CN110162851A - A kind of data calibration method of cable formation testing pumping numerical simulation and its process - Google Patents
A kind of data calibration method of cable formation testing pumping numerical simulation and its process Download PDFInfo
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Abstract
The invention discloses a kind of cable formation testing pumping numerical simulation and its data calibration methods of process, include the following steps: S1, judge that cable formation testing surveys the flow pattern of pressure data and seeks corresponding mobility；S2, probe open instrument connection on the borehole wall, invaded zone and formation fluid begin to flow to pit shaft, sampler extraction of formation fluid, and nowed forming and continuous conduction are flowed and formed to formation fluid moment, generation involves range, and involves range with what the continuous conduction of spheroid simulated formation fluid flowing was formed；S3, on the basis of given reservoir physical parameter, depth of invasion, seek obtaining according to algorithm surveys before prediction pumping break through, pump pure time and respective volume；S4, the actual effect of pumping is obtained in time, instructs engineer operation, to improve operating efficiency by optimization algorithm fitting function and simulation calculating to the realization correction of pumping result by cable formation testing pumping monitoring parameters, pickup pumping break through and volume.
Description
Technical Field
The invention relates to the technical field of petroleum and natural gas exploration and development, in particular to a numerical simulation method for a pumping numerical value of a cable stratum test and a numerical correction method for a process of the pumping numerical simulation method.
Background
The technology of cable formation testing began in 1950, and with the development of the technology, formation testing logging instruments have been able to meet five major application requirements of formation pressure testing, downhole fluid analysis, downhole fluid sampling, instability testing, micro fracturing and the like under different formation and borehole conditions.
The latest generation of cable formation testers are equipped with some necessary components. For example, an Optical Fluid Analyzer (OFA) can distinguish liquid from gas, can also distinguish water from oil, and the optical response of the OFA has good correlation with crude oil density, saturation pressure, crude oil compressibility, formation volume coefficient and gas-oil ratio.
With the development of formation testing acquisition technology, the schlumberger formation testing well logging interpretation software has also undergone many update upgrades from the original PDPlot software to the InSitu software and the InSitu Pro software, up to now the Techlog software. At present, a comprehensive analysis and application technology of Formation testing logging becomes an application module of Techlog software, namely a Formation testing suite Formation testing logging advanced analysis and application technology. While the development of Downhole fluid analysis technology (Downhole fluid analysis [ DFA ]) is rapid, DFA is mainly used for comprehensively analyzing the following data of the fluid in a pumping pipeline measured by a Downhole fluid identification module of a formation testing logging instrument, and the applied parameters include: resistivity, temperature, pressure, density, viscosity, fluorescence, bubble detection, absorption and diffraction spectra, PH, contamination level by oil-based mud.
However, the application of the current cable stratum test urgently needs to solve the following problems that 1, the mud cake plugging property is poor due to the influence of the performance of the drilling fluid, particularly in a low-porosity reservoir stratum, the invasion process of the drilling fluid is prolonged, the invasion amount is large, the reservoir stratum is seriously polluted, and the pumping effect is difficult to evaluate when the static invasion is continuously generated in the pumping and sampling stage; 2. establishing a design standard of pressure measurement sampling operation, forming a quantitative evaluation means for guiding real-time decision of pumping sampling, and solving the problem of decision standard of pressure measurement and pumping operation in production operation; establishing a pumping simulation model to provide reliable basis for operation key decision points so as to save operation time and reduce operation risk; 3. the method has the advantages that the fluid parameters are monitored by combining the simulation of the pumping process with the actual pumping, so that the representativeness of the long-time pumping sampling sample of the low-permeability reservoir is improved; and the research and application of parameters of each pumping process are deeply excavated, the reliable and effective permeability is obtained, and the DST test operation is guided.
Disclosure of Invention
The invention aims to provide a numerical simulation of pumping numerical simulation of cable formation testing and a numerical correction method of the process thereof.
In order to solve the above problems, the present invention provides a method for simulating pumping values of a cable formation test and correcting the pumping values of the cable formation test, the method comprising the steps of:
s1, obtaining basic parameters of the reservoir stratum, namely, the porosity, the permeability, the reservoir stratum thickness, the slurry performance, the borehole size, the pumping basic parameters of the cable stratum test pump and the slurry invasion condition by using conventional logging information, judging the flow pattern of the cable stratum test pressure measurement information and calculating the corresponding fluidity;
s2, opening a test hole on the well wall by a probe, enabling the invasion zone and formation fluid to start flowing to the well bore, extracting the formation fluid by a sampler, enabling the formation fluid to instantly flow and form a flowing form and continuous conduction to generate a swept range, and simulating the swept range formed by the continuous conduction of the formation fluid flow by an ellipsoid; the formation part of stratum flow outside the well cylinder and the part in the well cylinder are in a complementary relation and integrated into a complete ellipsoid, the size of the major axis and the minor axis of the ellipsoid depends on the permeability of a reservoir and the thickness of the reservoir, the volume relation among a cylinder, the ellipsoid and a cylindrical paraboloid in a volume model is obtained through calculation, the well cylinder is defined as a well cylinder, a pollution zone is the ellipsoid, the original formation fluid is the cylindrical paraboloid, the pressure measurement data of pumping operation is processed, and a pressure gradient curve, a spherical flow gradient curve and a radial flow gradient curve are combined together through analyzing the fluidity information of a pressure measurement point and the possible flow pattern characteristics of the pumping point, so that the flow form of the formation fluid is judged;
s3, inputting reservoir parameters, cable stratum test operation parameters and reservoir invasion depth, and calculating the volume among a cylinder (a shaft), an ellipsoid (a pollution zone) and a cylindrical projectile (undisturbed formation fluid) of the model; in formation pressure test and fluid sampling operation, oil gas breakthrough time and completion time are main time;
s4, when the pumping operation is tested in the cable formation, comprehensively analyzing the following data of the fluid in the pumping pipeline measured by the underground fluid identification module of the cable formation tester by utilizing an underground fluid analysis technology (DFA), and correcting the pumping result by optimizing an algorithm fitting function and simulating calculation, wherein the applied parameters comprise: the resistivity, temperature, pressure, density, water content, viscosity, fluorescence, bubble detection, absorption spectrum and diffraction spectrum, PH value and pollution degree of oil-based mud of the inflow/outflow pipeline; based on the pump breakthrough time, the radius of invasion of the invaded zone, which is an important basis for the calibration of the pumping process, can be calculated.
Further, the volume relationship among the cylinder, the ellipsoid and the cylindrical paraboloid of the model calculated in the step S3 is:
x-x0＝a2(y2+z2)，
(x+R)2+y2＝R2，
in the formula, x0The coordinate of the intersection point of the vertex of the revolution paraboloid on the x axis is shown;
a is a cylindrical paraboloid system,
b is the length of the horizontal axis of the ellipsoid in meters;
c is the length of the vertical axis of the ellipsoid in meters;
r is the radius of the cylinder and is measured in meters;
the region enclosed by the intersecting line of the cylindrical paraboloid and the ellipsoid is V1：
The volume of the truncated part of the ellipsoid by the cylinder is V2:
Wherein,a0＝-c,b0＝c，
n is an interval [ -c, c ],
intrusion into the space occupied by the fluid by the volume of the ellipsoid minus V1And V2Definition of V3Is the remaining volume of the ellipsoid cut by the formation virgin fluid and wellbore fluid:
further, the algorithm of the burst time and the completion time in step S3 is:
defining the volume percentage of the total test fluid occupied by the invaded zone fluid as the contamination rate, the breakthrough time of pumping is determined when the contamination rate is 95% and the completion time is determined when the contamination rate is 5% during the pumping process of the cable formation tester:
calculating the horizontal and vertical axes (b, c) of the ellipsoid, the units of b, c being m,
b＝c1×Qa×t×DP
c＝c2×Qa×t×DP)
calculating the time (t) of ellipsoid to reach the invaded zone0)，t0The unit of (a) is s,
b＝Di
calculating the speed of movement of the rotating projectile, sd0The unit of (a) is m/s,
sd0＝c3×DP×Qa
calculating the coefficient a of the ellipsoid, wherein the unit of a is m,
a＝c4×Kv/Kh
in the above formula, the first and second carbon atoms are,
h is the thickness of the stratum in m;
Khis the formation horizontal permeability in md;
Kv/Khis the anisotropy coefficient;
di is the depth of invasion in m;
uf is the formation fluid viscosity in cp;
um is the mud filtrate viscosity in cp;
ps is the position of the probe from the top boundary, the default center position is m;
r is the radius of the shaft and is m;
qa is the pump speed in m3/s；
t is pump discharge time in units of s;
DP is the differential pressure in MPa;
sd0the speed of the rotating projectile moving towards the probe;
t0the time for the outer boundary to reach the invaded zone during the expansion process of the ellipsoid;
b, the expression shows that the outer boundary of the ellipsoid reaches the invasion zone, and accordingly t is obtained0The expression of (1);
sd0means the speed of the rotating projectile moving in the direction of the probe;
Qathe physical meaning of x t is to reflect the speed of expansion of the ellipsoid;
c in the above equation1、c2、c3、c4The coefficients are relationships established between formation testing parameters Differential Pressure (DP), testing flow rate (Qa), and formation anisotropy coefficient (Kv/Kh),
c1unit is MPa-1*m-2；
c2Unit is MPa-1*m-2；
c3Unit is MPa-1*m-2；
c4The unit is m;
calculating x0Value (distance between the vertex of the cylindrical projectile and the probe point) when the pumping time t is greater than t0When the ellipsoid starts to be tangent to the cylindrical surface of the invasion zone, the cylindrical projectile (includingFormation virgin fluid) begins to taper inside the ellipsoid, i.e.:
t≥t0
x0＝Di-sd0(t-t0)
calculating the contamination ratio C according to V1, V2 and V3 obtained in step S2,
t≥t0
when t is less than or equal to t0When the contamination ratio c (t) is 1.0; t from t0Then the pollution rate C (t) begins to decrease; when c (t) is 0.95, the test elapsed time is the breakthrough time; when c (t) is 0.05 test elapsed time, it is completion time.
Further, in step S4, the pumping result is corrected by using a numerical simulation intelligent optimization algorithm, which establishes a fitting function and performs simulation calculation as follows:
and m kinds of logging data are set to participate in optimization calculation, represented by a vector a,
a＝(a1,a2,...,am)T
the vector x is m unknown parameters to be solved:
x＝(x1,x2,...,xm)T
based on the volume model changes employed above, the various response equations are expressed as:
ai＝fi(x,z),(i＝1,2,...,m)
wherein, the vector z is a regional interpretation parameter (stratum horizontal permeability Kh, anisotropy coefficient Kv/Kh and invasion depth Di), and the fitting function is as follows:
in the formula, ei and fi are the measurement error of the ith actual logging data and the error of the logging response equation respectively.
The invention has the beneficial effects that: according to the volume change of the mud pollution belt of the instrument probe accessory in the pumping process of the cable formation tester, the pumping efficiency of the instrument, the pumping breakthrough time and the pumping pure time are simulated, and meanwhile, the pumping prediction is corrected according to the detection parameters of the instrument in the pumping process, so that the purpose of utilizing the pumping operation prediction and correction is achieved, the pumping and sampling operation efficiency of the cable formation tester is improved, and the operation safety of the instrument is guaranteed.
Drawings
FIG. 1 is a flow chart of a numerical correction method in an embodiment of the present invention;
FIG. 2 is a schematic representation of a coordinate system for ellipsoidal formation fluid flow established in an embodiment of the invention;
FIG. 3 is a sampling graph showing pump breakthrough time and pump completion time in the embodiment of the present invention;
FIG. 4 is a parameter diagram illustrating the interaction between monitoring parameters of the instrument according to an embodiment of the present invention;
figure 5 is a graph of parameters for real-time pump breakthrough time pick-up provided in an embodiment of the present invention;
FIG. 6 is a graph of back calculated mud invasion depth data after pump breakthrough time pickup in an embodiment of the present invention;
fig. 7 is a comparison graph of the calibration of the pumping simulation results calculated in the example of the present invention.
Detailed Description
The technical solutions in the embodiments of the present invention will be clearly and completely described below with reference to the drawings in the embodiments of the present invention, and it is obvious that the described embodiments are only a part of the embodiments of the present invention, and not all of the embodiments. All other embodiments, which can be derived by a person skilled in the art from the embodiments given herein without making any creative effort, shall fall within the protection scope of the present invention.
Referring to fig. 1, a method for simulating pumping values of a cable formation test and correcting the pumping values of the cable formation test comprises the following steps:
s1, obtaining basic parameters (stratum porosity, permeability, reservoir thickness, slurry performance, borehole size, cable stratum test pumping basic parameters, slurry invasion condition and the like) of the reservoir by using conventional logging information, judging the flow pattern of the cable stratum test pressure measurement information and calculating the corresponding fluidity;
s2, opening a test hole on the well wall by a probe, enabling the invasion zone and formation fluid to start flowing to the well bore, extracting the formation fluid by a sampler, enabling the formation fluid to instantly flow and form a flowing form and continuous conduction to generate a swept range, and simulating the swept range formed by the continuous conduction of the formation fluid flow by an ellipsoid; the part formed by stratum flow outside the well cylinder and the part in the well cylinder are in a complementary relation and integrated into a complete ellipsoid, the size of the major axis and the minor axis of the ellipsoid depends on the permeability of the reservoir and the thickness of the reservoir, the volume relation among a cylinder, the ellipsoid and a cylindrical paraboloid in a volume model is obtained through calculation, the well cylinder is defined as a cylinder, the pollution zone is the ellipsoid, and the undisturbed stratum fluid is the cylindrical paraboloid; the flow form of the formation fluid is judged by combining a pressure gradient curve, a spherical flow gradient curve and a radial flow gradient curve together through analyzing the fluidity information of a pressure measuring point and the possible flow pattern characteristics of a pumping point;
s3, inputting reservoir parameters, cable formation test operation parameters, reservoir invasion depth, and calculating the volume between the cylinder (wellbore), ellipsoid (pollution zone) and cylindrical projectile (undisturbed formation fluid) as in the model of fig. 2.
The equations for defining the cylindrical projectile (undisturbed formation fluid), ellipsoid (pollution zone) and cylinder (wellbore) are respectively
x-x0＝a2(y2+z2)，
And
(x+R)2+y2＝R2，
wherein the parameter x0 is the intersection point coordinate of the vertex of the revolution paraboloid on the x axis, a is a cylindrical paraboloid system, b and c are the horizontal axis length and the vertical axis length of the ellipsoid respectively, and meter, R is the radius of the cylinder and meter.
The region enclosed by the intersecting line of the cylindrical paraboloid and the ellipsoid is V1：
The volume of the truncated part of the ellipsoid by the cylinder is V2:
Wherein,a0＝-c,b0c, n view range [ -c, c]Length-dependent, usually 80, intrusion into the space occupied by the fluid, i.e. the volume of the ellipsoid minus V1And V2I.e. the residual volume of the ellipsoid cut by the formation virgin fluid and the wellbore fluid is set as V3，
Calculating the breakthrough time and the pump pure time of pumping of the cable formation test, and defining the volume percentage of the invaded zone fluid occupying the total test fluid as a pollution rate, wherein in the pumping process of the cable formation tester, the moment when the pollution rate is equal to 95 percent is the breakthrough time of pumping, and the moment when the pollution rate reaches 5 percent is the pump pure (or completion time). Input parameters for contamination rate calculation:
h is the thickness of the stratum in m;
Khis the formation horizontal permeability in md;
Kv/Khis the anisotropy coefficient;
di is the depth of invasion in m;
uf is the formation fluid viscosity in cp;
um is the mud filtrate viscosity in cp;
ps is the position of the probe from the top boundary, the default center position is m;
r is the radius of the shaft and is m;
qa is the pump speed in m3/s；
t is pump discharge time in units of s;
DP is the differential pressure in MPa;
the horizontal and vertical axes (b, c) of the ellipsoid are calculated, with b, c being in meters.
b＝c1×Qa×t×DP
c＝c2×Qa×t×DP
The time for the ellipsoid to reach the invaded zone (t0) was calculated in seconds for t 0.
The velocity of the rotating projectile is calculated and sd0 has units of meters per second.
sd0＝c3×DP×Qa
The coefficients a of the ellipsoid are calculated in meters.
a＝c4×Kv/Kh
In the formula, t0Meaning the time for the outer boundary to reach the invaded zone during the expansion of the ellipsoid. See the expression of b, b ═ Di, which indicates that the outer boundary of the ellipsoid reaches the invasion zone, from which t is obtained0Is described in (1).
sd0Meaning the speed at which the rotating projectile moves in the direction of the probe.
QaThe physical meaning of x t is: reflecting the speed of expansion of the ellipsoid.
C in the above equation1、c2、c3、c4The coefficients are the relationships established between formation testing parameters Differential Pressure (DP), testing flow rate (Qa), and formation anisotropy coefficient (Kv/Kh), and are determined according to the existing international system of units, and the units of the coefficients are as follows.
| Parameter(s) | c1 | c2 | c3 | c4 |
| Dimension line | MPa-1*m-2 | MPa-1*m-2 | MPa-1*m-2 | m |
Calculating x0The value (distance between the vertex of the cylindrical projectile and the probe point), the current pumping time (t) being greater than t0At that time, i.e., the moment the ellipsoid begins to be tangent to the invaded cylindrical surface, the cylindrical paraboloid (containing the formation virgin fluid) begins to taper inwardly of the ellipsoid.
t≥t0
x0＝Di-sd0(t-t0)
V obtained according to step 3)1、V2、V3And calculating the pollution rate C of the waste water,
t≥t0
when t is less than or equal to t as shown in FIG. 30When the contamination ratio c (t) is 1.0; t from t0Then the pollution rate C (t) begins to decrease; when c (t) is 95% of the test elapsed time, defined as the breakthrough time; when c (t) is 5% of the elapsed time of the test, the completion time is defined.
S4, during the pumping operation of the cable formation testing, comprehensively analyzing the following data of the fluid in the pumping line measured by the Downhole fluid identification module of the cable formation tester by using a Downhole fluid analysis technique (DFA), and as shown in fig. 4, the applied parameters include: the resistivity, temperature, pressure, density, water content, viscosity, fluorescence, bubble detection, absorption spectrum and diffraction spectrum, PH value, contamination level of the oil-based mud of the inflow/outflow line, fig. 5 is an example diagram of real-time picking up the breakthrough time of pumping according to the above method, and according to the breakthrough time of pumping, as shown in fig. 6, the intrusion radius of the intrusion zone, which is an important basis for the calibration of the pumping process, can be calculated.
Referring to fig. 7, the intrusion depth of the intrusion zone obtained in the measurement is used, and the pumping result is corrected by using a numerical simulation intelligent optimization algorithm, wherein the main algorithm (establishing a fitting function and simulation calculation) is as follows:
and m kinds of logging data are set to participate in optimization calculation, represented by a vector a,
a＝(a1,a2,...,am)T；
the vector x is m unknown parameters to be solved:
x＝(x1,x2,...,xm)T
depending on the volumetric model variations employed above, various response equations can be abstractly expressed as:
ai＝fi(x,z),(i＝1,2,...,m)
wherein the vector z is a regional interpretation parameter (determined in the research as formation level permeability Kh, anisotropy coefficient Kv/Kh and invasion depth Di). We select a fitting function of the form:
in the formula, ei and fi are the measurement error of the ith actual logging data and the error of the logging response equation respectively.
In summary, the invention observes the ratio of the slurry filtrate entering the probe in the pumping stage to the total volume of the sample, the pumping time and the change of the pumping volume according to the volume model numerical simulation and intelligent optimization method on the basis of the classification of the flow pattern of the cable formation testing fluid, and calculates the breakthrough time and the completion time of the pumping of the cable formation testing, thereby realizing the establishment of the numerical simulation model of the pumping, carrying out the simulation and correction of the pumping by comparing the numerical simulation result with the detection parameter, estimating the operation time of the pumping point in advance, providing reference for the real-time decision of the pumping sampling, and improving the operation efficiency and the sampling success rate of the pumping.
Claims (4)
1. A numerical correction method for cable formation test pumping numerical simulation and a process thereof is characterized by comprising the following steps:
s1, judging the flow pattern of the pressure measurement data of the cable formation test and calculating the corresponding fluidity;
s2, opening a test hole on the well wall by a probe, enabling the invasion zone and formation fluid to start flowing to the well bore, extracting the formation fluid by a sampler, enabling the formation fluid to instantly flow and form a flowing form and continuous conduction to generate a swept range, and simulating the swept range formed by the continuous conduction of the formation fluid flow by an ellipsoid; the part formed by stratum flow outside the well cylinder and the part in the well cylinder are in a complementary relation and integrated into a complete ellipsoid, the size of the major axis and the minor axis of the ellipsoid depends on the permeability of the reservoir and the thickness of the reservoir, the volume relation among a cylinder, the ellipsoid and a cylindrical paraboloid in a volume model is obtained through calculation, the well cylinder is defined as a cylinder, the pollution zone is the ellipsoid, and the undisturbed stratum fluid is the cylindrical paraboloid;
s3, on the basis of giving reservoir physical property parameters and invasion depth, obtaining pre-measurement predicted pumping breakthrough time, completion time and corresponding volume according to an algorithm;
and S4, testing pumping monitoring parameters by the cable stratum, picking up pumping breakthrough time and volume, and correcting the pumping result by optimizing an algorithm fitting function and simulating calculation.
2. The method for numerical correction of pumping numerical simulation and process thereof for cable formation testing according to claim 1, wherein the volume relationship among the cylinder, ellipsoid and cylindrical paraboloid of the model calculated in step S3 is:
x-x0＝a2(y2+z2)，
(x+R)2+y2＝R2
in the formula, x0The coordinate of the intersection point of the vertex of the revolution paraboloid on the x axis is shown;
a is a cylindrical paraboloid system,
b is the length of the horizontal axis of the ellipsoid in meters;
c is the length of the vertical axis of the ellipsoid in meters;
r is the radius of the cylinder and is measured in meters;
the region enclosed by the intersecting line of the cylindrical paraboloid and the ellipsoid is V1：
The volume of the truncated part of the ellipsoid by the cylinder is V2:
Wherein,a0＝-c,b0＝c，
n is an interval [ -c, c ],
intrusion into the space occupied by the fluid by the volume of the ellipsoid minus V1And V2Definition of V3Is the remaining volume of the ellipsoid cut by the formation virgin fluid and wellbore fluid:
3. the method for simulating pumping numerical value of cable formation testing and calibrating the process thereof according to claim 1, wherein the algorithm of burst time and completion time in step S3 is:
defining the volume percentage of the total test fluid occupied by the invaded zone fluid as the contamination rate, the breakthrough time of pumping is determined when the contamination rate is 95% and the completion time is determined when the contamination rate is 5% during the pumping process of the cable formation tester:
calculating the horizontal and vertical axes (b, c) of the ellipsoid, the units of b, c being m,
b＝c1×Qa×t×DP
c＝c2×Qa×t×DP)
calculating the time (t) of ellipsoid to reach the invaded zone0)，t0The unit of (a) is s,
b＝Di
calculating the speed of movement of the rotating projectile, sd0The unit of (a) is m/s,
sd0＝c3×DP×Qa
calculating the coefficient a of the ellipsoid, wherein the unit of a is m,
a＝c4×Kv/Kh
in the above formula, the first and second carbon atoms are,
h is the thickness of the stratum in m;
Khis the formation horizontal permeability in md;
Kv/Khis the anisotropy coefficient;
di is the depth of invasion in m;
uf is the formation fluid viscosity in cp;
um is the mud filtrate viscosity in cp;
ps is the position of the probe from the top boundary, the default center position is m;
r is the radius of the shaft and is m;
qa is the pump speed in m3/s；
t is pump discharge time in units of s;
DP is the differential pressure in MPa;
calculating the x0 value (distance between the apex of the cylindrical projectile and the probe point), when the pumping time t is greater than t0, i.e. the ellipsoid starts to be tangent to the cylinder of the invaded zone, the cylindrical projectile (containing the original fluid of the formation) starts to taper inside the ellipsoid, i.e.:
t≥t0
x0＝Di-sd0(t-t0)
calculating the contamination ratio C according to V1, V2 and V3 obtained in step S2,
t≥t0
when t is less than or equal to t0When the contamination ratio c (t) is 1.0; t increases from t0 and the contamination rate C (t) decreases; when C (t) is 0.95, it is abruptBreaking time; when c (t) is 0.05, the completion time is.
4. The method for numerical calibration of cable formation testing pumping numerical simulation and process thereof according to claim 1, wherein the step S4 utilizes a numerical simulation intelligent optimization algorithm to calibrate the pumping result, which establishes a fitting function and the simulation calculation is:
and m kinds of logging data are set to participate in optimization calculation, represented by a vector a,
a＝(a1,a2,...,am)T
the vector x is m unknown parameters to be solved:
x＝(x1,x2,...,xm)T
based on the volume model changes employed above, the various response equations are expressed as:
ai＝fi(x,z),(i＝1,2,...,m)
wherein, the vector z is a regional interpretation parameter (stratum horizontal permeability Kh, anisotropy coefficient Kv/Kh and invasion depth Di), and the fitting function is as follows:
in the formula, ei and fi are the measurement error of the ith actual logging data and the error of the logging response equation respectively.
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