 method for estimating a higher equivalent fluid level in an underground wellbore, and method for cal
专利摘要:
method for estimating a higher equivalent fluid level in an underground wellbore, and method for calculating a theoretical surface ring backpressure in an underground wellbore a method for estimating a higher equivalent fluid level or anular ringbackpressure Theoretical surface in an underground wellbore includes the acquisition of first and second axially spaced pressure measurements in the wellbore. The pressure measurements can then be processed to calculate the upper equivalent fluid level and / or the theoretical drilling fluid surface annulus backpressure between the measurement locations. A tool column, including a large number of axially spaced pressure sensors (for example, four or more or even six or more) electronically coupled to a surface processor by wired drill pipe, may be used to obtain a plurality of values corresponding to various wellbore intervals. higher equivalent fluid level and / or theoretical surface ring backpressures can be used in automated managed pressure drilling operations. 公开号:BR102012021723A2 申请号:R102012021723-6 申请日:2012-08-24 公开日:2018-11-21 发明作者:John James；John C. Rasmus；William Lesso 申请人:Prad Research And Development Limited； IPC主号:
专利说明:
(54) Title: METHOD FOR ESTIMATING A TOP LEVEL OF EQUIVALENT FLUID IN AN UNDERGROUND WELL HOLE, AND METHOD FOR CALCULATING A THEORETICAL SURFACE ANNUAL CONTRAPRESSION IN AN UNDERGROUND WELL HOLE (51) Int. Cl .: E21 / 08; E21B 47/06. (30) Unionist Priority: 08/14/2012 US 13 / 585,650; 08/26/2011 US 61 / 527,948. (71) Depositor (s): PRAD RESEARCH AND DEVELOPMENT LIMITED. (72) Inventor (s): JOHN JAMES; JOHN C. RASMUS; WILLIAM LESSO. (57) Abstract: METHOD FOR ESTIMATING A TOP LEVEL OF EQUIVALENT FLUID IN AN UNDERGROUND WELL HOLE, AND METHOD FOR CALCULATING A THEORETICAL SURFACE ANNUAL CONTRAPRESSION IN AN UNDERGROUND WELL HOLE A method for estimating an equivalent upper fluid level a theoretical surface annular back pressure in an underground well hole includes the acquisition of first and second pressure measurements spaced axially in the well hole. The pressure measurements can then be processed to calculate the upper level of equivalent fluid and / or the theoretical surface annular pressure of drilling fluid between the measurement sites. A tool column, including a large number of axially spaced pressure sensors (for example, four or more or even six or more) electronically coupled to a surface processor via wire drill pipe, can be used to obtain a plurality of values corresponding to several well hole intervals. The upper level of equivalent fluid and / or theoretical surface annular backpressures can be used in automated managed pressure drilling operations. METHOD FOR ESTIMATING A TOP LEVEL OF EQUIVALENT FLUID IN AN UNDERGROUND WELL HOLE, AND METHOD FOR CALCULATING A THEORETICAL SURFACE ANNULAR BACKGROUND IN A UNDERGROUND WELL HOLE FIELD OF THE INVENTION The disclosed modalities generally refer to geotechnical field measurements and, more particularly, to Measurements Along the Column (Acronym for Along String Mesurements, ASM) that can be incorporated into the repeating hardware sections of the Wired Drill Pipe (WDP). The methods are disclosed to calculate the sequential and non-sequential pressure and temperature measurements on these repeaters as well as the measured pressures and temperatures components of the bottom composition (for the Bottom Hole Assembly, BHA). The methods are also disclosed for using these measurements to characterize the underground formations, the drilling fluid and the drilling process. BASE INFORMATION I, During drilling operations, measurements of conditions inside the well taken during drilling can provide valuable information that can be used by a drilling operator to improve efficiency and performance and minimize risk. Such measures, when t transmitted to the surface during drilling, can also provide an essentially real-time view of changes in conditions within the well allowing for essentially real-time performance improvements and risk prevention. There is great interest from the industry in risk prevention as even relatively minor disruptions to drilling operations can be prohibitively expensive. The recent introduction of the Wired Drilling Tube (WDP) significantly increased the communication bandwidth between the measurement sensors inside the well and the surface and therefore the total amount of data that can be transmitted to the surface during an operation drilling. For example, measurement data during drilling Drilling, acronym in including easily. drilling (ASM), by (in MWD) acronym in english to english data Profiling mesurements while for image logging of transmitted to the While drilling (in the Drilling, LWD), drilling, can be surface when using WDP. Measurements along the example column, including pressure along the column and temperature measurements, can also be transmitted to the surface during drilling. Although temperature and pressure measurements along the column are known in the art, there has been no disclosure of methods for calculating temperature range densities and sequential pressure and is . sequential nor any methods of using these gap densities to characterize underground formations, drilling fluid or the drilling process. There remains a need in the art for further development. SUMMARY Methods for pressure management using measured interval densities are disclosed. For example, a tool column, including at least 10 first and second axially spaced pressure sensors • can be implanted in an underground drilling well. The pressure measurements can then be used to calculate a higher level of equivalent fluid or a theoretical surface annular back pressure between the 15 pressure sensors (that is, between the first and second depths measured in the drilling well hole. ). The tool column may further include a large number of longitudinally spaced pressure sensors (for example, four or more or even six or more) 'electronically coupled with a surface processor (via wired drill pipes, thereby allowing that the upper level of equivalent fluid and the counter-pressure of the theoretical surface annular be measured at multiple intervals in the well bore. The disclosed modalities can provide several technical advantages. For example, several disclosed modalities provide automated back pressure control in certain managed pressure drilling operations. Changes in applied back pressure can be made automatically in response to various drilling conditions, for example, including a change in chip density, changes in well volume, such as flushing and clogging, flow of fluid from the formation to the well hole, lost circulation and changes in drilling fluid density. In a non-limiting embodiment, a method for estimating an equivalent upper fluid level in an underground well bore is disclosed. The method includes: (a). implant a tool column in the well, the tool column including first and second longitudinally spaced subsurface pressure sensors implanted in the corresponding first and second depths measured in the well bore, (b) make the first and second pressure sensors acquire the first and second annular drilling fluid pressure measurements at the first and second measured depths, and (c) having a processor process the first and second pressure measurements to compute an equivalent upper fluid level for a bore gap of well between the first and second measured depths. In a second non-limiting modality, a method for calculating a counterpressure of annular surface theorized in an underground well bore is disclosed. The method includes: (a) implanting a tool column in the well bore, the tool column including first and second longitudinally spaced subsurface pressure sensors 5 implanted in the corresponding first and second depths measured in the well bore, (b) making that the first and second pressure sensors acquire the first and second annular drilling fluid pressure measurements at the first and second depths 10 measurements, and (c) having a processor process the first and second pressure measurements to compute the back pressure of Theoretical surface ring for a borehole interval between the first and second measured depths. In a third non-limiting modality, a method for controlling surface annular back pressure in managed pressure drilling operations is disclosed. The method includes: (a) acquiring first and second annular drilling fluid pressure measurements at the first and second depths measured in an underground well 20 hole, (b) processing the first and second pressure measurements to calculate a back pressure to cancel the theoretical surface for a well hole interval between the first and second measured depths; (c) acquire a surface annular back pressure measurement; and (d) adjusting the surface annular back pressure so that the measured surface annular back pressure is substantially equal to the theoretical surface annular back pressure calculated in (b). This summary is provided to present a selection of concepts that are further described 5 below in the detailed description. This summary is not intended to identify the essential or key characteristics of the claimed matter, nor is it intended to be used as an aid in limiting the scope of the claimed matter. BRIEF DESCRIPTION OF THE DRAWINGS For a more complete understanding of the subject in question, and its advantages, reference is now made to the following description taken in conjunction with the attached drawings, in which: FIG. 1 represents an example of a conventional drilling platform, in which the disclosed methods can be used. FIG. 2 represents a flow diagram of an example of an embodiment of the method for obtaining an interval density of an underground well bore. FIG. 3 represents an example of a multidimensional depth i and time-based matrix (database), including two variables. FIG. 4 represents the density of modeled oil-based sludge (Oil Based Mud, OBM) 25 as a function of pressure and temperature. FIG. 5 represents an example of a record including calculated gap densities obtained during an ASM during the drilling operation. FIGS. 6, 7, and 8 represent a hypothetical example of a well drilling operation in which a change in formation lithology is found which results in a reduced chip density with FIG. 6 representing the hypothetical drilling operation at time ij = 0, FIG. 7 time represented ί 2 = ί; + Δί, and FIG. 8 representing time ί 3 = ί 2 + Δ /. FIGS. 6, 9 and 10 represent a hypothetical example of a well drilling operation in which a portion of the drilling hole becomes enlarged during the drilling operation with FIG. 6 representing the hypothetical drilling operation at time i, = 0, FIG. 9 representing time ί 2 = ί] + Δί, and FIG. 10 representing time ί 3 = ί 2 + Δί. FIGS. 11, 12 and 13 represent a hypothetical example of a well drilling operation in which the drilling well chips fall out of the suspension and form a packaging with FIG. 11 representing the hypothetical drilling operation at time Z, = 0 and FIGS. 12 and 13 representing different methodologies for calculating time gap densities t 2 = t x + Δ /. FIGS. 14, 15, 16 and 17 represent a hypothetical example of a well drilling operation including a formation fluid inflow event (also referred to as a kick) with FIG. 14 representing the hypothetical drilling operation at time t } = 0, FIG. 15 representing time t 2 ~ t } + Δί, FIG. 16 representing time t 3 = t 2 + Át, and FIG. 17 representing time ί 4 = ί 3 + Δί. FIG. 18 represents an example of a visual presentation illustrating inflow as a function of time and depth. FIGS. 14, 19, and 20 represent a hypothetical example of a well drilling operation including a fluid drilling outlet flow event with FIG. 14 representing the hypothetical drilling operation at time i, = 0 and FIGS. 19 and 20 representing time ί 2 = ί 1 + Δί. FIG. 20 differs from FIG. 19 due to the fact that the level of the drilling fluid fell below the first ASM. FIG. 21 represents an example of a record of a well drilling operation in which a drilling fluid flowed out of the well hole in the formation. FIGS. 22A and 22B represent the schematic depth versus pressure plots that illustrate the equivalent top of fluid level changes that can result from loss of circulation events. FIG. 23 represents another example of a record of the well drilling operation shown in FIG. 21. FIG. 24 represents yet another example of a record of the well drilling operation shown in FIG. 21. FIGS. 25 and 26 represent a hypothetical example of a well drilling operation in which chips are falling out of the suspension in the annular drilling fluid with FIG. 22 representing the hypothetical drilling operation at time i, = 0 and FIG. 23 representing time í 2 = /] + Δί. DETAILED DESCRIPTION FIG. 1 represents a drilling probe 10 suitable for using the various methods of the method described herein. A semi-submersible drilling rig 12 is positioned over an oil or gas formation (not shown) arranged under the seafloor 16. An underwater conduit 18 extends from deck 20 of the rig, 12 for a pressure loading installation well 22. The platform may include a drilling tower and a lifting device for raising and lowering a drilling column 30, which, as shown, extends into drilling hole 40 and includes a drill bit 32 implanted in the bottom end of the bottom composition (BHA) 50. In the embodiment shown, the drill string 30 includes a plurality of cable drill pipe joints and therefore provides a communication channel with high digital bandwidth (for example , a bandwidth of the order of 5 kilobits / second) between the BHA 50 and the surface. The drill string 30 includes a plurality of longitudinally spaced cable drill tube repeaters 34, at least some of which include annular pressure and annulus temperature sensors 36 and 38. These sensors containing repeater subs can be referred to herein as XLINKS and they can optionally include additional temperature and internal pressure sensors (not shown). It will be understood that the internal sensors are configured to measure the pressure and temperature of the drilling fluid in the drilling column 30, while the annular (or external) sensors are configured to measure the pressure and temperature of the drilling fluid in the annular between the drilling column 30 and the wall of the drilling well. The annular and internal temperature and pressure sensors can also be deployed inside the various MWD and / or LWD tools included in BHA 50. Examples of BHA pressure and temperature sensors are shown in 52 and 54. Temperature sensors and pressure mentioned above can be in communication with the surface through the high-bandwidth digital communications channel such that temperature and pressure measurements along the column can be transmitted to the surface during drilling. Pressure and temperature sensors (or 34 repeaters) can also include on-board memory to save temperature and pressure measurements for later analysis. Other column drilling components (although not explicitly described) may also contain annular and internal pressure and temperature sensors, for example, including EMAG repeaters, mud pulse signal boosters and acoustic telemetry boosters. The temperature and pressure measurements obtained through these sensors can also be transmitted to the surface during drilling used (or stored in the memory inside the well) in the modalities of the method disclosed hereinafter. Pressure and temperature sensors can have substantially any longitudinal spacing along the length of the drill string 30. For example, spaced pressure and temperature sensors can have a longitudinal spacing in the range of about 500 to about 5000 feet. measured depth. In addition, the spacing between the pressure and temperature sensors is not necessarily uniform. For example, a longitudinal spacing between the first and second sensors is not necessarily equal to the spacing between the second and third sensors. The disclosed modalities are not limited in this respect. The disclosed modalities are also not limited to the use of any particular type of pressure sensors from subs repeaters and / or BHA. Virtually all suitable pressure sensors can be used, as long as they provide sufficient precision and accuracy and are robust in environments within the well. For example, pressure sensors that use strain gauges (such as those that are commercially available from Paine Electronics, LLC) can be used. Likewise, silicon solid state pressure gauges in an insulator can also be used. It will be understood that the implantation illustrated in FIG. it is merely an example. The BHA can include substantially any suitable tool components from within the well, for example, including a steering tool such as a rotary steerable tool, a telemetry system from within the well, and one or more MWD or LWD tools including various sensors for detecting the characteristics of the well inside the drilling hole and the surrounding formations. The disclosed modalities are not limited in this respect. In addition, the disclosed methods can be used in well bore applications other than drilling applications, for example, including fluid sampling applications, well control during opening, well maintenance, and production and completion applications, and similar. It will also be understood that the disclosed modalities are not limited to use with a semi-submersible platform 12 as illustrated in FIG. 1. The disclosed modalities are also well suited for use with either onshore or offshore underground operations. In addition, it will be appreciated that the terms drilling well and well bore are used interchangeably here. The detailed description is divided into two main sections, the first describing the methodologies for computing range gradients for temperature and pressure measurements along the column. The second section describes methodologies for using computed interval gradients to interpret the various properties of drilling fluids and formations and the drilling process in general. INTERVAL DENSITY CALCULATION METHODOLOGIES FIG. 2 represents a flow diagram of an example of a method 100 method for determining an interval density in an underground well bore. A tool column (for example, drill column 30 shown in FIG.l or a production or completion column) is implanted in the well bore at 102. The tool column includes at least first and second subsurface pressure sensors (for example, example, annular pressure sensors or internal pressure sensors) implanted in the corresponding first and second measured depths in the well bore. Pressure sensors can be used to measure the corresponding first and second pressures at 104. The first and second pressures can then be processed to obtain the gap density at 106. It will be understood that tool columns employing three or more pressure sensors pressure can also be used and allow a plurality of gap densities to be obtained. The density of a fluid under static conditions within the range between two pressure measurements can be calculated from the knowledge of a vertical spacing between the pressure sensors and the actual pressure measurements. A temperature gradient can also be calculated. In general, given a number n of spaced pressure measurements, a corresponding number of intervals between all sensor combinations (neighboring and otherwise) can be calculated, for example, as follows: Number of intervals = y / ~ ”'(« - / ’) Equation 1 For example, given 2 spaced sensors, 1 range is available; given 3 spaced sensors, 3 intervals are available; data 4 spaced sensors, 6 intervals are available, data 5 spaced sensors, 10 intervals are available, and so on. In some of the modalities of the disclosed method the number of calculated interval densities N can, for example, be in the range of: n - <N <y ' n - i). Using any of the annular pressure measurements, a density of a fluid (for example, drilling fluid), under static conditions in a well bore can be calculated, for example, as follows: Annular density = ----— r Ic. = í | C. Equation 2 (Z mdC0 ^ Inc)) TVD) where the annular density represents an average density of the annular fluid (for example, in pounds per gallon), P represents the annular pressure (for example, in psia), Z mâ represents the measured depth of the well, TVD represents the true vertical depth of the well, Inc represents the mean slope of the well, and C l represents a unit conversion constant (for example, 19.25 ppg / psi / foot). It will be understood by those skilled in the art that the density of a fluid can be expressed in several units. The common unit of pounds of oil per gallon oilfield is given in Equation 2. The equivalent vertical pressure load can be used to express pressure in terms of the vertical height of a fluid column and can be calculated as follows: Vertical Equivalent Pressure Load = pc, average density Equation 3 where, as is known to those skilled in the art, the vertical pressure load refers to the hydraulic load (for example, in units of feet). Density Circulation of Annular Measure Range Of particular interest in the present disclosure are the methods for calculating gap densities (i.e., fluid density) between the various spaced sensors (for example, between the first and second sensors, or between the first, second, and third sensors ). Using the pressure measurements associated with the end points of a specific interval, the density of a fluid between the two sensors can be calculated for several specific cases, according to the methodologies that follow. For example, the gap density of a circulation fluid can be calculated as follows: MA_ICD, vg AP ATVD Ç, MA_ICD avg = (^ MD (ml) ~ ^ MO (n)) COS (/ MC )~ ^ 7VD (n)) _ Equation 4 where MA_ICD represents an average circulation density of interval of cancel measure Circular, AP represents an change in pressure in between the first and the second depths measures, ATVD represents a change at 20 depth vertical true between the first and second depths measures r and P „e represent at annular pressure measurements at the first and second depths nen + 1, and represent the first and second measured depths, Zjy D ^ e represent the true vertical depths of the first and second measured depths. Those skilled in the art will readily understand that the true vertical depth (or a change in the true vertical depth) can be represented by the measured depth (or a change in the measured depth) times the cosine of the mean wellhole slope within a range. Under dynamic conditions, for example, when circulating the drilling fluid during a drilling operation, MA_ICD includes the effects of temperature on the compressibility of the incoming drilling fluid, the effects of absolute pressure on the density, volume and mass of chips suspended flow inlet or outlet of the drilling fluid between the sensors, and pressure losses due to friction in the circulation mud. This calculated gap density (MA_ICD) is described in more detail below through various plots and comparisons with other calculated gap densities (for example, in FIGS. 6 through 26). Static Density of Measure Annular Interval Gap densities can also be calculated during non-circulating (static) conditions as well as using Equation 4. Such conditions are generally available at each connection when adding a pipe support or joint to the drill string and occasionally during drilling it is suspended while drilling a support. Under such static conditions, pressure losses by annular friction are absent and the only effects on gap densities are the effects of temperature, pressure, and suspended chips. This parameter is referred to as MA_ISD and is calculated using Equation 4, but under non-circulating, static conditions. The static density of the interval can also be calculated by subtracting the modeled frictional pressure losses or MA_ICD measurements as calculated in Equation 4, when calculated under circulation conditions. This approach allows for a substantially continuous determination of the static gap density and is referred to as MA_ISD mf . Equation 4 can be modified to include these friction pressure terms, as shown below in Equation MAJSD ^ where Pj represents the loss of pressure due to friction that acts on the fluid above sensor n and P f „+ represents the loss of pressure due to friction that acts on fluid above sensor n + 1. Two methods for calculating friction pressure loss are disclosed; a hydraulically modeled method and an in-situ measurement method. The hydraulic model makes use of various known or estimated fluids and bore properties to calculate frictional pressure loss. The properties may include, for example, temperature, pressure, compressibility, viscosity, flow rate, and the flow regime of the drilling fluid, the annular volume of the drilling well, the diameter and shape of the drilling well, the effects of rotation rate, and drilling well wall properties such as smoothness. The measurement method can calculate the gap density, for example, using Equation 4 under static non-pumping conditions to distinguish the borehole sections or intervals as a function of time. After the pumps are activated again and before drilling summaries, this amount can be used on the left side of Equation 5 together with the measured pressures to calculate Pf n _ l ^ Pf n for each distinct hole section in the well. The loss of pressure by dynamic friction is generally a strong function of the flow rate and the rotation rate for a given bore section and time period during well drilling. Therefore, this pressure loss is generally a value that varies slowly over time under steady-state flow conditions. For example, it can be in the range of 0.1 to 1 pound per gallon in a 10,000-foot vertical well. In this second method, an in-situ determination of friction pressure loss only needs to be performed periodically, as long as the drilling parameters do not change (for example, the rotation rate, flow rate, and the BHA components in each section different bore that may have a different pressure loss due to friction). When the drilling parameters change, the second method can be repeated. In practice, it can be advantageous to make use of both theoretical and measurement methodologies to calculate friction pressure losses. For example, when the two methods give similar values, the hydraulic model can be used with greater confidence. The differences between measured and modeled friction losses can also be used to calibrate the hydraulic model, calculate chip density, or signal certain drilling events of interest, as described in more detail below. When determining friction pressure losses, the MA_ISD mf measured gap gap density can be determined by circulating and drilling, replacing friction pressure losses in Equation 5. MA_ISD mf can be calculated at various time intervals during drilling. It should be understood that, in drilling operations where back pressure is applied to the annular fluid (for example, as it is done during controlled pressure drilling (MPD) applications), Equations 4 and 5 do not require a term in back pressure once what a pressure differential is used for to determine The density of interval. It should also be understood that the gradients of intervals are a direct function of pressure from inside the well and depth measurements. Therefore, any of the principles applied to interval gradient calculations apply to pressure measurements, whether measured or theoretical. Density of constituent mud components The MA_ISD measured or calculated MA_ISD m f annular gap static density can be taken as the sum of the individual densities of the individual components of the static annular fluid which can be valid for non-soluble components such as liquid forming fluids and chips of formation normally encountered during drilling. This can be expressed mathematically, for example, as follows and can allow specific gravities of the individual components to be calculated when their volumetric percentages are known: i = n (λ MA_ISD avg = ΣΙ ^ · I Equation 6 where MA_ISD avg represents a static mean gap density measured, M t represents the mass of the non-soluble component i, and V i represents the volume of the non-soluble component í. MA_ISD avg can also be expressed as a weighted average of the volume of the individual constituents in the drilling fluid mud. It should be noted that the product of volume and density also represents mass and can therefore be rewritten in terms of volumetric percentages as follows: MA_ISD mixture Equation 7 where MA ISD ^ t ^ represents the measured annular interval static density of a mixture, ^ represents the volume of component not soluble i, V misttlra represents the total volume of the mixture, and SG l represents mass specific (or density) of component 1. 0 drilling fluid flowing toward The surface in the annular usually includes a combination of the drilling fluid that is pumped down through the interior of the drill pipe and chips removed by the drill bit during drilling. The volumetric flow rate in the annular can be expressed as a combination of these two expected components plus an additional term that quantifies the increased or reduced flow due to the addition of an unexpected or unwanted constituent or loss of a constituent. The additional term can quantify, for example, an inlet flow of formation fluid into the annular or an outflow of drilling fluid in the formation. The inflow or outflow can involve either formations that have already been drilled or are currently drilled. Alternatively, the additional term can quantify additional chips that fragment from the drilling well wall after drilling. The corresponding gap density and ASM calculations can allow these inlet or outlet flow constituents to be identified and located along the length of the drilling well. As indicated above, the annular drilling fluid includes a combination of the drilling fluid that is pumped down through the interior of the drill pipe and chips removed by the drill bit. The volume of chips can be counted by integrating the flow rate into an annular fluid unit volume over a specified time interval and the flow rate out of the unit volume must equal the flow rate within the volume of the unit. In other words, the flow rate of the mixture can be set equal to the sum of the individual flow rates in this volume. The accumulated volume of the mixture flowing out of the annular volume of the unit over a given period of time can be expressed mathematically, for example, as follows: 12 12 f Q mix = f Qfora = J (Qlan.a + Q chips + Qx) ii ti il Equation 8 where Q mixture represents the volumetric flow rate of the mixture at time t, Q fara represents the volumetric flow rate outside the annular volume of the unit, Q mud represents the volumetric flow rate of the drilling fluid (mud) pumped in. of the annular volume of the unit at time t, Q chips represents the volumetric flow rate of chips that flows inward of the annular volume of the unit at time t, and Q x represents the volumetric flow rate of component x that flows inward or outward out of the annular volume of the unit at time t. Q mud and Q trimmings can be further defined, for example, as follows: Equation 9 where TFLO represents the drilling fluid flow rate in units of gallons per minute. TFLO can be determined on the surface using methods known to those skilled in the art, for example, using the probe's pumping stroke rate, the number of pump cylinders in use, their displacement / stroke, and the efficiency of the pump. When pumping a compressible fluid, such as synthetic oil-based mud (SOBM), flow rates within the well tend to change due to the effects of pressure and temperature on the properties of the fluid. The ASM temperatures and pressures measured from the interior drill pipe fluid properties can be used to measure the temperature and fluid density of the drill pipe in order to determine the compressibility of the fluid in situ and from there calculate the rate flow rate within the well given the surface flow rate. The flow rate from inside the well can also be measured inside the well. The rate of chip volume that is created and flows into the annular during the drilling operation can be considered an input variable and can be expressed mathematically, for example, as follows: Qaparas = π * r 2 * ROP ^^ (l - K * φ) Equation 10 where R represents the radius of the drilling well, ROP represents the penetration perforation rate, K represents the percentage of formation porosity destroyed by the action of drill crushing, and φ represents effective forming porosity. The percentage of formation porosity destroyed by the action of drill K can be estimated by observing the size of the chips during drilling. When K is defined as the unit, the crushing action of the drill destroys all porosity, creating chips similar to the individual grains of sand. For example, in unconsolidated sands, the size of the chips will be small and little present with predominantly individual grains of sand observed in the samples captured from shale shakers. In shale, competent or cemented rock formations, K is typically smaller than the unit due to the bit crushing component that is reduced (or minimized, depending on the degree of hardness of the formation). Determining a K value can be advantageous in certain drilling operations, for example, when a drill wants to calculate an expected volumetric flow rate of chips in certain chip control programs that determine the volume of chips remaining in the well of drilling and can potentially restrict the movement of BHA. However, in certain applications, it may be sufficient to define K for the unit in order to have Q chips representing the matrix or the volume of rock in the formation. This allows the density of the fluid contained within the pore volume to be explained separately in Equation 11.2, as described in more detail below. Formation porosity can be estimated, for example, from a standardized penetration rate (ROP) as disclosed in U.S. Patent 4,949,575 or in Rasmus and Stephens (SPE Paper 20443, Real Time Pore-Pressure Evaluation From MWD / LWD Measurements and Drilling-Derived Formation Strength). However, a fractional volume of fine grained clay / shale / sludge in the formation, V xist0 is generally necessary for this determination. V xlsl0 is normally calculated from LWD measurements such as measurements of natural gamma rays, however, such LWD measurements are not generally available on the drill. In certain applications, a dimensionless torque (TD) obtained, for example, from a Mechanical Efficiency Register can be used to differentiate between the drilling of a porous formation and a shale formation due to the signature of a single dimensionless torque and an increase in a porous formation in relation to shale. This differentiation can normally be made regardless of the type of drill bit. An example of a Mechanical Efficiency Record is given in Equation 11. V xisla can be estimated from T D and a dimensionless penetration rate (R D ), provided that both T D and R D are functions of clay volumes and effective porosity, regardless of drill wear conditions (see Burgess, Falconer, and Sheppard, Separating Bit and Lithology Effects From Drilling Mechanics Data, SPE 17191, 1988). Such K XÍJ measurements (0 can then be updated since the LWD data above the drill bit measures the forming properties. T D and R D can be expressed mathematically, for example, as follows: Ώ * DTOR DWOB * BS Equation 11 Where DTOR represents a torque measured inside the well or on the surface, DWOB represents a measure of weight inside the well or on the drill bit, and BS represents a diameter of the drill bit. „ROP * 0.2„ = R n = ------- Equation 11.1 D RPM * BS Where ROP represents a penetration rate and RPM represents a drilling column rotation rate in revolutions per minute. The pore fluid contained within the formation pore space can either be retained within the chip chip or released into the annular fluid depending on the crushing factor, K. Regardless of the degree of crushing, this will affect the measured gap densities of the annular fluid and can therefore be considered separately. Equation 11.2 where Qpco nuido represents volumetric flow rate of pore fluid within the annular in cubic feet per hour, R represents the radius of the drilling well, ROP represents the penetration rate, and φ represents the effective formation porosity. Ά flow rate of the drilling fluid (mud) leaving the annular surface, Q mixed or Q out , can also be considered a measurable inlet volume and can be measured, for example, by a paddle type measurement placed on the line output flow or by a type measurement Venturi or other means when using controlled pressure drilling (MPD) type equipment. This leaves the quantity Q x as the only unknown in the Equation In drilling operations, this represents a way of detecting an incoming flow of forming fluid or a kick (as it is better known) in the industry. However, under conditions where Q x has been found to be approximately equal to zero (for example, by stopping the mud pumps and performing a flow check), the can alternatively be used to measure the volume of chips flowing into the annular. However, in certain applications, it may be difficult to use the methodology described above to determine Q x given the measurements of, Q chips Q mud , and Q nllstura or Q off . This may be due to large variations in mud flow volumes, sometimes seen during drilling, which in turn may be due to erratic pump strokes, fluid compressibility, and inaccurate sensor measurements of these quantities. Equation 10 is often the most accurate means of determining chip volumes. Knowing the volume of chips generated and keeping track of the volume of chips coming out of the well hole, it is possible to determine the volume of chips, if any, that were left in the drilling well. However, it is desirable, not only to know the volume of chips that is generated, but the density of chips in the annular between any two ASM pressure measurements since this gives us information about the type of formation to be drilled. Within any two or more arbitrary depths in the annular, the relative volumetric percentage of the volume of chips in the annular constitutes a higher percentage than that calculated by Equation 8, due to the chips that travel upward through the annular at a lower speed than the drilling fluid. A corrected chip volume can be calculated by considering a sliding speed for the chips where V = V - V 'annular chip slip * A transport efficiency Fj - ^^ can be defined as the ratio of the speed of the chips to the average annular speed of the sludge and can be expressed mathematically, for example, as follows: VFJ τρ _ shavings _ T shavings ~ yryr ~ ^ mix * (cos (7nc /) 4- a * sin (/ Hc /)) Avpn * f z K ' u ring J shavings J Qlama Qx Qporo_fluido, 4rea a „ ei * (lf iparas} J Equation 12 where it represents the volumetric fraction of chips in the mud flowing in the annular, Area mel represents the cross sectional area of the annular at a given depth Z, Q mud represents the volume flow rate of mud from Equation 9, Q chips represents the volume flow rate of chips from Equation 10, Q pore fluid 0 represents the volume flow rate of the pore fluid of Equation 11.2, and a represents a transport coefficient of jump flow transport, which is generally a function of RPM and Qmisture * Transport efficiency can be calculated from empirical correlations, as disclosed in (i) Sifferman, et al., Drill Cutting Transport in Full-Scale Vertical Annuli, J. Pet. Tech., Nov 1974, 1295-1302; (ii) Moore, Drilling Practices Manual, Petroleum Publishing Co., Tulsa, 1974, and (iii) Sample and Bourgoyne, Development of Improved Laboratory and Field Procedures for Determíning the Carrying Capacity of Drilling Fluids, SPE 7497, 1978. The volumetric fraction of the chips that flow into the annular is also a function of slope of the borehole as the chips tend to fall out of the suspension in high slope sections. The constant a is used to explain the fact that as the well becomes closer to the horizontal, the chips tend to fall from the suspension and are transported along the well hole in a jump-type mechanism. The slope and jump terms in Equation 12 are intended to lead to an upward or vertical vertical sliding rate of chips. Equation 12 can then be rearranged to compute the terms f chips, for example, as shown in Equation 13. X * O r _ xZcuttmgs J cutttngs Y * () ip * 77) O 4-0 jx ^ cuttings ' Γ Ί cuttings in' z ^ x T pore_fluid / Equation 13 where X = cos Inc + asmlnc. Being liquid at temperatures and pressures inside the well, the volume of pore fluid from the formation that is released in the annular can have a negligible sliding speed in relation to the mud. fractional volume of pore fluid f k σ poro_fluid mud f J mud and inlet / outlet flow material can then be determined, for example, as follows in Equations 13.1 13.2, and 13.3. % * Ft * 0 _ fluid chips% * Qaparas + '' T_ chips * ^ Qlama _ in + + Qporo_fluido Equation 13.1 fx = _________________ * _ shavings * Q mud _ in________________ X * Qaparas + shavings * ^ Qlama _ in + Qx + Qporo_fluid7 Equation 13.2 Equation 13.3 Χ * Έτ * 0 ______________________ 1 1 shavings x _____________________ X * Qaparas + shavings * fèlama_em + Qx * Qporo_fluido In some applications, especially in depths smaller, the volume of pore fluid gives formation fporo_nuido that is released to the cancel may have an sliding speed in relation to the mud speed, when there are density differences between the two fluids. This sliding speed can generally be calculated and made available from a hydraulic module in commercial chip control or drilling well cleaning programs. Ά transformation of dimensions of volumetric or fractional flow to a depth dimension requires simultaneous consideration of transversal areas and fractional volumes. The annular volume can be represented mathematically, for example, as follows: Vol volul = p * r 2 * [Dbll 2 - Dp) dz Equation 14 z = n Where Vol anul is the annular volume between the two depths, z = nez = n + , .¾ the well diameter is, for example, obtained from the diameter of the drill or LWD measurements of caliper, and D p is drill pipe diameter located between z - nez = n + . Ação Equation 14 assumes a drilling well with a circular cross section. This assumption may be appropriate for many drilling operations, however, the modalities described are not limited in this regard. For example, a more general elliptical shape can be used. It will be understood that Equation 14 is expressed in terms of drilling well depth instead of time. It will also be understood that the connection between the volumes and the depth is the annular speed of the mixture of mud and chips, while the connection between the annular volume based on depth and time is the penetration rate. Thus, annular volumes and fluid flow rates can alternatively be expressed as functions of time or depth. For example, chip speed and fluid flow can be integrated over a specific period of time to determine chips as a function of depth. In an example workflow, an annular volume matrix at discrete depth intervals can be calculated using Equation 14. The matrix can be as thin as a few inches deep or as sparse as one to two feet deep. In the lower BHA (below an LWD caliper tool), the drill size can be used as the diameter of the well. The diameter can be updated using measured values when LWD caliper measurements become available at predefined depths. The diameter of the drill pipe can also be continuously updated using discrete time functions, as the various pipe diameters pass through these same depth points and the various chips are lifted from the face of the drills and taken to the volume cancel. The terms Qi love and Q shavings can be calculated from Equations 9 and 10, at discrete time intervals (for example, every few seconds). These volumes can then be used in Equation 13 to calculate the fractional volume of chips within each discrete time period. The chip speed can be integrated to obtain the corresponding depth position of the chip over time and can be expressed mathematically, for example, as follows: Equation 15 This can improve the accuracy for integrating annular mud speed (in opposition to or in addition to the chip speed), due to the higher fractional volume and higher volumetric flow rates. This can be expressed mathematically, for example, as follows: Equation 16 Equations 15 and / or 16 can be used to generate multidimensional matrices indexed by increments of depth. Each column represents a chosen time interval and can contain TIME, in addition to Area mul , Q ! Ama _ in t Qaparas rr Qporo fluid r ^^ chips θ ^^ mislura · θ tempO total time needed to circulate the chips outside the ring for the surface it dictates the total number of time intervals (steps). For example, if a 5 second time interval is used and it takes 1 hour to circulate the chips from the drill to the surface, then the die includes 720 time intervals (3600 s / 5 s.). Additional time intervals can be included to accommodate non-circulation periods (for example, a period of time in which a new pipe support is added to the drill string). An example of a multidimensional depth and time-based matrix (database) including multiple variables is shown in FIG. 3. For ease of illustration, only two of the many variables are shown in the example shown. It will be understood that the lines are typically added to the matrix in insofar as the well is perforated more deep in the earth.At quantities More of MA_ICD described above and calculated using the data from As me the Equation 5 can include multiple depth intervals within the depth matrix previously described. This multidimensional matrix can be integrated over the depth intervals corresponding to the ASM interval to derive an average density of the mixture that can be directly compared with the measured ASM values. A similar process can also be followed for the fractioned volume of chips. From Equation 7, MAjSDmiaura can be expressed mathematically, for example, as follows: MA_ISD mjs tu ra Japaras '^ Flour shavings _ fluid' ^^ potofluid Ί / mud inside ^^ / love inside / x Equation 17 Where f shavings r fporo _ fluid t / mud inside! fractionated of the shavings, the drilling, and constituents ^^ shavings r SG pom _liquid i ^^ iama inside f of the chips, f and x represent pore fluid volumes, inlet or outlet mud flow and and SG X represent the specific drilling, flow weights. pore fluid, sludge and inlet or outlet constituents Under conditions in which there is no inflow, outflow, or other event, such that constituent x is zero, Equation 17 can be used to calculate SG chips since all other variables can be determined using other means, as described above. These calculations are described in more detail below. Equation 17 can be further expanded considering that the pore fluid includes a combination of hydrocarbons and water that may or may not have been washed away by the drilling mud. The expanded form of Equation 17 can be represented mathematically, for example, as follows: NÍA_ISIj ^ jstur a - 7paras '' ^^ parings - ^ · ^ '' fporofluido + * ^^ Vporo_isenõ_gua t fporo_ fluid (1 ) ^^ pore ^ draarbonides + 0 ^) / pora_yZuít / c / ^^ 4ama_dcnto yiamadentro “ inside ^ G x Equation 17.1 where F represents a washing factor so that 1 <F <0 with F = 1 representing no washing and F = 0 representing complete washing, S ' u , represents the water saturation in the pores, 1-S 1 ^, represents the saturation of hydrocarbons in the pores, 5O pore jscnt0 water represents the density of water in the pores, represents the density of hydrocarbons in the pores, and SG mud denrr0 represents the density of inlet drilling fluid (mud). When drilling under conditions of no flow inlet or outflow (ie / x = 0), Equation 17.1 includes four unknowns (SG shavings , F, S w , and SG poroJlocarbons ) with the rest of the variables to be measured directly or calculated from other measurements. As described above, MEL can be used to determine whether the perforated formation is shale or a porous formation. When drilling through shale, water saturation can be considered to be 100%. In certain geological environments the lithology of a porous formation is known to be, for example, sandstone, limestone, or dolomite, such that SG * xis can be introduced. Equation 17.1 can be rearranged to solve S K as follows (recognizing that S hyr = (ϊ-S v ): - ^ Qnstura faparas ‘^^ trim ./iamadentro ^^ íaniainfluido ^^ amadentro fporo fluido‘ ^^ polio hydroarbonides fporo_ fluid rLT iseníi_water ‘^ ' Equation 17.2 Bearing in mind that equations 17.1 and 17.2 include at least four unknowns, several techniques can be used to determine which water saturation is appropriate. For example, assuming no washing (F = 1), the introduction of SG shavings from known lithology (eg shale or porous formation, as determined by MEL), and assuming a value for ^ ' Jr poro_hydrocarbons r allows S w to be calculated for various scenarios. A suitable scenario can be selected based on expected values. In one scenario, it can be assumed that hydrocarbons are present, but that the formation carries water In such a scenario, it would be expected that the calculated water saturation would be the unit. In another scenario, it can be assumed that hydrocarbons are present and that the formation is a hydrocarbon carrier. In such a scenario, the calculated water saturation would be expected to vary: between 0 and 1, but typically greater than 0.1-0.2. The calculation of S w requires that the density of the hydrocarbon be entered. Since this quantity is unknown, it can be calculated based on a first density of hydrocarbons representing gas (SG gfc ~ 0.2) and a second density of hydrocarbons representing oil (SG òieo »0.8). When the formation is a gas carrier, the calculated S w SG ók0 using is typically less than zero and, therefore, wrong. When the formation is oil bearing, the S w calculated using SG gis is, typically, between zero and one, but erroneously high. The calculated using SG ^ advantageously represents an upper limit on the actual water saturation. When the incoming flow is detected, the amount of fparasSQtms. It can be considered to be constant over a period of time. Ά Equation 17 can then be used to calculate f x SG x from which SG X can be calculated when / x is known (for example, from Equation 8). The determination (or estimation) of SG X can be advantageous in determining the type of fluid inlet flow into the well bore. Circulation Density and Measured Drill Tube Internal Interval Static The mentioned internal ASM pressure sensors that are implanted and configured to measure an internal drill pipe pressure (ASM FinKrna ) can be used to obtain internal fluid gradients inside the drill pipe under no flow (MIF_ISD) and flow conditions (MIF_ICD), for example, using Equation 4. The difference between MIF_ISD and MIF__ICD is usually due to friction losses in the drill pipe. When two pressure sensors are axially spaced close enough to the drill and separated in TVD, in order to adequately give high signal / noise measurements, the internal static density of the interval can be measured when not pumping. The internal static gap density can also be calculated using Equations 4 and 5, as described above to determine friction pressure losses and to subtract them from the internal dynamic gap density. Friction losses can also be calculated using a hydraulic model. The internal static density of the measured range (MIF_ISD) is a function of the density of the actual fluid to be pumped into the tube at the surface plus any pressure and temperature effects that affect the compressibility of the fluid. If the sensor pairs are too high above the drill, a temperature correction calculated for the static density of the gap can be applied using an appropriate hydraulic model that includes the effects of temperature and friction pressure. MIF_ISD represents the fluid that leaves the drill before any, chip loading effects and annular friction losses and therefore can be used as input for the calculation of the expected annular fluid gap static density described in more detail more forward. Circulation Density and Internal Static Expected Drill Pipe Interval Known hydraulic modeling techniques can be used to predict the density of the internal fluid as a function of pressure (predicted or measured) and internal temperature using the properties of surface mud density as a base fluid for modeling. The properties of surface mud are typically measured by mud recorders, but can also be measured by sensors on the surface. Accounting for the effects of pressure and temperature results in an expected static internal fluid gap density EIF_ISD. By taking into account the effects of modeled friction an expected internal fluid gap circulation density EIF_ICD can be obtained. The expected gap densities are also referred to here as modeled gap densities. The expected internal densities are generally equal to the measured quantities MIF_ISD and MIF_ICD when the hydraulic model is correct. A minimization process can be used to adjust the appropriate hydraulic parameters until a suitably accurate match is found. Expected annular fluid interval static density An expected annular fluid gap static density (EAF_ISD) can be obtained by correcting MIF_ISD for pressure and temperature effects as the inlet of mud flows from the top of the annular to the surface. EAF_ISD can be compared with the various interval densities measured to identify certain undesirable drilling events, as described in more detail below, in various applications in the INTERVAL DENSITY APPLICATIONS section of this disclosure. The annular pressure and temperature are typically measured by the ASM sensors in the WDP. When these measurements are not available, and only BHA sensors are present, pressure and temperature gradients can be assumed between the BHA sensors and the surface. Expected Annular Interval Static Density The fluid that comes out of the bit and is pumped into the annular is a fluid with properties defined by EAF_ISD, which, as described above, is MIF_ISD for the effects of pressure and temperature on density The chip load (with Q x = 0) calculated using one or more of Equations 8-16 can be added to obtain an expected annular gap static density EAF_ISD EA_ISD. The expected gap densities are also referred to here as modeled gap densities. EA_ISD represents a hypothetical fluid that has the properties of the sludge that is injected into the annular into the drill loaded with the drilled and suspended chips having a certain density range and can be expressed mathematically, for example, as follows: EA — ISD ./lama inside ^^ mud inside + faparas ^ shavings / mud inside • EAF_ISD + / operaj .SG apafas Equation 18 The difference between EAF_ISD and EA_ISD is due to the chip load. If the difference is minimal at the bottom of the hole, the calculated effects of the chip load and density using Equations 8-16 are likely to be correct. Given a discrepancy, the chip density can be adjusted. If MA_ISD decreases and falls below EA_ISD as the mud flows over the annular within the deviated section of the drilling well, this indicates that the chips may be falling from the suspension and settling at the bottom of the well. In addition, the inlet or outlet flow from the well hole can result in differences between these two calculated parameters and can be used to signal loss of circulation and gas kicks. Annular Interval Circulation Density Expected Taking the EA_ISD calculation and adding the pressure losses by annular friction to this results in an expected annular interval circulation density EA_ICD. This parameter is a function of the inlet sludge density adjusted for temperature, pressure, chip load, and pressure losses due to annular friction and is therefore comparable to MA_ICD. The expected and measured quantities (EA_ICD and MA_ICD) tend to be the same when the chip density and friction losses are entered correctly. When these quantities are not equal (or are not close to being equal), this can indicate a change in the chip density from the assumed chip density or inlet or outlet flow event (a Q .. event). EA_ICD can be expressed mathematically, for example, as follows: EA.ICD = A ^ EAF.ISD + f apams SG ^ Equation 19 where Ζτν Ώ („) and ^ zn> („ + i) represent the real vertical depths of the well at the first and second depths n η + 1 and P f represent the frictional pressure drop acting on the fluid above the sensors , as described above in relation to Equations 4 and 5. Equivalent Upper Fluid Level The true vertical depth or equivalent measure of the top of the liquid level can be calculated from the annular slurry gap density between the two pressure sensors, using the hydraulic pressure loading concept. This can be referred to as the equivalent upper part of the fluid level (ETOFL) and is intended to define the depth at the highest point or the level that a fluid would occupy if it were continuous and had the same properties as the fluid between the two pressures measures. Back pressure can sometimes be applied to annular strangulation during controlled pressure drilling (MPD) operations. With an incompressible fluid in the annular, the pressure can be subtracted from the measured pressure to calculate ETOFL. When the fluid is compressible, simply subtracting the back pressure cannot be adequately accurate to the extent that it may be necessary to calculate an equivalent back pressure in the sensor. Such calculations can be performed, for example, using hydraulic models. The following mathematical equations can be used to calculate ETOFL in the presence of an applied back pressure using previously calculated interval densities. In these equations, a positive ETOFL indicates that the calculated fluid level is below the surface, while a negative ETOFL indicates that the liquid level is above the surface. ETOFL Equation 20.1 ETOFL = Z TyD (n} p „-P / n -BPyC { MORE D Equation 20.2 where ETOFL represents the upper equivalent of fluid level which is essentially equivalent to the elevation of fluid in the well, including a fluid having a static density, P represents the measured pressure, P f represents the pressure loss through friction, BP represents the annular back pressure applied to the surface, n represents a pressure sensor at a certain measured depth, and n + 1 represents a pressure sensor at a certain measured deeper depth. Counter-pressure of annular extrapolated or theoretical surface In MPD operations, it can be useful to calculate a theoretical or extrapolated (BP) annular back pressure from the annular pressures measured inside the well and to compare the calculated values with the real surface annular pressure (SBP). Automated software routines can then be used to adjust the actual applied BP to minimize any differences to maintain a constant lower hole pressure (BHP). Equations 20.1 and 20.2 show that an increase in the gap density in a given BP results in an increase in ETOFL. This increase in interval density can cause the theoretical back pressure in Equations 20.1 and 20.2 to decrease and even become negative in some cases. In an event that causes a sudden increase in annular pressure measured by the lowest pair of sensors (for example, due to a restriction in the drill string above the sensors), the lower gap density remains substantially constant, ETOFL decreases, and the counterpressure of annular calculated surface (SBP) increases. Since the theoretical BP depends on the interval from which it is calculated and the impact that various events have on the interval density, the interpretation of the theoretical BP is dependent on the application, as described in more detail below with respect to Table 10. In general, the theoretical BP interpretation is used in combination with an interval density calculated in order to obtain the appropriate action to adjust the actual surface back pressure. Theoretical BP back pressure can be expressed mathematically, for example, as follows: BP = - (Z n ) * -rTH> (n + l) ^ TVD (n) Equation 21 where BP represents the theoretical back pressure, P „ and P„ + 1 represent the pressures measured in the sensors of nen + 1, and Z TOW and ^ rvD (.n + ) represent the actual vertical depths of sensors ne h + 1 . Speed and Acceleration of Interval Density Changes It is often desirable to know the direction and degree of change in the interval specific gravities calculated over time in order to determine whether the system is trending towards stability or instability, and, for example, to track an incoming flow as it moves over the ring. The rate of change of the gap density can be represented mathematically, for example, as follows: = - / 21) Equation 22 (fr V 2 _ί ι) where VID represents the rate of change of the gap density over time and represents one of the gap densities described above at time t. An additional derivative of the rate of change (ie, an acceleration) can also be useful in determining the direction of change and how quickly the gap density is changing in order to determine the reaction time required for the corrective action. Acceleration can also help to distinguish between inlet streams of gas jets versus water or oil. The acceleration of the gap density can be expressed mathematically, for example, as follows: AID = d ^ VID t2 —VID tl Equation 23 dt í 2 - í] where AID represents the rate speed change gives density interval with time (that is, the rate in interval density change) and VID t represents one of the velocities of time interval densities t. INTERVAL DENSITY APPLICATIONS In this section, methodologies for interpreting calculated gap densities are presented together with the various applications for using calculated gap densities to determine, diagnose, control and / or remedy various drilling events. Interpretative Methodology described DENSITY Table 1 summarizes the various range densities above in the section METHODOLOGIES OF CALCULATION OF INTERVAL and the physical effects that are included in each one. The mathematical equations listed above can be used to calculate the various interval densities. Calculations can be performed substantially in real time, while the well is being drilled or subsequent to the drilling operation using recorded historical data. The described modalities are not limited in this respect. The calculated interval densities, as well as their depth and time ratios, can be plotted on various cross plots or other displays that allow the drill (or a computer program) to recognize, differentiate and take mitigation control from the various situations discussed more later in this section. In addition, the use of calculated gap densities is not limited to drilling operations, but can also be useful in various completion and production operations. TABLE 1 Real a Real Modeled Modeled CO HΦΦ CO Φ Ό(Ü 1 ------- 1Φ ΌO Real null o ΌΦ Internal Real sideCalculation 0 P Φ O P Φsi — 1 Φ IP Φ TJ <05 PP CO CO 0 Ό O ω co Φ CO Φ Φ Φ P O P 3 CO IT CO ass P P •H s •H ω H Φ H Φ Φ PP O ρ (1) P Φ li u P P P £ ass Eh Q-i Hey < ΦPdensity rHΦ CO(D D Φ Φ Φ Φ Φ P Φ P OT5 ΌΌ Ό Ό Ό ç Ό P -H <IP P s of CO CO CO CO CO (0 (0CO'Φ0 0 O 0 O O O 0 O 0 PP -P P P P P P P P P ç Φ interval (D (D Φ Φ Φ Φ Φ P Φ P gP P P cp cp P P P P P 0ω ω M ω ω ω wM ç u MIF_ISD □ □ Friction effects internal are effectively removed ICD MIF □ □ □Measured during circulation EIF ISD □ □ To be compared to MIF_ISD EIF ICD □ □□ To be compared to MIF_ICD MORE D □ □ □Friction effects cancel are effectively removed by taking action whenare notcircling. MA_ISD mf □ □ □ □ Annular friction effects areeffectively removed bymodeling. MA ICD □ □ □□ Measured during circulation EAF_ISD □ □ EA_ISD □ □□ To becompared toMORE D EA_ICD □ □□□ To becompared toMA ICD EIF ICD and EIF ISD are the modeled (expected) internal static and interval gap densities calculated using the inlet mud properties at the surface, including pressure within the well and 5 temperature in the drill column at the depth of interest. The expected quantities can be compared directly with the measured internal circulation range and the static densities MIF_ICD and MIF_ISD. MIF_ISD can be obtained by subtracting an internal friction pressure loss from measured MIF_ICD or by direct measurement. Friction pressure losses can be obtained through modeling and / or measurements. For example, MIF_ICD can be measured directly by measuring MA_ISD when the mud pumps are turned off (for example, by adding a piece of the drill pipe to the drill column). The difference between MIF_ICD measurements made during circulation and non-circulation (when the pumps are turned on and off) can be considered as a direct measurement of pressure losses due to internal friction (LP_Internaf rlc ). The modeled EIF_ISD can be compared with MIF_ISD (which is MIF_ICD - □ P_Interna £ r i C when circulating and MIF_ISD when not circulating). An error minimization process (or a manual procedure) can be used to adjust the parameters of the hydraulic model that account for the effects of temperature and pressure on the drilling fluid such that EIF_ISD is equal to MIF_ISD. A subsequent error minimization process can then be used to adjust the parameters of the internal hydraulic model that represent the friction pressure losses in such a way that EIF_ICD is equal to MIF_ICD (that is, in such a way that the pressure loss is equal the modeled frictional pressure loss equals the measured frictional pressure loss □ P_Interna fr ic). Iterative minimization processes can be used to provide accurate results. The minimization processes can also be repeated at various flow rates and the results can be stored in a look-up table for future reference. The parameters of the hydraulic model previously obtained for the effects of pressure and temperature on the properties of the incoming sludge can be used in the annular environment as well. The properties of the annular fluid as a function of the annular pressure and temperature can be introduced into the hydraulic model to obtain a modeled (expected) EAF_ISD modeled static fluid gap density. This parameter represents the gap density of the annular fluid (without chips and friction effects) as a function of pressure and annular temperature as a function of depth and time. Calibration and determination of the effects of annular friction can be performed in the same way as described above for the effects of internal friction. For these minimizations, EA_ISD, EA_ICD, MA_ISD and MA_ICD are calculated in opposition to EIF_ISD, EIF_ICD, MIF_ISD and MIF_ISD as described in the previous paragraph. The EA_ISD modeled annular gap static density can be used as the incoming sludge properties with the effects of patterned chips and annular temperature and pressure included. EA_ISD can be equal to MA_ISD when the generation and transport of chips in the annular is properly modeled and the modeled frictional pressure losses that are subtracted from MA_ICD are correct. An error minimization process can be used to calculate the chip density using values appropriate to the friction transport efficiency, ROP, porosity, and the density of the chip-free fluid flowing in the annular determined from the minimization described above for the EAF_ISD. Changes in chip density calculated by the interval may indicate that the chips are falling out of the suspension as the modeled chip density is constant with depth. A chip control process can track the loss of chips in the ring and indicate the potential for undesirable drilling events, such as obstructions during drilling or during hole widening or tearing. The method modalities disclosed may also use measurements of the actual flow inside and outside each interval (for example, as described above with respect to Equation 8). These measurements provide a determination of Q x , and can therefore be used to differentiate between the effects of incoming or outgoing flow versus incorrect chip shaping effects, such as assumed chip density. When the flow of does not equal the flow from the outside, the differences can be attributed to the quantity f x -SG x in Equation 17 indicating flow from inside or outside the annular in the interval in which the differences occur. In certain applications, gap densities can then be used to calculate the fractional volume and density of a flow material (for example, using equations 8-17). This process can be useful for distinguishing between gas and salt water kicks, for example. MA_ICD and EA_ICD can be the same when the various parameters discussed above are modeled correctly. The differences between these two quantities can also indicate undesirable drilling events, as discussed above. In addition, the modeled friction effects may depend on the hole diameter. Using an LWD caliper, these effects can be properly accounted for. However, over time, the drilling well wall may experience washing or enlargement, for example, due to drilling practices, shale stability, or other geomechanical effects. Differences in MA_ICD and EA_ICD can be used to detect and monitor changes in the diameter of the drilling well. A minimization process can also be used to determine the average size of the drilling well within each interval, as a function of time. Losses of annular friction also depend on the rotation speed of the drill pipe (RPM) and the rate fluid flow. An time that these parameters can vary over time, the effects friction cancel also may be dependent of time is can be accounted for during drilling. Effects of Pressure and Temperature on Fluid Densities The fluid or mud that is being pumped into the well during drilling can be affected by the pressure and temperature changes it undergoes as it travels through the drill pipe and returns from the annular. For example, changes in pressure and temperature cause corresponding changes in fluid density. These changes can be measured using the above-mentioned ASM measurements and can allow the relationship between fluid density, pressure and temperature to be quantified and / or modeled which in turn allows other effects, such as chip loading and friction to be determined. The internal ASM pressures, temperatures, and calculated interval densities and temperature gradients can be used with a hydraulic model to calibrate model parameters. The hydraulic model can then be used to predict the effects of any other point in the system as a function of depth and time. Annular measurements can be used in the same way under non-perforation conditions (ie when there are no chips in the annular fluid). When the parameters of the hydraulic model are well defined and predictable for a particular drilling fluid, and in cases where either a measured temperature or a measured pressure is not available, the hydraulic model can be used to predict the missing measurement. FIG.4 represents the modeled oil-based sludge density (OBM) as a function of pressure and temperature. As indicated at 402 and 404, the density of the sludge increases with decreasing temperature 402 and increasing pressure 404. Under circulation conditions where the OBM temperature remains somewhat constant (that is, it does not increase significantly with depth) , the density increases with the OBM depth (and therefore the pressure), as indicated in 406. Under non-circulation conditions where the OBM temperature increases significantly with the depth, the effect of the temperature can overwhelm the effect of the pressure (ie that is, fluid density may decrease with increasing depth, as indicated in 408). FIG. 5 represents an example of a report including calculated interval densities obtained during an ASM in the drilling operation. Table 2 summarizes the relative locations of annular pressure measurements when the drill bit was located at a measured depth of 17,000 feet. The lower annular pressure measurement was made on a tool Schlumberger arcVISION® implanted in BHA. This pressure measurement is marked as APRS in lane 2 (at 502). The additional drill string included the first and second ASM annular pressure sensors marked 1231 and 5 1244 on lane 2. Sensor 1244 was located approximately 1259 feet (at measured depth) and 787 feet (at true vertical depth) above the BHA annular pressure measurement. Sensor 1231 was located about 5777 feet (at measured depth) and 5603 feet (at 10 true vertical depth) above sensor 1244. An SPPA surface measurement was located about 9934 feet above sensor 1231. TABLE 2 Sensor Drill depth Sensor displacement from the drill SensorMD Slopes SensorTVD Surface 17000 17000 0 0 0 ASM 1231 17000 7066 9934 0.2 9932 ASM 1244 17000 1289 15711 62 15535 APRS from 17000 30 16970 64 16322 toolarcVISIONin BHA Table 3 summarizes the parameters represented in the FIG. 5. Many of these parameters are described above in the INTERVAL DENSITY CALCULATION METHODOLOGIES section and are further described in more detail below with respect to the present example. TABLE 3 Track Curve name Definition 1 WDP status 0 = below 1 = : above2 APRS Pressure of Cancel per arcVISIONRing Pressure Pressure of Cancel in sensor ASM1231 # 1231 Ring Pressure Pressure of Cancel in sensor ASM1244 # 1244 SPPA Pressure in Pipe in Support in Surface 3 MA_ED_001 Calculation in ECD The leave in measurement in APRS using TVD in sensor MA_ED_003 Calculation in ECD The leave in measurement in ASM 1244 using TVD of sensorMA_ED_009 Calculation in ECD The leave in measurement in ASM 1231 using TVD of sensor 4 MA IED 003 001 Calculation density in Pressure intervalRing ASM sensor 1231 and surface. ofinMA_IED_009_003 Density calculation in Pressure interval of ASM 1244 sensor ring and ASM 1231 sensor. MA__IED_999_00 9 Density calculation in sensor interval ASM 1244 and surface sensor.5 MA TOM 003 001 Estimated ETOFL calculated The from pressure 1244 in APRS and ASM sensor. MA TOM 009 003 Estimated ETOFL calculated The from sensor pressures ASM 1244 and 1231. MA_TOM_009_001 Estimated ETOFL calculated The from pressures 1231 in APRS and ASM sensor.6 MA_TOM_003_001 Surface back pressure calculated using measurements in APRS sensor and 1244. MA_TOM_009_003 Surface back pressure calculated using measurements in sensor 1244 and 1231. With continued reference to FIG. 5, lane 7 (represented at 504) includes the densities and gap densities calculated between the pressure sensors referred to in the BHA and the drill string. The density of the annular sludge is calculated for each individual sensor and marked MA_EC (measured equivalent annular circulation density). MA_ED_001 corresponds to the equivalent density for the pressure measurement APRS, MA_ED_003 corresponds to the pressure measurement 1244, and MA_ED_009 corresponds to the pressure measurement 1231. These parameters tend to be insensitive to heterogeneities in the density of the local mud as illustrated in this example by fact that the values of each of the sensors are substantially identical and overlap each other on the graph. Although not shown in FIG. 5, the equivalent density calculated for each of the sensors has a value approximately equal to the density of the base OBM (about 7.9 ppg or 0.95 g / cm 3 ). When the pumps are switched off at the simulated connection (14:35 to 15:05 on track 1), these densities drop as expected, due to the lack of annular friction losses. The calculated gap densities are also shown in lane 4 (506) and are marked as MA_IED_003_001 (the gap density between APRS and 1244 sensors), MA_IED_003_009 (the gap density between sensors 1244 and 1231), and MA_IED_999_009 (a gap density between the 1244 ASM sensor and the annular surface pressure sensor). When the pumps are switched off at the connection, gap densities fall due to the elimination of annular friction losses. The gap densities are essentially the amounts of MA_ICD mentioned above when circulating and MA_ISD when not circulating. In this particular example, gap densities also closely represent EAF_ISD since the penetration rate (ROP) was low and there were long periods of circulation between the drilling events, which implies that there were few or no chips suspended in the annular fluid . The uppermost gap density (MA_IED_999_009) is approximately equal to the calculated equivalent densities shown in lane 3 (at 8 ppg). As shown in lane 4, gap densities decrease significantly with increasing depth, with MA_IED_003_009 being approximately equal to 7.6 ppg and MA_IED_003_001 being approximately equal to 7.3 ppg. Gap densities are likely to decrease due to the increase in lower well hole temperatures. In the absence of the effects of such temperatures, it would be expected that the density of a compressible fluid, such as an OBM, would increase with increasing depth. However, as shown in FIG. 4, increasing the drilling fluid temperature with increasing depth can result in a decrease in density. This can be observed directly using the gap densities disclosed here (as shown in FIG. 5). With further reference to FIG. 5, lanes 5 and 6 (shown in 508 and 510) represent the fluid equivalent top (ETOFL) and the calculated back pressure. In lane 5, the upper part of the fluid levels are marked MA_TOM_003_001 (the interval between APRS and 1244 sensors), MA_TOM_003_009 (the interval between sensors 1244 and 1231), and MA_TOM_009_001 (the interval between APRS and 1231 sensors). In lane 6, the return pressures are marked as MA_BP_003_001 (the interval between APRS and 1244 sensors) and MA_BP_003_009 (the interval between sensors 1244 and 1231). As shown, the calculated return pressures have positive values. The annular throttle pressure can be adjusted to a value equal to the value calculated for the pair in lower sensors (MA BP 003 _001 ) at lane 6 a end in maintain a pressure to cancel of hole of bottom constant when drilling through a window in Weight gives mud narrow After resuming circulation, the lowest sensor (APWD) measures the pressure for integral annular friction above the sensor (in addition to the static pressure), while the sensors located above the hole detect more decreasing friction losses. The resulting gap densities are therefore greater than the corresponding static gap densities. In well drilling operations, the temperature of the drilling well generally increases with increasing depth. In circulation (and drilling) conditions, the temperature of the drilling fluid is generally not a strong function of depth (due to the mixing of fluid and transport back to the surface). When circulation stops, the temperature generally increases with time and at any particular depth until a steady-state temperature is reached. As a result, the density of the drilling fluid can also be expected to decrease with time after circulation ceases. These time-dependent changes in density can also be observed using the above-mentioned interval densities. ASM temperature and pressure measurements and their relationship to the density of the fluid can also be used in refining and / or calibrating conventional hydraulic models. For example, measurements can be used to determine the coefficients in conventional API-13D equations: p base = (< , + b x P + c x P 2 ) + (a 2 + b 2 P + c 2 P 2 ) T Equation 24 Psaimour a = (a 2 + b 3 P + c 3 P 2 ) + (a 4 + b i P + c ^ P 2 ') T Equation 2 5 where p base represents the density of the base drilling OBM, represents the brine density, P represents pressure, T represents temperature, and a, b, and c represent adjustment coefficients. Table 4 includes sample book values for various conventional oil and / or brine solutions as well as statistics and validity ranges. TABLE 4 Calcium Chloride 19.3% by weight Diesel OilMineral OlefinInternal Paraffin Coefficients ofpressureai (lbm / gal) 9,9952 7.3183 6,9912 6.8358 6.9692 bi (lb m / gal / psi) 1.77 E- 5.27 2.25 E- 2.23 E- 3.35 E-05 E-05 05 05 05 Ci (lb m / gal / psi 2 ) 6 E-ll -8 E- -1 E-10 -2 E-10 -5 E-10 10 Coefficients ofTemperatureto 2 (lb m / gal / ° F) -2.75 -3.15 -3.28 -3, 39 -3.46 E-E-03 E-03 E-03 E-03 03 b 2 3.49 E- 7.46 1.17 E- 1.12 E- -1.64 E- (lb m / gal / psi / ° F) 08 E-08 07 07 08 c 2 -9 E-13 -1 AND- -3 E-12 -2 E-12 2 E-13 (lb m / gal / psi 2 / ° F)12 SettingsStatisticsfor DataModeledMean error% 0.135 0.237 0.166 0.194 0.214 Coefficient r z 0.998 0.997 0.998 0.998 0.999 RangeShelf lifeApplied PressureMax. (Psi) 20,300 20,000 20,300 24,000 14,500 Min. Temperature(° F) 77 40 77 56, 4 68 Max temperature.(° F) 392 400 392 392 302 It may be advantageous in certain applications to adjust these book values according to the conditions set. Once the oil-to-water ratio is known (which is normally controlled at the surface), the Equations 24 and 25 can be combined into a single equation that has six coefficients, for example, as follows: Piam »= (h + í p + kxP 2 ) + (i2 + j 2 P + k 2 P 2 ) T Equation 2 6 where p mud represents the density of the drilling fluid (the combination of base and brine) hey, j, and k represent the coefficients. This density can be measured in situ, for example, using the above-mentioned interval density calculations where the pressure and temperature values represent an average value for the interval. A drill string including six ASM pressure and temperature sensors, for example, can allow the six coefficients to be calculated. For example, six interval densities can be calculated using the corresponding six pressure and temperature measurements to obtain six equations with six unknowns (six coefficients). The values for the coefficients can then be determined using conventional root search algorithms. It should be understood that the number of intervals required can be reduced, for example, by using minimization techniques or using interval densities calculated at multiple times (or multiple depths) as long as the pressure and temperature measurements are sufficiently many different. Alternatively, Equations 24 and 25 can be combined into a single equation that has twelve coefficients, for example, as follows: Plama = MIF ISD = ^ Pbase + ^ brine P brine. r V mis Equation 27 MIFISD = V base [(«] + b i P + c l P 1 ) + {a2 + b2P + c2P 2 ) t] + (1 - ^ aie) [(« 3 + b 3 P + c 3 P 2 ) + (at 4 + bP + c 4 P 2 ) 7] Equation 28 where V base and V sa i maum represent the volume fractions of base and brine. The coefficients in Equations 27 and 28 can be obtained by making 12 independent interval density measurements, for example, in two different locations using the drill column described above having six ASM temperature and pressure sensors. In another alternative modality, the values for the brine coefficients (a 3 , b } , c 3 and a 4 , b 4 , c 4 in Equations 25 and 28) can be assumed and the six base coefficients evaluated, for example, using at least six independent interval density measurements. In the above embodiments, the coefficients can be determined using either internal gap density measurements or annular gap density measurements. Internal gap density measurements may be preferred due to the lack of chips inside the drill string, however, annular measurements can also be used when chips are counted using one or more of the techniques mentioned above. Chip Transport Efficiencies and Training Characterization ASM temperature and pressure measurements can be used to detect changes in chip densities and transport efficiencies and can therefore also be used to characterize the lithology of the formation to be drilled. As described above in relation to Equations 8-17, ASM pressure measurements can be used to determine the constituent densities of various materials in the drilling fluid. In operations where there is no input flow or annular output flow (that is, when Q x and x x are approximately equal to zero), the chip density can be readily determined using EA ISD and MA ISD. FIGS. 6, 7 and 8 represent a hypothetical example of a well drilling operation, in which a change in the formation of lithology is verified as resulting in a reduced chip density. In each of FIGS. 6, 7, and 8, lane 2 (shown at 604) schematically describes the lithology being drilled, for example, as determined by a calculated chip density and dimensionless torque. The drill pipe and drill bit are shown in 622 and 624, while. that the outline of the drilling well is shown in 626. The chips are further described in 628 as being carried to the surface in the drilling fluid that moves upward through the annular. The drilling column represented. includes four temperature and pressure sensors along column 630A, 630B, 630C and 630D and one surface sensor 632. It should be understood that the described modalities are not limited to any particular number of sensors of ASM. Lane 1 represents (in 602) MIF_ISD and EIF_ISD, the first of which is calculated from MIF_ICD by subtracting the friction effects from the modeled and / or measured internal drill pipe on the flowing mud. The EIF_ISD represents the density properties of the inlet mud corrected for the effects of measured and / or modeled pressures and temperatures of the internal drill pipe using a suitable hydraulic modeling program. The hydraulic modeling parameters needed for the effects of pressure and temperature can be determined by matching EIF_ISD to MIF_ISD during the intervals where MIF_ISD calculations are available. Lane 3 includes (in 606) the calculated annular gap densities, EAF_ISD, MA_ISD, EA_ISD, MA_ICD and EA_ICD. EAF_ISD represents the density of the chip-free inlet mud flowing over the annular corrected for the annular pressures and temperatures measured using the same hydraulic modeling parameters determined for the internal mud. The modeled chip load is added to EAF_ISD to obtain EA_ISD. The measured static interval density MA_ISD is equal to the measured circulation interval density MA_ICD minus annular friction losses, when the chip volume, density, and transport and friction flow parameters are appropriately modeled. A minimization program can be used in modeling, as described above, to achieve this as described above. Lane 4 describes (at 608) the calculated chip density. Other parameters are presented in Lanes 58 and discussed in more detail below in relation to the other examples. It should be understood in Figs. 6, 7, and 8 that when two parameters (for example, represented by dashed and solid curves) are equal to each other, they are shown with a slight separation (approximately one curve width), in order to make two curves visible. Such presentation is purely for convenience and is not intended to be limiting. The time differentials of the measured circulating and static interval densities MA_ISD and MA_ICD are shown in lane 5 to 610. The upper fluid ETOFL equivalent for the circulating and static fluid is shown in lane 6 to 612. Back pressure BP annular calculated for the circulating and static fluid is shown in lane 7 to 614 and the static and circulating pressures P of annular measurements are shown in lane 8 and 616. FIG. 6 represents the hypothetical drilling operation at time í] = 0. As shown in lane 3 (at 606), the measured and expected zero and circulation densities are equal to each other (ie, MA_ISD is approximately equal to EA_ISD and MA_ICD is approximately equal to EA_ICD). The calculated chip density shown in lane 4 is constant with the depth indicating that the time required for the chips to reach the surface is less than the time required to pierce the present formation layer. The chip volume fraction / decreases towards the top of the drilling well (as shown schematically in lane 2) and may be due, for example, to the effects of penetration rate, formation porosity, and / or transport of shavings as a function of time. These variables can be accounted for in the minimization process. The amount of fumes can also be shown in the log if desired. FIG. 7 represents the hypothetical drilling operation shown in FIG. 6 in time ί 2 = /] + Δί and includes the same tracks, as described above. As shown in lane 2, the drill bit penetrated a new formation having a lower density, thus resulting in 629 chips having a lower density than previously generated chips 628. As a direct result of the reduced chip density, MA_ISD is below of EA_ISD and MA — ICD is below EA_ICD in the lowest range (as described in 702 and 704 on track 3). It will be understood that the change in chip density can be identified by signatures other than those discussed above in relation to FIG. 7. Tables 5A and 5B list the expected signatures that result from such a change in chip density in the annular (typically as a result of drilling a new formation before the minimization process has calculated a new chip density value). Table 5A lists the signatures expected when drilling a formation that has a lower density, while Table 5B lists the signatures expected when drilling a formation that has a higher density. TABLE 5A Parameter Changes with Time ChangesDepth with the Q. Q x = 0; None ô x = 0; None changechange can change can change SG Calculated value goes ATshavings decrease MORE D MA_ISD <EA_ISD; Decrease in MA_ISD if vs. MA_ISD decreasing with moves up the hole EA_ISD the time until the insofar as theinterval contain shavings more light ifonly the new ones move up the holelighter shavings not cancelMA_ICD MA_ICD <EA_ICD; Decrease in MA_ICD if vs. MA_ICD decreasing with moves up the hole EA_ICD the time until the insofar as theinterval contain shavings more light ifonly the new ones move up the holelighter shavings. not cancelETOFL ETOFL decreases with ETOFL is lower intime over trim intervalsaffected range. lighter.BP of BP increases with BP is higher in breaks Surface time over with lighter shavings. and UndoCalculated affected range.Pressure Slight decrease Slight decrease from ASM with time over over intervals withthe affected range. lighter shavings. ASM temperature No changes No changes TABLE 5B Parameter Changes with Time Changes withDepth The Q x = 0; No changes ( x = 0; No change F x can change can change Ç (Zshavings Calculated valueincrease AT MORE D MA_ISD> EA_ISD Increase in MA ISD if vs. MA_ISD increasing with moves up the hole EA_ISD the time until the insofar as theinterval contain heavier shavings ifjust new shavings move up the holeheavier. do not cancel s MA_ICD MA_ICD> EA_ICD Increase in MA ICD if VS. MA_ICD increasing with moves up the hole EA_ICD the time until the insofar as theinterval contain heavier shavings ifonly the new ones move up the holeheavier shavings. not cancel ETOFL ETOFL increases with ETOFL is higher overtime over the of intervals with cutsaffected range. heavier. BP Override BP decreases with BP is lower at intervals in time over the with heavier shavings. Surface andCalculated affected range.Pressure Slight increase with Slight increase in from ASM time over the intervals having shavingsaffected range. heavier. ASM temperature No changes No changes FIG. 8 represents the hypothetical drilling operation shown in FIG. 6 at time t 3 = t 2 + At and includes the same tracks, as described above. When Q x = 0 um. minimization program can be used directly to determine the chip density. This density of the new chips is represented in lane 4 in 802 and indicates a reduced chip density as expected. The new chip density can also be used to calculate new expected static and circulation gap densities EA_ICD and EA__ISD, which are approximately equal to the corresponding measured gap densities MA_ICD and MA_ISD as shown in lane 3 to 804 and 806. SG ^^ chip density can be used, for example, to identify the lithology of the formation to be drilled (for example, sand, limestone, dolomite, shale, tar, salt, etc.). For example, quartz sandstone has a density of about 2.65, calcium carbonate limestone has a density of about 2.71, magnesium and calcium carbonate dolomite has a density of about SG of 2.85, mixed mineral shale formations have an average density in the range of about 2.6 to about 2.7, the halite salts have a density of about 2.17, the tar layers have a density in the range of about 0.8 to about 1.1, and anhydride has a density of about 2.97. Knowing the speed of the chips (or speeds) over time, allows the deep shavings assigned, which for your turn can to allow one register of lithology (for example, how represented at lane 2) be built . In the example represented in FIGS. 6-8 , the density of shavings in break a to be perforated is less than interval the previous one, which still helps in identifying the formation lithology. Those skilled in the art will immediately understand that the gross formation density is a widely used petrophysical parameter. This parameter is commonly used for applications ranging from overload calculations, geomechanical modeling, synthetic seismograms and determination of formation porosity. The soil density 'of the formation is generally a function of the lithology (or mineral content of the formation) and the type and volume of fluid in the formation. In drilling operations where the drilling process destroys the formation porosity, the calculated chip density can be used as the mineral density (formation matrix density), to calculate the porosity of a soil density measurement of the geophysics of the drilling well. Tar Matrix Identification Tar zones (also referred to in the art as tar mats) are a common threat in drilling operations and can sometimes pose a serious risk to the drilling operation. Since tar is difficult to identify on seismic maps, evasion can be challenging and is often based primarily on local experience. In addition, commonly used drilling technologies (LWD), such as gamma ray and resistivity measurements, are not always able to identify tar areas. As such, a drilling operator is sometimes unaware that a tar area has been intercepted until the ring is filled with tar. This can result in a clogged BHA situation. The ASM temperature and pressure measurements and interval densities described here can be used to quickly identify and mitigate the intercepted tar areas. The disclosed gap densities can be used to identify the tar in the annular by calculating the chip gap density, as described above with reference to FIG. 6-8 and Tables 5A and 5B. The presence of 'tar in the annular can be identified by a decrease in the density of the lower range. This decrease can be modeled as a corresponding decrease in the calculated chip density. Tar dies tend to cause a significant reduction in gap density for at least two reasons. First, the density of tar is significantly less than that of generally perforated rock formations 10 (for example, in a range of about 0.8 to about 1.1, compared to a range of about 2 to about of 3, for the perforated rock as described above). Second, tar matrices generally include a high volume fraction of tar 15 (many tar matrices are non-porous layers that are made up of about 100% tar) such that the volume fraction of tar in the range void location is also high. The early identification of tar matrices 20 allows the drilling operator to reduce the flow of tar entry into the well bore. The attenuation can include any number of techniques, for example, including the use of controlled pressure to artificially reinforce the pressure of compression or back pressure in the annular to maintain additional tar from the detachment inside the drilling well, moving the pipe above the point of the non-circulating tar matrix, then introducing a heavier slurry into the drilling well (called localized injection), lateral tracking around the tar, treating the tar with various chemical additives, and insulating the tar through the use of various types of coating. The disclosed modalities are obviously not limited to any specific mitigating action. Drilling Well Wash Due to various geomechanical and / or drilling practices, the drilling well may become enlarged over time during a drilling operation. Such an enlargement of the well can be detrimental for several reasons. For example, an enlarged hole can reduce the speed of chips by moving through the ring, thus increasing the possibility of chips falling from the suspension and obstruction of the drilling well. The enlarged drilling wells also require large volumes of cement during coating operations. FIGS. 6, 9 and 10 show a hypothetical example of another well drilling operation, in which a portion of the drilling well becomes enlarged during the drilling operation (FIGS. 9 and 10 represent the widening). This example again uses FIG. 6 to represent the hypothetical drilling operation at time t ] - 0. As described above, the measured and expected gap densities are substantially equal to each other over the length of the well (ie = MA_ISD EA_ISD and MA_ICD = EA_ICD as shown in lane 3), indicating that the effects of chip volume, density of chips, chip transport and fractional volume, and annular friction were adequately modeled. FIG. 9 represents the hypothetical drilling operation at time t 2 = t l + At and includes the same tracks, as described above in relation to FIG. 6. A wash zone with increased diameter is represented at 902 in lane 2. At lane 3 in 904, MA__ICD has decreased and is less than in the EA_ICD wash interval, however, MA_ISD remains substantially constant and is approximately equal to EA_ISD as shown in 90 6. The extended drilling well causes the annular friction pressure to decrease in the wash interval, thereby reducing the measured gap density in circulation, but not the expected gap densities that are calculated using a model that makes use of measurements with LWD caliper or drill size when the gap has been drilled. The static densities of measured and expected intervals remain substantially the same since the wash is at a constant depth and since the chips are not falling out of the suspension, in this example. The MA_ISD mf that is calculated by subtracting a modeled annular friction MA ICD also decreases in the wash interval as shown in 908. In lane 5 to 910, the MA_ICD derivative is negative, indicating a decrease in MA_ICD over time, as in which the drilling wells are washed (it becomes enlarged). FIG. 10 represents the hypothetical drilling operation in time ί 3 = ί 2 + Δ / '. A minimization process was instructed to calculate a new drilling well diameter such that the expected annular friction pressures are reduced and correspond to the measured interval circulation density. As shown in lane 3 to 1002, MA_ICD and EA_ICD are now the same in the wash interval (as a minimization process that creates a substantially larger result of the drilling well diameter). This new diameter can be stored as a function of time for plotting and analysis against drilling practices and time-dependent formation resistance parameters and determinations to further enhance understanding of formation resistance and recognition and prevention of drilling practices harmful in the future. In addition, the diameter of the drilling well calculated at the end of the drilling process can be used to calculate the volume of cement required in the post drilling coating operation. It will be understood that a change in the diameter of the perforation (for example, caused by a wash) can cause corresponding changes in some of the disclosed parameters other than those described above in relation to FIGS. 9-10. Table 6 shows the expected changes caused by washing or widening a 5-well well. TABLE 6 Parameter Change over time Change withdepth &No changes Q, = 0; None change THEIt can decrease and can Can decrease and can change over timechange as far asother intervals arewashedSG iparas None changeNo changes BAD_ ISD MORE D constant as MA_ISD = EA_ISD the same vstime is equal to EA_ISD interval in AND THE_ _ISD during the washing.depth, do not MORE D > MA_ISD mf moves above the hole aless than othersbreaks beextended.BAD_ _ICD MA_ICD decreasing as MA ICD less than EA ICD VStime is less than EA ICD over the AND THE_ ICD during the washing.depth affected,don't move above of hole unless other intervals are extended. ETOFL's Decreases as far as what Decreases as what circulation the wash expands with the washing is enlarged,O the time Static ETOFL Remains innot changing.fixed depths.BP of Increases as far as what Increases as what cancel from the wash expands with the washing is enlarged,superfici the time. Static BP not Remains in and changing. fixed depths.calculatedincirculationOPressure Slight decrease gives Slight decrease can from ASM pressure circulation change like othersduring the enlargementwashing intervals • Temperatu Light increase with 0 Slight increase due to of ASM time due The decreased speeddecreased speed flow in thatflow -depth. Drilling well obstruction As used in the art, an obstruction describes a situation in which the diameter of the drilling well has been reduced creating a strangulation of the fluid flowing upwards from the annular. This reduction can be caused, for example, by a large volume of chips that fell from the suspension in the annular or peeling off the wall of the drilling well in the annular. With insufficient annular fluid speed, mud viscosity, or in a very steep drilling well, chips can build up to a certain depth in the well and cause a restriction (obstruction). Depending on the severity of the obstruction, the pressure may increase to undesirable levels deeper in the well and may even cause the formations to rupture if corrective measures are not taken in time. Ά obstruction too may result in loss circulation that, for your time, can cause a loss in pressure hydrostatic and one flow of input possible 'or same a kick from an formation permeable. Severe obstruction can also result in a trapped BHA if sufficient chips are left to accumulate around the drill string. FIGS. 11, 12, and 13 represent a hypothetical example of a well drilling operation in which the drill cuttings fall out of the suspension and form an obstruction. Lane 2 of FIG. 11 includes an enlargement at 1102, as described above with reference to FIGS. 9 and 10. In FIGS. 12 and 13 an obstruction is shown just below the widening at 1202. FIGS. 11-13 exhibit the same tracks, as previously described in FIGS. 6-8. In this example, FIG. 11 'represents the hypothetical drilling operation in time /, = 0 (after the formation of the wash). It should be understood that the described modalities are not limited by the representation of a wash. In lane 35 of FIG. 11, the measured and expected gap densities are substantially equal to each other along the length of the well hole (ie = MA_ISD EA_ISD and MA_ICD = EA_ICD) which indicates that the effects of chip volume, chip density, chip transport and 10 of the fractional volume, and annular friction were adequately modeled. The obstruction is shown schematically in lane 3 (at 1202) in FIGS. 12 and 13. The restriction causes the annular circulation pressures further down the well 15 to increase, as shown at 1204 in lane 8 of FIG. 12. Circulation pressure above the limit can also decrease slightly as illustrated in 1206, if the flow rate is significantly reduced above the obstruction. At . conventional annular pressure measurements themselves can sometimes be used to identify the obstruction by monitoring changes in annular pressure over time and depth. The described gap densities can also be used to identify an obstruction and tend to provide a more definite signature. For example, as shown in FIG. 12, the gap densities covering the obstruction tend to increase while the densities of the gap above and below this range tend to remain unchanged. Within the scope of the obstruction, the measured gap densities MA_ISD mf and MA_ICD increase significantly over the corresponding expected (modeled) interval densities EA_ISD and EA_ICD as described in 1208 and 1210. When the pumps are brought down and the actual static density is measured, MA_ISD mf is also observed to be greater than the measured static interval density MA_ISD. In addition, MA__ISD can be approximately equal to (or possibly slightly greater than) EA__ISD as shown in 1212 as a function of the accumulated chip mass. It is also noted that it is approximately equal to zero, as indicated at 1214 in FIG. 12. These observed signatures tend to be exclusively attributable to obstructions (or other annular constraints) with the added feature that the aforementioned gap density differences remain at a fixed depth (since the obstruction itself remains at a fixed depth ). FIG. 13 is similar to FIG. 12, but represents an alternative methodology for calculating gap densities. In particular, each of the intervals used in FIG. 13 extends from the depth of the ASM sensor to the surface (instead of the gap between adjacent sensors as shown in FIG. 12). In FIG. 13, each of the circulation interval densities measured below the obstruction is greater than the corresponding expected circulation interval density as described in 1302 and 1304. The calculated ETOFL and BP are zero, by definition, when using this calculation technique as shown in lanes 6 and 7. In the methodology shown in FIG. 13, gap densities from the obstruction site to the drill bit increase. This can advantageously make the visual impact of the event more noticeable in certain display configurations and can even allow the axial location of the obstruction to be estimated. It should be understood that the development of an obstruction or restriction can cause corresponding changes in certain disclosed parameters other than those described above in relation to FIGS. 12 and 13. Table 7 lists the expected changes caused by an annular restriction or obstruction. TABLE 7 Parameter Change over time Change withdepth The The Q x = 0; No changes Q x = 0; No changes F x No changes No changes shavings No changes No changes MA_ISD mf MA_ISD mf > MA_ISD MA_ISD mf > EA_ISDvs. Increases over time in Over the range in MORE D insofar as depth inobstruction develops obstruction onlyMORE D MA_ISD »EA_ISD MA_ISD «EA_ISDVS.Over the range in EA ISDdepth in obstructionMA_ICD MA_ICD> EA__ICD MA_ICD> EA_ICDVS. Increases over time in Over the range in EA ICD insofar as depth inobstruction develops obstruction onlyPart Circulating ETOFL Circulating ETOFL higher increasing increasingof the fluid throughout the event, throughout the event, estimated slightly decreasing slightly decreasingbelow the event, and below the event, andno change above the no change above ofevent, all changing in event. 0 interval in as the obstruction develops. Static ETOFL is not affected if the obstruction interval is short. obstruction has greater ETOFL. Static ETOFL is not affected if the obstruction interval is short. BP Override Circulation BP Circulation BP in decreasing over the decreasing over the surface event, slightly event, slightly and increasing below the increasing below the calculated event, and none event, and nonechange above the event, change above the event.everyone changing to the extent 0 obstruction intervalwhere the obstruction is has the lowest BP.develops.Pressure The pressures of The pressures of from ASM circulation increase circulation increasebelow the obstruction, below the obstruction,no change above the no change above theobstruction, increases in obstruction.insofar as obstruction develops.Temperatu Slight increase with Slight increase below of ASM time below obstruction decreasesobstruction, decreases above above the obstructionobstruction The identification of the obstruction, observing annular pressures and gap densities, can be automated so that the signature shown in FIG. 12 (for example, MA_ISD> EA_ISD and MA_ICD> EA_ICD with the differences not changing over time) triggers an alarm that alerts the drilling operator. The automation routine can further reduce the circulation rate to reduce pressure build-up below the obstruction. The drilling operator can then initiate a sequence of steps designed to break or undo the obstruction (for example, by working the drilling column up and down in the drilling well during rotation). It should be understood that the modalities described are not limited in this regard. Inlet flow into the Drillhole Annular As is known to those skilled in the art, forming fluids tend to flow into the well bore during drilling when the formation has a higher pore pressure than the mud pressure at the depth of the formation. Such inflow events can occur higher above the drilling well if the mud column is dropped below the surface, for example, when firing the drill pipe out of the drilling well. Well cleaning events can also contribute to an inflow. Fluids in the formation, such as gas, oil, or synergistic water, generally exhibit a lower density than the drilling mud. Any inlet flow, therefore, tends to further reduce hydrostatic pressure, allowing the flow rate to increase until the borehole can no longer be controlled. Timely attenuation, therefore, requires early recognition of the inflow event. ASM temperature and pressure measurements and reported gap densities can be used to identify incoming flow events soon after they start. FIGS. 14, 15, 16, and 17 represent a hypothetical example of a well drilling operation including an input flow event in the formation (also referred to as a kick). Lane 2 of FIG. 14 represents the drill bit that penetrates a new formation 1402. In FIGS. 15-17 the fluid inlet flow in the formation is represented at 1502 in lane 2. FIGS. 14-17 exhibit the same tracks, as previously described in FIGS. 68. In this example, FIG. 14 represents the hypothetical drilling operation at time i, = 0 (after penetrating formation 1402, but before the fluid inlet flow event shown in FIGS. 15-17). It should be understood that the described modalities are not limited by the representation of the fluid flow that comes from the bottom of the well. The inlet flow can occur substantially anywhere along the length of the drilling well, as is known to those skilled in the art. In lane 3 of FIG. 14, the measured and expected interval densities are substantially equal to each other over the length of the well (ie = MA_ISD EA__ISD and MA_ICD = EA_ICD) which indicates that the effects of chip volume, chip density, chip transport and fractionated volume, and annular friction were adequately modeled. In addition, as shown in 1404, Q x is approximately equal to zero, indicating that there is no inflow. FIG. 15 represents the hypothetical drilling operation at time t 2 = t l + / Sí. The inflow event was initiated as represented in 1502 of lane 2 making Q x greater than zero as represented in 1508. The parameter Q x can be estimated by measuring the surface of the difference in flow rate between the flow outside the annular and the flow inside the drill string (a volume of differential flow). Equations 817 depicted above can be used to more accurately calculate or determine Q x . In some cases, a simple difference between the flow rate outside the annular and the flow rate inside the drill string may be adequate to estimate a value of Q x . More accurate values of Q x can be obtained, taking into account generated from the drilling operation as disclosed in Equations 8-17. In normal drilling operations, Q chips may be in a range, for example, from about 1 to about 5 percent of the drilling fluid flow rate. An inflow event (for example, a kick) can result in Q x being in a range, for example, from about 5 to about 100 percent or more of the drilling fluid flow rate. With continued reference to FIG. 15, the circulation and static interval densities measured MA_ISD and MA_ICD decreases below the corresponding 10 expected values of EA_ISD and EA__ICD as shown in 1504 and 1506 on track 3. Since Q x Ψ 0 the program logic retains the most recent value of SG ^^ as indicated in 1510 (and through the comparison of lane 4 in Figures 14 and 15). FIG. 16 represents the hypothetical drilling operation 15 in time ί 3 = Ζ 2 + Δί. A minimization process is used instead of calculating a value for the material density of the inlet flow, as indicated in 1610 in lane 4 of FIG. 16 (for example, using Equations 8-17). The calculated density of the incoming flow material SGc can then be used to estimate the type of fluid coming into the annular. For example, a gas inlet flow can have a density of less than about 0.6, an oil inlet flow can have a density in the range of about 0.6 to about 0.8, and a Inlet flow of synergetic water can have a density of about 1 to about 1.2. After assigning a value to SG X , the measured circulation and static interval densities MS_ISD and MS__ICD are again approximately equal to the expected values of ES_ISD and 5 ES_ICD as shown in 1602 and 1604. FIG. 17 represents the hypothetical drilling operation in time í 4 = í 3 + Δί. As the inlet flow rises or circulates over the annular as shown at 1702 in lane 2 of FIG. 17, the calculated SG X moves to 10 'above the annular as shown in 1710 on lane 4. This further illustrates the signature differences between an incoming flow and an obstruction or widening of the drilling well, where the disturbance of pressure remains at a constant depth. In addition, the derivative of the 15 gap densities (shown in 1612 and 1712 of FIGS. and 17) indicate the speed with which the inlet flow moves above the annular, thus facilitating the planning of the particular control methodology used to control the well. With continued reference to FIGS. 14-17, the fluid level ETOFL Equivalent upper part becomes negative at annular intervals with the inlet flow material (for example, as indicated in 1512 on lane 6 of FIG. 15). In addition, the calculated annular BP back pressure of the surface becomes positive at the annular intervals with the inlet flow material (for example, as indicated in 1514 in lane 7 of FIG. 15). As the flow material moves upward from the well hole, ETOFL decreases (or becomes negative) and BP increases (or becomes positive) at progressively higher intervals in the drilling well. FIG. 18 represents an example of a visual display illustrating the inflow as a function of time and depth. The depth is shown on the vertical axis, increasing in a downward direction. Time is shown on the horizontal axis increasing to the right. The range density values are plotted as outlines (for example, using pseudo-color highlighting with warm colors representing lower range density values - but using the gray scale outlines in the example shown, where a darker shade represents lower interval density values). The black regions are below the drill in the example shown below and therefore do not include any data. The left screen at time í, represents a snapshot of a time interval in which drilling is progressing. A lighter interval density is shown to be appearing in the lower range, to the right in 1802. Subsequent screens represent subsequent times t2, t $ and 4 when the kick of a relatively low density fluid moves upward from the annular with the time (the progression time is indicated in 1804, 1806, and 1808). It should be understood that the development of an input stream (or kick) can cause corresponding changes in certain disclosed parameters other than those described above in relation to FIGS. 14-17. Table 8 lists the expected changes caused by an input stream before SG x and Q x were calculated (for example, through the aforementioned minimization processes) and adjusted to the expected annular gap densities EA_ISD and EA_ICD. TABLE 8 Parameter Change over time Change withdepth The Q x Q x >0; You can change with a> o time F x No changes No changes aoaras No changes No changes MORE D MA_ISD <EA_ISD MA_ISD <EA_ISDvs. Difference increases with Moves up of EA ISD time if the flow of cancel over time if theentry continues input stream to be continuedMA_ICD MA_ICD <EA_ICD MA_ICD <EA_ICDVS. Difference increases with Moves up of EA ICD time if the flow of cancel over time if the 100 entry continues input stream to be continuedPart ETOFL is negative in ETOFL is negative we higher breaks breaksof the fluid containing the flow of containing the flow in equivalen entrance and input and the effect in you decreasing with time input stream ifif the input stream will move above the annulto be continued with timeAnnul BP BP is positive and increases BP is positive we in over time if the flow breakssurface input continues containing the flow in andinput, and the effect in calculatedinput stream will move up of cancel with timePressure It decreases over time if the Decreases in intervals from ASM input stream containing the flow into be continued input, and the effect in input stream moves up up the ring with the time.Temperatu Depends on temperature Highest rate of change at of ASM input stream, flow depth in 101 type of inlet flow, and if there are no Joule-Thomson pressure effects. It changes over time if the input flow rate changes. Inlet, changes migrate above the hole with the fluid from the inlet flow. During the formation fluid sampling operations, the formation fluid can be pumped (or released) into the annular. For example, the forming fluid is often pumped into the annular for a period of time before sampling the forming fluid to ensure that only virgin fluid is sampled (that is, that the sampled fluid is not contaminated with the fluid drilling or shavings). Up to one barrel or more of formation fluid can be released 10 into the annular for each sample acquired. The density of the annular fluid can be monitored during sampling, using the interval density techniques described here. In addition, after the samples are acquired, the forming fluid can be circulated to the surface and released through an annular choke. Gap densities can also be used to monitor the upward movement of the forming fluid through the annular, thereby saving considerable probe time. 102 When an inflow event (for example, a kick) is encountered, a drilling operator may decide to circulate through an annular choke while the heavy mud is pumped into the well. The disclosed gap densities can continue to be measured and calculated and used to determine when the bottom hole density and pressure is sufficient to interrupt the inlet flow. For example, a measured lower bore pressure can be used to conduct a choke to keep the pressure within a desired range when pumping heavy mud. Drilling Well Annular Outflow Annular fluids can flow into the formation, since it is perforated when the formation has a pore pressure less than the pressure of the drilling fluid at that depth. Such an outflow can happen at the drill bit or higher above the drilling well if the pressure of the drilling fluid is allowed to rise above the forming pressure. In some operations, an outflow reduces the hydrostatic pressure load, thereby causing the outflow rate to decrease until the well bore stabilizes. Such outflow events can be considered as self-attenuating. However, in other operations, the reduced hydrostatic pressure load caused by the outflow can trigger an inlet (or kick) flow in another formation (for example, in another location) 103 in the drilling well). As described above, inflow events can lead to highly dangerous and uncontrollable well conditions. Timely mitigation requires early recognition of the problem, and in line with the purposes of this section, timely recognition of the outflow event. ASM temperature and pressure measurements and reported gap densities can be used to identify flow outflow events soon after they start. FIGS. 14, 19, and 20 represent a hypothetical example of a well drilling operation, including a drilling fluid outflow event. Lane 2 of FIG. 14 represents the drill bit that penetrates a new formation 14 02, as described above in relation to FIGS. 14-17. In FIGS. 19 and 20, the outflow of the drilling fluid in the formation is described in 1902 in lane 2. FIGS. 14, 19, and 20 exhibit the same tracks, as previously described in FIGS. 6-8. In this example, FIG. 14 represents the hypothetical drilling operation at time / = 0 (after penetrating formation 1402, but before the fluid outflow event shown in FIGS. 19 and 20). It should be understood that the described modalities are not limited by the description of the fluid that leaves the bottom of the well. Outflow can occur substantially anywhere along the length of the drilling well, as is known to 104 skilled in the art. In lane 3 of FIG. 14, the measured and expected gap densities are substantially equal to each other along the length of the well hole (ie = MA_ISD EA_ISD and MA_ICD = EA_ICD) which indicates that the effects of chip volume, chip density, transport of shavings and fractional volume, and annular friction were properly modeled. In addition, as shown in 1404, Q x is approximately equal to zero, indicating that there is no inflow or outflow. With continued reference to FIG. 14, the upper circulating and static ETOFL fluid levels are shown in lane 6. These values can be calculated from the measured static interval densities MA_ISD (for example, according to Equation 20). As shown, ETOFL from the surface to the first pressure sensor is zero. ETOFL values tend to vary within the well, however, the sum or net average is approximately zero. The BP annular counterpressure of the calculated surface is anti-correlated with ETOFL (as shown in lane 7) and again counts approximately zero under the conditions of t = 0. FIG. 19 represents the hypothetical drilling operation shown in time /, = ί ι + Δί. The outflow event was initiated as described in 1902 of lane 2 causing Q x to be less than zero, as represented in 105 1908. The parameter can be obtained as described above in relation to FIG. 15. In the example shown, the level of drilling fluid in the annular dropped below the surface due to the outlet as shown in 1904 in lane 2 (for example, during static well-hole conditions). The measured circulating and static pressures are less than the pre-flow outlet values as described in 1912 and 1914 on lane 8. The MA_ICD and MA_ISD interval densities decreased in the interval containing the liquid level and any intervals above one as shown in 1906 and 1907 of runway 3. These values may (or may not) fall below EAF_ISD depending on the effects of liquid level, chip loading and annular friction. The derivatives of the static circulation range densities are negative within and above the range containing the liquid level and zero in the ranges below the range containing the liquid level as shown in 1916 and 1918 of runway 5. With continued reference to FIG. 19, the values of ETOFL increased at all intervals containing a column filled with drilling fluid as shown in 1922 in such a way that the sum or average became positive. FIG. 19 represents a scenario in which the fluid level is above the uppermost ASM 630D pressure sensor. In this example, the gap between the surface and the uppermost pressure has a zero value ETOFL by definition. O 106 range just below the range containing the liquid level can be made to have BP values and a high quality ETOFL. The calculated mean surface annular BP is negative. The average value represents the initial amount of reduction of the actual BPs for the MPD surface equipment. As blood pressure is lowered, gas or nitrogen may come out of the solution, thereby reducing the density of the annular fluid in a positive feedback condition. If no BP is being applied, the bottom hole pressure (BHP) of the lower sensor extrapolated to the total depth represents the pressure of the forming pores and the maximum BHP for the forward drilling. FIG. 20 is similar to FIG. 19, but represents a scenario in which the drilling fluid level has dropped to 15 below the first ASM (note that the 1904 fluid level is below the uppermost ASM sensor 2002). In this scenario, the range including the fluid level now has a non-zero ETOFL and BP, as shown in 2004 and 2006 on tracks 6 and 7. In addition, the density of 20 MA_ISD and MA_ICD intervals are close to zero in the longest range higher as shown in 2008 in lane 3 as this interval does not contain any fluid. The ETOFL and BP values can again be obtained from the first interval below the fluid level. It should be understood that, although the level of the annular fluid may drop during a lost circulation event, 107 the fluid level of the inner drill tube may or may not coincide with the annular fluid level due to different pressures above and below both fluid levels. This condition is often referred to in the art as ü-tube. Internal pressure measurements can be used to determine the level of the liquid inside the drill tube in a manner analogous to the method described above for the level of the annular fluid. In addition, in extreme lost circulation events, the fluid level in the annular 10 may drop during circulation while the drilling fluid is being pumped into the drilling column. It should be understood that the development of an output stream can cause corresponding changes in 15 certain parameters disclosed other than those described above in relation to FIGS. 14, 19, and 20. The Table shows the expected changes caused by an outflow. It should be understood that minimization may not be necessary to calculate the new expected range densities 20 EA_ISD and EA_ICD. 108 TABLE 9 Parameter Change over time Change with depth The Q x <0; You can change with Q x <0; You can change withtime depth F x No changes No changes çx ~ »shavings No changes No changes MORE D MA_ISD <EA_ISD MA ISD <EA_ISD vs. Difference changes Moves under the EA ISD until the liquid level cancel with time untilstabilizes. MORE D the liquid leveldecreases over time stabilizes.along the breaks MA ISD falls downaffected which are or close to EAF ISD inintervals above and interval having levelincluding the level of liquid. MA_ISD and MA ICDfluid. at intervals below the liquid level they are not affected. MA ICD MA ICD <EA ICD MA_ICD <EA_ICD VS. Difference changes Moves under the EA_ICD until the liquid level cancel with time untilstabilizes. MA ICD the liquid leveldecreases over time stabilizes. MA ICD fallsalong the breaks down or close to 109 affected what are EAF ISD in rangebreaks above and having liquid level.including The level in MA ICD approachesfluid. MA ISD in range containing the level of fluid and MA ISD equal at intervals above fluid level at which substances that are not liquids are gifts. Part Both static ETOFL Both static ETOFL higher how much of circulation how much circulation is of the fluid increase over time in positive in the intervals equivalen each interval below of lower and including the you interval containing O liquid level. Move-fluid level up what up down until theThe level of the fluid liquid levelstabilizes. Average in stabilizes. Intervalall the breaks is below the level ofpositive. fluid has ETOFL representative. Average of all intervals is positive. Annul BP Both the Static BP Both static BP 110 insurfaceandcalculated when circulating they decrease with time in each interval below the interval containing the fluid level until the fluid level stabilizes. how much circulation is negative in the intervals below and including the liquid level. Move down until the liquid level stabilizes. Average of all ranges is negative. ASM pressure Decreases on all sensors. Decreases over time if outflow continues It decreases on all sensors until the liquid level stabilizes. The amount of decrease will be the same for all sensors below the fluid level for incompressible fluids. ASM temperature Increases at all intervals due to lack of circulation. Increases over time. It may increase at affected intervals due to lack of circulation. In response to an outflow event, a drilling operator often closes the well, stops pumping, and closes the annular choke until pressures stabilize. Gap densities can be 111 used to determine the liquid level of the drilling fluid, while ASM and APWD measurements can be used to obtain BHP when the liquid level stabilizes. This BHP then becomes the maximum BHP that must be applied during future drilling operations. When drilling is restarted, the flow rate may be reduced and / or nitrogen may be injected into the inlet flow stream to reduce the density of the drilling fluid sufficiently so that the BHP remains below the maximum value. This calculated mean annular BP, or any of the calculated interval BP or annular pressures measured inside the well, can be used in an automatic throttling control. As disclosed here, the choke position can be controlled at intervals by an electromechanical server to reduce BP by the calculated amount until the system stabilizes. FIG. 21 (including FIGS. 21Ά and 21B) represents an example of recording from a well drilling operation in which the drilling fluid was lost during the drilling operation. The register shown is the time stamped on track 1 (Fig. 21A). The lower annular pressure measurement was performed using a Schlumberger arcVISION® tool implanted in the BHA. This pressure measurement is marked as APRS on runway 3. The additional drill column included the first and second 112 ASM ring pressure sensors marked as 1231 and 1244 on track 3. Density values based on a single sensor measurement are represented on track 4. MA_ED_001 corresponds to the APRS pressure measurement, MA_ED_003 corresponds to the pressure measurement 1244, and MA_ED_009 corresponds to the pressure measurement of 1231. The gap densities are plotted in lane 5 (FIG. 21B). MA_IED_003_001 corresponds to the interval between pressure measurements APRS and 1244, MA_IED_003_009 corresponds to the interval between pressure measurements of 1244 and 1231, and MA_IED_999_009 corresponds to the interval between pressure measurement of 1231 and the surface. The values of the top equivalent fluid for each of the above ranges are shown in lane 6. In the example shown, the dynamic sensors inside the well detected a high degree of adhesion / sliding in a depth range measured from about 5152 to about 5179 meters. A viscous plug was pumped on December 14 at 4 pm, while the back pressure was maintained at 350 psi. This was observed to stabilize the set and drilling continued at a controlled penetration rate of 5199 meters. On December 15, 07:20 the applied torque increased from 8000 to about 12700 foot pounds and partial fluid losses were considered to occur based on drill level observations. The pressures at 07:42 were observed as 113 decreasing significantly in response to a lost circulation event and a loss of hydrostatic pressure head. In the APRS sensor, the pressure dropped from about 7500 to about 6800 psi as indicated in 2102. The gap density between the APRS and 1244 pressure sensors also dropped from about 8.5 to about 5 ppg as indicated in 2104, while the other two gap densities remained approximately unchanged (from about 8.5 to about 8 ppg), as indicated in 2106. In addition to the ETOFL of the lowest range, the former enriched to a positive value before drop to about -10,000 feet as indicated by the envelope in 2108. These results strongly indicate a lost circulation event in the lower range, probably in the drill. Drilling and circulation were subsequently suspended. FIGS. 22A and 22B show the schematic depth versus pressure graphs illustrating the ETOFL changes that may result from missed circulation events. In FIG. 22A the lost circulation event occurs over (or close to) the drill. Before the event (at time t = 0), the depth versus pressure curve is approximately linear, as indicated in 2202. At time t = 1, the loss of the circulation event causes a pressure drop in the lower ASM1 sensor which may result in an increase in ETOFL (above the surface) in the longest range 114 lower (between ASM1 and ASM2), as indicated by the slope increase in 2204. As time progresses, ETOFL can decrease significantly, as indicated in 2206 (and 2108 of FIG. 21). FIG. 22B represents a schematic plot of depth versus pressure for a lost circulation event that occurs above the drill (between ASM2 and ASM4, in this example). Before the event, the depth versus pressure curve is approximately linear, as indicated in 2212. As the circulation is lost, the measured pressures fall on the ASM3 and ASM4 sensors. This can result in an increase in ETOFL (above the surface) in the interval between ASM3 and ASM4 sensors as indicated in 2214 and a decrease in ETOFL between ASM2 and ASM3 sensors as indicated in 2216. This signature strongly suggests a loss of circulation event above the drill (for example, in the vicinity of ASM3 in FIG. 22B). FIG. 23 (including FIGS. 23A and 23B) represents an example of recording the well drilling operation shown in FIG. 21 taken about a day later (morning of the 16th of December). The same tracks and data flow are represented. After drilling was stopped (as described above in relation to FIG. 21), the BHA was pulled up from the hole at 5093 meters of measured depth without circulation. An attempt was made to recover circulation at a low flow rate without 115 success. After pulling the BHA back into the casing for a period of time, then firing back to the bottom, the drilling fluid was pumped back into the well. The above-mentioned gap densities and fluid equivalent top were monitored during filling. The ETOFL can be seen to be increasing with filling in 2302. Pumping was suspended at 6:51 am and fluid level shots were performed using an Echometer. The Echometer detected a fluid depth of 2038 feet which is comparable to the average 2000 feet ETOFL shown at 2304 in FIG. 2 Pressure Controlled Drill Choke Adjustments During controlled pressure drilling (MPD) operations, the surface annular pressure (SBP) is maintained in such a way that the pressure of the bottom hole (BHP) remains within a predefined small range, in order to avoid both loss of circulation as well as setbacks or well hole stability problems. For example, as the mud pumps are brought down, the annular surface back pressure can be increased to compensate for the loss of annular friction and is also adjusted (up or down) to account for the possible phase changes when using aerated (or nitrogenous) drilling fluid. The control of 116 automatic feedback is desirable in order to make the adjustment faster and more accurate. In addition, automatic control may be even more desirable in the event of changes in drilling conditions (for example, a kick or change in chip density). The back pressure calculations described here can provide automated feedback. FIG. 24 (including FIGS. 24A and 24B) represents an example of recording the same well drilling operation as described in FIG. 21. Lanes 1 to 7 are identical to FIGS. 21 and 23. Lane 8 is added and includes a range BP back pressure calculated using Equation 21. MA_BP_003_001 corresponds to the BP calculated for the interval in between at measurements of pressure APRS and 1244, while MA IED 003_ 009 corresponds to calculated BP to interval in between at measurements of pressure 1244 and 1231. OPT_LINE_1 plot the actual SBP. At FIG. 24, profiling data are shown that correspond to a time interval before making a connection (13 December 23: 10-23: 30), in which the pumps were closed, but the cable drill pipe remained connected. The annular back pressure was being applied, however there was no nitrogen injection. The average back pressure during the previous drilling (for example, at 22:20) was about 350 psi. When closing the pumps under 23:10, the back pressure was increased by 275 psi to 625 psi 117 to compensate for the loss of annular friction. Pressure measurements inside the well on the APRS sensors, 1231, 1244 are seen increasing from about 100-150 psi above the drilling value at 2402, 2403, 2404 and on lane 3 (FIG. 24A). The APRS pressure measurement is reproduced in lane 7 at 2406 using the same resolution as the SBP (FIG. 24B). In this operation, the objective was to minimize excess pressure and reduce the pressure to the drilling value. The excess was reduced, decreasing the back pressure over the next 10 minutes (23: 10— 23:20), as indicated in 2408. In this operation, a back pressure of about 525-550 psi seems ideal to compensate for the loss of losses due to annular friction. Therefore, the annular pressure losses due to friction were about 175 psi, instead of 275 psi initially assumed. Such a back pressure calibration can improve stability and eliminate inlet flow problems at connections. Lane 8 displays the calculated BP. These calculated return pressures indicate the efficiency with which the SBP is being transmitted to the drilling fluid in the annular at any particular interval. The calculated BP can be compared directly in a control circuit to obtain a desirable SBP, for example, by adjusting the SBP in such a way that the calculated SBP and BP are approximately equal. Since constant BHP is desirable, 118 MA_BP_003_001 can be used directly in the control circuit. In FIG. 24 there are several intervals in which the cleaning effects are observed, for example, between 23:22 and 23:27. In such cases, the calculated BP is greater than the actual SBP implying that the SBP must be increased, which in turn decreases the calculated BP. The aforementioned control circuit can be configured, for example, to incrementally increase SBP until SBP is approximately equal to the calculated BP. Such a cycle tends to be inherently stable since these quantities generally move in opposite directions (for example, the increase in SBP decreases BP and the decrease in SBP increases BP). When peak effects occur (for example, 22: 5022: 55), the calculated BP is less than the actual SBP. SBP should therefore be reduced. The methodology described above for controlling back pressure during controlled pressure drilling operations can advantageously be highly stable since the calculated back pressure (from Equation 21) is sensitive to the transmission efficiency of the SBP applied to the annular fluid. By maintaining a desired BHP during MPD operations, the inlet flow rate can be adjusted, the weight of the sludge can be adjusted, the volume of injected nitrogen varied, or the BP can be adjusted. In many cases, two or more of these parameters can be adjusted so 119 substantially simultaneously. In addition, the calculated mean void BP or any of the interval calculated BP or the void pressure measured within the well can be used in an automatic throttling control methodology. The choke position can be controlled, for example, in incremental steps by an electromechanical device until the system stabilizes and BP and SBP are substantially the same as described above. Table 10 lists the direction of change for the calculation of theoretical BP across depth intervals, while certain other drilling events occur (other than compensation for annular friction losses as described above). These events are listed in column 1. Column 2 presents the desired change in surface BP during MPD operations, in order to neutralize the event within the well and to maintain a substantially constant BHP (or to maintain BHP within a window mud weight safety). 120 TABLE 10 Theoretical BP du Calculated Event BP adjustment Event at Event belowof surfacewanted BP long from BP Shavings BP increase BP of AT drillinglighter of surface circulation and static will increase in the lower pair of sensorsShavings Decrease in BP of AT Drilling BP of circulation andmoreheavy surface static will decrease in the lowest pair of sensorsWashing BP increase BP of Noneof surface circulation will increase over the wash. Static BP change 121 constantObstruction Decrease in BP of BP ofBP of circulation circulationsurface will decrease increase along the lightly obstruction. BP below static obstruction constantKick BP increase BP of BP ofof surface circulation and circulation and static will static increase to will decrease over the lightly interval of below the kick interval of kick if applicable Lost of Decrease in BP of BP of Circulation BP of circulation and circulation andsurface static will static decrease will decrease by lightly all the over the breaks level of below the fluid level of 122 fluid Changes in Decrease in If the AT property BP of density of.or rheology surface already intervalof the mud that BHP will be increases, BPresulting decreasing circulationinand staticincreases ofwill decrease.density in interval Changes in BP increase If the AT property of surface density ofor rheology since BHP intervalof the mud will be decreases, BPresulting decreasing circulationinand staticdecreaseswill increase.in density in interval In-situ monitoring of fluid quality Drilling As described above, pressures and temperatures 123 internal ASMs can be used to measure the density of the incoming slurry and temperature profiles. Internal ASM measurements can also be used to calculate hydraulic modeling parameters that are used to predict the subsequent pressure and temperature effects on the annular fluid that moves upwards from the annular. Changing the weight of the sludge or other properties such as viscosity, during a viscous sweep, can be beneficial to know where the sludge (or buffer) is in the system. When the mud becomes uniform within the system, drilling can be resumed. A circulation time or time above the bottom can be used to determine the depth from which the chips collected on the surface have come. Often the perforator will circle the bottom before P.O.O.H (Pull Out Of Hole). This is estimated using an estimated drilling well diameter and volume that may be in error. Since the time required to clean the drilling well from all chips is not well defined, a safety factor of 1.5 to 2 is generally used, which means that the circulation time is increased by these factors to ensure a clean hole before POOH The gap and annular friction densities tend not to change over time since the mud is homogeneous. The gap densities that do not change can therefore be 124 used to determine when the mud density is homogeneous within the drilling well volumes. When the annular is free of chips, annular gap densities tend to reflect the density of the input mud corrected for the effects of pressure and temperature. Circulation can then be stopped in order to perform P.O.O.H. One or both of Equations 22 and 23 can be used to determine when the mud system is homogeneous and other drilling operations have resumed. Production Analysis Obtaining production from wells, especially side wells, is often complicated by transport issues. In a side well, the implantation of tools into the well through a standard gravity descent cannot be possible. To overcome this difficulty, tools can be pushed or pulled into the well, through profiling assisted by drilling pipes, pipe transport, with tractors, propelled with a piston cup, or some other means. Accumulation of debris during the transportation of various production tools into the well can be particularly problematic in horizontal or near-horizontal wells. In addition, excessive probe time is often necessary for the transmission of tools with conventional cables (WL) in horizontal wells such that WL tools are often not used. 125 Production analysis tools carried with cable often include numerous measurement sensors implanted at various depths in the well. Such measurement sensors can, alternatively, be implanted using wired drill pipe transport. The use of WDP allows substantially identical sensors to be deployed in the same configuration and at multiple depths in the well bore. The implantation of the sensor can be carried out by triggering WDP in the drilling well. The surface pressure can be adjusted in such a way that the forming fluids flow into the well hole and upwards inside the drill part, where they can be vented through a choke surface or sent to the production facilities. . The temperature and pressure measurements along the column, as well as the calculated interval densities and temperature gradients can then be used to assess the type and rate of fluid flow from the various intervals. In addition, by controlling the pressure above the borehole, the effect of pressure variability on the properties of the fluid within the well can be assessed - such as phase changes, flow rate changes, fluid retention changes, and the like . Chip Transport Control Proper transport of chips from the drill bit to the surface is necessary in order to 126 avoid various drilling problems, such as friction caused by the accumulation of chips, the generation of an obstruction around the BHA or other locations in the drill string, and stuck drill pipe. Increased friction due to increased chip volume or a drop of barite in the drilling fluid can delay chip removal and result in one or more of the above problems. Chip transport problems, if not properly identified and mitigated, can quickly get out of control, for example, from increased friction, to an obstruction, a stuck drill pipe. In high-angle wells, for example, including horizontal and near-horizontal wells, there is a greater tendency for chips to fall from the suspension. This can occur for at least two reasons, including the non-uniform annular flow profile with increasing stagnation towards the bottom of the drilling well and the action of gravity, in a direction perpendicular to the flow speed. Having only a short distance to fall into the stagnant flow profile at the bottom of the drilling well, the aforementioned problems of chip transport can therefore manifest quickly in high-angle wells. Various factors such as the drilling column rotation rate, drilling fluid flow rate, and periodic BHA and axial drill pipe movements help 127 to keep the bed of chips shaken and suspended. However, at the time of this disclosure, there is no known definite well measurement available to measure the degree of success of these practices at specific depth intervals. Drill personnel generally expect to determine whether or not target chips appear approximately on shale shakers (for example, 20-90 minutes after the penetration of the particular formation). Current practice may also make use of single sensor BHA measurements from which drilling personnel look for increases in overall annular density, with time to detect chip build-up. However, such accumulation may also be due to the drilling of denser rock with a high penetration rate or obstructions located above the BHA. It is generally considered that a decrease in annular density over time corresponds to a better cleaning of the bore and the transport of chips. In reality, the chips that fall out of the solution can give the same signature. In contrast, the measurements in temperature and ASM pressure, densities interval here calculated, and at its derivatives can be used for distinguish at shavings that fall from other effects and locate the affected depth ranges. FIGS. 25 and 26 represent a hypothetical example of a well drilling operation in which the cuttings from the drilling well that fall from the suspension into a well 128 bypass drilling. Lane 2 of FIG. 25 includes an enlargement of 2502, as described above with reference to FIGS. 9 and 10. FIGS. 25 and 26 show the same tracks, as previously described in FIGS. 6-8. In this example, FIG. 25 represents the hypothetical drilling operation at time η = 0 (after the formation of the wash, but before the chips fall out of the suspension). It should be understood that the described modalities are not limited by the representation of a wash. In lane 3 of FIG. 25, the measured and expected gap densities are substantially equal to each other over the length of the well (ie = MA_ISD EA ISD and MA_ICD = EA__ICD) which indicates that the effects of chip volume, chip density, transport of shavings and fractional volume, and annular friction were adequately modeled. FIG. 26 represents the hypothetical drilling operation in time Ζ 2 = ί 1 + Δ / in which the chips are falling from the suspension. Fallen chips are shown schematically in lane 2 (at 2602) in FIG. 26. As the chips move above the hole from the drill, the chip density remains approximately constant and can be controlled as a function of time and depth (for example, after SG apams stabilize). When the chips fall out of the suspension, SG chips can significantly reduce (for example, by about 10 to about 129 of 50 percent). An automatic routine can be used to identify and quantify the severity of a chip transport problem (for example, drop of chips from the annular volume) as a function of time and depth before executing the aforementioned minimization routine. When the chips fall from the suspension, MA_ISD decreases below EA_ISD and approaches (or is substantially equal to) EAF_ISD (as can be seen by comparing FIGS. 25 and 26 in 2504 and 2604). MA_ICD also decreases below EA_ICD as described in 2606 of FIG. 26. The upper part of the ETOFL equivalent fluid may also decrease while the BP annular back pressure increases as described in 2608 and 2610. Although changes in interval density tend to mimic those of a kick signature and / or a loss of circulation signature, transport problems with chips can be easily identified by noting that Q x = 0 in FIGS. 25 and 26. This distinguishes the chip transport from the incoming or outgoing flow events. It is also noted that the routine keeps SG s constant, according represented in 2612. At the in which case ^^ shavings θ calculated wrongly in instead of to be kept constant by program, the value of çz * »'' J shavings can fall to a value approximately equal to the density of the mud that during a 130 kick (especially a gas kick), SG shavings falls below the mud density. It must be understood that the transportation problems of. chips, especially in inclined wells, can cause corresponding changes in some of the disclosed parameters other than those described above in relation to FIGS. 25 and 26. Table 11 lists certain changes caused by chips that fall from the annular suspension. These changes are observed before a minimization routine has 10 calculated new interval density values and adjusted to the expected void quantities (EA) accordingly. 131 TABLE 11 Parameter Change over time Change withdepth The The a = o α = θ F x Can change Can change SG AT ATMORE D MA ISD is equal to The signatures of DSI VS. EA ISD until the tend to be affected in EA_ISD shavings fall particular intervalsoccurs at the moment where the chip dropthat MA ISD falls to It is more likely, perbelow EA ISD and if example, 40-65 degreesapproaches density of inclination. Theof the mud. Differences breaks inincrease with time depth that create theuntil punch takes fall tend not to to changecorrective measures. with time. MA ISD <Unlike a MA_ISD mf . wash where MA ISD remains constant and MA ICD is affected. MA_ICD MA ICD and EA_ICD Same subscriptions what VS. tend to mimic the the ISD curves.EA_ICD DSI subscriptions, although the effect may 132 higher or lower, depending on the volume of the fall and the net effect on thefriction cancel.Equivalent fluid top ETOFL decreases with the pace during the affected intervals as the chips fall. ETOFL decreases over the intervals when the chips are falling. Slight increase below the affected intervals. Superfici's BP andCalculated BP increases with time as the chips fall. BP increases with time as the chips fall. Slight decrease below the affected intervals. ASM pressure Slightly decreases Slightly decreases ASM temperature No changesexpected No changes expected A driller may decide to respond to chip transport problems, such as chips that fall out of the suspension in the annular, using a series of mitigation techniques. For example, a drilling operator may decide (i) to increase the rotation rate of the drilling column to promote turbulent mixing of the 133 annular fluid, (ii) increase the flow rate of the drilling fluid, (iii) reduce the penetration rate (for example, via weight reduction on the drill), or (iv) replace the drill bit with a less aggressive drill or a drill that has a different nozzle configuration. Other components of BHA can also be replaced in order to change the pressure drop between the surface and the drill bit. The described modalities are not limited by any of these aspects. Internal and External Temperature Gradients Internal and annular temperature measurements made as a function of depth and time can be used to calculate the various temperature gradients in the drilling well. For example, internal and external (annular) temperature gradients can be determined along the length of the drill string (as a function of measured depth). In addition, radial gradients across the drill string between internal and external temperature measurements can be determined. These temperature gradients can be used to evaluate various conditions related to the drill string and the tool, as well as various conditions related to formation. In one embodiment, temperature gradients 134 can be calculated as a function of time and depth along the drill string to predict when the temperature of the drill well in the BHA may exceed the nominal tool temperatures. These measurements can be made in both static and circulation conditions. In a high temperature formation, the temperature of the drilling well can increase with time and depth during static conditions. Therefore, the measured temperature gradients can allow the determination of a time in which the nominal tool temperatures are exceeded. For example, sampling fluid sampling operations LWD are generally performed under static conditions. The temperature gradients mentioned above may allow an update per maximum station to be determined during which time the sampling operation will have to be completed. circulation can then be resumed in order to cool BHA. can In another modality, they can be used for internal and external measurements to model a radial heat transfer coefficient of the drilling column or tool inside the well. Such modeling may also include a third temperature measurement to be made between internal and external fluids (for example, 'on an internal circuit board). The use of three temperature measurements can allow non-linear effects of 135 heat are evaluated. Such measurements can be made during circulation and / or static conditions. These temperature measurements can be included in a model to predict drill column temperatures for numerous drilling conditions. For example, temperature gradients can be evaluated at various drilling column rotation rates (for example, 50 rpm, 100 rpm and 200 rpm) and at various drilling fluid flow rates (for example, 300 gpm, 500 gpm and 800 gpm). This can allow the effects of various parameters, including the rotation rate of the drilling column and the flow rate of the drilling fluid, to mitigate drilling situations with high temperature. The development of a heat transfer model, for example, as described in the preceding paragraph may also allow the measured temperatures to be used for calculating a static formation temperature. Obtaining the static formation temperature can be highly valuable in that it is related to several parameters of interest, including the heat transfer capacity of the formation which is, in turn, related to the fluid content and the lithology of the formation, which is even more related to porosity, hydrocarbon saturation, and pore pressure. The determination of the 136 static formation can also allow static and circulation temperatures of the drilling well to be predicted long before the well is completed. Phase changes can also be identified. In addition, knowledge 5 of the static formation temperature can allow the platform planes to be refined during the journey inside hot wells. Although numerous methods for calculating and using well hole interval densities and certain advantages 10 of them have been described in detail, it should be understood that various changes, substitutions and alternations can be made in this document without departing from the spirit and scope of the disclosure as defined by the appended claims.
权利要求:
Claims (11) [1] - CLAIMS - 1. METHOD FOR ESTIMATING A TOP LEVEL OF EQUIVALENT FLUID IN AN UNDERGROUND WELL HOLE, the method characterized by comprising: (a) implanting a tool column in the well bore, the tool column including at least first and second longitudinally spaced subsurface pressure sensors implanted in the corresponding first and second depths measured in the well bore; (b) having the first and second pressure sensors acquire the first and second annular drilling fluid pressure measurements at the first and second measured depths, and (c) having a processor process the first and second pressure measurements pressure to calculate a higher level of equivalent fluid for a borehole interval between the first and second measured depths. [2] 2. Method according to claim 1, characterized by: the tool column includes first, second and third subsurface pressure sensors spaced longitudinally at the corresponding first, second and third depths; (b) understanding that the first, second and third pressure sensors acquire first, second and third pressure measurements of annular drilling fluid; and (c) understanding processing the first, second and third measurements to calculate a first upper level 5 of equivalent fluid for a well hole interval between the first and second measured depths and a second upper level of equivalent fluid for an interval of borehole between the second and third measured depths. Method according to claim 1, characterized in that: drilling fluid is being circulated in the tool column and the well hole is being drilled in (b). 4. Method, in according to claim 1, 15 characterized by: drilling fluid be static in tool column in (B) . 5. Method, in according to claim 1, characterized in that the upper level of equivalent fluid is calculated in (c) according to the following equation: ETOFL fc-P - / »>)« C - Atd (o) where ETOFL represents the upper level of equivalent fluid, Ζ τνβ ^ and Z „, D ( 2 ) represent the true vertical depths in the first and second measured depths, Ρ λ and P 2 represent the first and the second pressure measurements, represent pressure losses due to friction in the first and second sensors, BP represents a back pressure applied to the annular surface and C, represents a unit conversion constant. [3] 6. Method according to claim 1, characterized by (c) further comprising: (i) processing the first and second pressure measurements to calculate a static annular gap density measured; and (ii) processing the measured annular gap static density and the first pressure measurement to calculate the upper equivalent fluid level. [4] Method according to claim 6, characterized in that the upper level of equivalent fluid is calculated in (c) according to the following equation: ETOFL = MAJSD where ETOFL represents the upper equivalent fluid level, Z-mAj) represents a true vertical depth of the first measured depth, P } represents the first temperature measurement, P f represents friction pressure loss in the first pressure sensor, BP represents a back pressure applied to the annular surface, C represents a unit conversion constant and MA_ISD represents the measured annular interval static density. [5] Method according to claim 1, characterized in that the pressure measurements in the annular are acquired in a surface processor in (b) via a wired drill pipe communications channel. [6] 9. METHOD FOR CALCULATING AN THEORETICAL SURFACE ANNEX BACKGROUND IN A UNDERGROUND WELL HOLE, the method being characterized by comprising: (a) implanting a tool column in the well hole, the tool column including first and second subsurface spaced pressure sensors implanted in the corresponding first and second depths measured in the well hole; (b) causing the first and second pressure sensors to acquire first and second annular drilling fluid pressure measurements at the first and second measured depths; and (c) having a processor process the first and second pressure measurements to calculate the theoretical surface annulus back pressure for a well hole interval between the first and second measured depths. [7] Method according to claim 9, characterized by: the tool column includes first, second and third longitudinally spaced subsurface pressure sensors at the corresponding first, second and third measured depths; (b) understanding that the first, second and third pressure sensors acquire first, second and third pressure measurements of annular drilling fluid; and (c) understanding the processing of the first, second and third pressure measurements to calculate a first theoretical surface annular pressure for a well hole interval between the first and second measured depths and a second theoretical surface annular pressure for a borehole interval between the second and third measured depths. [8] 11. Method according to claim 9, characterized in that drilling fluid is being circulated in the tool column and the well hole is being drilled in (b). [9] Method according to claim 9, characterized in that the drilling fluid is static in the tool column in (b). [10] 13. Method, according to claim 9, characterized in that the counterpressure of the annular theoretical surface is calculated in (c) according to the following equation 'TVL> w, / 0 (1) + P, where BP represents the theoretical surface annulus back pressure, P x represents the first pressure measurement, P 2 represents the second pressure measurement; and 5 Z TI , DiX) and Z TyDm represent a true vertical depth in the first and second measured depths. [11] Method according to claim 9, characterized in that the annular pressure measurements are acquired on a surface processor in (b) through a wired drill pipe communications channel. 1/29 30___ -—18 2/29 100 s / depth Time = T0 Time = TO + DT Time = T1 + DT Time = T2 + JX / 1000 MAJSD = 9.5 MA_ISD = 9.7 MAJSD = 9.8 MAJSD / Ô, 6 1000.5 MAJSD = 9.5 MA_ISD = 9.7 MA_ISD = 9.8 MA _ ^ = 9.6 depthTime = T0Time = T0 + DT Time = T1 + Dt Time = T2 + DT JSD = 9.6 1000 36 = 2.6 36 = 2.7 36 = 2.5 36 = 2.6 JSD = 9.6 100 (1.5 36 = 2.6 36 = 2.7 36 = 2.5 36 = ^ 6 ISD ^ 9.6 1001 36 = 2.6 86 = 2.7 36 = 2.5 S6 = 2.6 JSD = 9.6 1001.5 36 = 2.6 36 = 2.7 86 = 35 86 = 2.6 / 1002 36 = 2.6 36 = 2.7 SG-2.5 36 = 2.6 1002.5 36 = 2.6 SG-2.7 36-215 SG = 2.6
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2018-11-21| B03A| Publication of an application: publication of a patent application or of a certificate of addition of invention| 2018-11-27| B08F| Application fees: dismissal - article 86 of industrial property law|Free format text: REFERENTE A 6A ANUIDADE. | 2019-03-12| B08K| Lapse as no evidence of payment of the annual fee has been furnished to inpi (acc. art. 87)|Free format text: REFERENTE AO ARQUIVAMENTO PUBLICADO NA RPI 2499 DE 27/11/2018. |
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申请号 | 申请日 | 专利标题 US201161527948P| true| 2011-08-26|2011-08-26| US61/527,948|2011-08-26| US13/585,650|US9134451B2|2011-08-26|2012-08-14|Interval density pressure management methods| US13/585,650|2012-08-14| 相关专利
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