CN115481578A - Construction method of compact rock core relative permeability model considering imbibition - Google Patents
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Abstract
The invention discloses a method for constructing a compact rock core relative permeability model considering imbibition, which considers that the oil saturation caused by imbibition in the process of stewing after pressure is reduced to cause the defects of the traditional relative permeability curve, provides a compact rock core capillary force model based on a fractal theory, and respectively constructs a capillary force model and a relative permeability model analytic solution without considering the imbibition and the imbibition on the basis of the capillary force model and the relative permeability model analytic solution, has important significance for improving the recovery efficiency mechanism in the process of stewing after pressure relief, and can be popularized and applied in the field of improving the recovery efficiency in unconventional reservoir fracturing modification.
Description
Technical Field
The invention relates to the technical field of enhanced recovery of a compact oil reservoir, in particular to a method for constructing a compact core relative permeability model considering an imbibition effect.
Background
China has abundant dense oil resources, and the amount of the main basin dense oil geological resources is primarily evaluated to be 126 hundred million tons. At present, 3 10-hundred million-ton oil regions are implemented and mainly distributed in basins such as Ordos, songliao, bohai Bay, sichuan and the like, have great development potential and are important take-over resources. Through years of practice, technologies such as compact oil resource evaluation, dessert optimization, well drilling and completion technology, horizontal well volume fracturing and the like are gradually improved, a development mode of 'long horizontal section horizontal well + volume fracturing modification' is preliminarily formed, the single well yield is improved, and effective utilization of a compact oil reservoir is realized. But at present, the problems of fast yield decrease, short stable production time, low recovery ratio and the like still exist. Researches find that after large-scale volume fracturing, the well is not closed for a period of time (well soaking), the retention liquid quantity is increased, so that the imbibition process is promoted, the stratum energy is supplemented, and the yield of the oil-gas well is improved. However, the internal mechanism of improving the production capacity by soaking is still unclear, and one reason of the mechanism is that the oil-water phase seepage rule in the soaking process is unclear, so that a large error exists in the production capacity model calculation.
At present, a tight sandstone core phase-permeability model is kept unchanged by default in an application process, in fact, oil-water phase permeability of a tight oil reservoir is dynamically changed due to the influence of an imbibition displacement effect, and the influence of the imbibition effect on a phase-permeability rule is neglected in the existing research.
Therefore, in order to deeply explain the intrinsic mechanism of the imbibition displacement effect for improving the recovery efficiency, the research on the phase permeation law considering the imbibition effect is urgently needed to be developed.
Disclosure of Invention
In order to improve the internal mechanism of recovery efficiency by the imbibition displacement effect in the process of stewing after deep-entry decompression, the invention provides a method for constructing a compact core relative permeability model considering the imbibition effect, wherein the model is based on a fractal theory and obtains a capillary force curve of residual oil saturation after imbibition by fitting, thereby constructing a relative permeability curve considering the influence of the imbibition effect.
In order to achieve the purpose, the invention adopts the following technical scheme:
a method for constructing a compact rock core relative permeability model considering imbibition comprises the following steps:
constructing a capillary force model of the compact rock core based on a fractal theory, and further constructing an oil-water relative permeability model;
carrying out a high-speed centrifugation experiment, determining a capillary force curve, fitting according to an experiment result to obtain a fractal dimension in a capillary force model, and obtaining an analytical expression of the capillary force model without considering the imbibition effect and a relative permeability model;
carrying out a spontaneous imbibition experiment, and determining the saturation of the residual oil at the end of the imbibition experiment;
and extending the capillary force curve determined by the high-speed centrifugation experiment to the residual oil saturation at the end of the imbibition according to a curve extension rule, fitting by using a capillary force model without taking the imbibition into consideration to obtain an analytical expression of the capillary force model with the imbibition into consideration, and obtaining a corresponding analytical expression of the relative oil-water permeability.
The invention discloses a compact rock core relative permeability new model considering imbibition, and relates to the following four technical theories, namely a relative permeability model constructed based on a fractal theory, capillary force curve determination by a high-speed centrifugation method, a relative permeability model verified by an unsteady state method and a spontaneous imbibition experiment.
Constructing a relative permeability model based on a fractal theory: the relative permeability model of the compact rock core is based on a fractal theory, a capillary force model is obtained through deduction on the assumption that the compact rock core is composed of different capillaries with distribution characteristics meeting fractal dimensions, and then an oil-water relative permeability model is constructed by combining a Hagen-Poiseuille equation.
Determining a capillary force curve by a high-speed centrifugation method: the centrifugal method is an experimental method for indirectly measuring capillary force curve, and the centrifugal force generated by a high-speed centrifuge is used as an external displacement pressure to achieve the core displacement effect. And fitting to obtain a fractal dimension in the capillary force model based on the capillary force curve experimental result, and further determining an analytical expression of the capillary force model and the relative permeability model which accord with the characteristics of the compact rock core.
The unsteady state method verifies a relative permeability model: in order to verify the calculation result of the theoretical model, the relative permeability is measured by adopting an unsteady state method, which is based on the core displacement experiment and carries out theoretical derivation by applying Darcy law and B-L equation. In conjunction with experimental requirements, the following assumptions were made: (1) the reservoir is a uniform porous medium; (2) the oil and water properties are stable and do not react with each other; (3) neglecting the compression properties of reservoir and displacement oil water; and (4) neglecting the oil-water gravity effect.
Spontaneous imbibition experiment: spontaneous imbibition is one of the important mechanisms for improving the recovery ratio of unconventional oil reservoirs, and oil-water displacement action generated in the soaking process after pressing is favorable for reducing the oil saturation, so that the relative permeability curve of a compact oil reservoir in the soaking process is a dynamic change process, the relative permeability curve after imbibition is still based on the relative permeability curve constructed by a fractal theory, and a capillary force curve of residual oil saturation after imbibition is achieved by fitting, so that a relative permeability curve under the influence of the imbibition action is constructed.
According to the construction method, preferably, a capillary force model of the compact rock core is constructed based on a fractal theory, and the oil-water relative permeability model is constructed by combining a Hagen-Poiseuille equation.
According to the construction method of the invention, preferably, in the step of constructing the oil-water relative permeability model by combining the Hagen-Poiseuille equation, the oil-water relative permeability model comprises the water phase relative permeability and the oil phase relative permeability.
According to the construction method of the present invention, preferably, the analytical expressions of the relative permeability of the aqueous phase and the relative permeability of the oil phase are as follows:
wherein the content of the first and second substances,
in the formula, K rw Relative permeability of water phase; k ro Relative permeability of the oil phase; s w Is the water phase saturation; s. the wr Irreducible water saturation; s. the or Residual oil saturation; λ =3-D f ，D f Is a fractal dimension; p is a radical of e The radius of a capillary of a tight sandstone core is r max Capillary force, r, corresponding to max The maximum capillary radius of the tight sandstone core; α = (p) e /p max ) -λ ，p max To the capillary force corresponding at irreducible water saturation; p c The method is characterized in that the method is the capillary force corresponding to the compact sandstone core capillary with the radius r;
according to the construction method of the invention, preferably, the developing of the high-speed centrifugation experiment includes simulating an oil displacement process and a water displacement process, and a capillary force curve of the displacement process and a capillary force curve of the suction process are respectively and correspondingly obtained.
According to the construction method of the present invention, preferably, the high-speed centrifugation experiment comprises:
and performing a core centrifugation experiment by using an ultracentrifuge, wherein the core centrifugation experiment comprises a process of centrifuging saturated water cores to a bound water state, namely the oil flooding water, and a process of centrifuging bound water cores to a residual oil state, namely the water flooding oil.
According to the construction method, preferably, a fractal dimension is obtained by fitting a capillary force curve of a displacement process obtained in the oil-water displacement process, and the relative permeability K of the water phase is calculated rw (ii) a Then obtaining fractal dimension by fitting capillary force curve of the suction process obtained in the oil-water displacement process, and calculating the relative permeability K of the oil phase ro 。
According to the construction method of the invention, the pretreatment of the core sample before the high-speed centrifugation experiment preferably comprises oil washing, drying, vacuumizing and saturation of 2% potassium chloride solution.
According to the construction method of the present invention, after obtaining the analytical expressions of the capillary force model and the relative permeability model without considering the imbibition, before the performing the spontaneous imbibition experiment, the method further includes: and (3) measuring the oil-water relative permeability of the compact rock core by using an unsteady state method, and verifying the calculation result of a relative permeability model without considering the imbibition effect.
The unsteady state method refers to a method for measuring relative permeability of two-phase fluid in rock of national standard GB/T28912-2012, and the relative permeability of oil and water of the compact rock core measured by the unsteady state method is compared with a calculation result of a relative permeability model without considering the imbibition; the comparison is not so large that a theoretical model is considered feasible. The most important parameter fractal dimension of the theoretical model is obtained according to the experimental result, and generally no large deviation exists, if errors exist possibly, and the fractal dimension test result has large errors possibly, the core of the same layer of the same reservoir is selected to carry out multiple centrifugal experiments, and an average value is selected as a comprehensive fractal dimension result, so that the theoretical model is corrected.
According to the construction method of the invention, preferably, when the unsteady state method is used for measuring the oil-water relative permeability of the compact core, a compact core sample with physical property parameters similar to those of the core sample used in the high-speed centrifugation experiment is selected.
The beneficial effects of the invention include:
the method considers that the oil saturation caused by imbibition in the soaking process after pressure is reduced, so that the traditional relative permeability curve has defects, provides a compact core capillary force model based on a fractal theory, and respectively constructs a capillary force model and a relative permeability model analytic solution without and with the imbibition being considered on the basis of the capillary force model and the relative permeability model, has important significance for improving the recovery efficiency mechanism in the soaking process after pressure release, and can be popularized and applied in the field of improving the recovery efficiency in unconventional reservoir fracturing modification.
Drawings
FIG. 1 is a flow chart of a compact core relative permeability model with imbibition considerations in an embodiment of the invention.
Fig. 2 is a capillary force curve and a fitting curve of an experimental test in a core a11 oil-water flooding process in an embodiment of the invention.
Fig. 3 is a capillary force curve and a fitting curve of an experimental test in a core a11 water flooding process in an embodiment of the invention.
FIG. 4 is a calculation result of a theoretical model of a compact core A11 oil-water relative permeability curve in an embodiment of the invention.
FIG. 5 is a comparison of the oil-water relative permeability curves for the dense core A12 of the examples of the present invention.
Fig. 6 is a capillary force curve fitting result of the tight core a11 in consideration of imbibition in the example of the present invention.
Fig. 7 is a graph of oil-water relative permeability of the dense core a11 in consideration of imbibition in an example of the present invention.
FIG. 8 is a comparison of the oil-water relative permeability curves before and after imbibition of the dense core A11 in an example of the invention.
Detailed Description
In order to more clearly illustrate the invention, the invention is further described below in connection with preferred embodiments. It is to be understood by persons skilled in the art that the following detailed description is illustrative and not restrictive, and is not to be taken as limiting the scope of the invention.
In the present invention, the principle is based on: constructing a capillary force model and a relative permeability model of the compact rock core without considering the imbibition based on a fractal theory, and determining an important parameter fractal dimension in the theoretical model through a high-speed centrifugation experiment; then, testing the relative permeability by using an unsteady state method, and verifying a theoretical model; and finally, carrying out a spontaneous imbibition experiment, determining the saturation of the residual oil, extending a capillary force curve measured by the high-speed experiment to the saturation of the residual oil at the end of imbibition according to a curve extension rule, fitting to obtain a capillary force model analytical expression considering the imbibition effect, and obtaining a corresponding oil-water relative permeability analytical expression.
As shown in fig. 1, in an embodiment of the present invention, a method for constructing a new dense core relative permeability model considering imbibition is provided, where the method includes:
s101: a compact core capillary force model is constructed based on a fractal theory, and an oil-water relative permeability model is constructed by combining a Hagen-Poiseuille equation.
S102: and (3) carrying out a high-speed centrifugation experiment, determining a capillary force curve of the compact rock core, fitting according to an experiment result to obtain a fractal dimension in a capillary force model, and obtaining an analytic expression of the capillary force model without considering the imbibition effect and a relative permeability model.
S103: and measuring the oil-water relative permeability of the compact rock core by using an unsteady state method, and verifying the calculation result of the theoretical model.
S104: and (5) carrying out a spontaneous imbibition experiment, and determining the residual oil saturation at the end of the imbibition experiment.
S105: and (3) extending the capillary force curve measured by a high-speed experiment to the residual oil saturation at the end of imbibition according to a curve extension rule, fitting by using a capillary force model without taking the imbibition effect into consideration to obtain an analytical expression of the capillary force model with the imbibition effect into consideration, and obtaining a corresponding analytical expression of the oil-water relative permeability.
By utilizing the method, a relative permeability model without considering the imbibition is constructed, and a compact sandstone sample of a long 6-component 284-block of an oil field in an Eldos basin Hua Qing is selected to carry out a high-speed centrifugation experiment, an unsteady-state water flooding experiment and a spontaneous imbibition experiment, and a theoretical model is combined with an experiment result to finally obtain a compact core relative permeability curve with considering the imbibition. The method comprises the following specific steps:
1) Constructing a compact rock core capillary force model based on a fractal theory, and constructing an oil-water relative permeability model by combining a Hagen-Poiseuille equation; the specific process is as follows:
assuming that the compact rock core is composed of different capillaries, the distribution characteristics of the compact rock core meet fractal dimension characteristics, as shown in formula (1):
wherein N is the number of capillaries with a capillary radius larger than r, and D f Is the fractal dimension, r max Is the maximum capillary radius.
Obtaining the total pore volume of the compact rock core according to the formula (1):
in the formula, V total Is the total volume of pores, L f Is a characteristic length, r min Is the minimum capillary radius.
In the centrifugation process, the pore volume occupied by the oil phase in the compact core is as follows:
in the formula V o The pore volume occupied by the oil phase in the compact rock core, and r is the minimum capillary radius occupied by the oil phase.
The oil phase saturation S of the compact rock core can be known from the formulas (2) and (3) o Comprises the following steps:
the capillary force can be expressed by the following formula:
in the formula P c The method is characterized in that the method is the capillary force corresponding to the compact sandstone core capillary with the radius of r, sigma is the oil-water interfacial tension, and theta is the oil-water two-phase contact angle.
From the formula (5), the radius of the capillary is r max And r min The corresponding capillary forces are respectively:
substituting equations (5) - (7) into equation (4) can result:
corresponding water phase saturation S w And irreducible water saturation S wr Can be expressed as:
in the formula, p max To constrain the corresponding capillary forces at water saturation.
For convenient calculation, the water phase saturation is normalized to obtain:
substituting equations (8) - (10) into equation (11) can result:
obtaining capillary force P after finishing c Comprises the following steps:
in the centrifugal experiments, the centrifugal force was considered to be equal to the capillary force. Therefore, the fractal dimension D can be obtained by fitting a capillary force curve obtained by a centrifugal experiment f And obtaining the analytical expression of the capillary force model.
The relative permeability (K) of the water phase can be obtained by combining a Hagen-Poiseuille equation and a capillary force model rw ) Relative permeability (K) to oil phase ro )：
Wherein λ =3-D f ；α＝(p e /p max ) -λ ；
In general, K ro And K rw The calculation results of the saturation values of the irreducible water and the residual oil are respectively 1 (0) and 0 (1) which have larger difference from the actual situation, so as to solve the problem that the actual saturation values of the irreducible water and the residual oil are different from the actual saturation valuesIn the application process, a fractal dimension is obtained by fitting a capillary force curve obtained in the first oil-water displacement process in a high-speed centrifugation experiment (such as the following step 2) in the displacement process, and K is calculated rw (ii) a Fitting capillary force curve in the suction process obtained by the second water flooding to obtain fractal dimension, and calculating K ro 。
2) Selecting 6 groups of compact sandstone samples A11 in an Eldos basin Hua Qing in a long oil field, carrying out a high-speed centrifugation experiment, simulating oil displacement and water displacement processes, determining a corresponding capillary force curve, fitting to obtain a fractal dimension, and finally obtaining a relative permeability curve. The specific process is as follows:
before the centrifugal experiment, the core sample is pretreated, including washing oil (solvent extraction method of toluene and ethanol, 30 days), drying (sealed oven at 105 ℃,2 days), vacuumizing and saturating 2% potassium chloride solution; afterwards, an Optim XPN type ultracentrifuge was used to perform a core centrifugation experiment, which included two parts, namely saturated water core centrifugation to bound water state (oil flooding), bound water state core centrifugation to residual oil state (water flooding).
The actually measured capillary force curve and fitting curve of the oil-water flooding process and the water-oil flooding process are shown in fig. 2 and fig. 3.
According to the experimental test result and the fitting result, the parameter P determined in the oil-water flooding process of the compact rock core A11 can be known e And fractal dimension D f Respectively 0.97MPa and 2.13, parameter P determined in the oil-water displacement process e And fractal dimension D f 0.55MPa and 2.74 respectively. Substituting the obtained parameters into the formulas (14) and (15) to obtain an oil-water relative permeability curve based on a fractal theory, as shown in fig. 4.
3) Selecting a compact rock core A12 with physical parameters similar to those of the rock core A11, and determining an oil-water relative permeability curve of the rock core sample A12 according to a national standard GB/T28912-2012 method for determining relative permeability of two-phase fluid in rock, as shown in FIG. 5. It can be seen that the relative permeability curve measured by the experimental method is not greatly different from the result obtained by fractal theory calculation, the relative permeability change rule of the oil phase is basically consistent, and the relative permeability of the water phase is slightly different but not obvious. Overall, the effect of this effect on the relative permeability curve is substantially negligible. Therefore, a theoretical model is considered feasible.
The theoretical model is obtained by deduction with reference to previous research results, large deviation generally does not exist, the most important parameter fractal dimension is obtained according to experimental results, if errors possibly exist and the fractal dimension test result has large errors, cores of the same layer of the same reservoir are selected to carry out multiple centrifugal experiments, and an average value is selected as a comprehensive fractal dimension result, so that the theoretical model is corrected.
4) And (3) placing the compact rock core A11 after the second centrifugation in an Amott imbibition bottle, and carrying out a spontaneous imbibition experiment to obtain the residual oil saturation of 24.13% at the end of the imbibition experiment.
5) And (3) extending the capillary force curve measured by the high-speed centrifugation experiment to the residual oil saturation (shown in figure 6) at the end of imbibition according to the curve extension rule, fitting to obtain a new capillary force curve, and predicting that the capillary force reaching the residual oil saturation is 13.25MPa. Then, based on the fitted capillary force curve, a relative permeability curve (as shown in fig. 7) is obtained that takes the imbibition into account.
The imbibition results in a decrease in residual oil saturation and a relatively significant change in the relative permeability curve. Comparing the oil-water relative permeability curves before and after the imbibition (as shown in fig. 8), it can be seen that the imbibition causes the range of the oil-water two-phase percolation region to be enlarged compared with that before the imbibition, and at the same time, near the saturation of the residual oil, the oil phase relative permeability is slightly higher than that before the imbibition. According to the conclusion, the internal mechanism of improving the capacity of the compact oil reservoir by the soaking operation after the fracturing construction can be explained, namely the saturation of residual oil is reduced by the seepage action, the oil-water two-phase seepage area is enlarged, the flow of the crude oil in the matrix is favorably improved, and the recovery ratio is improved.
By adopting the method, a new compact core relative permeability model considering the imbibition effect is effectively constructed, the obtained result has important significance for improving the recovery efficiency mechanism in the stewing process after pressure release, and the method can be popularized and applied in the field of improving the recovery efficiency in unconventional reservoir fracturing modification.
It should be understood that the above-mentioned embodiments of the present invention are only examples for clearly illustrating the present invention, and are not intended to limit the embodiments of the present invention, and it will be obvious to those skilled in the art that other variations or modifications may be made on the basis of the above description, and all embodiments may not be exhaustive, and all obvious variations or modifications may be included within the scope of the present invention.
Claims (10)
1. A method for constructing a compact rock core relative permeability model considering imbibition is characterized by comprising the following steps:
constructing a capillary force model of the compact rock core based on a fractal theory, and further constructing an oil-water relative permeability model;
carrying out a high-speed centrifugal experiment, determining a capillary force curve, fitting according to an experiment result to obtain a fractal dimension in a capillary force model, and obtaining an analytical expression of the capillary force model without considering the imbibition and a relative permeability model;
carrying out a spontaneous imbibition experiment, and determining the saturation of the residual oil at the end of the imbibition experiment;
and extending the capillary force curve measured by the high-speed centrifugation experiment to the residual oil saturation at the end of the imbibition experiment according to a curve extension rule, fitting by using a capillary force model without taking the imbibition into consideration to obtain an analytical expression of the capillary force model with the imbibition into consideration, and obtaining a corresponding analytical expression of the relative oil-water permeability.
2. The construction method according to claim 1, characterized in that a capillary force model of the compact core is constructed based on a fractal theory, and the oil-water relative permeability model is constructed by combining a Hagen-Poiseuille equation.
3. The construction method according to claim 2, wherein in the step of constructing the oil-water relative permeability model in combination with the Hagen-Poiseuille equation, the oil-water relative permeability model includes an oil phase relative permeability and an aqueous phase relative permeability.
4. The construction method according to claim 3, wherein the analytical expressions of the water phase relative permeability and the oil phase relative permeability are as follows:
wherein the content of the first and second substances,
in the formula, K rw Relative permeability of the water phase; k is ro Relative permeability of the oil phase; s w Is the water phase saturation; s wr Irreducible water saturation; s or Residual oil saturation; λ =3-D f ，D f Is a fractal dimension; p is a radical of e The radius of a capillary of a tight sandstone core is r max Capillary force, r, corresponding to max The maximum capillary radius of the tight sandstone core; α = (p) e /p max ) -λ ，p max The corresponding capillary force at irreducible water saturation; p c The method is characterized in that the method is the capillary force corresponding to the compact sandstone core capillary with the radius r;
5. the construction method according to claim 4, wherein the developing of the high-speed centrifugation experiment includes simulating an oil flooding process and a water flooding process, and obtaining a capillary force curve of a displacement process and a capillary force curve of a suction process respectively.
6. The method of construction according to claim 5, wherein the high speed centrifugation experiment comprises:
and performing a core centrifugation experiment by using an ultracentrifuge, wherein the core centrifugation experiment comprises a process of centrifuging saturated water cores to a bound water state, namely the oil flooding water, and a process of centrifuging bound water cores to a residual oil state, namely the water flooding oil.
7. The construction method according to claim 6, wherein a fractal dimension is obtained by fitting a capillary force curve of a displacement process obtained in the oil-water displacement process, and a water phase relative permeability K is calculated rw (ii) a Fitting a capillary force curve obtained in the oil-water displacement process in the suction process to obtain a fractal dimension, and calculating the relative permeability K of the oil phase ro 。
8. The construction method according to claim 6, wherein the high-speed centrifugation experiment is preceded by pretreatment of the core sample, which comprises oil washing, drying, vacuum pumping and saturation of 2% potassium chloride solution.
9. The method according to any one of claims 1 to 8, wherein after obtaining the analytical expressions of the capillary force model and the relative permeability model without considering the imbibition, and before performing the spontaneous imbibition test, the method further comprises: and (3) measuring the oil-water relative permeability of the compact rock core by using an unsteady state method, and verifying the calculation result of a relative permeability model without considering the imbibition effect.
10. The construction method according to claim 9, wherein when the unsteady state method is used for measuring the oil-water relative permeability of the compact core, a compact core sample with physical parameters similar to those of the core sample used in the high-speed centrifugation experiment is selected.
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Cited By (2)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| CN117233065A (en) * | 2023-11-16 | 2023-12-15 | 中国地质大学（武汉） | Shale relative permeability determination method and device and electronic equipment |
| CN117664804A (en) * | 2024-02-01 | 2024-03-08 | 中国地质大学（北京） | Relative permeability curve correction method considering end face effect and application thereof |
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Cited By (3)
| Publication number | Priority date | Publication date | Assignee | Title |
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| CN117233065A (en) * | 2023-11-16 | 2023-12-15 | 中国地质大学（武汉） | Shale relative permeability determination method and device and electronic equipment |
| CN117664804A (en) * | 2024-02-01 | 2024-03-08 | 中国地质大学（北京） | Relative permeability curve correction method considering end face effect and application thereof |
| CN117664804B (en) * | 2024-02-01 | 2024-04-26 | 中国地质大学（北京） | Relative permeability curve correction method considering end face effect and application thereof |
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