A method for determining gas and water relative permeability of a reservoir

Abstract

The application discloses a reservoir gas-water relative permeability determination method, and relates to the field of reservoir permeability determination. The method comprises the following steps: obtaining a core sample of a target reservoir and determining the geometric size of the core sample; injecting simulated formation water into the core sample until the core sample is saturated, and performing nuclear magnetic scanning to obtain a reference nuclear magnetic signal and an initial porosity distribution; performing a multistage gas injection pressure experiment in an intermittent displacement mode to obtain quasi-steady-state displacement data; constructing a two-phase percolation numerical model with phase permeability curve parameters and capillary pressure curve parameters as to-be-inverted parameters; constructing a target function based on the quasi-steady-state data and performing inversion solving to obtain optimal parameters; and determining the phase permeability curve and the capillary pressure curve based on the optimal parameters. The application obtains the fluid distribution inside the core through nuclear magnetic resonance, obtains quasi-steady-state data in combination with intermittent displacement, and inversely solves the phase permeability and the capillary pressure, so that the problem that the fluid distribution inside the core cannot be accurately reflected and the multi-solution problem cannot be solved is solved, and the influence of the capillary end effect is eliminated.

Description

Technical Field

[0001] This application relates to the field of reservoir permeability determination technology, and in particular to a method for determining the relative permeability of gas and water in a reservoir. Background Technology

[0002] The gas-water relative permeability curve is a key basic parameter for evaluating reservoir productivity, formulating development plans, and conducting numerical simulations. Accurately determining the gas-water relative permeability of a reservoir is of great significance for the efficient development of unconventional oil and gas reservoirs.

[0003] Traditional methods for determining relative permeability include steady-state and unsteady-state methods. However, for unconventional reservoirs with ultra-low permeability, strong heterogeneity, and significant capillary end-effects, traditional methods suffer from severe measurement biases in practical applications. Specifically, traditional methods struggle to accurately reflect the fluid distribution within the core through fluid metering during experiments, and they neglect the nonlinear controlling effect of the initiation pressure gradient and capillary force on fluid displacement in low-permeability media. Consequently, the determined gas-water relative permeability fails to accurately reflect the actual reservoir conditions.

[0004] Therefore, there is an urgent need for a method to determine the relative permeability of gas and water in reservoirs, in order to solve the measurement deviation problem caused by the inability to accurately reflect the fluid distribution inside the core, thereby improving the accuracy and reliability of the determination of the relative permeability of gas and water. Summary of the Invention

[0005] The purpose of this application is to provide a method for determining the relative permeability of gas and water in reservoirs, which can accurately reflect the fluid distribution inside the core, eliminate the influence of capillary end effect and unsteady displacement on the measurement results, thereby improving the accuracy and reliability of determining the relative permeability of gas and water.

[0006] To achieve the above objectives, this application provides the following solution:

[0007] This application provides a method for determining the relative permeability of gas and water in a reservoir, including:

[0008] Obtain core samples from the target reservoir and determine the geometric dimensions of the core samples;

[0009] Simulated formation water was injected into the core sample until it reached a fully saturated state, and nuclear magnetic resonance scanning was performed on the core sample under simulated formation overburden conditions to obtain the spatial distribution of the baseline nuclear magnetic resonance signal and the initial porosity distribution of the core sample under a fully saturated state.

[0010] Under simulated formation overburden conditions, a multi-stage gas injection pressure displacement experiment was conducted on the core sample using an intermittent displacement method to obtain quasi-steady-state displacement data of the core sample at each gas injection pressure. The quasi-steady-state displacement data includes the spatial distribution of water saturation, cumulative gas production, and cumulative water production.

[0011] Based on the geometric dimensions and initial porosity distribution of the core sample, a one-dimensional two-phase flow numerical model was constructed with the parameters of the gas-water relative permeability curve and the capillary pressure curve as the parameters to be inverted.

[0012] Construct an objective function based on the quasi-steady-state displacement data;

[0013] Based on the objective function, an optimization algorithm is used to iteratively invert and solve the one-dimensional two-phase flow numerical model until a preset stopping condition is met, and the inversion stops to obtain the optimal gas-water relative permeability curve parameters and the optimal capillary pressure curve parameters. The preset stopping condition includes the rate of change of the objective function value within a preset number of consecutive iterations being less than a preset change threshold, or the number of iterations reaching a preset maximum number of iterations.

[0014] The gas-water relative permeability curve of the target reservoir is determined based on the optimal gas-water relative permeability curve parameters, and the capillary pressure curve of the target reservoir is determined based on the optimal capillary pressure curve parameters.

[0015] According to the specific embodiments provided in this application, the following technical effects are disclosed:

[0016] This application provides a method for determining the relative permeability of gas and water in reservoirs. By injecting simulated formation water into core samples until they are fully saturated, and performing nuclear magnetic resonance (NMR) scanning under simulated formation overburden conditions, the spatial distribution of the baseline NMR signal and the initial porosity distribution are obtained. This solves the problem of not being able to obtain the internal pore structure distribution of the core and achieves quantitative characterization of core heterogeneity. By conducting multi-stage gas injection pressure displacement experiments on core samples under simulated formation overburden conditions using an intermittent displacement method, quasi-steady-state displacement data at each injection pressure level are obtained. This solves the problem of unstable fluid distribution caused by viscous fingering and capillary end effect in traditional continuous displacement methods and achieves the acquisition of fluid distribution under quasi-static capillary equilibrium. By constructing a one-dimensional two-phase flow numerical model with the parameters of the gas-water relative permeability curve and the parameters of the capillary pressure curve as the parameters to be inverted, and constructing an objective function based on the quasi-steady-state displacement data for iterative inversion solution, this solves the problem of multiple solutions in inversion caused by traditional methods relying only on inlet and outlet metering data. This achieves the joint determination of gas-water relative permeability and capillary pressure, improving the uniqueness and stability of the inversion results. Attached Figure Description

[0017] To more clearly illustrate the technical solutions in the embodiments of this application or the prior art, the drawings used in the embodiments will be briefly introduced below. Obviously, the drawings described below are only some embodiments of this application. For those skilled in the art, other drawings can be obtained based on these drawings without creative effort.

[0018] Figure 1 This is a flowchart illustrating a method for determining the relative permeability of reservoir gas and water in one embodiment of this application. Detailed Implementation

[0019] The technical solutions of the embodiments of this application will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of this application, and not all embodiments. Based on the embodiments of this application, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of this application.

[0020] To make the above-mentioned objectives, features and advantages of this application more apparent and understandable, the application will be further described in detail below with reference to the accompanying drawings and specific embodiments.

[0021] like Figure 1 As shown, this application provides a method for determining the relative permeability of reservoir gas and water, including the following steps 201 to 207. Wherein:

[0022] Step 201: Obtain a core sample from the target reservoir and determine the geometric dimensions of the core sample.

[0023] Step 202: Inject simulated formation water into the core sample until it reaches a fully saturated state, and perform nuclear magnetic resonance scanning on the core sample under simulated formation overburden conditions to obtain the spatial distribution of the reference nuclear magnetic signal and the initial porosity distribution of the core sample under a fully saturated state.

[0024] Step 203: Under simulated formation overburden conditions, a multi-stage gas injection pressure displacement experiment is conducted on the core sample using an intermittent displacement method to obtain quasi-steady-state displacement data of the core sample at each gas injection pressure; the quasi-steady-state displacement data includes the spatial distribution of water saturation, cumulative gas production, and cumulative water production.

[0025] Step 204: Based on the geometric dimensions and initial porosity distribution of the core sample, construct a one-dimensional two-phase flow numerical model with the parameters of the gas-water relative permeability curve and the capillary pressure curve as the parameters to be inverted.

[0026] Step 205: Construct an objective function based on the quasi-steady-state displacement data.

[0027] Step 206: Based on the objective function, an optimization algorithm is used to iteratively invert and solve the one-dimensional two-phase flow numerical model until a preset stopping condition is met, and the inversion stops to obtain the optimal gas-water relative permeability curve parameters and the optimal capillary pressure curve parameters. The preset stopping condition includes the rate of change of the objective function value within a preset number of consecutive iterations being less than a preset change threshold, or the number of iterations reaching a preset maximum number of iterations.

[0028] Step 207: Determine the gas-water relative permeability curve of the target reservoir based on the optimal gas-water relative permeability curve parameters, and determine the capillary pressure curve of the target reservoir based on the optimal capillary pressure curve parameters.

[0029] By implementing steps 201 to 207 above, this application obtains the fluid distribution inside the core through nuclear magnetic resonance scanning, obtains quasi-steady-state data by combining intermittent displacement, and solves the relative permeability of gas and water and capillary pressure through joint inversion. This effectively eliminates the influence of capillary end effect and unsteady displacement on the measurement results, solves the problem that traditional methods cannot accurately reflect the fluid distribution inside the core and the multiple solutions of inversion, improves the accuracy and reliability of determining the relative permeability of gas and water, and can provide more reliable basic data for the productivity evaluation and numerical simulation of unconventional oil and gas reservoirs.

[0030] In another exemplary embodiment of this application, step 202 specifically includes:

[0031] After the core sample is evacuated, simulated formation water is injected under high pressure until the core sample reaches a state of complete saturation.

[0032] Under simulated formation overburden conditions, nuclear magnetic resonance (NMR) scans were performed on core samples that had reached full saturation to obtain the spatial distribution of baseline NMR signals.

[0033] The initial porosity distribution was calculated based on the spatial distribution of the reference NMR signal and the NMR signal-simulated formation water quality standard curve.

[0034] In another exemplary embodiment of this application, step 203 specifically includes:

[0035] Multiple injection pressure levels are determined and sorted in ascending order to obtain a pressure level sequence.

[0036] By traversing each injection pressure in the pressure series, displacement experiments were conducted on the core samples at the current injection pressure using the following intermittent displacement steps:

[0037] Initialize the number of iterations i = 1.

[0038] Maintaining a constant current injection pressure, the core sample is subjected to the i-th displacement. Displacement is stopped after a first preset time, and the gas production and water production of the i-th displacement are obtained.

[0039] After waiting for the second preset time, the core sample after the i-th displacement is subjected to nuclear magnetic resonance scanning to obtain the nuclear magnetic resonance T2 spectrum and spatial distribution of nuclear magnetic signals of the i-th displacement at the current gas injection pressure. Based on the spatial distribution of nuclear magnetic signals of the i-th displacement at the current gas injection pressure and the spatial distribution of reference nuclear magnetic signals, the spatial distribution of water saturation of the i-th displacement is determined.

[0040] If the displacement equilibrium condition is met, the cumulative gas production of the current stage gas injection pressure is obtained by summing the gas production of all displacements at the current stage gas injection pressure, and the cumulative water production of the current stage gas injection pressure is obtained by summing the water production of all displacements at the current stage gas injection pressure. The cumulative gas production, cumulative water production, and spatial distribution of water saturation of the current stage gas injection pressure are used as quasi-steady-state displacement data under the current stage gas injection pressure. The displacement equilibrium condition includes that the rate of change of water saturation at at least one axial position of the core sample is less than a first preset rate of change threshold. The rate of change of water saturation is calculated based on the spatial distribution of water saturation of the (i-1)th displacement and the spatial distribution of water saturation of the ith displacement when i≥2.

[0041] If the displacement equilibrium condition is not met when i=1 or i≥2, then repeat the above intermittent displacement steps to perform the (i+1)th displacement experiment at the current stage injection pressure.

[0042] If the termination condition is met, the displacement experiment ends, and quasi-steady-state displacement data of the core sample under each injection pressure level are obtained. The termination condition includes the completion of pressure level sequence traversal, or the nuclear magnetic resonance T2 spectrum showing only bound water signal, or the rate of change of the overall water saturation of the core sample under the current injection pressure level within a consecutive preset number of levels being less than a second preset rate of change threshold. The overall water saturation is the arithmetic mean of the water saturation at all axial positions of the core sample in the spatial distribution of water saturation under the current injection pressure level.

[0043] If the termination condition is not met, the next level of gas injection pressure displacement experiment will be carried out on the core sample.

[0044] In another exemplary embodiment of this application, the objective function is:

[0045] .

[0046] Where J represents the value of the objective function; Indicates the first The cumulative gas production obtained from a one-dimensional two-phase flow numerical model at each state point; j={1,2,3,...,n} This represents the total number of state points that record cumulative gas production and water production data. Indicates the first The cumulative gas production measured in experiments at each state point; Indicates the first The cumulative water production obtained from the one-dimensional two-phase flow numerical model at each state point; Indicates the first Cumulative water production measured in experiments at each state point; Indicates the first The monitoring time, the Water saturation obtained from a one-dimensional two-phase flow numerical model at the axial position of a core sample; Indicates the first The monitoring time, the The experimentally measured water saturation at axial locations of core samples; t={1,2,3,...,m} This represents the total number of times when NMR scans were performed to measure the spatial distribution of water saturation; l = {1, 2, 3, ..., L}. Indicates the total number of core samples at axial positions; , and These represent the weighting coefficients for cumulative gas production, cumulative water production, and spatial distribution of water saturation, respectively.

[0047] In another exemplary embodiment of this application, the one-dimensional two-phase flow numerical model includes a gas phase equation, a water phase equation, and an auxiliary equation.

[0048] The gas phase equation is as follows:

[0049] .

[0050] The aqueous phase equation is:

[0051] .

[0052] The auxiliary equation is:

[0053] .

[0054] .

[0055] in, Indicates the axial position of the core sample; Indicates time; This indicates the absolute permeability of the core sample; and These represent the relative permeability of the gas phase and the relative permeability of the aqueous phase, respectively. and These represent the gas phase pressure and the water phase pressure, respectively. Indicates the pressure in the air-water capillary tube; and These represent the viscosity of the gas phase and the viscosity of the aqueous phase, respectively. and These represent the volume coefficients of the gas phase and the aqueous phase, respectively. Indicates the porosity of the core sample; and These represent gas saturation and water saturation, respectively. and These represent the source and sink terms in the gas phase and the source and sink terms in the aqueous phase, respectively.

[0056] In another exemplary embodiment of this application, the gas-water relative permeability curve of the target reservoir is determined based on the optimal gas-water relative permeability curve parameters, and the capillary pressure curve of the target reservoir is determined based on the optimal capillary pressure curve parameters, specifically including:

[0057] The normalized water saturation at each axial location point of the core sample is calculated using the following formula:

[0058] .

[0059] in, This represents the normalized water saturation at the axial position x of the core sample. This indicates the water saturation at the axial position x of the core sample; Indicates the degree of bound water saturation; This indicates the critical gas saturation.

[0060] The relative permeability of the gas phase and the relative permeability of the water phase at the normalized water saturation corresponding to the axial position of each core sample are calculated using the following formula, thus obtaining the gas-water relative permeability curve:

[0061] .

[0062] .

[0063] in, and These represent the relative permeability of the water phase and the relative permeability of the gas phase at the normalized water saturation at the axial position x of the core sample, respectively. and These represent the relative permeability of the aqueous phase at the endpoint and the relative permeability of the gas phase at the endpoint, respectively. and These represent the water phase permeability index and the gas phase permeability index, respectively.

[0064] The capillary pressure values ​​under different normalized water saturation levels are calculated using the following formula, thus obtaining the capillary pressure curve:

[0065] .

[0066] in, This represents the capillary pressure value corresponding to the normalized water saturation at the axial position x of the core sample. Indicates the inlet capillary pressure; This represents the pore size distribution index.

[0067] In another exemplary embodiment of this application, the optimization algorithm includes the Levenberg-Marquardt algorithm or a genetic algorithm.

[0068] In another exemplary embodiment of this application, the NMR signal-simulated formation water quality standard curve is obtained by performing NMR scans on multiple sets of simulated formation water of different qualities to establish a linear quantitative relationship between the simulated formation water quality and the total amplitude of the NMR signal.

[0069] The expression for the NMR signal-simulated formation water quality standard curve is:

[0070] .

[0071] in, This indicates the simulated formation water quality; Nuclear magnetic resonance signal - linear scaling factor for simulating formation water quality; This represents the total amplitude of the nuclear magnetic resonance signal; This represents the correction factor.

[0072] In another exemplary embodiment of this application, the formula for calculating water saturation is:

[0073] .

[0074] in, This indicates the water saturation at the axial position x of the core sample at time t; The nuclear magnetic resonance signal represents the axial position x of the core sample at time t; The reference NMR signal represents the axial position x of the core sample.

[0075] In another exemplary embodiment of this application, the constraints of the one-dimensional two-phase flow numerical model include: spatial distribution constraints of water saturation.

[0076] In another exemplary embodiment of this application, the target reservoir includes a coal-rock reservoir or a tight sandstone reservoir.

[0077] The following example illustrates this application using a specific process for determining the relative permeability of gas and water in a reservoir.

[0078] Step 1: Core preprocessing and NMR signal quantization calibration.

[0079] ① Core preparation: Select representative cores from the target reservoir (coal reservoir or tight sandstone reservoir) and process them into standard plunger samples (2.5cm in diameter).

[0080] ②Preparation of experimental fluid: Prepare simulated formation water with the same salinity as the reservoir formation water to obtain direct water phase signals.

[0081] ③ Establish a standard curve for NMR signal-simulated formation water quality: Take no fewer than 5 sets of simulated formation water samples of different masses (e.g., 2g, 5g, 8g, 10g, 12g, etc.) and scan them in an NMR spectrometer. Establish a water quality standard curve. With the total amplitude of the NMR signal The linear regression equation: Because the total NMR signal amplitude is strictly proportional to the number of hydrogen nuclei (i.e., water content) in the examined volume, a linear calibration equation can be established by performing NMR scans on at least five sets of simulated formation water of known mass. Requirements: This serves as the benchmark for calculating water saturation in real time by converting NMR signals into water content in subsequent experiments.

[0082] The formula for calculating the linear correlation coefficient r is as follows:

[0083] .

[0084] in, Indicates the first The total amplitude of the nuclear magnetic resonance signal of the simulated formation water; Indicates the first The group simulated the actual mass of formation water; and These are the arithmetic mean of the total amplitude of the NMR signals of all simulated formation water groups and the arithmetic mean of the actual mass of all simulated formation water groups, respectively. 2 It equals the square of r. R 2 A value >0.99 means that more than 99% of the variation in water quality can be explained by changes in the amplitude of the NMR signal.

[0085] Step 2: High-pressure saturated water in the core.

[0086] ① Vacuum pressure saturation: The core sample is placed in a saturation container, and a vacuum is drawn to -0.1 MPa and maintained for more than 4 hours. Then, simulated formation water is injected. High pressure saturation of 15 MPa-20 MPa is applied for 24-48 hours to ensure that the water phase completely enters the micro-nano pores.

[0087] ② Initial state scan: After the core was saturated with water, it was placed in a non-magnetic core holder and put into an online nuclear magnetic resonance imaging system. Confining pressure (3-5 MPa higher than the maximum injection pressure in the experiment) was applied to simulate the overburden pressure.

[0088] ③ Baseline data acquisition: Nuclear magnetic resonance T2 spectroscopy and slice imaging scans were performed to obtain the signal distribution map of the core sample when it reached a fully saturated state (100% water saturation). The signal distribution map is used as a normalization benchmark. The horizontal axis represents the axial position of the core (along the path, usually in mm), and the vertical axis represents the total amplitude of the NMR signal. In step two, the core is already in a 100% high-pressure saturation state, therefore the water saturation under this state is defined as 100% across the entire range. The initial pore distribution is obtained using the signal distribution map obtained from NMR scanning. Combined with the linear regression equation from step one, the signal amplitude at each location is converted into water content, and then into the corresponding pore volume.

[0089] Step 3: Low-pressure start-up and intermittent unsteady-state displacement.

[0090] ① Set the starting pressure: Set the first-stage gas injection pressure For low-permeability cores, It should be slightly higher than the estimated initiation pressure gradient of the core macropores or fractures.

[0091] ② Intermittent injection: The core displacement system opens the gas injection valve in its gas injection circuit to maintain constant pressure. Perform for a short time (first preset time) (e.g., 1 minute) displacement, and the gas production during that period is recorded using a flow metering unit. and water production .

[0092] ③ Stop Injection Equilibrium: The inlet and outlet valves at both ends of the core holder are closed by the core displacement system, so that the core sample is in a sealed state and displacement is stopped. It is then left to stand for a second preset time (e.g., 10 minutes). During the stop injection period, the fluid inside the core undergoes spontaneous redistribution under capillary pressure. The water phase is drawn back into the small pores, and the gas phase migrates into the large pores, eliminating the unstable fluid distribution caused by viscous fingering and making the fluid distribution tend towards quasi-static capillary equilibrium.

[0093] ④ Steady-state monitoring: Perform NMR scanning at the end of the settling period (including overall NMR T2 spectrum and spatial distribution of water saturation in the slices).

[0094] ⑤ Cyclic judgment: Maintain pressure Repeat steps ② through ④, and compare the spatial distribution of water saturation in NMR slices during the two injection-free periods. If the rate of change of saturation at a certain location ( If the first preset rate of change threshold (e.g., 0.5%) is indicated, then the displacement at that pressure level is determined to have reached equilibrium, and the process proceeds to the next step; otherwise, the cyclic displacement continues at that pressure. When the injection-stop-equilibrium-monitoring cycle is repeated multiple times until the injection pressure level is determined to have reached displacement equilibrium, the system records the cumulative gas production and cumulative water production obtained at that pressure level, and uses this data for fitting calculations of a multi-objective function.

[0095] As an optional implementation, the water saturation at any axial position x at time t is calculated. It uses a ratio conversion logic:

[0096] .

[0097] in, The nuclear magnetic resonance signal of the axial position x of the core sample at time t; The reference NMR signal representing the axial position x of the core sample is the reference NMR signal at the same position under 100% water saturation recorded in step two. By using this ratio of current signal to full-scale signal, the influence of the heterogeneity of the core pore structure on saturation calculation can be eliminated, and an accurate local saturation field can be directly obtained, thus avoiding the drawback of the traditional outlet measurement method, which cannot characterize the internal fluid distribution.

[0098] Step 4: Gradually increase the injection pressure for displacement.

[0099] ① Increase the injection pressure: Increase the injection pressure in stages to ,in

[0100] ② Repeated cycle: at each pressure level Next, repeat steps ② to ⑤ in step 3. In the low-pressure stage, the water in the fractures and large pores is mainly displaced. As the pressure gradually increases, the gas gradually overcomes the capillary resistance of the micropore throats and enters the matrix, thereby completely scanning the pore structure of the core through the pressure change process.

[0101] ③ Termination condition: Until the injection pressure reaches the limit of the experimental system or the maximum pressure difference of the simulated formation. Furthermore, the NMR T2 spectrum shows only bound water signals (short relaxation components), and the overall water saturation of the core no longer decreases. The criterion for determining that the NMR T2 spectrum shows only bound water signals is: when the signal amplitude in the NMR T2 spectrum with a relaxation time greater than the empirical T2 cutoff value of the reservoir core (or the T2 cutoff value obtained from centrifugation calibration) decays to zero, and the total signal amplitude consists only of short relaxation components smaller than this T2 cutoff value, it is determined that only bound water signals remain. Here, the NMR T2 spectrum showing only bound water signals (short relaxation components) and the overall water saturation of the core no longer decreasing are the same state, but the characterization methods are different: The overall water saturation no longer decreasing indicates that the current displacement pressure difference can no longer overcome the capillary resistance in smaller pores, and macroscopically, no more water is produced. Only bound water signals indicate that the mobile water in large and medium pores has been completely displaced, and the water phase is only bound in micropores. These two conditions are physically equivalent and are both criteria for determining that the core has reached the bound water state.

[0102] Step 5: Historical fitting and inversion of the phase permeation curve.

[0103] ① Establish a numerical model: Based on the core geometry, establish a one-dimensional or two-dimensional numerical model of two-phase flow. Use the initial porosity distribution obtained from NMR imaging in step two. The values ​​are assigned to the grid of the one-dimensional two-phase flow numerical model to characterize the heterogeneity of the core.

[0104] ② Construct the objective function: Construct a multi-objective deviation function that includes cumulative water production, cumulative gas production, and water saturation distribution along the pipeline:

[0105] .

[0106] Where J represents the value of the objective function; Indicates the first The cumulative gas production obtained from a one-dimensional two-phase flow numerical model at each state point; j={1,2,3,...,n} This represents the total number of state points that record cumulative gas production and water production data. Indicates the first The cumulative gas production measured in experiments at each state point; Indicates the first The cumulative water production obtained from the one-dimensional two-phase flow numerical model at each state point; Indicates the first Cumulative water production measured in experiments at each state point; Indicates the first The monitoring time, the Water saturation obtained from a one-dimensional two-phase flow numerical model at the axial position of a core sample; Indicates the first The monitoring time, the The experimentally measured water saturation at axial locations of core samples; t={1,2,3,...,m} This represents the total number of times when NMR scans were performed to measure the spatial distribution of water saturation; l = {1, 2, 3, ..., L}. Indicates the total number of core samples at axial positions; , and These represent the weighting coefficients for cumulative gas production, cumulative water production, and spatial distribution of water saturation, respectively.

[0107] ③ Introduce water saturation distribution along the core axis at different times measured by nuclear magnetic resonance. As a strong constraint, the problem of multiple solutions in relative permeability inversion is solved. By adjusting the parameters of the relative permeability curve, the root mean square error (RMSE) between the spatial distribution profile of water saturation generated by numerical simulation and the spatial distribution profile of quasi-steady-state water saturation measured by nuclear magnetic resonance is minimized, and the residuals of the spatial discrete points of saturation at each pressure level are all within the convergence accuracy range of the algorithm.

[0108] ④ History fitting: Using the Levenberg-Marquardt algorithm or genetic algorithm, adjust the parameters of the gas-water relative permeability curve (such as the relative permeability of the water phase at the endpoint). Relative permeability of gas phase at endpoints Vapor permeability index It is a fitting parameter that controls the shape and curvature of the relative permeability curve of the gas phase, and the relative permeability index of the water phase. It is a fitting parameter that controls the shape and curvature of the relative permeability curve of the water phase, and the bound water saturation. ) and capillary pressure curve parameters (inlet capillary pressure) Pore ​​size distribution index ), making the objective function Minimization. The principle is that the relative permeability of gas and water determines the fluid's velocity in a porous medium, while the capillary pressure parameter controls the spatial arrangement of the fluid phases. By continuously adjusting these control parameters, a one-dimensional two-phase flow numerical model is driven to generate different dynamic production sequences and saturation field distributions. The optimization algorithm compares the gas / water production and saturation distribution along the flow path generated by the numerical simulation with the measured physical data point by point, calculating the value of the multi-objective deviation function J. As the algorithm searches within the parameter space, the numerical simulation results gradually approach the observed physical values. When the multi-objective deviation function J reaches its minimum and the fit converges, the corresponding parameter combination eliminates unsteady-state disturbances such as capillary end effects, thereby determining the true relative permeability curve of gas and water covering the full pore size of the target reservoir.

[0109] As an optional implementation, when the optimization algorithm is the Levenberg-Marquardt algorithm, based on the objective function, the optimization algorithm is used to iteratively invert and solve the one-dimensional two-phase flow numerical model until a preset stopping condition is met, at which point the inversion stops, obtaining the optimal gas-water relative permeability curve parameters and the optimal capillary pressure curve parameters, specifically including:

[0110] Step 1, Parameter Initialization: Set the initial parameter vectors for the gas-water relative permeability curve parameters and capillary pressure curve parameters to be inverted. :

[0111] .

[0112] And initialize the damping factor (usually taken) =0.01) is used to balance the Gauss-Newton method and the gradient descent method, and to set the iteration counter a=0.

[0113] Step 2, Forward Modeling and Residual Evaluation: The parameter vector P from the a-th iteration... a Substitute the values ​​into a one-dimensional two-phase flow numerical model to calculate the simulated values ​​at each experimental point (axial position of the core sample). And combined with experimental measurement data Calculate the objective function value and residual vector .

[0114] .

[0115] .

[0116] Step 3, Jacobian matrix construction: Calculate the sensitivity of each observation to the inversion parameters using the numerical perturbation method, and construct the Jacobian matrix H for the a-th iteration. a .

[0117] .

[0118] in, Indicates the first Simulated values ​​obtained from a one-dimensional two-phase flow numerical model at each state point; This represents the value of the k-th inversion parameter in the a-th iteration; This indicates the total number of inversion parameters.

[0119] Step 4, Parameter Update Iteration: Calculate the parameter increment according to the Levenberg-Marquardt formula. :

[0120] .

[0121] The parameter vector is updated to obtain the parameter vector for the (a+1)th iteration. :

[0122] .

[0123] Where T denotes transpose; I denotes identity matrix; This represents the damping factor in the a-th iteration.

[0124] Step 5, Convergence Determination: If the decrease in the objective function value J is less than the preset threshold or the maximum number of iterations is reached, then stop the iteration and output the current parameters as the optimal result. Otherwise, adjust the damping factor and let a = a + 1, then return to the forward calculation and residual evaluation steps.

[0125] The specific method for adjusting the damping factor is as follows: If (If step size is effective), then reduce the damping factor (e.g.) This biases the algorithm towards the Gauss-Newton method to accelerate convergence. If (If step size is ineffective), then increase the damping factor (e.g.) This makes the algorithm biased towards gradient descent to stabilize the search.

[0126] As an optional implementation, when the optimization algorithm is a genetic algorithm, based on the objective function, the optimization algorithm is used to iteratively invert and solve the one-dimensional two-phase seepage numerical model until a preset stopping condition is met, at which point the inversion stops, obtaining the optimal gas-water relative permeability curve parameters and the optimal capillary pressure curve parameters, specifically including:

[0127] Step 1, Population initialization: Within the reasonable physical range of relative permeability and capillary pressure parameters, several parameter combinations are randomly generated to form an initial population. Each parameter combination is regarded as an individual (chromosome).

[0128] Step 2, Fitness Evaluation: Substitute the parameters of each individual in the population into the one-dimensional two-phase flow numerical model for simulation calculation, use the objective function J to calculate its residual, and convert it into a fitness value (for example, take the reciprocal of the objective function, the smaller the residual, the higher the fitness).

[0129] Step 3, Selection Operation: Using roulette wheel or tournament methods, select superior individuals from the current population as parents based on their fitness values.

[0130] Step 4, Crossover and Mutation: Perform crossover operations on the selected parent individuals to recombine parameters, and perform gene mutation operations (randomly perturb a certain parameter) with a certain probability to generate a new offspring population.

[0131] Step 5, Iteration and Termination: Replace the parent population with the offspring population and repeat steps 2 to 4. Continue until the highest fitness value in the population remains unchanged for multiple generations, or the set maximum number of generations is reached. Stop the inversion and output the individual with the highest fitness as the optimal parameter.

[0132] ⑤ Output relative permeability: The parameter curve obtained after fitting convergence is the gas-water relative permeability curve of the target reservoir under the control of the real pore structure.

[0133] As an optional implementation, the Brooks-Corey empirical formula is used as the mathematical representation of the relative permeability and capillary pressure curves. The parameters of the optimal gas-water relative permeability curve and the optimal capillary pressure curve are the fitting coefficients in this empirical formula. The specific determination method is as follows:

[0134] Based on the optimal parameters obtained from the inversion (such as relative end-point permeability) Relevance index , Bound water saturation Inlet capillary pressure and pore size distribution index Substituting the following formula will generate the full-range curve:

[0135] The normalized water saturation at each axial location point of the core sample is calculated using the following formula:

[0136] .

[0137] in, This represents the normalized water saturation at the axial position x of the core sample. This indicates the water saturation at the axial position x of the core sample; Indicates the degree of bound water saturation; This indicates the critical gas saturation.

[0138] The relative permeability of the gas phase and the relative permeability of the water phase at the normalized water saturation corresponding to the axial position of each core sample are calculated using the following formula, thus obtaining the gas-water relative permeability curve:

[0139] .

[0140] .

[0141] in, and These represent the relative permeability of the water phase and the relative permeability of the gas phase at the normalized water saturation at the axial position x of the core sample, respectively. and These represent the relative permeability of the aqueous phase at the endpoint and the relative permeability of the gas phase at the endpoint, respectively. and These represent the water phase permeability index and the gas phase permeability index, respectively.

[0142] The capillary pressure values ​​under different normalized water saturation levels are calculated using the following formula, thus obtaining the capillary pressure curve:

[0143] .

[0144] in, This represents the capillary pressure value corresponding to the normalized water saturation at the axial position x of the core sample. Indicates the inlet capillary pressure; This represents the pore size distribution index.

[0145] This application also provides an application scenario in which the above-mentioned method for determining the relative permeability of reservoir gas and water is applied. Specifically, the method for determining the relative permeability of reservoir gas and water provided in this embodiment can be applied to the scenario of production capacity evaluation and development plan formulation in the development of unconventional oil and gas reservoirs. This scenario includes a core experiment stage, a data inversion stage, and a production capacity prediction stage. Core samples are obtained from the field drilling and coring stage, and quasi-steady-state displacement data are obtained through nuclear magnetic resonance scanning and intermittent displacement experiments, and then enter the data inversion stage. In the data inversion stage, a one-dimensional two-phase flow numerical model and an objective function are constructed and iteratively inverted to obtain the relative permeability curve of gas and water and the capillary pressure curve, and then enter the production capacity prediction stage. In the production capacity prediction stage, numerical simulation is performed based on the obtained relative permeability curve of gas and water and the capillary pressure curve to predict the production capacity of unconventional oil and gas reservoirs. The method for determining the relative permeability of reservoir gas and water provided in this embodiment belongs to the core experiment and data inversion stage in the development of unconventional oil and gas reservoirs. Specifically, this method obtains the fluid distribution inside the core through nuclear magnetic resonance scanning, obtains quasi-steady-state data by combining intermittent displacement, and solves the relative permeability of gas and water and capillary pressure through joint inversion, providing accurate basic parameters for subsequent production capacity prediction.

[0146] In summary, this application effectively avoids saturation errors caused by state changes during scanning: a quasi-steady-state saturation field is obtained through "gas injection—injection stop—scanning—convergence criterion"; a spatially resolved saturation profile is obtained: slice scanning provides the spatial distribution of water saturation along the path, which can significantly reduce inversion bias caused by end-effects; gradually increasing the injection pressure expands the measurable saturation range; and the combined inversion of relative permeability and capillary pressure is achieved by simultaneously fitting the boundary production / pressure difference with the internal water saturation spatial distribution profile, improving the uniqueness and stability of the inversion. Furthermore, it can provide more reliable basic data for the productivity evaluation and numerical simulation of unconventional oil and gas reservoirs.

[0147] It should be noted that the user information (including but not limited to user device information, user personal information, etc.) and data (including but not limited to data used for analysis, data stored, data displayed, etc.) involved in this application are all information and data authorized by the user or fully authorized by all parties, and the collection, use and processing of the relevant data must comply with relevant regulations.

[0148] The technical features of the above embodiments can be combined in any way. For the sake of brevity, not all possible combinations of the technical features in the above embodiments are described. However, as long as there is no contradiction in the combination of these technical features, they should be considered to be within the scope of this specification.

[0149] This document uses specific examples to illustrate the principles and implementation methods of this application. The descriptions of the above embodiments are only for the purpose of helping to understand the methods and core ideas of this application. Furthermore, those skilled in the art will recognize that, based on the ideas of this application, there will be changes in the specific implementation methods and application scope. Therefore, the content of this specification should not be construed as a limitation of this application.

Claims

1. A method for determining the relative permeability of gas and water in a reservoir, characterized in that, include: Obtain core samples from the target reservoir and determine the geometric dimensions of the core samples; Simulated formation water was injected into the core sample until it reached a fully saturated state, and nuclear magnetic resonance scanning was performed on the core sample under simulated formation overburden conditions to obtain the spatial distribution of the baseline nuclear magnetic resonance signal and the initial porosity distribution of the core sample under a fully saturated state. Under simulated formation overburden conditions, a multi-stage gas injection pressure displacement experiment was conducted on the core sample using an intermittent displacement method to obtain quasi-steady-state displacement data of the core sample at each gas injection pressure. The quasi-steady-state displacement data includes the spatial distribution of water saturation, cumulative gas production, and cumulative water production. Based on the geometric dimensions and initial porosity distribution of the core sample, a one-dimensional two-phase flow numerical model was constructed with the parameters of the gas-water relative permeability curve and the capillary pressure curve as the parameters to be inverted. Construct an objective function based on the quasi-steady-state displacement data; Based on the objective function, an optimization algorithm is used to iteratively invert and solve the one-dimensional two-phase flow numerical model until a preset stopping condition is met, and the inversion stops to obtain the optimal gas-water relative permeability curve parameters and the optimal capillary pressure curve parameters. The preset stopping condition includes the rate of change of the objective function value within a preset number of consecutive iterations being less than a preset change threshold, or the number of iterations reaching a preset maximum number of iterations. The gas-water relative permeability curve of the target reservoir is determined based on the optimal gas-water relative permeability curve parameters, and the capillary pressure curve of the target reservoir is determined based on the optimal capillary pressure curve parameters.

2. The method for determining the relative permeability of reservoir gas and water according to claim 1, characterized in that, Simulated formation water was injected into the core sample until it reached full saturation. Under simulated formation overburden conditions, nuclear magnetic resonance (NMR) scanning was performed on the core sample to obtain the spatial distribution of the baseline NMR signal and the initial porosity distribution of the core sample under full saturation. Specifically, this included: After vacuuming the core sample, simulated formation water was injected under high pressure until the core sample reached a fully saturated state. Under simulated formation overburden conditions, nuclear magnetic resonance (NMR) scans were performed on core samples that had reached full saturation to obtain the spatial distribution of baseline NMR signals. The initial porosity distribution was calculated based on the spatial distribution of the reference NMR signal and the NMR signal-simulated formation water quality standard curve.

3. The method for determining the relative permeability of reservoir gas and water according to claim 1, characterized in that, Under simulated formation overburden conditions, multi-stage gas injection pressure displacement experiments were conducted on the core samples using an intermittent displacement method to obtain quasi-steady-state displacement data of the core samples at each gas injection pressure, specifically including: Determine the injection pressure at multiple levels and sort them in ascending order to obtain a pressure level sequence; By traversing each injection pressure in the pressure series, displacement experiments were conducted on the core samples at the current injection pressure using the following intermittent displacement steps: Initialize the number of iterations i = 1; Maintaining a constant current injection pressure, the core sample is subjected to the i-th displacement. Displacement is stopped after a first preset time, and the gas production and water production of the i-th displacement are obtained. After waiting for the second preset time, the core sample after the i-th displacement is subjected to nuclear magnetic resonance scanning to obtain the nuclear magnetic resonance T2 spectrum and nuclear magnetic signal spatial distribution of the i-th displacement at the current gas injection pressure. Based on the nuclear magnetic signal spatial distribution of the i-th displacement at the current gas injection pressure and the reference nuclear magnetic signal spatial distribution, the spatial distribution of water saturation of the i-th displacement is determined. If the displacement equilibrium condition is met, the cumulative gas production of the current stage gas injection pressure is obtained by summing the gas production of all displacements at the current stage gas injection pressure, and the cumulative water production of the current stage gas injection pressure is obtained by summing the water production of all displacements at the current stage gas injection pressure. The cumulative gas production, cumulative water production, and spatial distribution of water saturation of the current stage gas injection pressure are used as quasi-steady-state displacement data under the current stage gas injection pressure. The displacement equilibrium condition includes that the rate of change of water saturation at at least one axial position of the core sample is less than a first preset rate of change threshold. The rate of change of water saturation is calculated based on the spatial distribution of water saturation of the (i-1)th displacement and the spatial distribution of water saturation of the ith displacement when i≥2. If the displacement equilibrium condition is not met when i=1 or i≥2, then repeat the above intermittent displacement steps to perform the (i+1)th displacement experiment at the current stage injection pressure. If the termination condition is met, the displacement experiment ends, and quasi-steady-state displacement data of the core sample under each injection pressure level are obtained. The termination condition includes the completion of pressure level sequence traversal, or the nuclear magnetic resonance T2 spectrum showing only bound water signal, or the rate of change of the overall water saturation of the core sample under the current injection pressure level within a consecutive preset number of levels being less than a second preset rate of change threshold. The overall water saturation is the arithmetic mean of the water saturation at all axial positions of the core sample in the spatial distribution of water saturation under the current injection pressure level. If the termination condition is not met, the next level of gas injection pressure displacement experiment will be carried out on the core sample.

4. The method for determining the relative permeability of reservoir gas and water according to claim 1, characterized in that, The objective function is: ； Where J represents the value of the objective function; Indicates the first The cumulative gas production obtained from a one-dimensional two-phase flow numerical model at each state point; j={1,2,3,...,n} This represents the total number of state points that record cumulative gas production and water production data. Indicates the first The cumulative gas production measured in experiments at each state point; Indicates the first The cumulative water production obtained from the one-dimensional two-phase flow numerical model at each state point; Indicates the first Cumulative water production measured in experiments at each state point; Indicates the first The monitoring time, the Water saturation obtained from a one-dimensional two-phase flow numerical model at the axial position of a core sample; Indicates the first The monitoring time, the The experimentally measured water saturation at axial locations of core samples; t={1,2,3,...,m} This represents the total number of times when NMR scans were performed to measure the spatial distribution of water saturation; l = {1, 2, 3, ..., L}. Indicates the total number of core samples at axial positions; , and These represent the weighting coefficients for cumulative gas production, cumulative water production, and spatial distribution of water saturation, respectively.

5. The method for determining the relative permeability of reservoir gas and water according to claim 1, characterized in that, The one-dimensional two-phase flow numerical model includes the gas phase equation, the aqueous phase equation, and auxiliary equations; The gas phase equation is as follows: ； The aqueous phase equation is: ； The auxiliary equation is: ； ； in, Indicates the axial position of the core sample; Indicates time; This indicates the absolute permeability of the core sample; and These represent the relative permeability of the gas phase and the relative permeability of the aqueous phase, respectively. and These represent the gas phase pressure and the water phase pressure, respectively. Indicates the pressure in the air-water capillary tube; and These represent the viscosity of the gas phase and the viscosity of the aqueous phase, respectively. and These represent the volume coefficients of the gas phase and the aqueous phase, respectively. Indicates the porosity of the core sample; and These represent gas saturation and water saturation, respectively. and These represent the source and sink terms in the gas phase and the source and sink terms in the aqueous phase, respectively.

6. The method for determining the relative permeability of reservoir gas and water according to claim 1, characterized in that, The gas-water relative permeability curve of the target reservoir is determined based on the optimal gas-water relative permeability curve parameters, and the capillary pressure curve of the target reservoir is determined based on the optimal capillary pressure curve parameters, specifically including: The normalized water saturation at each axial location point of the core sample is calculated using the following formula: ； in, This represents the normalized water saturation at the axial position x of the core sample. This indicates the water saturation at the axial position x of the core sample; Indicates the degree of bound water saturation; Indicates critical gas saturation; The relative permeability of the gas phase and the relative permeability of the water phase at the normalized water saturation corresponding to the axial position of each core sample are calculated using the following formula, thus obtaining the gas-water relative permeability curve: ； ； in, and These represent the relative permeability of the water phase and the relative permeability of the gas phase at the normalized water saturation at the axial position x of the core sample, respectively. and These represent the relative permeability of the aqueous phase at the endpoint and the relative permeability of the gas phase at the endpoint, respectively. and These represent the water phase permeability index and the gas phase permeability index, respectively. The capillary pressure values ​​under different normalized water saturation levels are calculated using the following formula, thus obtaining the capillary pressure curve: ； in, This represents the capillary pressure value corresponding to the normalized water saturation at the axial position x of the core sample. Indicates the inlet capillary pressure; This represents the pore size distribution index.

7. The method for determining the relative permeability of reservoir gas and water according to claim 1, characterized in that, The optimization algorithm includes the Levenberg-Marquardt algorithm or a genetic algorithm.

8. The method for determining the relative permeability of reservoir gas and water according to claim 2, characterized in that, The NMR signal-simulated formation water quality standard curve is obtained by performing NMR scans on multiple sets of simulated formation water with different masses, and establishing a linear quantitative relationship between the simulated formation water quality and the total amplitude of the NMR signal. The expression for the NMR signal-simulated formation water quality standard curve is: ； in, This indicates the simulated formation water quality; Nuclear magnetic resonance signal - linear scaling factor for simulating formation water quality; This represents the total amplitude of the nuclear magnetic resonance signal; This represents the correction factor.

9. The method for determining the relative permeability of reservoir gas and water according to claim 3, characterized in that, The formula for calculating water saturation is: ； in, This indicates the water saturation at the axial position x of the core sample at time t; The nuclear magnetic resonance signal represents the axial position x of the core sample at time t; The reference NMR signal represents the axial position x of the core sample.

10. The method for determining the relative permeability of reservoir gas and water according to claim 1, characterized in that, The target reservoirs include coal-rock reservoirs or tight sandstone reservoirs.

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