MODIFIED FLOW RATE ANALYSIS

Abstract

Methods, systems, devices, and products for estimating a parameter of interest of an earth formation. The method may include using a correction factor to conduct a flow rate analysis on fluid sampled from the formation via a probe contacting a wall of the borehole, wherein the correction factor compensates for total compressibility; determining at least one of: i) the product of formation porosity and total compressibility; ii) system compressibility; and iii) initial formation pressure; or determining a mobility of the formation using a slope of a linear relationship of a time-dependent pressure of the fluid with respect to a formation flow rate. The parameter of interest may be i) formation mobility or ii) formation permeability. The correction factor may be determined using formation compressibility. The correction factor may be determined using at least one of: i) gas saturation; ii) oil saturation; and iii) water saturation.

Description

FIELD OF THE DISCLOSURE

This disclosure generally relates to borehole tools, and in particular to methods and apparatuses for conducting downhole measurements.

BACKGROUND OF THE DISCLOSURE

Historically, flow rate analysis has been used to determine parameters of interest such as formation permeability and fluid mobility. Tools configured to extract formation fluids from the wall of a borehole are well known. Generally, such tools include a fluid entry port which may be part of a probe associated with a pad engageable to the wall of the borehole. One or more packers may also be used. Fluids (liquids, gases, mixtures, and so on) from the formation may be drawn in to the port and to a chamber while the pressure and volume are measured.

Conventionally, a draw down test method may be used for determining permeability. With the probe engaged against the borehole wall, a measured volume of fluid is withdrawn from the formation. The method may include reducing pressure in a flow line that is in fluid communication with a borehole wall. A piston may be used to increase the flow line volume, thereby decreasing the flow line pressure. The rate of pressure decrease is such that formation fluid entering the flow line combines with fluid leaving the flow line to create a substantially linear pressure decrease. Generally, the fluid pressure in the formation at the wall of the wellbore is monitored until equilibrium pressure is reached. Conversely, in the buildup method, fluid is withdrawn from the reservoir using a probe and the flow of fluid is terminated. The subsequent buildup in pressure is measured.

In some techniques, a “best straight line fit” is used to define a straight-line reference for a predetermined acceptable deviation determination. The acceptable deviation may be 2σ from the straight line. Once the straight-line reference is determined, the volume increase is maintained at a steady rate. At a first time, the pressure exceeds the 2σ limit and it is assumed that the flow line pressure being below the formation pressure causes the deviation. Draw down is discontinued and the pressure is allowed to stabilize. Additional draw down cycles may be repeated. Various improvements to the tool have occurred over time, allowing faster, safer or more accurate determination of pressure and/or volume.

In other methods, draw down may continue at an established rate until the formation fluid entering the tool stabilizes the tool pressure. Then the pressure is allowed to rise and stabilize by stopping the draw down. Other methods may include incrementally decreasing the pressure within the test volume at a variable rate to allow periodic measurements of pressure as the test volume pressure decreases. Adjustments to the rate of decrease may be carried out before the pressure stabilizes.

SUMMARY OF THE DISCLOSURE

In aspects, the present disclosure is related to methods and apparatuses for estimating at least downhole parameter relating to an earth formation intersected by a borehole.

One general method embodiment according to the present disclosure may include using a correction factor to conduct a flow rate analysis on fluid sampled from the formation via a probe contacting a wall of the borehole, wherein the correction factor compensates for total compressibility. The method may include determining at least one of: i) the product of formation porosity and total compressibility; ii) system compressibility; and iii) initial formation pressure. The method may include determining a mobility of the formation using a slope of a linear relationship of a time-dependent pressure of the fluid with respect to a formation flow rate. The method may include applying the correction factor to pressure measurements of the sampled fluid to derive the time-dependent pressure. The method may include sampling the fluid from the formation; taking fluid pressure measurements over time; determining a volume of the sampled fluid as a function of time; and determining a corresponding draw rate of the formation fluid as a function of time.

The parameter of interest may be at least one of: i) formation mobility; and ii) formation permeability. The correction factor may be determined using at least one of: i) a complementary error function; and ii) numerical inversion of laplace transform. The correction factor may be determined using estimated formation porosity and at least one of: i) predicted formation permeability; and ii) predicted formation mobility. The correction factor may be determined using a geometric factor. The correction factor may be determined using both draw-down and build-up measurements. The correction factor may be determined using superposition. The correction factor may be determined using formation compressibility. The correction factor may be determined using at least one of: i) gas saturation; ii) oil saturation; and iii) water saturation.

Another general method embodiment includes modeling the formation using an adjusted time-dependent pressure of a fluid sampled from the formation through a probe extending to the formation through a wall of the borehole, wherein the adjusted time-dependent pressure is determined by applying a correction factor compensating for total compressibility to time-dependent pressure measurements of the fluid.

Apparatus embodiments may include a tool body; a fluid sampling unit associated with the tool body configured to sample fluid from the formation while in the borehole, the fluid sampling unit including a probe configured to contact a wall of the borehole; and a processor configured to use a correction factor to conduct a flow rate analysis on fluid sampled from the formation by the fluid sampling unit, wherein the correction factor compensates for total compressibility.

The processor may be configured to carry out the methods described above. The processor may be configured to determine at least one of: i) the product of formation porosity and total compressibility; ii) system compressibility; and iii) initial formation pressure. The processor may be configured to determine a mobility of the formation using a slope of a linear relationship of a time-dependent pressure of the fluid with respect to a formation flow rate. The processor may be configured to apply the correction factor to pressure measurements of the sampled fluid to derive the time-dependent pressure.

Further embodiments may include a non-transitory computer-readable medium product having instructions thereon that, when executed, cause at least one processor to perform a method as described above. The product may have instructions thereon that cause the at least one processor to use a correction factor to conduct a flow rate analysis on fluid sampled from the formation via a probe contacting a wall of the borehole, wherein the correction factor compensates for total compressibility. The non-transitory computer-readable medium product may include at least one of: (i) a ROM, (ii) an EPROM, (iii) an EEPROM, (iv) a flash memory, or (v) an optical disk.

Examples of some features of the disclosure may be summarized rather broadly herein in order that the detailed description thereof that follows may be better understood and in order that the contributions they represent to the art may be appreciated.

BRIEF DESCRIPTION OF THE DRAWINGS

For a detailed understanding of the present disclosure, reference should be made to the following detailed description of the embodiments, taken in conjunction with the accompanying drawings, in which like elements have been given like numerals, wherein:

FIG. 1 schematically illustrates a drilling system in accordance with embodiments of the present disclosure;

FIG. 2 is a section of drill string in accordance with embodiments of the present disclosure;

FIG. 3 illustrates a formation sampling tool in accordance with embodiments of the present disclosure;

FIG. 4 illustrates a wireline tool in accordance with embodiments of the present disclosure in communication with the formation;

FIG. 5 shows a downhole formation multi-tester instrument in accordance with embodiments of the present disclosure;

FIGS. 6A and 6B show charts of dimensionless adjustment pressure with respect to dimensionless time;

FIG. 7A compares an FRA plot created using the prior art method against a corrected FRA plot;

FIG. 7B shows adjustment pressure with respect to time;

FIG. 8 shows a flow chart for estimating a parameter of interest of an earth formation intersected by a borehole in accordance with embodiments of the present disclosure;

FIG. 9 shows a flow chart for using a correction factor to conduct a flow rate analysis on the fluid sampled from the formation in accordance with embodiments of the present disclosure.

DETAILED DESCRIPTION

In aspects, this disclosure relates to estimating a parameter of interest of an earth formation intersected by a borehole. The at least one parameter of interest may include, but is not limited to, one or more of: (i) mobility, (ii) permeability, (iii) viscosity. The method may include using a correction factor to conduct a flow rate analysis on fluid sampled from the formation via a probe contacting a wall of the borehole. The correction factor may compensate for total compressibility.

Various analysis techniques have been used to analyze the information gathered using a formation testing tool. One drawdown mobility calculation incorporates the pressure drawdown corresponding to the piston drawdown rate in Darcy's equation to calculate near wellbore mobility. Flow geometry may be modeled as a hemispherical flow about the probe of the tool. Mobility estimates of low permeability formations are problematic using these techniques due to tool storage effects.

New techniques were developed to calculate mobility using a formation rate analysis (FRA) methods accounting for storage effects. For example, some FRA methods account for storage effects using an estimated fluid compressibility within the tool volume during drawdown. For example, formation flow rate may be calculated from the piston drawdown rate using Darcy's equation and the material balance in the tool,

q_ac=q_f−q_dd

wherein q_ac represents accumulation, q_f represents formation flow and q_dd represents piston drawdown. A small density variation is implicitly assumed. Time dependent pressure, p(t), may be calculated. A plot of p(t) with respect to formation rate should approach a straight line with negative slope and intercept p* at the p(t) axis. Formation mobility and/or permeability may be calculated from the slope. The FRA plot should yield identical slopes for both buildup and drawdown in the case of constant compressibility.

However, in the case of very low mobility (VLM) formations, this FRA methodology does not produce reliable results. Specifically, the resulting FRA curve demonstrates significant deviation from a straight line, resulting in erroneously high mobility estimates. In VLM formations, accuracy may be significantly improved by accounting for effects outside of the tool volume in order to estimate total compressibility of the fluid system. For example, FRA may be carried out by modeling the system including interactions between the fluid outside of the tool and the rock of the formation.

Aspects of the present disclosure allow for estimating a parameter of interest of an earth formation intersected by a borehole. The method may include using a correction factor to conduct a flow rate analysis on fluid sampled from the formation via a probe contacting a wall of the borehole, wherein the correction factor compensates for total compressibility. Total compressibility may be defined as compressibility of the fluid system modeled by taking into account compressibilities and saturations of predominant fluids in the tool-formation system along with the compressibility of the rock matrix corresponding to the portion of the formation containing such fluids and interacting with the sampling tool. For example, total compressibility may be defined as compressibility of the fluid system modeled as a function of rock compressibility, oil compressibility, water compressibility, oil compressibility, gas compressibility, oil saturation, water saturation, gas saturation, and so on, or combinations of the same.

Some aspects include using information obtained from sensors associated with FRA instruments (FRA information). For example, such FRA information may include volume and pressure measurements with respect to time. Each of the embodiments herein may be used in a variety of settings in both drilling and non-drilling environments. In some implementations, the disclosed embodiments may be used as part of a drilling system. An example drilling system for use in conjunction with LWD is illustrated herein.

FIG. 1 schematically illustrates a drilling system 100 having a downhole tool 112 configured to acquire information for downhole fluid analysis in a borehole 104 intersecting a formation 119 using a test apparatus 116. The system 100 includes a drilling rig 102 having a drill string 106 extending therefrom. The drill string 106 has attached thereto a bottom hole assembly (BHA) 108 including a drill bit for drilling borehole 104. Drill string may include jointed tubing, coiled tubing, or other small diameter work string such as snubbing pipe. Other embodiments may include a slickline, an e-line, a wireline, etc. Thus, depending on the configuration, the tool may be used during drilling and/or after the wellbore (borehole) has been formed. The drillstring or other carrier may include embedded conductors for power and/or data for providing signal and/or power communication between the surface and downhole equipment.

The drilling rig 102 is shown positioned on a drilling ship 122 with a riser 124 extending from the drilling ship 122 to the sea floor 120. While a subsea system is shown, the teachings of the present disclosure may also be utilized in land applications. Any drilling rig configuration may be adapted to implement the present disclosure. If applicable, the drill string 106 may have a downhole drill motor (e.g., mud motor) 110. Incorporated in the drill string 106 above the BHA 108 is a typical testing unit, which can have one or more sensors 114 to sense downhole characteristics of the borehole, the BHA, the formation and/or the reservoir, with such sensors being well known in the art. Sensors 114 may detect one or more parameters of a formation. Parameters of a formation may include information relating to a geological parameter, a geophysical parameter, a petrophysical parameter, and/or a lithological parameter. Thus, the sensors 114 may include sensors for estimating formation resistivity, dielectric constant, the presence or absence of hydrocarbons, acoustic porosity, bed boundary, formation density, nuclear porosity and certain rock characteristics, permeability, capillary pressure, and relative permeability. Sensors 114 may detect one or more parameters of the wellbore, including parameters relating to downhole fluids. Non-limiting examples of downhole fluids include drilling fluids, return fluids, formation fluids, production fluids containing one or more hydrocarbons, oils and solvents used in conjunction with downhole tools, water, brine, engineered fluids, and combinations thereof. A useful application of the sensor(s) 114 is to determine direction, azimuth and orientation of the drill string 106, e.g., wherein the sensor may be an accelerometer or similar sensor. The BHA also contains a formation test apparatus 116 according to the present disclosure, which will be described in greater detail below.

In order to operate the downhole tool 112 and/or provide a communications interface with at least one processor at the surface, the downhole tool 112 may include a downhole processor 117. In one embodiment, electronics (not shown) associated with the sensors may be configured to record information related to the parameters to be estimated. In some embodiments, the parameter of interest may be estimated using the recorded information.

In other embodiments, such electronics may be located elsewhere (e.g., at the surface). To perform estimation of a parameter during a single trip, the tool may use a “high bandwidth” transmission to transmit the information acquired by sensors to the surface for analysis. For instance, a communication line for transmitting the acquired information may be an optical fiber, a metal conductor, or any other suitable signal conducting medium. It should be appreciated that the use of a “high bandwidth” communication line may allow surface personnel to monitor and control the treatment activity in “real time.”

In some embodiments, processors may include electromechanical and/or electrical circuitry configured to control one or more components of the tool 112. In other embodiments, processors may use algorithms and programming to receive information and control operation of the tool 112, including the test apparatus 116. Therefore, processors may include an information processor that is in data communication with a data storage medium and a processor memory. The data storage medium may be any standard computer data storage device, such as a USB drive, memory stick, hard disk, removable RAM, EPROMs, EAROMs, flash memories and optical disks or other commonly used memory storage system known to one of ordinary skill in the art including Internet based storage. The data storage medium may store one or more programs that when executed causes information processor to execute the disclosed method(s). Herein, “information” may include raw data, processed data, analog signals, and digital signals.

FIG. 2 is a section of drill string 106 in accordance with embodiments of the present disclosure. The tool section may be located in the BHA 108 close to the drill bit (not shown). The tool includes a communication unit 218 and power supply 220 for two-way communication to the surface and supplying power to the downhole components. A downhole controller and processor 117 in accordance with the present disclosure carry out subsequent control. Stabilizers 208 and 210 for stabilizing the tool section of the drill string 106 and packers 204 and 206 for sealing a portion of the annulus. A circulation valve disposed preferably above the upper packer 204 is used to allow continued circulation of drilling mud above the packers 204 and 206 while rotation of the drill bit is stopped. A separate vent or equalization valve (not shown) may be used to vent fluid from the test volume between the packers 204 and 206 to the upper annulus. This venting reduces the test volume pressure, which is required for a draw down test. It is also contemplated that the pressure between the packers 204 and 206 could be reduced by drawing fluid into the system or venting fluid to the lower annulus, but in any case some method of increasing the volume of the intermediate annulus to decrease the pressure will be required. In one embodiment of the present disclosure an extendable pad-sealing element 202 for engaging the borehole wall (FIG. 2) may be disposed between the packers 204 and 206 on the test apparatus 216 of the present disclosure. The pad-sealing element 202 could be used without the packers 204 and 206, because a sufficient seal with the well wall can be maintained with the pad 202 alone.

If packers 204 and 206 are not used, a counterforce may be provided so pad 202 can maintain sealing engagement with the wall of the borehole 104. The seal creates a test volume at the pad seal. One way to ensure the seal is maintained is to stabilize the drill string 106. Selectively extendable gripper elements 212 and 214 could be incorporated into the drill string 106 to anchor the drill string 106 during the test. Grippers 212 and 214 are shown incorporated into the stabilizers 208 and 210 in this embodiment. Grippers 212 and 214 may protect other elements from damage due to tool movement (e.g, in offshore systems).

FIG. 3 illustrates a formation sampling tool in accordance with embodiments of the present disclosure. Selectively extendable gripper elements 212 engage the borehole wall 105 to anchor the drill string 106. Packer elements 204 and 206 extend to engage the borehole wall 105. The extended packers separate the well annulus into three sections, an upper annulus 302, an intermediate annulus 304 and a lower annulus 306. The sealed annular section (or simply sealed section) 304 is adjacent a formation 119. Mounted on the drill string 106 and extendable into the sealed section 204 is the selectively extendable pad sealing element 202. A fluid line providing fluid communication between pristine formation fluid 308 and tool sensors such as pressure sensor 324 is shown extending through the pad member 202 to provide a port 320 in the sealed annulus 304. Packers 304 and 306 may be sealingly urged against the wall 105 and may have a sealed relationship between the wall 105 and extendable element 202 to ensure pristine fluid is tested or sampled. Reducing pressure in sealed section 304 prior to engaging the pad 202 will initiate fluid flow from the formation into the sealed section 304. The port 320 extending through the pad 220 will be exposed to pristine fluid 308.

FIG. 4 illustrates a wireline tool in accordance with embodiments of the present disclosure in communication with the formation. Borehole 410 intersects a portion of the earth formation 411. Disposed within the borehole 410 by means of a conveyance device 412 is a sampling and measuring instrument 413. Conveyance device 412 may be a drill string, coiled tubing, a slickline, an e-line, a wireline, etc. The sampling and measuring instrument includes hydraulic power system 414, a fluid sample storage section 415 and a sampling mechanism section 416. Sampling mechanism section 416 includes selectively extensible well engaging pad member 417, a selectively extensible fluid admitting sampling probe member 418 and bi-directional pumping member 419. Specific configuration of the components with respect to one another may vary.

In operation, sampling and measuring instrument 413 is positioned within borehole 410 via conveyance device 412 (e.g., by winding or unwinding cable 412 from a hoist (not shown)). Depth information from a depth indicator 421 is coupled to signal processor 422 and recorder 423 when instrument 413 is disposed adjacent an earth formation of interest. Control signals from control circuitry 424 are transmitted through electrical conductors contained within conveyance device 412 to instrument 413. Any or all of signal processor 422, control circuitry 424 and recorder 423 may be implemented with one more processors.

Electrical control signals activate an operational hydraulic pump within the hydraulic power system 414 shown, which provides hydraulic power causing the well engaging pad member 417 and the fluid admitting member 418 to move laterally from instrument 413 into engagement with the earth formation 411 and the bi-directional pumping member 419. Fluid admitting member or sampling probe 418 can then be placed in fluid communication with the earth formation 411, such as, for example, via electrical control signals from control circuits 424 selectively activating solenoid valves within instrument 413 for the taking of a sample of connate fluids contained in the earth formation of interest, or via other actuation techniques.

FIG. 5 shows a down hole formation multi-tester instrument in accordance with embodiments of the present disclosure. Instrument 500 includes a bi-directional formation fluid pump which may be included in formation testing instrument 413. The pump of FIG. 5 is configured to pump formation fluid into the well bore during pumping to free the sample of filtrate and pump formation fluid into a sample tank after sample clean up.

Formation testing instrument 413 includes a bi-directional piston pump mechanism 524. Within the instrument body 413 is also provided one or more sample tanks, 526 and 528. The piston pump mechanism 524 defines a pair of opposed pumping chambers 562 and 564 which are disposed in fluid communication with the respective sample tanks via supply conduits 534 and 536. Discharge from the respective pump chambers 562, 564 to the supply conduit of a selected sample tank 526 or 528 is controlled by electrically energized three-way valves 527 and 529 or by any other suitable control valve arrangement enabling selective filling of the sample tanks. The respective pumping chambers 562 and 564 are also shown to have the capability of fluid communication with the subsurface formation of interest via pump chamber supply passages 538 and 540, which are defined by the sample probe 418 (FIG. 12) and which are controlled by appropriate valving. The supply passages 538 and 540 may be provided with check valves 539 and 541 to permit overpressure of the fluid being pumped from the chambers 562 and 564 if desired. Position Sensor Resistor LMP 47 tracks the position and speed of pistons 558 and 560 from which pumping volume, over time, for a known piston cylinder size can be determined, as known in the art.

A point of novelty of the systems and devices illustrated in FIGS. 1-5 is that the surface processor and/or the downhole processor (and/or other circuitry) are configured to perform certain methods (discussed below) that are not in prior art.

Generally, embodiments of the present disclosure relate to estimation of an adjustment pressure which may be used as a correction factor when determining p(t). Dimensionless adjustment pressure, p_a,d, may be calculate according to:

$\begin{array}{cc}{p}_{a,d}=\frac{1}{\sqrt{1-4c_d}}\left({}^{{\beta }_1^2t_d}·\mathrm{erfc}\left({\beta }_1\sqrt{t_d}\right)-{}^{{\beta }_2^2t_d}·\mathrm{erfc}\left({\beta }_2\sqrt{t_d}\right)\right)& \left(1\right)\end{array}$

which may be calculated using

${\beta }_1=\frac{1-\sqrt{1-4c_d}}{2c_d},{\beta }_2=\frac{1+\sqrt{1-4c_d}}{2c_d},c_d=\frac{V_sc_s}{4\pi r_s^3\phi c_t},t_d=\frac{\mathrm{tk}}{r_s^2\mathrm{\mu \phi }c_t},r_s=\frac{G_or_p}{4\pi },\mathrm{and}$ $c_t=c_r+S_o·c_o+S_w·c_w+S_g·c_g,$

wherein:
c_d is dimensionless tool storage;
t_d is dimensionless time;
t is time;
r_s is effective probe radius;
r_p is probe radius;
k is predicted formation permeability;
φ is formation porosity;
μ is formation fluid viscosity;
q is constant drawdown rate;
G_o is geometric factor;
V_s is system volume;
c_s is tool system compressibility;
c_t is total compressibility;
c_r is rock (formation) compressibility;
c_o is oil compressibility;
c_w is water compressibility;
c_g is gas compressibility;
S_o is oil saturation;
S_w is water saturation; and
S_g is gas saturation.

The term φc_t may be treated as a single unknown factor. The adjustment pressure p_a can be calculated from dimensionless adjustment pressure using Eq. (2).

$\begin{array}{cc}{p}_a=p_{a,d}·\frac{q\mu }{G_or_pk}& \left(2\right)\end{array}$

Adjustment pressure may be expressed as a function of time, t. Adjustment pressure may be added to initial formation pressure p_i, or subtracted from measured pressure p(t). The modified p(t) as used in FRA may thus be described by Eq. 3.

$\begin{array}{cc}p\left(t\right)=p_i+p_a-\frac{V_sc_s\mu }{G_or_pk}\frac{p}{t}-\frac{q\mu }{G_or_pk}& \left(3\right)\end{array}$

FIGS. 6A and 6B show charts of dimensionless adjustment pressure, p_a,d, with respect to dimensionless time, t_d. Each curve 602-620 represents one of five typical values of dimensionless tool storage. FIG. 6A illustrates a case where the rate is constant. FIG. 6B reflects a pretest of a draw-down and a build-up. FIG. 6B illustrates a case where the rate during build-up is zero. The dimensionless p_a,d under this condition can be obtained by superposition. FIG. 6B shows curves of dimensionless p_a,d with respect to dimensionless t_d where build-up starts at t_d=10. An FRA plot according to prior art methods will exhibit a hockey-stick shape when pretest is conducted in a very low mobility formation (see FIG. 7A). The plot of p_a,d as shown in FIG. 6B helps to explain this effect. During draw-down and early time of build-up, the adjustment pressure p_a,d is greater than zero. Consequently, the pressure measurement p(t) is overvalued by the amount of p_a. By subtracting p_a from the pressure measurement p(t), the hockey-stick shape will be transformed into a straight line.

The correction of estimated parameter values resulting from the embodiments described herein may be illustrated using the following example case. Taking an example wherein total test time is 2000 seconds, and the drawdown rate is 1.0 cubic centimeters with a duration of 1.5 seconds, the following table provides the relevant system parameters.

TABLE 1
Input Parameters
Probe radius               rp = 0.635 cm
Wellbore radius            rw = 10.795 cm (diameter is 8.5 inch)
Porosity                   φ = 0.2
Permeability               k = 0.01 mD
Viscosity                  μ = 1.0 cp
Initial formation Pressure pi = 5000 psi
Total compressibility      ct = 9e−6 psi−1
System compressibility     cs = 3e−6 psi−1
System volume              Vs = 131 cm3

FIG. 7A compares an FRA plot 702 created using the prior art method against an FRA plot 704 determined by correcting p(t) as determined according to the prior art method using an adjustment pressure correction factor according to the present disclosure. It is apparent that the modified FRA plot is a straight line. That overlapping of plots 702 and 704 during late build-up portion (from 3500 to 5000 psi) suggests accurate formation mobility can be estimated from late build-up portion of plot 702 using the prior art method. FIG. 7B shows the adjustment pressure 706 for this case with respect to time. The maximum value of the adjustment pressure for this case is 1196.9 psi at the end of draw-down (1.5 second). The maximum value of dimensionless adjustment pressure can be obtained given estimated formation mobility. Then the dimensionless tool storage can be estimated from a chart similar to FIG. 6B by matching the maximum value of dimensionless adjustment pressure.

FIG. 8 shows a flow chart 800 for estimating a parameter of interest of an earth formation intersected by a borehole in accordance with embodiments of the present disclosure. Optional step 810 of the method comprises obtaining flow rate analysis information relating to fluid sampling. This may be carried out by sampling fluid from the formation via a probe contacting a wall of the borehole; taking fluid pressure measurements over time; and determining a volume of the sampled fluid as a function of time. The information may be used in determining a corresponding draw rate and/or a corresponding build-up rate of the formation fluid as a function of time.

Optional step 820 may include determining the correction factor. The correction factor compensates for total compressibility. The correction factor may be determined using a complementary error function with estimated dimensionless tool storage, or by using estimated formation porosity and estimated formation permeability (or mobility). Determining the correction factor may be carried out using a geometric factor. The geometric factor G₀ may function to extend application of the method from isotropic formations to anisotropic formations. Superposition may also be used, such as, for example, in variable-rate applications. Determining the correction factor may be determined using both draw-down and build-up measurements.

Step 830 comprises using a correction factor to conduct a flow rate analysis on the fluid sampled from the formation. At step 840, the parameter of interest is estimated. Estimating the parameter of interest may be carried out by determining a mobility of the formation using a slope of a linear relationship of a time-dependent pressure of the fluid with respect to a formation flow rate. In some embodiments, the parameter of interest is the mobility. In other embodiments, a parameter of interest such as permeability or viscosity may be determined using the mobility.

FIG. 9 shows a flow chart 900 for using a correction factor to conduct a flow rate analysis on the fluid sampled from the formation in accordance with embodiments of the present disclosure. At step 910, at least one of i) system compressibility; ii) initial formation pressure; and a product of formation porosity and total compressibility is determined. Step 920 comprises applying the correction factor to pressure measurements of the sampled fluid to derive the time-dependent pressure. At step 930, a mobility of the formation is determined using a slope of a linear relationship of a time-dependent pressure of the fluid with respect to a formation flow rate.

The term “conveyance device” as used above means any device, device component, combination of devices, media and/or member that may be used to convey, house, support or otherwise facilitate the use of another device, device component, combination of devices, media and/or member. Exemplary non-limiting conveyance devices include drill strings of the coiled tube type, of the jointed pipe type and any combination or portion thereof. Other conveyance device examples include casing pipes, wirelines, wire line sondes, slickline sondes, drop shots, downhole subs, BHA's, drill string inserts, modules, internal housings and substrate portions thereof, self-propelled tractors. As used above, the term “sub” refers to any structure that is configured to partially enclose, completely enclose, house, or support a device. The term “information” as used above includes any form of information (Analog, digital, EM, printed, etc.). The term “processor” herein includes, but is not limited to, any device that transmits, receives, manipulates, converts, calculates, modulates, transposes, carries, stores or otherwise utilizes information. A processor refers to any circuitry performing the above, and may include a microprocessor, resident memory, and/or peripherals for executing programmed instructions, application specific integrated circuits (ASICs), field programmable gate arrays (FPGAs), or any other circuitry configured to execute logic to perform methods as described herein. The term very low mobility, as described herein refers to mobility below 1.0 millidarcy per centipoise, 0.75 millidarcy per centipoise, 0.5 millidarcy per centipoise, 0.3 millidarcy per centipoise, 0.1 millidarcy per centipoise, or lower. Fluid, as described herein, may refer to a liquid, a gas, a mixture, and so on. Predicted formation permeability and predicted formation mobility refer to values predicted for the formation and used to estimate the correction factor. Predicted values may be predicted from lithology, estimated from other estimation techniques, obtained by analogy, and so on, but are distinguished from parameters of interest estimating according to the methods disclosed herein.

While the foregoing disclosure is directed to the one mode embodiments of the disclosure, various modifications will be apparent to those skilled in the art. It is intended that all variations be embraced by the foregoing disclosure.

Claims

1. A method for estimating a parameter of interest of an earth formation intersected by a borehole, the method comprising:

using a correction factor to conduct a flow rate analysis on fluid sampled from the formation via a probe contacting a wall of the borehole, wherein the correction factor compensates for total compressibility.

2. The method of claim 1, further comprising determining at least one of: i) the product of formation porosity and total compressibility; ii) system compressibility; and iii) initial formation pressure.

3. The method of claim 1, further comprising determining a mobility of the formation using a slope of a linear relationship of a time-dependent pressure of the fluid with respect to a formation flow rate.

4. The method of claim 3, further comprising applying the correction factor to pressure measurements of the sampled fluid to derive the time-dependent pressure.

5. The method of claim 4, further comprising:

sampling the fluid from the formation;

taking fluid pressure measurements over time;

determining a volume of the sampled fluid as a function of time; and

determining a corresponding draw rate of the formation fluid as a function of time.

6. The method of claim 1, wherein the parameter of interest is at least one of: i) formation mobility; and ii) formation permeability.

7. The method of claim 1, wherein the correction factor is determined using at least one of: i) a complementary error function; and ii) a numerical inversion of a laplace transform.

8. The method of claim 1, wherein the correction factor is determined using estimated formation porosity and at least one of: i) predicted formation permeability; and ii) predicted formation mobility.

9. The method of claim 1, wherein the correction factor is determined using a geometric factor.

10. The method of claim 1, wherein the correction factor is determined using both draw-down and build-up measurements.

11. The method of claim 1, wherein the correction factor is determined using superposition.

12. The method of claim 1, wherein the correction factor is determined using formation compressibility.

13. The method of claim 1, wherein the correction factor is determined using at least one of: i) gas saturation; ii) oil saturation; and iii) water saturation.

14. An apparatus for estimating a parameter of interest of an earth formation intersected by a borehole, the apparatus comprising:

a tool body;

a fluid sampling unit associated with the tool body configured to sample fluid from the formation while in the borehole, the fluid sampling unit including a probe configured to contact a wall of the borehole; and

a processor configured to use a correction factor to conduct a flow rate analysis on fluid sampled from the formation by the fluid sampling unit, wherein the correction factor compensates for total compressibility.

15. The method of claim 14, further comprising determining at least one of: i) the product of formation porosity and total compressibility; ii) system compressibility; and iii) initial formation pressure.

16. The apparatus of claim 14, wherein the processor is configured to determine a mobility of the formation using a slope of a linear relationship of a time-dependent pressure of the fluid with respect to a formation flow rate.

17. The apparatus of claim 16, wherein the processor is configured to apply the correction factor to pressure measurements of the sampled fluid to derive the time-dependent pressure.

18. A method for estimating a parameter of interest of an earth formation intersected by a borehole, the method comprising:

modeling the formation using an adjusted time-dependent pressure of a fluid sampled from the formation through a probe extending to the formation through a wall of the borehole, wherein the adjusted time-dependent pressure is determined by applying a correction factor compensating for total compressibility to time-dependent pressure measurements of the fluid.

19. A non-transitory computer-readable medium product having instructions thereon that, when executed, cause at least one processor to perform a method, the method comprising:

using a correction factor to conduct a flow rate analysis on fluid sampled from the formation via a probe contacting a wall of the borehole, wherein the correction factor compensates for total compressibility.

20. The non-transitory computer-readable medium product of claim 19 further comprising at least one of: (i) a ROM, (ii) an EPROM, (iii) an EEPROM, (iv) a flash memory, or (v) an optical disk.