Non-steady relative permeability algorithm considering end effect

Abstract

This invention provides an unsteady phase permeability algorithm considering end-face effects, comprising: Step 1: Establishing a saturation profile equation based on Darcy's law and the saturation equation; Step 2: Fitting and calculating the optimal model for different reservoir conditions; Step 3: Determining the relationship function between core distance and unwetting phase saturation; Step 4: Obtaining conventional parameters such as the flow rate and viscosity of the wetting and unwetting phases; Step 5: Determining the relationship function between the water phase saturation at the inlet end and the relative permeability of the oil phase when the water flow rate is zero, and the average water saturation of the entire core; Step 6: Obtaining the saturation correction value at the core inlet end; Step 7: Calculating the relative permeability of the oil phase and the relative permeability of the water phase based on the optimal phase permeability model. This algorithm obtains the true relative phase permeability and saturation of the core, solving the problem of overestimation of the wetting phase saturation caused by end-face effects. Furthermore, the optimal model for different reservoirs lays the foundation for ensuring data accuracy.

Description

Technical Field

[0001] This invention relates to the field of oilfield development technology, and in particular to an unsteady-state phase permeation algorithm that considers end-face effects. Background Technology

[0002] Relative permeability data is fundamental for studying two-phase flow in porous media, and laboratory experiments often employ unsteady-state multiphase flow testing methods. However, during experiments, the capillary force disappears at the core outlet, leading to the accumulation of the wetted phase at the core end. This phenomenon, where capillary force discontinuity has an impact, is called the end-face effect. The end-face effect can cause significant errors in the saturation and relative permeability calculated based on pressure drop information and production. Therefore, correcting for the end-face effect is crucial for low-permeability reservoirs with strong capillary forces.

[0003] Existing methods for correcting end-face effects can be divided into three categories. The first category involves increasing the displacement velocity in high-permeability cores during laboratory experiments to reduce the end-face effect; however, this method is less applicable to low-permeability reservoirs with low permeability. The second category utilizes numerical simulation models to fit typical relative permeability curves and establish graphs for unsteady-state testing methods, or iterative algorithms to correct laboratory relative permeability curves. These methods all use traditional JBN calculation methods to obtain corrected relative permeability, and the selection of empirical formulas for relative permeability is relatively limited, making them unsuitable for complex and variable formation conditions. The third category is based on extensive experimental data to correct the endpoints of the relative permeability curve, thereby constructing a formula for relative permeability curves with end-face effects. However, this method requires numerous experiments and is difficult to widely implement.

[0004] Chinese patent application CN 108489878 A discloses a method for correcting relative permeability curves based on numerical simulation iteration to eliminate end-effects. This method mainly comprises three parts: unsteady-state method for determining rock relative permeability, establishment of a numerical simulation model considering end-effects, and iterative correction of the relative permeability curve. First, a one-dimensional core two-phase displacement numerical simulation model considering end-effects is established. Then, combined with the relative permeability curves measured under the influence of end-effects in laboratory experiments, the relative permeability curves are corrected based on the numerical simulation model and iterative algorithm, forming a complete method for correcting relative permeability curves to eliminate the influence of end-effects. However, the method in this patent uses the traditional JBN relative permeability curve calculation method to obtain water cut, saturation, and average relative permeability, and does not consider the adaptability of this method to different reservoirs.

[0005] Chinese patent application CN 108487904 A discloses a method for correcting relative permeability curves to eliminate end-effects based on a chart. This method mainly comprises four parts: determining the relative permeability of rock using an unsteady-state method, establishing a numerical simulation model considering end-effects, establishing a chart for correcting relative permeability characterization parameters considering end-effects, and relative permeability correction. Based on the generation mechanism of end-effects, this invention considers the influence of capillary force on the oil-water two-phase flow pattern in the core. It uses a virtual mesh to simulate the influence area of ​​end-effects and uses linear relative permeability to characterize the influence area. For the first time, a one-dimensional numerical simulation model of two-phase displacement in the core considering end-effects is established, simulating the effect of end-effects. However, the virtual network used in this invention to simulate the influence area of ​​end-face effects deviates somewhat from the actual influence area in the laboratory core.

[0006] In the October 2016 issue of *China Offshore Oil & Gas*, an improved method for correcting the end-effect of oil-water re-permeability experiments was proposed. Starting from the formation mechanism of the end-effect, it utilizes extensive historical experimental data and statistical regression to obtain the dimensionless ratio of the end-effect, thereby establishing an improved re-permeability curve correction method. Based on this, the morphology and saturation endpoints of the early-stage re-permeability curve of the reservoir were corrected. However, this method relies on a large amount of experimental data to construct a re-permeability curve formula for correcting end-face effects, involves numerous experiments, and mainly focuses on correcting the saturation endpoints, with less consideration given to correcting end-face effects during seepage.

[0007] The existing technologies described above are significantly different from the present invention and have failed to solve the technical problem we want to address. Therefore, we have invented a new unsteady phase permeation algorithm that considers end-face effects. Summary of the Invention

[0008] The purpose of this invention is to provide a nonsteady-state phase permeation algorithm that considers not only the influence of end-face effects on the endpoints, but also the influence of end-face effects during the seepage process, making the model more comprehensive and efficient in taking end-face effects into account.

[0009] The objective of this invention can be achieved through the following technical measures: an unsteady-state phase permeation algorithm considering end-face effects. This unsteady-state phase permeation algorithm considering end-face effects includes:

[0010] Step 1: Establish a two-phase saturation profile equation considering capillary forces based on Darcy's law and the saturation equation;

[0011] Step 2: Fit the calculation to obtain the optimal model for different reservoir conditions, including the optimal wetting phase model, the optimal non-wetting phase model, and the optimal capillary force model;

[0012] Step 3: Based on the optimization model and the one-dimensional two-phase saturation profile equation considering capillary force, determine the relationship function between core distance and wetting phase saturation;

[0013] Step 4: Use the unsteady-state method to test the relative permeability of oil and water to obtain conventional parameters such as the flow rate and viscosity of the wetting and unwetting phases;

[0014] Step 5: Determine the relationship between the water phase saturation at the inlet and the relative permeability of the oil phase when the water flow rate is zero, and the average water saturation of the entire core.

[0015] Step 6: Obtain the pressure drop in the region unaffected by the end-face effect, establish the relationship between the relative permeability of the oil phase at the end of the core and the pressure drop, and thus obtain the saturation correction value at the core inlet.

[0016] Step 7: Using the obtained inlet saturation correction value, calculate the relative permeability of the oil phase and the relative permeability of the water phase based on the optimal relative permeability model.

[0017] The objective of this invention can also be achieved through the following technical measures:

[0018] In step 1, considering the influence of capillary force, based on Darcy's law and the capillary pressure saturation equation, the two-phase saturation profile equation can be obtained:

[0019]

[0020] In the formula: K represents the air permeability of the experimental test core, 10 -3 μm 2 A represents the cross-sectional area of ​​the experimental test core, in cm². 2 ;q w The core wetting phase flow rate, μ w Indicates the viscosity of the wetting phase; k rw q represents the relative permeability of the wetting phase; nw The flow rate of the non-wetting phase in the core is expressed in μ. nw Indicates the viscosity of the non-wetting phase; k rnw P represents the relative permeability of the non-wetting phase. c S represents the capillary force in the rock core. w It represents the wetting phase saturation; x represents the distance from the core inlet.

[0021] In step 2, using a large amount of existing indoor experimental relative permeability test data, the cores are divided into five reservoir property types: ultra-low porosity and low permeability, low porosity and low permeability, medium porosity and medium permeability, high porosity and high permeability, and ultra-high porosity and high permeability. The optimal model fitting selects multiple models such as capillary force regression model and wettable phase Gorkwyn model.

[0022] In step 3, based on the optimization model and the one-dimensional two-phase saturation profile equation considering capillary force, the relationship function between the length of the core displacement inlet and the wetted phase saturation is determined.

[0023]

[0024] In the formula, L represents the total length of the core; x represents the distance from the core inlet end; Snw represents the residual saturation of the non-wetting phase measured at the outlet end; the wetting phase commonly used in the phase permeability test is the water phase, and the non-wetting phase is the oil phase;

[0025] In step 4, the parameters such as water phase flow rate, oil phase flow rate, production pressure difference, and fluid viscosity are determined by the unsteady-state relative permeability test experiment.

[0026] 1) Fluid preparation: The experimental oil was a simulated oil prepared by adding neutral kerosene to fresh degassed crude oil, and the fluid used in the experiment was simulated formation water; the viscosity and density of the prepared fluid were recorded;

[0027] 2) First, weigh the dry core and measure the air permeability of the core. Then, saturate the formation with vacuum water. Finally, weigh the wet weight of the rock sample after saturation with fluid. From this, the effective pore volume and porosity can be obtained.

[0028] 3) Establish bound water saturation: Inject oil into a core saturated with formation water to displace it to a bound water state, displacing at least 10 times the pore volume, record the amount of water displaced, and calculate the oil phase permeability and bound water saturation.

[0029] 4) Water-driven oil phase permeability test: Establish a certain pressure at the rock sample inlet; accurately record the cumulative oil production q. nw Cumulative water production q w The pressure difference between the two ends of the rock sample; after injecting water 30 times the pore volume, the displacement experiment was stopped, and the water phase saturation and residual oil saturation were calculated.

[0030] In step 5, the relationship function between the water phase saturation at the inlet end and the relative permeability of the oil phase and the average water saturation of the entire core are determined when the water flow rate is zero.

[0031] 1) To simplify the model, the water phase saturation is calculated when the water phase flow rate is 0.

[0032]

[0033] 2) When the core distance is 0, obtain the relationship function between the water phase saturation and the relative permeability of the oil phase at the core inlet end;

[0034]

[0035] In the formula It is the standardized wetting phase saturation;

[0036] It is the saturation of the wetting phase at the inlet end;

[0037] 3) Obtain the average water saturation of the entire core.

[0038]

[0039] In step 6, the pressure drop ΔP| in the region unaffected by end-face effects can be obtained. x Saturation correction value at the core inlet;

[0040] 1) Since the entire core is in a stable state without water injection, integrating Darcy's equation for oil yields the pressure drop ΔP| at a distance x from the core inlet, unaffected by end-face effects. x :

[0041]

[0042] In the formula, ΔP| x It is the average pressure from the inlet to the outlet;

[0043] p| x It is the pressure at a distance x from the inlet end;

[0044] p|0 is the pressure at the inlet end;

[0045] It is the capillary force under standardized aqueous phase saturation;

[0046] It is the initial capillary force under standardized aqueous phase saturation;

[0047] 2) Establish the relationship between the relative permeability of the oil phase at the end of the core and the pressure drop, so as to obtain the saturation correction value at the core inlet.

[0048] In step 7, the relative permeability of the oil phase and the relative permeability of the water phase are calculated based on the optimal relative permeability model using the obtained inlet saturation correction value.

[0049] This invention presents an unsteady-state relative permeability algorithm considering end-face effects, applicable to oilfield development technologies such as reservoir seepage theory research, oilfield development dynamic analysis, numerical simulation, production prediction, and various engineering operation planning. It provides an algorithm that considers end-face effects. While the original invention used the traditional JBN algorithm to obtain a corrected model relative permeability, this invention primarily constructs optimized relative permeability models and capillary force models for different reservoir properties to obtain corrected relative permeability. This method more closely approximates the actual seepage conditions and broadly considers corrected relative permeability models for different reservoir properties. The original literature aimed to reduce the influence of end-face effects by correcting the saturation endpoints. This invention introduces a correction coefficient, ensuring data accuracy while establishing the relationship between actual and experimental saturation. It considers not only the influence of end-face effects on the endpoints but also the influence of end-face effects during the seepage process, making the model more comprehensive and efficient. This method has the following advantages: 1. It obtains correction results based on experimental data from core samples, not only relying on the selection of empirical formulas for relative permeability, thus eliminating errors from human factors and resulting in more accurate correction results. 2. The optimal selection of relative permeability models and capillary force models under different reservoir properties was completed, solving the problem of a single model for correcting end-face effects. 3. By using data fitting methods to correct the end-face effect of experimental saturation on the true saturation throughout the unsteady-state method, the corrected relative permeability value of the non-wetting phase, unaffected by end-face effects, can be obtained. This provides a simple, effective, and feasible method for correcting the end-face effect problem in unsteady-state relative permeability measurement experiments. Attached Figure Description

[0050] Figure 1 This is a flowchart illustrating the implementation of the unsteady phase permeation algorithm of the present invention, which considers the end-face effect. Detailed Implementation

[0051] It should be noted that the following detailed descriptions are exemplary and intended to provide further illustration of the invention. Unless otherwise specified, all technical and scientific terms used herein have the same meaning as commonly understood by one of ordinary skill in the art to which this invention pertains.

[0052] It should be noted that the terminology used herein is for the purpose of describing particular embodiments only and is not intended to limit the exemplary embodiments of the present invention. As used herein, the singular form is intended to include the plural form as well, unless the context clearly indicates otherwise. Furthermore, it should be understood that when the terms "comprising" and / or "including" are used in this specification, they indicate the presence of features, steps, operations, and / or combinations thereof.

[0053] The unsteady phase permeation algorithm of this invention, which considers end-face effects, includes the following:

[0054] Step 1: Establish a two-phase saturation profile equation considering capillary forces based on Darcy's law and the saturation equation;

[0055] Step 2: Fit the calculation to obtain the optimal model for different reservoir conditions, including the optimal wetting phase model, the optimal non-wetting phase model, and the optimal capillary force model;

[0056] Step 3: Based on the optimization model and the one-dimensional two-phase saturation profile equation considering capillary force, determine the relationship function between core distance and wetting phase saturation;

[0057] Step 4: Use the unsteady-state method to test the relative permeability of oil and water to obtain conventional parameters such as the flow rate and viscosity of the wetting and unwetting phases;

[0058] Step 5: Determine the relationship between the water phase saturation at the inlet and the relative permeability of the oil phase when the water flow rate is zero, and the average water saturation of the entire core.

[0059] Step 6: Obtain the pressure drop in the region unaffected by the end-face effect, establish the relationship between the relative permeability of the oil phase at the end of the core and the pressure drop, and thus obtain the saturation correction value at the core inlet.

[0060] Step 7: Using the obtained inlet saturation correction value, calculate the relative permeability of the oil phase and the relative permeability of the water phase based on the optimal relative permeability model.

[0061] This unsteady phase permeation algorithm, which considers end-face effects, introduces a saturation profile equation that takes into account capillary forces and an optimization model for different reservoirs. It removes the regions affected by end-face effects from participating in phase permeation calculations, obtains the true phase permeability and saturation of the core, and solves the problem of high wetted phase saturation in the core caused by end-face effects. At the same time, the optimization model for different reservoirs lays the foundation for ensuring data accuracy.

[0062] The following are several specific embodiments of the application of the present invention.

[0063] Example 1

[0064] In a specific embodiment 1 of the present invention, the low-porosity, low-permeability unsteady-state phase permeation algorithm considering end-face effects includes:

[0065] Step 1, considering the influence of capillary force, based on Darcy's law and the capillary pressure saturation equation, the two-phase saturation profile equation can be obtained:

[0066]

[0067] In the formula: K represents the air permeability of the experimental test core, 10 -3 μm 2 A represents the cross-sectional area of ​​the experimental test core, in cm². 2 ;q w The core wetting phase flow rate, μ wIndicates the viscosity of the wetting phase; k rw q represents the relative permeability of the wetting phase; nw The flow rate of the non-wetting phase in the core is expressed in μ. nw Indicates the viscosity of the non-wetting phase; k rnw P represents the relative permeability of the non-wetting phase. c S represents the capillary force in the rock core. w It represents the wetting phase saturation; x represents the distance from the core inlet.

[0068] Step 2: Based on existing indoor unsteady-state relative permeability test data for low-porosity and low-permeability reservoirs, the optimal oil phase relative permeability model, optimal water phase relative permeability model, and optimal capillary force model for this type of reservoir are fitted as follows: and

[0069] In the formula: a, b, c, n are parameters obtained by fitting the capillary pressure curve; g, e are parameters obtained by fitting the relative permeation curve; It is the standardized wetting phase saturation; S wi It is the bound water saturation;

[0070] Step 3: Based on the optimization model and the one-dimensional two-phase saturation profile equation considering capillary force, determine the relationship function between the length of the core displacement inlet and the wetted phase saturation.

[0071]

[0072] In the formula, L represents the total length of the core sample; x represents the distance from the core inlet; S nw This indicates the residual saturation of the non-wetting phase measured at the outlet end;

[0073] Step 4: Use the unsteady-state method to test relative permeability to determine parameters such as water phase flow rate, oil phase flow rate, production pressure difference, and fluid viscosity.

[0074] 1) Fluid preparation: The experimental oil was a simulated oil prepared by adding neutral kerosene to fresh degassed crude oil, and the fluid used in the experiment was simulated formation water; the viscosity and density of the prepared fluid were recorded;

[0075] 2) First, weigh the dry core and measure the air permeability of the core. Then, saturate the formation with vacuum water. Finally, weigh the wet weight of the rock sample after saturation with fluid. From this, the effective pore volume and porosity can be obtained.

[0076] 3) Establish bound water saturation: Inject oil into a core saturated with formation water to displace it to a bound water state, displacing at least 10 times the pore volume, record the amount of water displaced, and calculate the oil phase permeability and bound water saturation.

[0077] 4) Water-driven oil phase permeability test: Establish a certain pressure at the rock sample inlet; accurately record the cumulative oil production q. nw Cumulative water production q w The pressure difference between the two ends of the rock sample; after injecting water 30 times the pore volume, the displacement experiment was stopped, and the water phase saturation and residual oil saturation were calculated.

[0078] Step 5: Determine the relationship between the water phase saturation at the inlet and the relative permeability of the oil phase when the water flow rate is zero, and the average water saturation of the entire core.

[0079] 1) To simplify the model, the water phase saturation is calculated when the water phase flow rate is 0.

[0080]

[0081] 2) When the core distance is 0, obtain the relationship function between the water phase saturation and the relative permeability of the oil phase at the core inlet end;

[0082]

[0083] In the formula It is the standardized wetting phase saturation;

[0084] It is the saturation of the wetting phase at the inlet end;

[0085] 3) Obtain the average water saturation of the entire core.

[0086]

[0087] Step 6: Since the entire core is in a stable state without water injection, integrating the Darcy equation for oil yields the pressure drop ΔP| at a distance x from the core inlet, unaffected by end-face effects. x To establish the relationship between the relative permeability of the oil phase at the end of the core and the pressure drop, thereby obtaining the saturation correction value at the core inlet;

[0088] 1) Pressure drop ΔP at a distance x from the core inlet is unaffected by end-face effects. x :

[0089]

[0090] In the formula, ΔP| x It is the average pressure from the inlet to the outlet;

[0091] p| x It is the pressure at a distance x from the inlet end;

[0092] p|0 is the pressure at the inlet end;

[0093] It is the capillary force under standardized aqueous phase saturation;

[0094] It is the initial capillary force under standardized aqueous phase saturation;

[0095] 2) Establish the relationship between the relative permeability of the oil phase at the core tip and the pressure drop, thereby obtaining the saturation correction value at the core inlet.

[0096]

[0097] Step 7: Utilize the obtained inlet saturation correction value Based on the optimal relative permeability model, the relative permeability of the oil phase and the relative permeability of the water phase were calculated as follows:

[0098]

[0099] Example 2

[0100] In a specific embodiment 2 of the present invention, the algorithm for unsteady phase permeation in the mesopore considering end-face effects includes:

[0101] Step 1, considering the influence of capillary force, based on Darcy's law and the capillary pressure saturation equation, the two-phase saturation profile equation can be obtained:

[0102]

[0103] In the formula: K represents the air permeability of the experimental test core, 10 -3 μm 2 A represents the cross-sectional area of ​​the experimental test core, in cm². 2 ;q w The core wetting phase flow rate, μ w Indicates the viscosity of the wetting phase; k rw q represents the relative permeability of the wetting phase; nw The flow rate of the non-wetting phase in the core is expressed in μ. nw Indicates the viscosity of the non-wetting phase; k rnw P represents the relative permeability of the non-wetting phase. c S represents the capillary force in the rock core. w It represents the wetting phase saturation; x represents the distance from the core inlet.

[0104] Step 2: Based on existing indoor unsteady-state relative permeability test data for low-porosity and low-permeability reservoirs, the optimal oil phase relative permeability model, optimal water phase relative permeability model, and optimal capillary force model for this type of reservoir are fitted as follows: and

[0105] In the formula: a, b, c, n are parameters obtained by fitting the capillary pressure curve; g, e are parameters obtained by fitting the relative permeation curve; It is the standardized wetting phase saturation; S wi It is the bound water saturation;

[0106] Step 3: Based on the optimization model and the one-dimensional two-phase saturation profile equation considering capillary force, determine the relationship function between the length of the core displacement inlet and the wetted phase saturation.

[0107]

[0108] In the formula, L represents the total length of the core sample; x represents the distance from the core inlet; S nw This indicates the residual saturation of the non-wetting phase measured at the outlet end;

[0109] Step 4: Use the unsteady-state method to test relative permeability to determine parameters such as water phase flow rate, oil phase flow rate, production pressure difference, and fluid viscosity.

[0110] 1) Fluid preparation: The experimental oil was a simulated oil prepared by adding neutral kerosene to fresh degassed crude oil, and the fluid used in the experiment was simulated formation water; the viscosity and density of the prepared fluid were recorded;

[0111] 2) First, weigh the dry core and measure the air permeability of the core. Then, saturate the formation with vacuum water. Finally, weigh the wet weight of the rock sample after saturation with fluid. From this, the effective pore volume and porosity can be obtained.

[0112] 3) Establish bound water saturation: Inject oil into a core saturated with formation water to displace it to a bound water state, displacing at least 10 times the pore volume, record the amount of water displaced, and calculate the oil phase permeability and bound water saturation.

[0113] 4) Water-driven oil phase permeability test: Establish a certain pressure at the rock sample inlet; accurately record the cumulative oil production q. nw Cumulative water production q w The pressure difference between the two ends of the rock sample; after injecting water 30 times the pore volume, the displacement experiment was stopped, and the water phase saturation and residual oil saturation were calculated.

[0114] Step 5: Determine the relationship between the water phase saturation at the inlet and the relative permeability of the oil phase when the water flow rate is zero, and the average water saturation of the entire core.

[0115] 1) To simplify the model, the water phase saturation is calculated when the water phase flow rate is 0.

[0116]

[0117] 2) When the core distance is 0, obtain the relationship function between the water phase saturation and the relative permeability of the oil phase at the core inlet end;

[0118]

[0119] In the formula It is the standardized wetting phase saturation;

[0120] It is the saturation of the wetting phase at the inlet end;

[0121] 3) Obtain the average water saturation of the entire core.

[0122]

[0123] Step 6: Since the entire core is in a stable state without water injection, integrating the Darcy equation for oil yields the pressure drop ΔP| at a distance x from the core inlet, unaffected by end-face effects. x To establish the relationship between the relative permeability of the oil phase at the end of the core and the pressure drop, thereby obtaining the saturation correction value at the core inlet;

[0124] 1) Pressure drop ΔP at a distance x from the core inlet is unaffected by end-face effects. x :

[0125]

[0126] In the formula, ΔP| x It is the average pressure from the inlet to the outlet;

[0127] p| x It is the pressure at a distance x from the inlet end;

[0128] p|0 is the pressure at the inlet end;

[0129] It is the capillary force under standardized aqueous phase saturation;

[0130] It is the initial capillary force under standardized aqueous phase saturation;

[0131] 2) Establish the relationship between the relative permeability of the oil phase at the core tip and the pressure drop, thereby obtaining the saturation correction value at the core inlet.

[0132]

[0133] Step 7: Utilize the obtained inlet saturation correction value Based on the optimal relative permeability model, the relative permeability of the oil phase and the relative permeability of the water phase were calculated as follows:

[0134]

[0135] Example 3

[0136] In a specific embodiment 3 of the present invention, the high-porosity, high-permeability unsteady-state phase permeation algorithm considering end-face effects includes:

[0137] Step 1, considering the influence of capillary force, based on Darcy's law and the capillary pressure saturation equation, the two-phase saturation profile equation can be obtained:

[0138]

[0139] In the formula: K represents the air permeability of the experimental test core, 10 -3 μm 2 A represents the cross-sectional area of ​​the experimental test core, in cm². 2 ;q w The core wetting phase flow rate, μ w Indicates the viscosity of the wetting phase; k rw q represents the relative permeability of the wetting phase; nw The flow rate of the non-wetting phase in the core is expressed in μ. nw Indicates the viscosity of the non-wetting phase; k rnw P represents the relative permeability of the non-wetting phase. c S represents the capillary force in the rock core. w It represents the wetting phase saturation; x represents the distance from the core inlet.

[0140] Step 2: Based on existing indoor unsteady-state relative permeability test data for low-porosity and low-permeability reservoirs, the optimal oil phase relative permeability model, optimal water phase relative permeability model, and optimal capillary force model for this type of reservoir are fitted as follows:

[0141] and

[0142] In the formula: a, b, c, n are parameters obtained by fitting the capillary pressure curve; g, e, m are parameters obtained by fitting the relative permeability curve. It is the standardized wetting phase saturation; S wi It is the bound water saturation;

[0143] Step 3: Based on the optimization model and the one-dimensional two-phase saturation profile equation considering capillary force, determine the relationship function between the length of the core displacement inlet and the wetted phase saturation.

[0144]

[0145] In the formula, L represents the total length of the core sample; x represents the distance from the core inlet; S nwThis indicates the residual saturation of the non-wetting phase measured at the outlet end;

[0146] Step 4: Use the unsteady-state method to test relative permeability to determine parameters such as water phase flow rate, oil phase flow rate, production pressure difference, and fluid viscosity.

[0147] 1) Fluid preparation: The experimental oil was a simulated oil prepared by adding neutral kerosene to fresh degassed crude oil, and the fluid used in the experiment was simulated formation water; the viscosity and density of the prepared fluid were recorded;

[0148] 2) First, weigh the dry core and measure the air permeability of the core. Then, saturate the formation with vacuum water. Finally, weigh the wet weight of the rock sample after saturation with fluid. From this, the effective pore volume and porosity can be obtained.

[0149] 3) Establish bound water saturation: Inject oil into a core saturated with formation water to displace it to a bound water state, displacing at least 10 times the pore volume, record the amount of water displaced, and calculate the oil phase permeability and bound water saturation.

[0150] 4) Water-driven oil phase permeability test: Establish a certain pressure at the rock sample inlet; accurately record the cumulative oil production q. nw Cumulative water production q w The pressure difference between the two ends of the rock sample; after injecting water 30 times the pore volume, the displacement experiment was stopped, and the water phase saturation and residual oil saturation were calculated.

[0151] Step 5: Determine the relationship between the water phase saturation at the inlet and the relative permeability of the oil phase when the water flow rate is zero, and the average water saturation of the entire core.

[0152] 1) To simplify the model, the water phase saturation is calculated when the water phase flow rate is 0.

[0153]

[0154] 2) When the core distance is 0, obtain the relationship function between the water phase saturation and the relative permeability of the oil phase at the core inlet end;

[0155]

[0156] In the formula It is the standardized wetting phase saturation;

[0157] It is the saturation of the wetting phase at the inlet end;

[0158] 3) Obtain the average water saturation of the entire core.

[0159]

[0160] Step 6: Since the entire core is in a stable state without water injection, integrating the Darcy equation for oil yields the pressure drop ΔP| at a distance x from the core inlet, unaffected by end-face effects. x To establish the relationship between the relative permeability of the oil phase at the end of the core and the pressure drop, thereby obtaining the saturation correction value at the core inlet;

[0161] 1) Pressure drop ΔP at a distance x from the core inlet is unaffected by end-face effects. x :

[0162]

[0163] In the formula, ΔP| x It is the average pressure from the inlet to the outlet;

[0164] p| x It is the pressure at a distance x from the inlet end;

[0165] p|0 is the pressure at the inlet end;

[0166] It is the capillary force under standardized aqueous phase saturation;

[0167] It is the initial capillary force under standardized aqueous phase saturation;

[0168] 2) Establish the relationship between the relative permeability of the oil phase at the core tip and the pressure drop, thereby obtaining the saturation correction value at the core inlet.

[0169]

[0170] Step 7: Utilize the obtained inlet saturation correction value Based on the optimal relative permeability model, the relative permeability of the oil phase and the relative permeability of the water phase were calculated as follows:

[0171]

[0172] Finally, it should be noted that the above description is merely a preferred embodiment of the present invention and is not intended to limit the present invention. Although the present invention has been described in detail with reference to the foregoing embodiments, those skilled in the art can still modify the technical solutions described in the foregoing embodiments or make equivalent substitutions for some of the technical features. Any modifications, equivalent substitutions, improvements, etc., made within the spirit and principles of the present invention should be included within the protection scope of the present invention.

[0173] Except for the technical features described in the specification, all other technologies are known to those skilled in the art.

Claims

1. An unsteady phase permeation algorithm considering end-face effects, characterized in that, The unsteady phase permeation algorithm that considers end-face effects includes: Step 1: Establish a two-phase saturation profile equation considering capillary forces based on Darcy's law and the saturation equation; Step 2: Fit the calculation to obtain the optimal model for different reservoir conditions, including the optimal wetting phase model, the optimal non-wetting phase model, and the optimal capillary force model; Step 3: Based on the optimization model and the one-dimensional two-phase saturation profile equation considering capillary force, determine the relationship function between core distance and wetting phase saturation; Step 4: Use the unsteady-state method to test the relative permeability of oil and water to obtain conventional parameters such as the flow rate and viscosity of the wetting and unwetting phases; Step 5: Determine the relationship between the water phase saturation at the inlet and the relative permeability of the oil phase when the water flow rate is zero, and the average water saturation of the entire core. Step 6: Obtain the pressure drop in the region unaffected by the end-face effect, establish the relationship between the relative permeability of the oil phase at the end of the core and the pressure drop, and thus obtain the saturation correction value at the core inlet. Step 7: Using the obtained inlet saturation correction value, calculate the relative permeability of the oil phase and the relative permeability of the water phase based on the optimal relative permeability model.

2. The unsteady phase permeation algorithm considering end-face effects according to claim 1, characterized in that, In step 1, considering the influence of capillary force, based on Darcy's law and the capillary pressure saturation equation, the two-phase saturation profile equation can be obtained: In the formula: K represents the air permeability of the experimental test core, 10 -3 μm 2 A represents the cross-sectional area of ​​the experimental test core, in cm². 2 ;q w The core wetting phase flow rate, μ w Indicates the viscosity of the wetting phase; k rw q represents the relative permeability of the wetting phase; nw The flow rate of the non-wetting phase in the core is expressed in μ. nw Indicates the viscosity of the non-wetting phase; k rnw P represents the relative permeability of the non-wetting phase. c S represents the capillary force in the rock core. w It represents the wetting phase saturation; x represents the distance from the core inlet.

3. The unsteady-state phase permeation algorithm considering end-face effects according to claim 1, characterized in that, In step 2, using a large amount of existing indoor experimental relative permeability test data, the optimal relative permeability model and the optimal capillary force model under different physical property conditions are fitted to obtain them.

4. The unsteady phase permeation algorithm considering end-face effects according to claim 1, characterized in that, Step 2 specifically includes: based on existing relative permeability laboratory test data, the core is divided into five reservoir property types: ultra-low porosity and low permeability, low porosity and low permeability, medium porosity and medium permeability, high porosity and high permeability, and ultra-high porosity and high permeability. The optimal model fitting selects multiple models such as capillary force regression model and wettable phase Gorkwyn model.

5. The unsteady phase permeation algorithm considering end-face effects according to claim 1, characterized in that, In step 3, based on the optimization model and the one-dimensional two-phase saturation profile equation considering capillary force, the relationship function between the length of the core displacement inlet and the wetted phase saturation is determined. In the formula, L represents the total length of the core sample; x represents the distance from the core inlet; S nw This indicates the residual saturation of the non-wetting phase measured at the outlet end; q w The core wetting phase flow rate, μ w q represents the viscosity of the wetting phase; nw The flow rate of the non-wetting phase in the core is expressed in μ. nw Indicates the viscosity of the non-wetting phase; In the phase permeation test, the commonly used wetting phase is the aqueous phase, and the non-wetting phase is the oil phase.

6. The unsteady-state phase permeation algorithm considering end-face effects according to claim 1, characterized in that, In step 4, the parameters such as water phase flow rate, oil phase flow rate, production pressure difference, and fluid viscosity are determined by the unsteady-state relative permeability test experiment.

7. The unsteady-state phase permeation algorithm considering end-face effects according to claim 1, characterized in that, Step 4 specifically includes: 1) Fluid preparation: The experimental oil was a simulated oil prepared by adding neutral kerosene to fresh degassed crude oil, and the fluid used in the experiment was simulated formation water; the viscosity and density of the prepared fluid were recorded; 2) First, weigh the dry core and measure the air permeability of the core. Then, saturate the formation with vacuum water. Finally, weigh the wet weight of the rock sample after saturation with fluid. From this, the effective pore volume and porosity can be obtained. 3) Establish bound water saturation: Inject oil into a core saturated with formation water to displace it to a bound water state, displacing at least 10 times the pore volume, record the amount of water displaced, and calculate the oil phase permeability and bound water saturation. 4) Water-driven oil phase permeability test: Establish a certain pressure at the rock sample inlet; accurately record the cumulative oil production q. nw Cumulative water production q w The pressure difference between the two ends of the rock sample; after injecting water 30 times the pore volume, the displacement experiment was stopped, and the water phase saturation and residual oil saturation were calculated.

8. The unsteady phase permeation algorithm considering end-face effects according to claim 1, characterized in that, In step 5, the relationship function between the water phase saturation at the inlet end and the relative permeability of the oil phase when the water flow rate is zero and the average water saturation of the entire core are determined respectively.

9. The unsteady phase permeation algorithm considering end-face effects according to claim 1, characterized in that, Step 5 specifically includes: 1) To simplify the model, the water phase saturation is calculated when the water phase flow rate is 0. 2) When the core distance is 0, obtain the relationship function between the water phase saturation and the relative permeability of the oil phase at the core inlet end; In the formula It is the standardized wetting phase saturation; It is the saturation of the wetting phase at the inlet end; 3) Obtain the average water saturation of the entire core. Where K represents the air permeability of the experimental test core, 10 -3 μm 2 A represents the cross-sectional area of ​​the experimental test core, in cm². 2 ;q nw The flow rate of the non-wetting phase in the core is expressed in μ. nw S represents the viscosity of the non-wetting phase. w It represents the wetting phase saturation; x represents the distance from the core inlet.

10. The unsteady phase permeation algorithm considering end-face effects according to claim 1, characterized in that, In step 6, the pressure drop in the region unaffected by the end-face effect is obtained, and the relationship between the relative permeability of the oil phase at the end of the core and the pressure drop is established, thereby obtaining the saturation correction value at the core inlet.

11. The unsteady-state phase permeation algorithm considering end-face effects according to claim 1, characterized in that, Step 6 specifically includes: 1) Pressure drop ΔP at a distance x from the core inlet is unaffected by end-face effects. x : In the formula, ΔP| x It is the average pressure from the inlet to the outlet; p| x It is the pressure at a distance x from the inlet end; p|0 is the pressure at the inlet end; It is the capillary force under standardized aqueous phase saturation; It is the initial capillary force under standardized aqueous phase saturation; q nw Indicates the flow rate of the non-wetting phase in the core; μ nw Indicates the viscosity of the non-wetting phase; K represents the air permeability of the experimental test core, 10 -3 μm 2 ; A represents the cross-sectional area of ​​the experimental test core, in cm². 2 ; 2) Establish the relationship between the relative permeability of the oil phase at the end of the core and the pressure drop, so as to obtain the saturation correction value at the core inlet.

12. The unsteady-state phase permeation algorithm considering end-face effects according to claim 1, characterized in that, In step 7, the relative permeability of the oil phase and the relative permeability of the water phase are calculated based on the optimal relative permeability model using the obtained inlet saturation correction value.

Images