A method for constructing a relative permeability model for tight cores that considers seepage.

Abstract

This invention discloses a method for constructing a relative permeability model of tight cores that considers the effect of seepage. This method takes into account the reduction in oil saturation caused by seepage during the post-fracturing well stagnation process, which leads to the inadequacy of traditional relative permeability curves. A capillary force model of tight cores based on fractal theory is proposed. Based on this, analytical solutions for capillary force models and relative permeability models that do not consider seepage and those that do consider seepage are constructed respectively. This is of great significance for explaining the mechanism of enhanced oil recovery during the post-fracturing well stagnation process and can be widely applied in the field of enhanced oil recovery through fracturing in unconventional reservoirs.

Description

Technical Field

[0001] This invention relates to the field of enhanced oil recovery technology for tight oil reservoirs, specifically to a method for constructing a relative permeability model for tight core samples that takes into account the effects of seepage and absorption. Background Technology

[0002] China possesses abundant tight oil resources, with preliminary assessments indicating geological resources of 12.6 billion tons in major basins. Currently, three oilfields with reserves exceeding 1 billion tons have been identified, primarily distributed in the Ordos, Songliao, Bohai Bay, and Sichuan basins, representing significant development potential and important replacement resources. Through years of practice, technologies such as tight oil resource evaluation, sweet spot selection, drilling and completion techniques, and horizontal well volumetric fracturing have been gradually improved, initially forming a development model of "long horizontal well sections + volumetric fracturing stimulation," which has increased single-well production and achieved effective utilization of tight oil reservoirs. However, problems such as rapid production decline, short stable production time, and low recovery rates still exist. Research has found that after large-scale volumetric fracturing, shutting in the well for a period without flowback (well shut-in) and increasing the amount of retained fluid helps promote the permeation process, replenish formation energy, and increase oil and gas well production. However, the underlying mechanism by which well shut-in improves production capacity remains unclear, partly due to a lack of understanding of the oil-water interphase permeability during well shut-in, leading to significant errors in production capacity model calculations.

[0003] Currently, the phase permeability model of tight sandstone cores is assumed to remain unchanged during application. In fact, due to the influence of permeation and replacement, the oil-water phase permeability of tight oil reservoirs is dynamic. Existing studies have neglected the influence of permeation on phase permeability patterns.

[0004] Therefore, in order to deeply explain the intrinsic mechanism of enhanced oil recovery through permeation and displacement, it is urgent to carry out research on the relative permeation law that takes into account permeation. Summary of the Invention

[0005] To gain a deeper understanding of the intrinsic mechanism by which the permeation and replacement effect enhances oil recovery during the post-pressure well simmering process, this invention proposes a method for constructing a relative permeability model of tight core samples that considers permeation. This model is based on fractal theory and obtains the capillary force curve of residual oil saturation after permeation by fitting, thereby constructing a relative permeability curve that considers the influence of permeation.

[0006] To achieve the above objectives, the present invention adopts the following technical solution:

[0007] A method for constructing a relative permeability model for tight cores that considers permeation includes the following steps:

[0008] Based on fractal theory, a capillary force model of dense rock cores is constructed, and then an oil-water relative permeability model is constructed.

[0009] High-speed centrifugation experiments were conducted to determine the capillary force curve. Based on the experimental results, the fractal dimension in the capillary force model was obtained by fitting the model, and analytical expressions for the capillary force model and the relative permeability model without considering the osmosis effect were obtained.

[0010] Conduct spontaneous percolation experiments to determine the residual oil saturation at the end of the percolation experiment;

[0011] The capillary force curve measured by high-speed centrifugation experiment was extended to the residual oil saturation at the end of the percolation according to the curve extension law. The capillary force model without considering the percolation effect was used for fitting to obtain the analytical expression of the capillary force model considering the percolation effect, and the corresponding analytical expression of the relative permeability of oil and water was obtained.

[0012] This invention aims to construct a new model for the relative permeability of dense cores that takes into account the permeation effect. It involves the following four aspects of technical theory: constructing a relative permeability model based on fractal theory, determining the capillary force curve using the high-speed centrifugation method, verifying the relative permeability model using the unsteady-state method, and conducting spontaneous permeation experiments.

[0013] A relative permeability model based on fractal theory is constructed: The relative permeability model of tight core is based on fractal theory. It assumes that the tight core is composed of capillaries with different distribution characteristics that satisfy the fractal dimension, and derives the capillary force model. Then, the oil-water relative permeability model is constructed by combining the Hagen-Poiseuille equation.

[0014] High-speed centrifugation method for determining capillary force curves: The centrifugation method is an experimental method for indirectly measuring capillary force curves. It uses the centrifugal force generated by a high-speed centrifuge as an external displacement pressure to achieve the core displacement effect. Based on the experimental results of the capillary force curves, the fractal dimension in the capillary force model is fitted, and then analytical expressions for the capillary force model and relative permeability model that conform to the characteristics of dense cores are determined.

[0015] Verification of the relative permeability model using the unsteady-state method: To verify the calculation results of the theoretical model, the relative permeability was measured using the unsteady-state method. This method is based on core displacement experiments and uses Darcy's law and the BL equation for theoretical derivation. In accordance with the experimental requirements, the following assumptions need to be made: (1) The reservoir is a homogeneous porous medium; (2) The oil and water properties are stable and do not react with each other; (3) The compressibility of the reservoir and the displaced oil and water is ignored; (4) The gravitational effect of oil and water is ignored.

[0016] Spontaneous Immersion Experiment: Spontaneous immersion is one of the important mechanisms for improving the recovery rate of unconventional oil reservoirs. The oil-water replacement that occurs during the well-steaming process after pressure is beneficial to reducing the oil saturation. Therefore, the relative permeability curve of tight oil reservoirs during the well-steaming process is a dynamic process. The relative permeability curve after immersion is still based on the relative permeability curve constructed by fractal theory. By fitting the capillary force curve that reaches the residual oil saturation after immersion, a relative permeability curve considering the influence of immersion is constructed.

[0017] According to the construction method of the present invention, preferably, a capillary force model of a dense core is constructed based on fractal theory, and the oil-water relative permeability model is constructed by combining the Hagen-Poiseuille equation.

[0018] According to the construction method of the present 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 includes the relative permeability of the water phase and the relative permeability of the oil phase.

[0019] According to the construction method of the present invention, preferably, the analytical expressions for the relative permeability of the aqueous phase and the relative permeability of the oil phase are as follows:

[0020]

[0021]

[0022] in,

[0023]

[0024] In the formula, K rw K represents the relative permeability of the aqueous phase. ro S represents the relative permeability of the oil phase. w S represents the water phase saturation. wr S represents the bound water saturation. or Residual oil saturation; λ = 3 - D f D f p is the fractal dimension; e The core capillary radius of the dense sandstone is r. max The capillary force corresponding to time, r max The maximum capillary radius of the dense sandstone core; α=(p e / p max ) -λ p max P represents the capillary force corresponding to the bound water saturation level. c The capillary force corresponding to a capillary radius of r in a dense sandstone core;

[0025] According to the construction method of the present invention, preferably, the high-speed centrifugation experiment includes simulating an oil-driven water displacement process and a water-driven oil displacement process, respectively obtaining the capillary force curves of the displacement process and the capillary force curves of the suction process.

[0026] According to the construction method of the present invention, preferably, the high-speed centrifugation experiment includes:

[0027] Core centrifugation experiments were conducted using an ultracentrifuge, including centrifuging saturated water cores to a bound water state, i.e., the oil-driven water process, and centrifuging bound water cores to a residual oil state, i.e., the water-driven oil process.

[0028] According to the construction method of the present invention, preferably, the fractal dimension is obtained by fitting the capillary force curve of the displacement process obtained by the oil-water displacement process, and the relative permeability K of the aqueous phase is calculated. rw Then, by fitting the capillary force curve of the suction process obtained from the water-drive oil process, the fractal dimension is obtained, and the relative permeability K of the oil phase is calculated. ro .

[0029] According to the construction method of the present invention, preferably, the core sample is pretreated before the high-speed centrifugation experiment, including washing off oil, drying, vacuuming and saturating with 2% potassium chloride solution.

[0030] According to the construction method of the present invention, preferably, after obtaining the analytical expressions of the capillary force model and the relative permeability model without considering the seepage effect, before carrying out the spontaneous seepage experiment, the method further includes: using the unsteady-state method to determine the oil-water relative permeability of the tight core and verifying the calculation results of the relative permeability model without considering the seepage effect.

[0031] The unsteady-state method refers to the national standard GB / T 28912-2012 "Method for Determination of Relative Permeability of Two-Phase Fluids in Rocks". The oil-water relative permeability of tight core samples measured using the unsteady-state method is compared with the calculation results of a relative permeability model that does not consider seepage. If the difference is not significant, the theoretical model is considered feasible. The most important parameter of the theoretical model, the fractal dimension, is obtained from experimental results and generally does not have a large deviation. If there is a possibility of error, it may be due to a large error in the fractal dimension test results. In this case, multiple centrifugation experiments are conducted on core samples from the same reservoir and the same stratigraphic level, and the average value is selected as the comprehensive fractal dimension result to correct the theoretical model.

[0032] According to the construction method of the present invention, preferably, when measuring the relative oil-water permeability of tight cores using the unsteady-state method, a tight core sample with similar physical property parameters to the core sample used in the high-speed centrifugation experiment is selected.

[0033] The beneficial effects of this invention include:

[0034] This invention considers the decrease in oil saturation caused by seepage during the post-fracturing well-suppression process, which leads to the inadequacy of traditional relative permeability curves. It proposes a capillary force model for tight cores based on fractal theory. Based on this model, analytical solutions for capillary force models and relative permeability models that do not consider seepage and those that do consider seepage are constructed respectively. This is of great significance for explaining the mechanism of enhanced oil recovery during the post-fracturing well-suppression process and can be widely applied in the field of enhanced oil recovery through fracturing in unconventional reservoirs. Attached Figure Description

[0035] Figure 1 This is a flowchart illustrating the construction of a relative permeability model for a tight core considering the seepage effect in an embodiment of the present invention.

[0036] Figure 2 The capillary force curve and fitting curve are obtained from the experimental test of the oil flooding process in core A11 in this embodiment of the invention.

[0037] Figure 3 These are the capillary force curves and fitted curves obtained from the experimental testing of the water-drive oil recovery process in core A11 in this embodiment of the invention.

[0038] Figure 4 The calculation results are from the theoretical model of the relative permeability curve of oil and water in the tight core A11 in this embodiment of the invention.

[0039] Figure 5 This is a comparison of the oil-water relative permeability curves of the tight core A12 in the embodiments of the present invention.

[0040] Figure 6 The capillary force curve fitting results for dense core A11 in the embodiments of the present invention, considering the permeation effect.

[0041] Figure 7 The oil-water relative permeability curves for dense core A11 in this embodiment of the invention, considering the seepage effect.

[0042] Figure 8 This is a comparison of the relative permeability curves of oil and water before and after the absorption of A11 in the tight core in this embodiment of the invention. Detailed Implementation

[0043] To more clearly illustrate the present invention, the following description, in conjunction with preferred embodiments, further clarifies the invention. Those skilled in the art should understand that the specific descriptions below are illustrative rather than restrictive, and should not be construed as limiting the scope of protection of the present invention.

[0044] The principles underlying this invention are as follows: A capillary force model and a relative permeability model for tight core samples without considering permeation are constructed based on fractal theory. The fractal dimension, a key parameter in the theoretical model, is determined through high-speed centrifugation experiments. Subsequently, the relative permeability is tested using an unsteady-state method to verify the theoretical model. Finally, spontaneous permeation experiments are conducted to determine the residual oil saturation. The capillary force curve measured by the high-speed experiments is then extended according to the curve extension law to the residual oil saturation at the end of permeation. Based on this, an analytical expression for the capillary force model considering permeation is obtained, along with the corresponding analytical expression for the relative permeability of oil and water.

[0045] like Figure 1 As shown, this embodiment of the invention provides a method for constructing a new model of relative permeability of tight core samples that considers seepage and absorption. The method includes:

[0046] S101: Based on fractal theory, a capillary force model of tight core was constructed, and combined with the Hagen-Poiseuille equation, an oil-water relative permeability model was constructed.

[0047] S102: Conduct high-speed centrifugation experiments to determine the capillary force curve of the dense core, and obtain the fractal dimension in the capillary force model based on the experimental results, and obtain the analytical expressions of the capillary force model and the relative permeability model without considering the seepage effect.

[0048] S103: The relative permeability of oil and water in tight cores was measured using the unsteady-state method to verify the calculation results of the theoretical model.

[0049] S104: Conduct spontaneous percolation experiments to determine the residual oil saturation at the end of the percolation experiment.

[0050] S105: Extend the capillary force curve determined by the high-speed experiment to the residual oil saturation at the end of the percolation according to the curve extension law, fit it with the capillary force model that does not consider the percolation effect, obtain the analytical expression of the capillary force model that considers the percolation effect, and obtain the corresponding analytical expression of the relative permeability of oil and water.

[0051] Using the method of this invention, a relative permeability model was constructed without considering percolation. High-speed centrifugation experiments, unsteady-state waterflooding experiments, and spontaneous percolation experiments were conducted on tight sandstone samples from Block 284 of the Chang 6 group in the Huaqing Oilfield of the Ordos Basin. By combining the theoretical model with the experimental results, the relative permeability curve of the tight core considering percolation was finally obtained. The specific steps are as follows:

[0052] 1) A capillary force model for tight core samples was constructed based on fractal theory, and an oil-water relative permeability model was built by combining it with the Hagen-Poiseuille equation; the specific process is as follows:

[0053] Assuming that the dense core is composed of different capillaries, and that their distribution characteristics satisfy the fractal dimension characteristics, as shown in formula (1):

[0054]

[0055] In the formula, N is the number of capillaries with a capillary radius greater than r, and D f Let r be the fractal dimension. max This represents the maximum capillary radius.

[0056] The total pore volume of the compacted core can be obtained according to formula (1):

[0057]

[0058] In the formula, V total L represents the total pore volume. f r is the feature length. min This is the minimum capillary radius.

[0059] During centrifugation, the pore volume occupied by the oil phase in the tight core is:

[0060]

[0061] In the formula V o R is the pore volume occupied by the oil phase in the dense core, and r is the minimum capillary radius occupied by the oil phase.

[0062] From formulas (2) and (3), it can be seen that the oil phase saturation S in tight cores is... o for:

[0063]

[0064] Capillary force can be expressed by the following formula:

[0065]

[0066] In the formula P c σ represents the capillary force corresponding to a capillary radius of r in a tight sandstone core, σ represents the oil-water interfacial tension, and θ represents the contact angle between the oil and water phases.

[0067] From formula (5), we know that the capillary radius is r. max and r min The corresponding capillary forces are as follows:

[0068]

[0069]

[0070] Substituting formulas (5)-(7) into formula (4) yields:

[0071]

[0072] Corresponding water phase saturation S w and bound water saturation S wr It can be represented as:

[0073]

[0074]

[0075] In the formula, p max This represents the capillary force corresponding to the bound water saturation level.

[0076] For ease of calculation, the water phase saturation is normalized to obtain:

[0077]

[0078] Substituting formulas (8)-(10) into formula (11) yields:

[0079]

[0080] After simplification, the capillary force P is obtained. c for:

[0081]

[0082] In centrifugation experiments, the centrifugal force is assumed to be equal to the capillary force. Therefore, the fractal dimension D can be obtained by fitting the capillary force curve obtained from the centrifugation experiment. f Thus, the analytical expression for the capillary force model can be obtained.

[0083] Combining the Hagen-Poiseuille equation and the capillary force model, the relative permeability of the aqueous phase (K) can be obtained. rw ) and oil phase relative permeability (K ro ):

[0084]

[0085]

[0086] In the formula, λ=3-D f ; α=(p e / p max ) -λ ; In general, K ro and K rwThe calculated values ​​of 1(0) and 0(1) under bound water saturation and residual oil saturation differ significantly from the actual situation. To address this issue, in practical applications, the fractal dimension is obtained by fitting the capillary force curve of the displacement process obtained in the first oil-water displacement experiment in a high-speed centrifuge experiment (e.g., step 2 below), and K is calculated. rw Then, by fitting the capillary force curve of the suction process obtained from the second water-driven oil recovery, the fractal dimension is obtained, and K is calculated. ro .

[0087] 2) A11 tight sandstone sample from the Chang 6 group of the Huaqing Oilfield in the Ordos Basin was selected for high-speed centrifugation experiments to simulate oil-water flooding and water-oil flooding processes. The corresponding capillary force curves were determined and fitted to obtain the fractal dimension, ultimately yielding the relative permeability curve. The specific process is as follows:

[0088] Before centrifugation, the core samples were pretreated, including oil washing (solvent extraction with toluene and ethanol, 30 days), drying (sealed oven at 105℃, 2 days), vacuuming, and saturation with 2% potassium chloride solution. Then, the core samples were centrifuged using an Optim XPN ultracentrifuge, which consisted of two parts: centrifuging the saturated water core to the bound water state (oil-driven water), and centrifuging the bound water core to the residual oil state (water-driven oil).

[0089] The measured capillary force curves and fitted curves for oil-driven water and water-driven oil processes are shown below. Figure 2 and Figure 3 As shown.

[0090] Based on the experimental test results and fitting results, the parameter P determined during the oil-water displacement process in the tight core A11 is... e and fractal dimension D f The parameters P determined for the water-driven oil recovery process are 0.97 MPa and 2.13 MPa, respectively. e and fractal dimension D f The pressures are 0.55 MPa and 2.74 MPa, respectively. Substituting the obtained parameters into formulas (14) and (15), the oil-water relative permeability curves based on fractal theory can be obtained, as shown below. Figure 4 As shown.

[0091] 3) Select a tight core A12 with similar physical properties to the A11 core. Measure the oil-water relative permeability curve of the core sample A12 according to the national standard GB / T 28912-2012 "Method for Determination of Relative Permeability of Two-Phase Fluids in Rock". Figure 5 As shown, the relative permeability curves measured by the experimental method are not significantly different from those calculated by fractal theory. The variation law of relative permeability in the oil phase is basically consistent, while the relative permeability in the water phase differs slightly, but not significantly. Overall, this influence on the relative permeability curve is negligible. Therefore, the theoretical model is considered feasible.

[0092] The theoretical model is derived from previous research results and generally does not have a large deviation. The most important parameter, fractal dimension, is obtained from experimental results. If there may be an error, it may be that the fractal dimension test results have a large error. In this case, multiple centrifugation experiments are carried out on cores from the same reservoir and the same layer, and an average value is selected as the comprehensive fractal dimension result, thereby correcting the theoretical model.

[0093] 4) The dense core A11 after the second centrifugation was placed in an Amott percolation bottle and a spontaneous percolation experiment was carried out. The residual oil saturation at the end of the percolation experiment was 24.13%.

[0094] 5) Extend the capillary force curve obtained from the high-speed centrifugation experiment according to the curve extension law to the residual oil saturation at the end of the percolation (e.g., Figure 6 As shown in the figure, a new capillary force curve was obtained by fitting the curve, and the capillary force at residual oil saturation was predicted to be 13.25 MPa. Then, based on the fitted capillary force curve, a relative permeability curve considering osmosis was obtained (as shown in the figure). Figure 7 (As shown).

[0095] Immersion leads to a decrease in residual oil saturation, resulting in a significant change in the relative permeability curve. Compare the oil-water relative permeability curves before and after immersion (e.g., ...). Figure 8 As shown in the figure, it can be seen that compared with before the percolation, the percolation increases the area of ​​the oil-water two-phase flow zone. Simultaneously, near the residual oil saturation, the relative permeability of the oil phase is slightly higher than before the percolation. Based on this conclusion, the underlying mechanism by which well-clogging operations after fracturing improve the productivity of tight oil reservoirs can be explained: the percolation reduces the residual oil saturation, expands the oil-water two-phase flow zone, which is conducive to improving the fluidity of crude oil within the matrix and increasing the recovery rate.

[0096] This method effectively constructs a new model of relative permeability of tight cores that takes into account the seepage effect. The results obtained are of great significance for explaining the mechanism of enhanced oil recovery in the post-fracturing well simmering process and can be promoted and applied in the field of enhanced oil recovery through fracturing in unconventional reservoirs.

[0097] Obviously, the above embodiments of the present invention are merely examples for clearly illustrating the present invention, and are not intended to limit the implementation of the present invention. For those skilled in the art, other variations or modifications can be made based on the above description. It is impossible to exhaustively list all the implementation methods here. All obvious variations or modifications derived from the technical solutions of the present invention are still within the protection scope of the present invention.

Claims

1. A method for constructing a relative permeability model of a tight core considering imbibition, characterized in that, The construction method includes the following steps: Based on fractal theory, a capillary force model of dense rock cores is constructed, and then an oil-water relative permeability model is constructed. High-speed centrifugation experiments were conducted to determine the capillary force curve. Based on the experimental results, the fractal dimension in the capillary force model was obtained by fitting the model, and analytical expressions for the capillary force model and the relative permeability model without considering the osmosis effect were obtained. Conduct spontaneous percolation experiments to determine the residual oil saturation at the end of the percolation experiment; The capillary force curve measured by the high-speed centrifugation experiment was extended to the residual oil saturation at the end of the percolation experiment according to the curve extension law. The capillary force model without considering the percolation effect was used for fitting to obtain the analytical expression of the capillary force model considering the percolation effect, and the corresponding analytical expression of the relative permeability of oil and water was obtained.

2. The construction method of claim 1, wherein, A capillary force model for dense cores was constructed based on fractal theory, and the oil-water relative permeability model was constructed by combining the Hagen-Poiseuille equation.

3. The construction method of claim 2, wherein, In the step of constructing the oil-water relative permeability model by combining the Hagen-Poiseuille equation, the oil-water relative permeability model includes the relative permeability of the water phase and the relative permeability of the oil phase.

4. The construction method according to claim 3, characterized in that, The analytical expressions for the relative permeability of the aqueous phase and the relative permeability of the oil phase are as follows: in, In the formula, K rw K represents the relative permeability of the aqueous phase. ro S represents the relative permeability of the oil phase. w S represents the water phase saturation. wr S represents the bound water saturation. or Residual oil saturation; λ = 3 - D f D f p is the fractal dimension; e The core capillary radius of the dense sandstone is r. max The capillary force corresponding to time, r max The maximum capillary radius of the dense sandstone core; α=(p e / p max ) -λ p max P represents the capillary force corresponding to the bound water saturation level. c The capillary force corresponding to a capillary radius of r in a dense sandstone core; 5. The construction method according to claim 4, characterized in that, The high-speed centrifugation experiment included simulating oil-driven water displacement and water-driven oil displacement processes, respectively obtaining capillary force curves for the displacement process and capillary force curves for the intake process.

6. The construction method according to claim 5, characterized in that, The high-speed centrifugation experiment includes: Core centrifugation experiments were conducted using an ultracentrifuge, including centrifuging saturated water cores to a bound water state, i.e., the oil-driven water process, and centrifuging bound water cores to a residual oil state, i.e., the water-driven oil process.

7. The construction method according to claim 6, characterized in that, The fractal dimension is fitted by the capillary force curve of the displacement process obtained by the oil-water displacement process, and the relative permeability K of the water phase is calculated rw The fractal dimension is fitted by the capillary force curve of the suction process obtained by the water-oil displacement process, and the relative permeability K of the oil phase is calculated ro .

8. The construction method according to claim 6, characterized in that, The high-speed centrifugation experiment also includes pretreatment of the core sample, including washing off oil, drying, vacuuming, and saturating with a 2% potassium chloride solution.

9. The construction method according to any one of claims 1-8, characterized in that, After obtaining the analytical expressions for the capillary force model and the relative permeability model that do not consider the seepage effect, before conducting the spontaneous seepage experiment, the method further includes: using the unsteady-state method to determine the oil-water relative permeability of the tight core and verifying the calculation results of the relative permeability model that does not consider the seepage effect.

10. The construction method according to claim 9, characterized in that, When measuring the relative oil-water permeability of tight cores using the unsteady-state method, a tight core sample with similar physical properties to the core sample used in the high-speed centrifugation experiment is selected.

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