CN117664804A - Relative permeability curve correction method considering end face effect and application thereof - Google Patents
Relative permeability curve correction method considering end face effect and application thereof Download PDFInfo
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- 230000035699 permeability Effects 0.000 title claims abstract description 170
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- 238000009736 wetting Methods 0.000 claims abstract description 130
- XLYOFNOQVPJJNP-UHFFFAOYSA-N water Substances O XLYOFNOQVPJJNP-UHFFFAOYSA-N 0.000 claims abstract description 81
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- 230000008569 process Effects 0.000 claims abstract description 17
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- 230000002776 aggregation Effects 0.000 claims abstract description 4
- 238000003825 pressing Methods 0.000 claims abstract description 4
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- 230000008859 change Effects 0.000 claims description 12
- 229920006395 saturated elastomer Polymers 0.000 claims description 12
- 239000011148 porous material Substances 0.000 claims description 5
- 239000008346 aqueous phase Substances 0.000 claims description 4
- 238000001035 drying Methods 0.000 claims description 3
- 238000005325 percolation Methods 0.000 claims description 3
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- QSHDDOUJBYECFT-UHFFFAOYSA-N mercury Chemical compound [Hg] QSHDDOUJBYECFT-UHFFFAOYSA-N 0.000 description 8
- 229910052753 mercury Inorganic materials 0.000 description 8
- 238000004458 analytical method Methods 0.000 description 4
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- 230000007547 defect Effects 0.000 description 3
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- 238000005259 measurement Methods 0.000 description 3
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- 239000007788 liquid Substances 0.000 description 1
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- 239000003208 petroleum Substances 0.000 description 1
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Abstract
The invention discloses a relative permeability curve correction method considering end face effect and application thereof, comprising the following steps: developing a relative permeability test experiment to obtain relative permeability curve data of the core; carrying out a core mercury-pressing experiment to obtain capillary force data of the core; establishing a saturation profile equation of a wetting phase in a one-dimensional two-phase seepage process of core outlet section aggregation; after the water phase permeability model, the oil phase permeability model and the capillary force model are obtained, the corrected oil phase permeability and/or the corrected water phase permeability are calculated by using a correction formula. The oil phase permeability or the water phase permeability after correction is calculated by using a correction formula based on conventional testing, can be popularized to a multi-reservoir type core, does not limit the length of the core, can overcome the requirement on core samples, and can also overcome the influence of end face effect on test results.
Description
Technical Field
The invention relates to the technical field of oil reservoir engineering in petroleum development, in particular to a relative permeability curve correction method considering end face effect and application thereof.
Background
The relative permeability is the basis for researching two-phase seepage in a porous medium, and is an indispensable important data in the aspects of dynamic analysis, numerical simulation, yield prediction, construction operation and the like of compact oil field development. It was found that the relative permeability test process was significantly affected by the "end-face effect" resulting in a deviation of the measurement results. Therefore, correcting the end-face effect is important to obtain an accurate relative permeability curve, and plays a vital role in oil field production, productivity and water content prediction. The current methods for correcting the end-face effect can be divided into three main categories:
(1) Long core experimental method
And (3) carrying out an oil-water two-phase relative permeability experiment by using a long core, and weakening the influence of an end face effect on a saturation profile of a wetting phase by increasing the length of the core. But it is not suitable for all rock samples because not all cores are provided with the experimental conditions of long cores.
(2) Steady state experimental numerical calculation method
And carrying out a steady-state experiment, and obtaining the relative permeability which is not influenced by the end-face effect by establishing the relation between the end-face effect and the pressure drop and the core length influenced by the end-face effect. However, the steady-state experiment method requires more experiment times, takes longer time, has larger workload and is not convenient for obtaining the correction result quickly.
(3) Unsteady state experiment numerical value calculation method
And carrying out an unsteady state experiment, and establishing a saturation profile equation of the wetting phase to obtain the relative permeability which is not influenced by the end face effect. The two-phase flow saturation is small, and the two-phase flow saturation is more serious particularly for water wet cores, heterogeneous cores and low-viscosity fluids.
Therefore, although the three methods in the prior art can calculate the relative permeability, certain defects still exist in accuracy, and the methods have corresponding limitations, so that the popularization of the methods in practical application is affected.
Disclosure of Invention
The invention aims to provide a relative permeability curve correction method considering an end face effect and application thereof, so as to solve the technical problem that accuracy defects exist in calculating the relative permeability when the end face effect is considered in the prior art.
In order to solve the technical problems, the invention specifically provides the following technical scheme:
a relative permeability curve correction method considering end face effect includes the following steps:
developing a relative permeability test experiment to obtain relative permeability curve data of the core;
carrying out a core mercury-pressing experiment to obtain capillary force data of the core;
establishing a saturation profile equation of a wetting phase in a one-dimensional two-phase seepage process of core outlet section aggregation;
after the water phase permeability model, the oil phase permeability model and the capillary force model are obtained, the corrected oil phase permeability and/or the corrected water phase permeability are calculated by using a correction formula.
Further, the relative permeability curve data of the core includes an oil phase permeability model and a water phase permeability model.
Further, the method for carrying out the relative permeability test experiment to obtain the relative permeability curve data of the core comprises the following steps:
vacuumizing and drying the rock core, then placing the rock core into a rock core holder, and weighing the rock core after the rock core is saturated with water under high pressure by a constant-speed constant-pressure pump;
wherein:
the saturated water core is put back into the core holder, saturated oil is carried out in a constant-speed oil displacement mode, the flow of discharged water is measured by using a cylinder at the outlet end until the water is not discharged any more, and displacement parameters of the constant-speed oil displacement are recorded to calculate and obtain an oil phase permeability model;
and (3) carrying out the saturated oil core in a constant-speed water flooding mode, measuring the flow of discharged oil by using a cylinder at an outlet end until no water is discharged, and recording displacement parameters of the constant-speed water flooding to calculate and obtain the water phase permeability model.
Further, the capillary force data of the core includes a capillary force model.
Further, the method for constructing the saturation profile equation in the one-dimensional two-phase seepage process comprises the following steps:
obtaining seepage equations of a wetting phase and a non-wetting phase according to Darcy's law:the method comprises the steps of carrying out a first treatment on the surface of the Wherein (1)>Is non-wetting phase flow, m/s; />For wetting phase flow, m/s; k is absolute permeability, D; />Relative permeability, D, for the non-wetting phase; a is the cross-sectional area of the core, cm 2 ；/>Viscosity of non-wetting phase, mpa·s; />D, relative permeability for the wet phase; />Viscosity of the wetting phase, mpa·s; let capillary pressure +.>Pressure +.>Pressure>The difference is recorded asThe method comprises the steps of carrying out a first treatment on the surface of the In the one-dimensional core, if the distance from any position of the core to the inlet end is x, x is E [0, L]L is the length of the core, cm, then: capillary pressure->Gradient change expression along x: />The method comprises the steps of carrying out a first treatment on the surface of the Wherein the gradient expression of the capillary pressure Pc along x is rewritten as saturation of the capillary pressure Pc along the wetting phase +.>Is a gradient change expression of (2):the method comprises the steps of carrying out a first treatment on the surface of the Wherein (1)>Saturation for the wet phase; and combining the gradient change expression of the capillary pressure along the saturation of the wetting phase and the gradient change expression of the capillary pressure along x to obtain a one-dimensional two-phase seepage equation containing the saturation gradient:；
since the wet phase saturation is a function of time t and distance x, in an unsteady experiment, when time t goes to infinity, the displacement system no longer changes with time, correspondingly wet phase saturation S w Irrespective of time t, then the one-dimensional two-phase percolation equation with saturation gradient is converted into:the method comprises the steps of carrying out a first treatment on the surface of the And integrating the above on the whole rock core to obtain the section equation of the saturation of the wetting phase at different distances from the inlet end of the rock core: />The method comprises the steps of carrying out a first treatment on the surface of the Wherein (1)>Saturation of the wetting phase for the outlet end;
the section equation of the saturation of the wetting phase of the core with the length of the inlet end is converted into the section equation of the saturation of the wetting phase of the core with the length of the inlet end when the time tends to infinity:the method comprises the steps of carrying out a first treatment on the surface of the Wherein (1)>Is the saturation of the non-wetting phase. Further, the correction method for the relative oil phase permeability and the relative water phase permeability specifically comprises the following steps:
correcting the relative permeability of the oil phase when the non-wetting phase displaces the wetting phase;
correction of relative permeability of the aqueous phase as the wetting phase displaces the non-wetting phase.
Further, when the non-wetting phase displaces the wetting phase, the saturation of the core inlet end is:；/>normalized saturation for the wetting phase of the inlet section, < >>Normalized saturation for the wet phase;
under the steady state condition that the core is not injected with the wetting phase, the Darcy equation of the non-wetting phase is integrated to obtain the pressure drop at the position x away from the inlet end of the core, wherein the pressure drop is as follows:the method comprises the steps of carrying out a first treatment on the surface of the P is pressure, atm; Δp is the differential pressure, atm; x is the distance from the inlet end of the core, cm; />Pressure of x, atm; />Pressure at x is 0, atm; />Capillary force for the inlet end; />Normalizing saturation to wetting phaseCapillary forces of the associated cores; />Capillary force for the core; wherein, when x=l: />The method comprises the steps of carrying out a first treatment on the surface of the Wherein S is wi Saturation of the wet phase in the bound state; k (k) rnw (S wi ) av For the relative permeability of the non-wetting phase measured at the average bound wetting phase saturation; />Is the capillary force when normalized wet phase saturation is 1; then: />；
Wherein,to bind the relative permeability of the non-wetting phase measured at saturation of the wetting phase.
Further, when the wetting phase displaces the non-wetting phase, q nw =0；
Section equation of the wet phase saturation of the core with distance from the inlet end when time goes to infinity:；
wherein,saturation of the wetting phase for the outlet end;
when x is 0, the saturation of the core inlet end is:；/>normalized saturation for the wetting phase of the inlet section, < >>Normalized saturation for the wet phase;
because the core is in a steady state without injecting the wetting phase, the pressure drop at the position x from the inlet end of the core is obtained by integrating the Darcy equation of the wetting phase:the method comprises the steps of carrying out a first treatment on the surface of the P is pressure, atm; Δp is the differential pressure, atm; x is the distance from the inlet end of the core, cm; />Pressure of x, atm; />Pressure at x is 0, atm;capillary force for the inlet end; />Capillary force of the core relative to saturation normalized to wetting phase; />Capillary force for the core;
wherein, when x=l:the method comprises the steps of carrying out a first treatment on the surface of the Wherein: />Relative permeability of the wet phase as measured at average residual non-wet phase saturation;
then:；
wherein,is the relative permeability of the wet phase measured at the saturation level of the residual non-wet phase.
Further, the correction method is expanded to different reservoir types, wherein the reservoir types comprise five cores of ultra-low pore hypotonic, medium pore hypotonic, high Kong Gaoshen and ultra-high pore hypertonic;
further, the method for determining the optimized water phase permeability model, the oil phase permeability model and the capillary force model of different reservoir types is to optimally fit the water phase permeability model, the oil phase permeability model and the capillary force model by adopting a global optimization algorithm, and compare and select the optimized water phase permeability model, the oil phase permeability model and the capillary force model. Compared with the prior art, the invention has the following beneficial effects:
based on conventional tests, such as relative permeability curve data and capillary force data, the method calculates corrected oil phase permeability or water phase permeability by using a correction formula based on a water phase permeability model, an oil phase permeability model and a capillary force model, can be popularized to multi-reservoir type cores, and does not limit the core length;
the method is based on a saturation profile equation in a one-dimensional two-phase seepage process, not only can the requirements on a core sample be overcome, but also the influence of an end face effect on a test result can be overcome, and particularly for a sample with a defect core, a more accurate correction result can be obtained through limited times of tests.
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In order to more clearly illustrate the embodiments of the present invention or the technical solutions in the prior art, the drawings used in the description of the embodiments or the prior art will be briefly described below. It will be apparent to those of ordinary skill in the art that the drawings in the following description are exemplary only and that other implementations can be obtained from the extensions of the drawings provided without inventive effort.
FIG. 1 is a schematic flow chart of an embodiment of the present invention;
FIG. 2 is a diagram of a numerical simulation model according to an embodiment of the present invention.
Detailed Description
The following description of the embodiments of the present invention will be made clearly and completely with reference to the accompanying drawings, in which it is apparent that the embodiments described are only some embodiments of the present invention, but not all embodiments. All other embodiments, which can be made by those skilled in the art based on the embodiments of the invention without making any inventive effort, are intended to be within the scope of the invention.
As shown in fig. 1, the invention provides a relative permeability curve correction method considering end-face effect, and aims at the problems that three current methods for correcting end-face effect cannot obtain very accurate results and each has limitation, the invention is based on a third type correction method, and based on the establishment of a saturation profile equation of a wetting phase, the end-face effect correction of the whole process of a non-steady state relative permeability measurement experiment is obtained through the analysis of the saturation profile of two processes of non-wetting phase displacement wetting phase and wetting phase displacement non-wetting phase, and the end-face effect correction method suitable for multiple reservoir type cores is obtained through the classification of reservoirs, the analysis of relative permeability models and the analysis of capillary pressure models.
In order to realize end-face effect correction, the method specifically comprises the following steps:
developing a relative permeability test experiment to obtain relative permeability curve data of the core;
carrying out a core mercury-pressing experiment to obtain capillary force data of the core;
establishing a saturation profile equation of a wetting phase in a one-dimensional two-phase seepage process of core outlet section aggregation;
after obtaining a water phase permeability model, an oil phase permeability model and a capillary force model, calculating by using a correction formula to obtain corrected oil phase permeability and/or water phase permeability;
expanding the method to different reservoir types, and determining an optimized water phase permeability model, an oil phase permeability model and a capillary force model of different reservoir types;
and calculating the oil phase permeability and/or the water phase permeability corrected by different reservoir types by using a correction formula.
In the invention, based on a saturation profile equation in a one-dimensional two-phase seepage process, conventional tests such as relative permeability curve data and capillary force data are utilized, and corrected oil phase permeability or water phase permeability is calculated by using a correction formula based on a water phase permeability model, an oil phase permeability model and a capillary force model.
The core testing device can overcome the requirement on core samples, can also overcome the influence of end-face effect on testing results, can obtain more accurate correction results through limited tests particularly for core defective samples, and can be popularized to different reservoir types to obtain oil phase permeability and/or water phase permeability after correction of different reservoir types.
Further, the relative permeability curve data of the core includes an oil phase permeability model and a water phase permeability model.
Further, the method for carrying out the relative permeability test experiment to obtain the relative permeability curve data of the core comprises the following steps:
vacuumizing and drying the core, placing the core into a core holder, and weighing the core after the core is saturated with water for 12 hours under high pressure by a constant-speed constant-pressure pump;
wherein:
the saturated water core is put back into the core holder, saturated oil is carried out in a constant-speed oil flooding mode at the injection speed of 0.1mL/min, the flow of discharged water is measured by using a cylinder at the outlet end until no water is discharged, the displacement parameters of the constant-speed oil flooding are recorded (the total volume of the discharged water and the inlet pressure of the core are recorded, and the original oil saturation, the irreducible water saturation and the oil phase permeability in the condition of the irreducible water can be calculated) so as to obtain an oil phase permeability model through calculation;
and (3) carrying out the saturated oil core in a constant-speed water flooding mode, measuring the flow of discharged oil by using a cylinder at an outlet end until water is not discharged, and recording displacement parameters (displacement time, accumulated oil yield, accumulated liquid yield, displacement pressure difference and temperature in the displacement process) of the constant-speed water flooding so as to calculate and obtain a water phase permeability model.
Further, the capillary force data of the core includes a capillary force model. The method is used for accurately representing the relationship between capillary pressure and wet phase saturation, and comprises the following experimental steps:
loading a core sample into an instrument, and changing sample information and vacuum time;
entering an instrument autottorun interface, and operating according to the specified requirement of the instrument;
and after the experiment is finished, deriving an experiment result. Experimental data are read by using Aspedas software to obtain mercury inlet pressure, mercury inlet saturation, mercury removal pressure and mercury removal saturation.
(4) After the water phase permeability model, the oil phase permeability model and the capillary force model are obtained, corrected irreducible water saturation, residual oil saturation, and oil phase permeability in the irreducible water state and water phase permeability in the residual oil are calculated according to the formulas. Wherein the relative permeability of the non-wetting phase in the binding state of the wetting phase and the relative permeability of the wetting phase in the displacement process of the wetting phase are obtained by using a wetting phase saturation profile equation considering capillary force, respectively, and correction of the oil phase permeability and the water phase permeability is performed.
And establishing a saturation profile equation in the one-dimensional two-phase seepage process according to the physical meaning generated by the end face effect, namely that the wetting phase gathers in the core outlet section. The hypothetical conditions for the equation are:
1) The two fluids are incompressible;
2) The two fluids are not miscible;
3) Gravity is not considered;
4) Capillary pressure is considered.
The method for constructing the saturation profile equation in the one-dimensional two-phase seepage process comprises the following steps:
obtaining seepage equations of a wetting phase and a non-wetting phase according to Darcy's law:(1) The method comprises the steps of carrying out a first treatment on the surface of the Wherein, is>Is non-wetting phase flow, m/s; />For wetting phase flow, m/s; k is absolute permeability, D; />Relative permeability, D, for the non-wetting phase; a is the cross-sectional area of the core, cm 2 ；/>Viscosity of non-wetting phase, mpa·s; />D, relative permeability for the wet phase; />The viscosity of the wet phase, mPas.
Because the end-face effect is caused by the discontinuous capillary pressure, the capillary pressure needs to be considered in the equation when the seepage equation is constructed, so that the influence of the capillary pressure on the seepage result can be reflected. Thus, let the capillary pressurePressure +.>Pressure>The difference is noted as: />；
Combining equation (1) with equation (2) to obtain capillary pressureGradient change expression along x:（3）；
in the one-dimensional core, if the distance from any position of the core to the inlet end is x, x epsilon [0, L ], L is the length of the core, and cm is: when x=0, is the inlet end of the core; when x=l, it is the exit end of the core.
Since capillary pressure is a function of not only x but also water saturation, the gradient expression of capillary pressure Pc along x is rewritten as saturation of capillary pressure Pc along the wetting phaseIs a gradient change expression of (2): />（4）；
Wherein,saturation for the wet phase. And combining the gradient change expression of the capillary pressure along the saturation of the wetting phase and the gradient change expression of the capillary pressure along x to obtain a one-dimensional two-phase seepage equation containing the saturation gradient:（5）；
since the wet phase saturation is a function of time t and distance x, in an unsteady experiment, when time t goes to infinity, the displacement system no longer changes with time, correspondingly wet phase saturation S w Irrespective of time t, then the one-dimensional two-phase percolation equation with saturation gradient is converted into:（6）；
and integrating the above on the whole rock core to obtain the section equation of the saturation of the wetting phase at different distances from the inlet end of the rock core:(7) The method comprises the steps of carrying out a first treatment on the surface of the Wherein (1)>Saturation of the wetting phase for the outlet end;
equation 7 is the saturation profile equation of the wetting phase at different distances from the core inlet end. The upper limit of the right integral is the water saturation at the core exit end. Due to capillary tubeAs a result, a relatively large amount of wetting phase may accumulate at the core outlet end face. Therefore, within the error allowance range, S w,out Can be assumed to be 100%, S in the presence of residual oil w,out Can be assumed to be 1-S nw . Namely: the section equation of the saturation of the wetting phase of the core with the length of the inlet end is converted into the section equation of the saturation of the wetting phase of the core with the length of the inlet end when the time tends to infinity:(8) The method comprises the steps of carrying out a first treatment on the surface of the Wherein (1)>Is the saturation of the non-wetting phase. The correction method for the relative permeability of the oil phase and the relative permeability of the water phase specifically comprises the following steps:
correcting the relative permeability of the oil phase when the non-wetting phase displaces the wetting phase;
correction of relative permeability of the aqueous phase as the wetting phase displaces the non-wetting phase.
In one aspect, when the non-wetting phase displaces the wetting phase, the saturation of the core inlet end is:（9）；/>normalized saturation for the wetting phase of the inlet section, < >>Normalized saturation for the wet phase;
and obtaining the saturation correction value of the core inlet end according to the relation between the relative permeability of the wetting phase at the core end obtained through experiments and the pressure drop.（10）；
Under the steady state condition that the core is not injected with the wetting phase, the Darcy equation of the non-wetting phase is integrated to obtain the pressure drop at the position x away from the inlet end of the core, wherein the pressure drop is as follows:（11）；
p is pressure, atm; Δp is the differential pressure, atm; x is the distance from the inlet end of the core, cm;pressure of x, atm;pressure at x is 0, atm; />Capillary force for the inlet end; />Capillary force of the core relative to saturation normalized to wetting phase; />Is the capillary force of the core.
Wherein, when x=l:（12）；
bringing Δp in equation (12) into equation (10) yields:(13) The method comprises the steps of carrying out a first treatment on the surface of the Wherein S is wi Saturation of the wet phase in the bound state; k (k) rnw (S wi ) av For the relative permeability of the non-wetting phase measured at the average bound wetting phase saturation; />Is the capillary force when normalized to wet phase saturation of 1. And k is rnw (S wi ) av 、L、q nw 、u nw K, A can be measured by oil-water relative permeability experiments. P (P) c (S w * ) Can be measured by mercury intrusion experiments. S can be obtained from equation (13) w * in . Due to k rnw Is about k rnw (S wi ) And S is equal to w * Is the function of (1): />（14）；
Wherein,to bind the relative permeability of the non-wetting phase measured at saturation of the wetting phase.
In the whole rock core, the saturation is integrated and then averaged, and the average water saturation of the whole rock core can be obtained as follows:（15）；
based on the obtained S w * av S is obtained wi The method comprises the following steps:（16）。
on the other hand, when the core is filled with the non-wetting phase and the trapped wetting phase, a displacement process of the wetting phase is carried out, and when the wetting phase displaces the non-wetting phase, q nw =0；
Section equation of the wet phase saturation of the core with distance from the inlet end when time goes to infinity:（17）；
wherein,saturation of the wetting phase for the outlet end;
when x is 0, the saturation of the core inlet end is:（18）；/>normalized saturation for the wetting phase of the inlet section, < >>Normalized saturation for the wet phase;
in the experiments, the relative permeability of the wet phase at the end of the core was calculated from the pressure drop across the core. The pressure drop needs to be corrected due to capillary end effects. And obtaining a saturation correction value of the inlet end of the core according to the relation between the relative permeability of the wetting phase at the tail end of the core obtained through experiments and the pressure drop.（19）；
Because the core is in a steady state without injecting the wetting phase, the pressure drop at the position x from the inlet end of the core is obtained by integrating the Darcy equation of the wetting phase:(20) The method comprises the steps of carrying out a first treatment on the surface of the P is pressure, atm; Δp is the differential pressure, atm; x is the distance from the inlet end of the core, cm; />Pressure of x, atm; />Pressure at x is 0, atm;capillary force for the inlet end; />Capillary force of the core relative to saturation normalized to wetting phase; />Is the capillary force of the core.
Wherein, when x=l:（21）；
bringing Δp in equation (21) into equation (19) yields:（22）；
wherein:relative permeability of the wet phase as measured at average residual non-wet phase saturation;、L、q w 、u w k, A can be measured by oil-water relative permeability experiments. P (P) c (S w * ) Can be measured by mercury intrusion experiments. P can be found according to equation 22 c (S w * ) in 。/>（23）；
S is obtainable according to formula (23) w * in . Due to k rw Is about k rw (S or ) And S is equal to w * So that k can be obtained from the formula (24) rw (S or )。（24）；
To this end S can be obtained or * K rw (S or )：。
Wherein,is the relative permeability of the wet phase measured at the saturation level of the residual non-wet phase.
Based on the foregoing, in the present embodiment:
the oil phase relative permeability correction procedure is as follows:
k in the relative permeability curve test experiment rnw (S wi ) av 、L、q nw 、u nw P in the mercury intrusion experiments, K, A c (S w * ) Brought into equation 13 to find S w * in ；
Due to k rnw Is about k rnw (S wi ) And S is equal to w * We have found the relationship between relative permeability of the non-wetting phase (oil phase) and water saturation during the data processing stage, so k can be found according to equation 14 rnw （S wi ) The method comprises the steps of carrying out a first treatment on the surface of the The water saturation of the whole rock core is integrated and then averaged to obtain the average water saturation of the whole rock core, as shown in the formula (15), at the moment, S can be obtained according to the formulas (15) - (16) wi 。
The relative permeability correction process for the aqueous phase is as follows: k in the relative permeability curve test experiment rw (S or ) av 、L、q w 、u w P in the mercury intrusion experiments, K, A c (S w * ) Brought into equation 23 to obtain S w * in The method comprises the steps of carrying out a first treatment on the surface of the Due to k rw Is about k rw (S or ) And S is equal to w * We have found the relation between relative permeability of the non-wetting phase (oil phase) and water saturation during the data processing stage, so k can be found according to equation 24 rw (S or ) The method comprises the steps of carrying out a first treatment on the surface of the S is obtained according to formula (25) or 。
Expanding the method to different reservoir types, and determining an optimized water phase permeability model, an oil phase permeability model and a capillary force model of different reservoir types, wherein the model optimization result is shown in figure 2;
and calculating to obtain oil phase permeability and/or water phase permeability after correction of different reservoir types by using a correction formula, wherein the formula 14, the formula 23 and the formula 24 can preferably find an optimization model corresponding to the reservoir type, so as to obtain the oil phase permeability and/or water phase permeability after correction of different reservoir types.
Therefore, in the present embodiment, the oil-water relative permeability curve considering the end effect can be obtained by inputting the core basic physical properties, the unsteady state relative permeability measurement experimental conditions, and the data of the to-be-corrected permeability curve.
In addition, in combination with the comparison of the two models in fig. 2, that is, the model 1 uses the oil-water two-phase relative permeability data before correction to perform simulation, and the model 2 uses the corrected oil-water two-phase permeability data to perform simulation. Model 1 contains an end face grid; the mesh does not contain an end face mesh in the model 2.
The water content curves of the model 1 and the model 2 are compared, the error is smaller than 1%, and the method is considered to be not influenced by the end-face effect in the core experiment and is close to the relative permeability of the core in the true state of the oil reservoir.
The above embodiments are only exemplary embodiments of the present application and are not intended to limit the present application, the scope of which is defined by the claims. Various modifications and equivalent arrangements may be made to the present application by those skilled in the art, which modifications and equivalents are also considered to be within the scope of the present application.
Claims (10)
1. The method for correcting the relative permeability curve by considering the end face effect is characterized by comprising the following steps of:
developing a relative permeability test experiment to obtain relative permeability curve data of the core;
carrying out a core mercury-pressing experiment to obtain capillary force data of the core;
establishing a saturation profile equation of a wetting phase in a one-dimensional two-phase seepage process of core outlet section aggregation;
after the water phase permeability model, the oil phase permeability model and the capillary force model are obtained, the corrected oil phase permeability and/or the corrected water phase permeability are calculated by using a correction formula.
2. The method of claim 1, wherein the relative permeability profile data of the core comprises an oil phase permeability model and a water phase permeability model.
3. The method of claim 2, wherein the step of performing a relative permeability test to obtain the relative permeability curve data of the core comprises:
vacuumizing and drying the rock core, then placing the rock core into a rock core holder, and weighing the rock core after the rock core is saturated with water under high pressure by a constant-speed constant-pressure pump;
wherein:
the saturated water core is put back into the core holder, saturated oil is carried out in a constant-speed oil displacement mode, the flow of discharged water is measured by using a cylinder at the outlet end until the water is not discharged any more, and displacement parameters of the constant-speed oil displacement are recorded to calculate and obtain an oil phase permeability model;
and (3) carrying out the saturated oil core in a constant-speed water flooding mode, measuring the flow of discharged oil by using a cylinder at an outlet end until no water is discharged, and recording displacement parameters of the constant-speed water flooding to calculate and obtain the water phase permeability model.
4. A method of correcting a relative permeability curve taking into account end effects as defined in claim 3, wherein the capillary force data of the core comprises a capillary force model.
5. The method for correcting a relative permeability curve considering an end-face effect according to claim 4, wherein the method for constructing a saturation profile equation in a one-dimensional two-phase seepage process is as follows:
obtaining seepage equations of a wetting phase and a non-wetting phase according to Darcy's law:the method comprises the steps of carrying out a first treatment on the surface of the Wherein (1)>Is non-wetting phase flow, m/s; />For wetting phase flow, m/s; k is absolute permeability, D; />Relative permeability, D, for the non-wetting phase; a is the cross-sectional area of the core, cm 2 ；/>Viscosity of non-wetting phase, mpa·s; />D, relative permeability for the wet phase; />Viscosity of the wetting phase, mpa·s; let capillary pressure +.>Pressure +.>Pressure>The difference is marked as->The method comprises the steps of carrying out a first treatment on the surface of the In the one-dimensional core, if the distance from any position of the core to the inlet end is x, x is E [0, L]L is the length of the core, cm, then: capillary pressure->Gradient change expression along x: />The method comprises the steps of carrying out a first treatment on the surface of the Wherein the gradient expression of the capillary pressure Pc along x is rewritten as saturation of the capillary pressure Pc along the wetting phase +.>Is a gradient change expression of (2): />The method comprises the steps of carrying out a first treatment on the surface of the Wherein (1)>Saturation for the wet phase; and combining the gradient change expression of the capillary pressure along the saturation of the wetting phase and the gradient change expression of the capillary pressure along x to obtain a one-dimensional two-phase seepage equation containing the saturation gradient: />；
Since the wet phase saturation is a function of time t and distance x, in an unsteady experiment, when time t goes to infinity, the displacement system no longer changes with time, correspondingly wet phase saturation S w Irrespective of time t, then the one-dimensional two-phase percolation equation with saturation gradient is converted into:；
and integrating the above on the whole rock core to obtain the section equation of the saturation of the wetting phase at different distances from the inlet end of the rock core:the method comprises the steps of carrying out a first treatment on the surface of the Wherein (1)>Saturation of the wetting phase for the outlet end;
the section equation of the saturation of the wetting phase of the core with the length of the inlet end is converted into the section equation of the saturation of the wetting phase of the core with the length of the inlet end when the time tends to infinity:；
wherein,is the saturation of the non-wetting phase.
6. The method for correcting relative permeability curves considering end effects according to claim 5, wherein the method for correcting relative permeability of oil phase and relative permeability of water phase specifically comprises:
correcting the relative permeability of the oil phase when the non-wetting phase displaces the wetting phase;
correction of relative permeability of the aqueous phase as the wetting phase displaces the non-wetting phase.
7. A method for correcting a relative permeability curve taking into account end-face effects as defined in claim 6,
when the non-wetting phase displaces the wetting phase, the saturation of the core inlet end is:；/>normalized saturation for the wetting phase of the inlet section, < >>Normalized saturation for the wet phase;
under the steady state condition that the core is not injected with the wetting phase, the Darcy equation of the non-wetting phase is integrated to obtain the pressure drop at the position x away from the inlet end of the core, wherein the pressure drop is as follows:the method comprises the steps of carrying out a first treatment on the surface of the P is pressure, atm; Δp is the differential pressure, atm; x is the distance from the inlet end of the core, cm; />Pressure of x, atm; />Pressure at x is 0, atm;capillary force for the inlet end; />Capillary force of the core relative to saturation normalized to wetting phase; />Capillary force for the core;
wherein, when x=l:the method comprises the steps of carrying out a first treatment on the surface of the Wherein S is wi Saturation of the wet phase in the bound state; k (k) rnw (S wi ) av For the relative permeability of the non-wetting phase measured at the average bound wetting phase saturation; />Is the capillary force when normalized wet phase saturation is 1; then: />The method comprises the steps of carrying out a first treatment on the surface of the Wherein (1)>To bind the relative permeability of the non-wetting phase measured at saturation of the wetting phase.
8. A method for correcting a relative permeability curve taking into account end-face effects as defined in claim 6,
q when the wetting phase displaces the non-wetting phase nw =0; section equation of the wet phase saturation of the core with distance from the inlet end when time goes to infinity:the method comprises the steps of carrying out a first treatment on the surface of the Wherein (1)>Saturation of the wetting phase for the outlet end;
when x is 0, the saturation of the core inlet end is:；/>normalized saturation for the wetting phase of the inlet section, < >>Normalized saturation for the wet phase;
because the core is in a steady state without injecting the wetting phase, the pressure drop at the position x from the inlet end of the core is obtained by integrating the Darcy equation of the wetting phase:the method comprises the steps of carrying out a first treatment on the surface of the P is pressure, atm; Δp is the differential pressure, atm; x is the distance from the inlet end of the core, cm; />Pressure of x, atm; />Pressure at x is 0, atm; />Capillary force for the inlet end; />Capillary force of the core relative to saturation normalized to wetting phase; />Capillary force for the core;
wherein, when x=l:；
wherein:relative permeability of the wet phase as measured at average residual non-wet phase saturation;
then:the method comprises the steps of carrying out a first treatment on the surface of the Wherein (1)>Is the relative permeability of the wet phase measured at the saturation level of the residual non-wet phase.
9. The method for correcting the relative permeability curve considering the end-face effect according to claim 8, wherein according to the clastic rock reservoir physical property classification standard, five types of cores of ultra-low pore hypotonic, medium pore hypotonic, high Kong Gaoshen and ultra-high Kong Gaoshen are used, and an optimized water phase permeability model, an oil phase permeability model and a capillary force model of different reservoir types are obtained through an optimized fitting means;
and after the optimized water phase permeability model, the oil phase permeability model and the capillary force model are obtained, calculating by using a correction formula to obtain the corrected oil phase permeability and/or water phase permeability of different reservoir types.
10. Use of a relative permeability curve correction method taking into account end effects according to any of claims 1-9, characterized in that the relative permeability curve correction method taking into account end effects is extended to different reservoir types, and water phase permeability models, oil phase permeability models and capillary force models of different reservoir types are determined;
and calculating the oil phase permeability and/or the water phase permeability corrected by different reservoir types by using a correction formula.
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