A method for simulating variable reservoir effect caused by downhole throttling of gas well

Abstract

The application discloses a method for simulating the variable well storage effect caused by downhole throttling of a gas well, which comprises the following steps: step 1) establishing a dimensionless wellbore material balance equation under downhole throttling conditions to obtain a dimensionless pressure value under the downhole throttling conditions; step 2) drawing a double-log pressure derivative curve chart based on the dimensionless pressure value in step 1) to simulate the variable well storage effect under different parameter combinations under the downhole throttling conditions; and step 3) making a normalized pseudo-pressure difference and its derivative and a measured curve chart of the shut-in time based on actual pressure buildup data under the throttling conditions, and drawing the measured curve chart on the double-log pressure derivative curve chart in step 2) to keep the measured curve chart coinciding with the double-log pressure derivative curve chart, and solving relevant parameters of the variable well storage stage according to a fitting key point, so that the variable well storage effect caused by the downhole throttling of the gas well is described through the relevant parameters.

Description

TECHNICAL FIELD

[0001] The application belongs to the technical field of gas field development, and particularly relates to a simulation method of variable well storage effect caused by downhole throttling of a gas well. BACKGROUND

[0002] At present, three methods are used to describe the variable well storage effect at home and abroad, which are Fair method, Hegman method and Spivey method. The Fair method is mainly used to simulate the variable well storage effect caused by wellbore phase separation and thermal effect. The Hegman method is an improvement of the Fair method, and the two methods simulate the same mechanism of the variable well storage effect, with the only difference being that the mathematical models for describing the phase transition pressure are different. The Fair method adopts an exponential method, and the Hegman method adopts an error function. The Spivey method simulates the variable well storage phenomenon caused by the sealing leakage of the oil-casing annular space and the short and wide fracture-wellbore near the well. Although the above methods can simulate the variable well storage effect, the application has certain specificity, and the simulation method needs to be selected according to the mechanism of the variable well storage phenomenon. The analysis of the actual pressure buildup test data shows that the variable well storage effect exists under the downhole throttling condition of the tight gas reservoir, but the mechanism is different from the variable well storage mechanism simulated by the above three methods. The adaptability of the above three methods for simulating the variable well storage phenomenon under the downhole throttling condition of the gas well is poor, and the simulation result has low reliability. Therefore, in order to improve the description of the downhole throttling variable well storage effect, it is urgent to study the downhole throttling variable well storage model, research the characteristics of the downhole throttling variable well storage effect, and improve the reliability of the downhole throttling variable well storage interpretation. SUMMARY

[0003] The application aims to overcome the above problems of the prior art, and provides a simulation method of variable well storage effect caused by downhole throttling of a gas well, which overcomes the problems of the prior art, such as 1: the existing description method is not suitable for the variable well storage effect existing under the downhole throttling condition of a tight gas reservoir; 2: the mechanism of the variable well storage effect existing under the downhole throttling condition of the tight gas reservoir is different from the variable well storage mechanism simulated by the existing method, and the adaptability of the existing method for simulating the variable well storage phenomenon under the downhole throttling condition of the gas well is poor; and 3: the simulation result of the existing method has low reliability.

[0004] In order to solve the technical problem, the technical scheme of the application is as follows:

[0005] Step 1) establishing a dimensionless wellbore material balance equation under the downhole throttling condition to obtain a dimensionless pressure value under the downhole throttling condition;

[0006] Step 2) drawing a double-logarithmic pressure derivative curve graph based on the dimensionless pressure value in step 1) to simulate the variable well storage effect change characteristics under different parameter combinations under the downhole throttling condition;

[0007] Step 3) Based on the actual pressure buildup data under the throttling condition, a normalized pseudo pressure difference and its derivative versus shut-in time measured curve is drawn, and is plotted on the log-log pressure derivative curve chart in step 2), the measured curve is kept coinciding with the log-log pressure derivative curve chart, and the relevant parameters of the variable reservoir stage caused by the downhole throttling are solved according to the fitting key points, and the variable reservoir effect caused by the downhole throttling of the gas well is described by the relevant parameters.

[0008] Preferably, the step 1) is to establish the dimensionless wellbore material balance equation under the downhole throttling condition, wherein the dimensionless wellbore material balance equation is:

[0009]

[0010] Wherein:

[0011] - is the symbol of partial differential;

[0012] - is the dimensionless pseudo pressure;

[0013] - is the dimensionless pseudo pressure difference;

[0014] - is the dimensionless distance;

[0015] - is the wellbore storage coefficient at the upper end of the throttle;

[0016] - is the wellbore storage coefficient at the lower end of the throttle;

[0017] - is the dimensionless depth of the throttle;

[0018] - is the dimensionless time;

[0019] - is the dimensionless time related to the change of pressure difference.

[0020] Preferably, the step 1) is to solve the dimensionless wellbore material balance equation by Laplace transform, and the stehfest method is used to calculate the Laplace space solution to obtain the dimensionless pressure value under the downhole throttling condition.

[0021] Preferably, the double logarithmic pressure derivative graph pattern in step 2) includes pressure and pressure derivative graphs under different dimensionless choke depths, pressure and pressure derivative graphs under different dimensionless time related to pressure difference changes, pressure and pressure derivative graphs under different ratios of reservoir coefficients above and below the choke, and pressure and pressure derivative graphs under different dimensionless pseudo pressure differences, which simulate the variable well storage effect under different parameter combinations under the downhole throttling condition.

[0022] Preferably, the pressure and pressure derivative graphs under different dimensionless choke depths, the pressure and pressure derivative graphs under different dimensionless time related to pressure difference changes, the pressure and pressure derivative graphs under different ratios of reservoir coefficients above and below the choke, and the pressure and pressure derivative graphs under different dimensionless pseudo pressure differences can all obtain the change trend of the initial wellbore reservoir coefficient and the final wellbore reservoir coefficient.

[0023] Preferably, in step 3), the measured curve is plotted on the graph pattern of the double logarithmic pressure derivative graph in step 2), the double logarithmic pressure derivative graph pattern that best matches the measured curve is found, the measured curve is kept coinciding with the graph pattern of the double logarithmic pressure derivative graph, the fitting points are selected, the variable well storage model related parameters are solved by using nonlinear regression, and the variable well storage effect caused by the downhole throttling of the gas well is described by the related parameters.

[0024] Preferably, the variable well storage model related parameters include the final wellbore reservoir coefficient, the initial wellbore reservoir coefficient value, and the variable well storage transition time, and the variable well storage effect caused by the downhole throttling of the gas well is described by the variable well storage model related parameters.

[0025] Compared with the prior art, the application has the following advantages:

[0026] (1) The application creates a downhole and throttling outlet pressure difference mathematical model, describes the pressure difference change between the downhole and the throttling outlet in the initial pressure recovery stage by using the mathematical model, introduces a wellbore material balance equation to obtain a dimensionless pressure value under the downhole throttling condition, then plots a double logarithmic pressure derivative graph pattern based on the dimensionless pressure value, simulates the variable well storage effect under different parameter combinations under the downhole throttling condition, then makes a normalized pseudo pressure difference and its derivative and a measured curve of the shut-in time based on the actual pressure recovery data under the throttling condition, plots the measured curve on the graph pattern of the double logarithmic pressure derivative graph, keeps the measured curve coinciding with the graph pattern of the double logarithmic pressure derivative graph, solves the related parameters of the variable well storage stage according to the fitting key points, describes the variable well storage effect caused by the downhole throttling of the gas well by using the related parameters, and realizes the model establishment, simulation and description analysis of the variable well storage effect caused by the downhole throttling.

[0027] (2) The application establishes a corresponding simulation analysis method for the variable well storage effect under the downhole throttling condition, realizes effective simulation of the variable well storage effect caused by the downhole throttling effect of the gas well, simulates and analyzes the variable well storage effect in the early stage of pressure recovery, realizes the interpretation and analysis of the variable well storage phenomenon under the downhole throttling condition, and improves the reliability of the interpretation result.

[0028] (3) The simulation method of the application is simple, fast, practical, and has high reliability of the described variable well storage effect, and the described variable well storage effect provides a favorable basis for later gas field development. BRIEF DESCRIPTION OF DRAWINGS

[0029] Figure 1 The pressure graph under different dimensionless throttling device depth conditions in the embodiment 8 of the application;

[0030] Figure 2 The pressure derivative graph under different dimensionless throttling device depth conditions in the embodiment 8 of the application;

[0031] Figure 3 The pressure graph under different dimensionless time conditions related to the change of dimensionless pressure difference in the embodiment 8 of the application;

[0032] Figure 4 The pressure derivative graph under different dimensionless time conditions related to the change of dimensionless pressure difference in the embodiment 8 of the application;

[0033] Figure 5 The pressure graph under different ratios of wellbore storage coefficients above and below the throttling device in the embodiment 8 of the application;

[0034] Figure 6 The pressure derivative graph under different ratios of wellbore storage coefficients above and below the throttling device in the embodiment 8 of the application;

[0035] Figure 7 The pressure graph under different dimensionless pseudo pressure difference conditions in the embodiment 8 of the application;

[0036] Figure 8 The pressure derivative graph under different dimensionless pseudo pressure difference conditions in the embodiment 8 of the application;

[0037] Figure 9 The fitting graph of the measured curve and the simulation fitting curve in the embodiment 8 of the application. DETAILED DESCRIPTION

[0038] The specific embodiment of the application will be described below in combination with the embodiments:

[0039] It should be noted that the structure, proportion, size, etc. shown in the specification are only used to understand and read the content disclosed by the skilled in the art, and are not used to limit the conditions that can be implemented by the application. Any modification of structure, change of proportion relationship or adjustment of size, which does not affect the effect and purpose that can be achieved by the application, should still fall within the scope covered by the disclosed technology.

[0040] Meanwhile, the terms such as "upper", "lower", "left", "right", "middle" and "one" used in the specification are only for the convenience of clear description, and are not used to limit the scope of the application. The change or adjustment of the relative relationship is also considered as the implementation of the application without substantial change of the technical content.

[0041] The Laplace transform is a mathematical transform method, which aims to eliminate time from the partial differential equation and convert it into a first-order differential equation.

[0042] The stehfest method is a calculation method of Laplace numerical inversion, which inverts the Laplace space solution to the real space.

[0043] Embodiment 1

[0044] The application discloses a simulation method of variable well storage effect caused by downhole throttling of a gas well, comprising the following steps:

[0045] Step 1) establishing a dimensionless wellbore material balance equation under downhole throttling conditions to obtain a dimensionless pressure value under downhole throttling conditions;

[0046] Step 2) based on the dimensionless pressure value in step 1), a double logarithmic pressure derivative curve chart is drawn to simulate the variable well storage effect under different parameter combinations under downhole throttling conditions;

[0047] Step 3) based on the actual pressure recovery data under throttling conditions, a normalized pseudo-pressure difference and its derivative and a measured curve graph of shut-in time are made, and are plotted on the double logarithmic pressure derivative curve chart in step 2), so that the measured curve graph and the double logarithmic pressure derivative curve chart are kept coincident, the related parameters of the variable well storage stage are solved according to the fitting key points, and the variable well storage effect caused by downhole throttling of the gas well is described through the related parameters.

[0048] Embodiment 2

[0049] The application discloses a simulation method of variable well storage effect caused by downhole throttling of a gas well, comprising the following steps:

[0050] Step 1) establishing a dimensionless wellbore material balance equation under downhole throttling conditions to obtain a dimensionless pressure value under downhole throttling conditions;

[0051] Step 2) based on the dimensionless pressure value in step 1), a double logarithmic pressure derivative curve chart is drawn to simulate the variable well storage effect under different parameter combinations under the downhole throttling condition;

[0052] Step 3) based on the actual pressure recovery data under the throttling condition, a measured curve chart of normalized pseudo-pressure difference and its derivative and shut-in time is made, and is plotted on the double logarithmic pressure derivative curve chart in step 2), the measured curve chart is kept coinciding with the double logarithmic pressure derivative curve chart, the related parameters of the variable well storage stage are solved according to the fitting key points, and the variable well storage effect caused by the downhole throttling of the gas well is described through the related parameters.

[0053] Preferably, the dimensionless wellbore material balance equation under the downhole throttling condition is established in step 1), wherein the dimensionless wellbore material balance equation is:

[0054]

[0055] Wherein:

[0056] - the symbol of partial differential;

[0057] - dimensionless pseudo-pressure;

[0058] - dimensionless pseudo-pressure difference;

[0059] - dimensionless distance;

[0060] - wellbore storage coefficient at the upper end of the throttling device;

[0061] - wellbore storage coefficient at the lower end of the throttling device;

[0062] - dimensionless depth of the throttling device;

[0063] - dimensionless time;

[0064] - dimensionless time related to the change of pressure difference.

[0065] Example 3

[0066] The application discloses a variable well storage effect simulation method caused by downhole throttling of a gas well, which comprises the following steps:

[0067] Step 1) a dimensionless wellbore material balance equation under the downhole throttling condition is established, and a dimensionless pressure value under the downhole throttling condition is obtained.

[0068] Step 2) Based on the dimensionless pressure value in step 1), a double logarithmic pressure derivative curve chart is drawn to simulate the variable well storage effect under different parameter combinations under downhole throttling conditions;

[0069] Step 3) Based on the actual pressure recovery data under throttling conditions, a measured curve of normalized pseudo-pressure difference and its derivative and shut-in time is made, and is plotted on the double logarithmic pressure derivative curve chart in step 2), the measured curve and the double logarithmic pressure derivative curve chart are kept coincident, the relevant parameters of the variable well storage stage are solved according to the fitting key points, and the variable well storage effect caused by downhole throttling of the gas well is described by the relevant parameters.

[0070] Preferably, the dimensionless wellbore material balance equation under downhole throttling conditions is established in step 1), wherein the dimensionless wellbore material balance equation is:

[0071]

[0072] Wherein:

[0073] - is the symbol of partial differential;

[0074] - dimensionless pseudo-pressure;

[0075] - dimensionless pseudo-pressure difference;

[0076] - dimensionless distance;

[0077] - wellbore storage coefficient at the upper end of the choke;

[0078] - wellbore storage coefficient at the lower end of the choke;

[0079] - dimensionless choke depth;

[0080] - dimensionless time;

[0081] - dimensionless time related to pressure difference change.

[0082] Preferably, step 1) is to solve the dimensionless wellbore material balance equation by Laplace transform, and the stehfest method is used to calculate the Laplace space solution to obtain the dimensionless pressure value under downhole throttling conditions.

[0083] Example 4

[0084] The application discloses a method for simulating variable well storage effect caused by downhole throttling of a gas well.

[0085] Step 1) establishing a dimensionless wellbore material balance equation under downhole throttling conditions to obtain a dimensionless pressure value under downhole throttling conditions;

[0086] Step 2) based on the dimensionless pressure value in step 1), a double-log pressure derivative curve chart is drawn to simulate the variable well storage effect under different parameter combinations under downhole throttling conditions;

[0087] Step 3) based on actual pressure recovery data under throttling conditions, a normalized pseudo-pressure difference and its derivative and a measured curve of shut-in time are drawn on the double-log pressure derivative curve chart in step 2), the measured curve and the double-log pressure derivative curve chart are kept coincident, relevant parameters of the variable well storage stage are solved according to a fitting key point, and the variable well storage effect caused by downhole throttling of the gas well is described through the relevant parameters.

[0088] Preferably, the dimensionless wellbore material balance equation under downhole throttling conditions in step 1) is as follows:

[0089]

[0090] Wherein,

[0091] is a symbol of partial differential;

[0092] is a dimensionless pseudo-pressure;

[0093] is a dimensionless pseudo-pressure difference;

[0094] is a dimensionless distance;

[0095] is a wellbore storage coefficient at an upper end of a throttle;

[0096] is a wellbore storage coefficient at a lower end of the throttle;

[0097] is a dimensionless throttle depth;

[0098] is a dimensionless time;

[0099] is a dimensionless time related to pressure difference change.

[0100] Preferably, the step 1) is to solve the dimensionless wellbore material balance equation under the downhole throttling condition by Laplace transform, and to calculate the dimensionless pressure value under the downhole throttling condition by using the stehfest method.

[0101] Preferably, the double logarithmic pressure derivative curve chart in the step 2) includes pressure and pressure derivative graphs under different dimensionless throttling depth conditions, pressure and pressure derivative graphs under different dimensionless time conditions related to dimensionless pressure difference changes, pressure and pressure derivative graphs under different dimensionless reservoir coefficient ratio conditions above and below the throttling device, and pressure and pressure derivative graphs under different dimensionless pseudo pressure difference conditions, so as to simulate the variable well storage effect under different parameter combinations under the downhole throttling condition by the double logarithmic pressure derivative curve chart.

[0102] Preferably, the pressure and pressure derivative graphs under different dimensionless throttling depth conditions, the pressure and pressure derivative graphs under different dimensionless time conditions related to dimensionless pressure difference changes, the pressure and pressure derivative graphs under different dimensionless reservoir coefficient ratio conditions above and below the throttling device, and the pressure and pressure derivative graphs under different dimensionless pseudo pressure difference conditions can all obtain the change trend of the initial wellbore reservoir coefficient and the final wellbore reservoir coefficient.

[0103] Embodiment 5

[0104] The application discloses a variable well storage effect simulation method caused by downhole throttling of a gas well.

[0105] Step 1) establishing a dimensionless wellbore material balance equation under the downhole throttling condition to obtain a dimensionless pressure value under the downhole throttling condition;

[0106] Step 2) based on the dimensionless pressure value in the step 1), a double logarithmic pressure derivative curve chart is drawn to simulate the variable well storage effect under different parameter combinations under the downhole throttling condition;

[0107] Step 3) based on the actual pressure recovery data under the throttling condition, a normalized pseudo pressure difference and its derivative and a measured curve graph of the shut-in time are drawn on the chart of the double logarithmic pressure derivative curve chart in the step 2), the measured curve graph and the chart of the double logarithmic pressure derivative curve chart are kept coincident, relevant parameters of the variable well storage stage are solved according to a fitting key point, and the variable well storage effect caused by the downhole throttling of the gas well is described through the relevant parameters.

[0108] Preferably, the step 1) establishes the dimensionless wellbore material balance equation under the downhole throttling condition, wherein the dimensionless wellbore material balance equation is:

[0109]

[0110] In the formula, P is a dimensionless pressure, t is a dimensionless time, and K is a dimensionless reservoir coefficient.

[0111] - symbol of partial derivative;

[0112] - dimensionless pseudo pressure;

[0113] - dimensionless pseudo pressure difference;

[0114] - dimensionless distance;

[0115] - wellbore storage coefficient at the upper end of the choke;

[0116] - wellbore storage coefficient at the lower end of the choke;

[0117] - dimensionless choke depth;

[0118] - dimensionless time;

[0119] - dimensionless time related to the change of pressure difference.

[0120] Preferably, the step 1) is to solve the dimensionless wellbore material balance equation by Laplace transform, and to calculate the Laplace space solution by Stehfest method to obtain the dimensionless pressure value under the downhole throttling condition.

[0121] Preferably, the graph of the double logarithmic pressure derivative curve in the step 2) includes pressure and pressure derivative graphs under different dimensionless choke depths, pressure and pressure derivative graphs under different dimensionless times related to the change of pressure difference, pressure and pressure derivative graphs under different ratios of wellbore storage coefficients above and below the choke, and pressure and pressure derivative graphs under different dimensionless pseudo pressure differences, so as to simulate the change characteristics of the variable well storage effect under different parameter combinations under the downhole throttling condition by the double logarithmic pressure derivative curve.

[0122] Preferably, the pressure and pressure derivative graphs under different dimensionless choke depths, the pressure and pressure derivative graphs under different dimensionless times related to the change of pressure difference, the pressure and pressure derivative graphs under different ratios of wellbore storage coefficients above and below the choke, and the pressure and pressure derivative graphs under different dimensionless pseudo pressure differences can all obtain the change trend of the initial wellbore storage coefficient and the final wellbore storage coefficient.

[0123] Preferably, the step 3) is that the measured curve is plotted on the graph of the double logarithmic pressure derivative curve in step 2), the double logarithmic pressure derivative curve graph that matches the measured curve is found, the measured curve is kept coinciding with the graph of the double logarithmic pressure derivative curve, the fitting points are selected, the relevant parameters of the variable well storage model are solved by using the nonlinear regression, and the variable well storage effect caused by the downhole throttling of the gas well is described through the relevant parameters.

[0124] Embodiment 6

[0125] The application discloses a simulation method for a variable well storage effect caused by downhole throttling of a gas well.

[0126] The step 1) is to establish a dimensionless wellbore material balance equation under the downhole throttling condition, and a dimensionless pressure value under the downhole throttling condition is obtained.

[0127] The step 2) is to plot a double logarithmic pressure derivative curve graph based on the dimensionless pressure value in step 1), and to simulate the variable well storage effect under different parameter combinations under the downhole throttling condition.

[0128] The step 3) is to make a measured curve of a normalized pseudo pressure difference and its derivative and a shut-in time based on actual pressure recovery data under the throttling condition, to plot the measured curve on the graph of the double logarithmic pressure derivative curve in step 2), to keep the measured curve coinciding with the graph of the double logarithmic pressure derivative curve, to solve the relevant parameters of the variable well storage stage according to the fitting key points, and to describe the variable well storage effect caused by the downhole throttling of the gas well through the relevant parameters.

[0129] Preferably, the step 1) is to establish a dimensionless wellbore material balance equation under the downhole throttling condition, and the dimensionless wellbore material balance equation is as follows:

[0130]

[0131] Wherein:

[0132] - the symbol of the partial differential;

[0133] - the dimensionless pseudo pressure;

[0134] - the dimensionless pseudo pressure difference;

[0135] - the dimensionless distance;

[0136] - the wellbore storage coefficient at the upper end of the throttler;

[0137] - the wellbore storage coefficient at the lower end of the throttler;

[0138] - dimensionless choke depth;

[0139] - dimensionless time;

[0140] - dimensionless time related to differential pressure change.

[0141] Preferably, the step 1) is to solve the dimensionless wellbore material balance equation by Laplace transform, and to calculate the dimensionless pressure value under the downhole throttling condition by using the stehfest method for the Laplace space solution.

[0142] Preferably, the log-log pressure derivative curve chart in the step 2) includes pressure and pressure derivative charts under different dimensionless choke depths, pressure and pressure derivative charts under different dimensionless times related to differential pressure change, pressure and pressure derivative charts under different ratios of wellbore storage coefficients above and below the choke, and pressure and pressure derivative charts under different dimensionless pseudo-pressure differences, so as to simulate the variable well storage effect under different parameter combinations under the downhole throttling condition by the log-log pressure derivative curve.

[0143] Preferably, the pressure and pressure derivative charts under different dimensionless choke depths, the pressure and pressure derivative charts under different dimensionless times related to differential pressure change, the pressure and pressure derivative charts under different ratios of wellbore storage coefficients above and below the choke, and the pressure and pressure derivative charts under different dimensionless pseudo-pressure differences can all obtain the change trend of the initial wellbore storage coefficient and the final wellbore storage coefficient.

[0144] Preferably, in the step 3), the measured curve is plotted on the chart of the log-log pressure derivative curve in the step 2), the log-log pressure derivative curve chart that best matches the measured curve is found, the measured curve and the chart of the log-log pressure derivative curve are kept coincident, the fitting points are selected, the variable well storage model related parameters are obtained by using the nonlinear regression, and the variable well storage effect caused by the downhole throttling of the gas well is described by the variable well storage model related parameters.

[0145] Preferably, the variable well storage model related parameters include the final wellbore storage coefficient, the initial wellbore storage coefficient value, and the variable well storage transition time, and the variable well storage effect caused by the downhole throttling of the gas well is described by the variable well storage model related parameters.

[0146] Example 7

[0147] Establishing the dimensionless wellbore material balance equation under the downhole throttling condition

[0148] Through in-depth study, it is shown that the main reason for the variable well storage phenomenon of the wellbore under the downhole throttling process condition is that the pressure difference between the well bottom and the throttling outlet changes nonlinearly in the initial stage of pressure recovery, thereby causing the variable well storage effect. Therefore, a mathematical model of the pressure difference between the well bottom and the throttling outlet is created, the change of the pressure difference between the well bottom and the throttling outlet in the initial stage of pressure recovery is described by the mathematical model, and the wellbore material balance equation is introduced to realize the model establishment and simulation analysis of the variable well storage effect caused by the downhole throttling.

[0149] 1) Description of variable well storage effect under downhole throttling condition

[0150] When the gas well is produced in the downhole throttling process mode, the throttling action causes the pressure difference between the throttling inlet and the throttling outlet. When the well is shut in for pressure recovery, the pressure difference between the well bottom and the throttling outlet changes nonlinearly in the initial stage of pressure recovery, the wellbore storage coefficients above and below the throttling also change nonlinearly, causing the nonlinear change of the wellbore storage coefficient, which is also called the variable well storage effect.

[0151] 2) Model of the change of the pressure difference ΔP between the well bottom and the throttling outlet with time in the pressure recovery process

[0152] The main reason for the variable well storage phenomenon under the throttling condition is the pressure difference ΔP, and it is crucial to establish the model of the change of the pressure difference ΔP with time in the wellbore pressure recovery process. For the first time, the function of the pressure difference and time is defined as an exponential form (the function of the pressure difference and time is defined as an exponential form because the formula is simple in the Laplace space form, and it is consistent with the actual situation, and it is more convenient to solve later) :

[0153] (1)

[0154] Wherein:

[0155] ΔP is the pressure difference between the well bottom and the throttling outlet;

[0156] ΔPmax is the maximum value of the pressure difference;

[0157] ΔPmin is the minimum value of the pressure difference;

[0158] t is the time related to the change of the pressure difference;

[0159] t is the pressure recovery time.

[0160] 3) Establishment of wellbore material balance equation

[0161] According to the material balance theory, the mathematical relationship between the pressure difference between the throttling outlet and the well bottom established above is substituted into the wellbore material balance equation of the flow continuation section, and the wellbore material balance equation of the flow continuation section in the initial stage of pressure recovery under the downhole throttling condition is established, which is shown in formula 2:

[0162] (2)

[0163] where:

[0164] B is the choke upper-end wellbore storage coefficient;

[0165] B is the choke lower-end wellbore storage coefficient;

[0166] P is the bottomhole pressure;

[0167] Q is the flowing-face production rate;

[0168] Q is the surface production rate.

[0169] 4) Dimensionless wellbore material balance equation

[0170] Introducing relevant dimensionless quantities, the wellbore material balance equation is converted to the form under the condition of pseudo-pressure, see Equation 3:

[0171] (3)

[0172] where:

[0173] - is the symbol of partial derivative;

[0174] - is the dimensionless pseudo-pressure;

[0175] - is the dimensionless pseudo-pressure difference;

[0176] - is the dimensionless distance;

[0177] - is the choke upper-end wellbore storage coefficient;

[0178] - is the choke lower-end wellbore storage coefficient;

[0179] - is the dimensionless choke depth;

[0180] - is the dimensionless time;

[0181] - is the dimensionless time related to the change of pressure differential.

[0182] Example 8

[0183] The dimensionless wellbore mass balance equation under downhole throttling conditions in Example 7 was subjected to a Laplace transform. The Stehfest method was used to calculate the Laplace space solution to obtain the dimensionless pressure value under downhole throttling conditions. Based on the dimensionless bottom hole pressure value, a double logarithmic pressure derivative curve was plotted (see Appendix). Figures 1-8 , attached Figures 1-8 The variation characteristics of reservoir effect under different parameter combinations under throttling conditions were simulated.

[0184] Figure 1 and Figure 2 Pressure versus pressure derivative plots under different dimensionless throttle depth conditions

[0185] pass Figure 1 It can be seen that the dimensionless pressure first increases rapidly with dimensionless time, and then increases slowly; through Figure 2 It can be seen that the dimensionless pressure derivative first increases with dimensionless time, then decreases rapidly, and then increases again; from Figure 1 and 2 It can be seen that as the depth of the throttle increases (Hd is 0.6, 0.7, 0.8), the dimensionless pressure and pressure derivative curves shift to the left, thus the initial wellbore reservoir coefficient decreases and the final wellbore reservoir coefficient increases.

[0186] Figure 3 and Figure 4 Pressure and pressure derivative plots under dimensionless time conditions related to dimensionless pressure difference changes.

[0187] Under dimensionless time conditions related to dimensionless pressure difference changes, through Figure 3 It can be seen that the dimensionless pressure first increases rapidly with dimensionless time, and then increases slowly; through Figure 4 It can be seen that the dimensionless pressure derivative first increases with dimensionless time, then decreases rapidly, and then increases again; from Figure 3 and Figure 4 It can be seen that as the dimensionless time related to the dimensionless pressure difference increases ( (For values ​​of 0.005, 0.01, and 0.05), the dimensionless pressure and pressure derivative curves shift to the right, and the degree of concavity in the dimensionless pressure derivative curve decreases; therefore, the initial wellbore storage coefficient decreases, while the final wellbore storage coefficient remains unchanged, and the duration of the variable well storage effect is reduced.

[0188] Figure 5 and Figure 6 Pressure and pressure derivative diagrams under different reservoir coefficient ratios above and below the throttle.

[0189] pass Figure 5 It can be seen that the dimensionless pressure first increases rapidly with dimensionless time, and then increases slowly; from Figure 6It can be seen that the dimensionless pressure derivative first increases with dimensionless time, then decreases rapidly, and then increases again; from Figure 5 and Figure 6 It can be seen that as the ratio of the reservoir coefficient above the throttle to the reservoir coefficient below the throttle increases ( / (For values ​​of 1.1, 1.5, and 2), the dimensionless pressure and pressure derivative curves shift to the left; therefore, the initial wellbore reservoir coefficient decreases, and the final wellbore reservoir coefficient increases, but the change is not significant.

[0190] Figure 7 and Figure 8 Pressure and pressure derivative plots under different dimensionless pseudo-pressure difference conditions

[0191] pass Figure 7 It can be seen that the change trend of dimensionless pressure with dimensionless time differs depending on the dimensionless initial pressure difference; when the dimensionless pressure difference is small, the dimensionless pressure first increases rapidly with dimensionless time, then increases slowly; when the dimensionless pressure difference is large, the dimensionless pressure first increases rapidly with dimensionless time, then decreases slowly. Figure 8 It can be seen that the trend of the dimensionless pressure derivative with dimensionless time differs depending on the dimensionless initial pressure difference. When the dimensionless pressure difference is small, the dimensionless pressure derivative first increases with dimensionless time, then decreases rapidly, and then increases again. When the dimensionless pressure difference is large, the dimensionless pressure derivative first increases with dimensionless time, then decreases rapidly, becomes negative, and then increases again. Figure 7 and Figure 8 It can be seen that as the dimensionless initial pressure difference increases ( (For values ​​of 0.2, 0.5, and 2), the dimensionless pressure and pressure derivative curves shift to the left; therefore, the initial wellbore storage coefficient decreases, the final wellbore storage coefficient increases, and the influence time of the variable well storage phenomenon is longer.

[0192] The double logarithmic pressure derivative curve chart is shown in... Figures 1-8 Select one of the following lines to form a chart: Figure 1 and Figure 2 The dimensionless throttles have the same depth. Figure 3 and Figure 4 In order to ensure that the dimensionless time related to the dimensionless pressure difference change is the same, Figure 5 and Figure 6 The ratio of the reservoir coefficient above and below the throttle is the same. Figure 7 and Figure 8 The dimensionless pseudo-pressure difference is the same.

[0193] like Figure 9 Specifically, taking the SX well as an example, the pressure recovery data of the SX well was plotted as a double logarithmic curve, see [link / details]. Figure 9 The measured curves are plotted on a double logarithmic pressure derivative curve graph.Figures 1-8 ) to find the best match of the measured curve, see Figure 9 ) the best match of the measured curve, then select the fitting point (see Figure 9 ) the fitting point) on the best match of the measured curve, and use nonlinear regression to obtain the final wellbore storage coefficient of 0.56 m 3 / MPa, the initial wellbore storage coefficient value of 0.39 m 3 / MPa, and the variable well storage transition time of 1.8 hours.

[0194] The present application creates a mathematical model of the pressure difference between the bottom hole and the choke outlet, uses the mathematical model to describe the change of the pressure difference between the bottom hole and the choke outlet in the early stage of pressure recovery, introduces the wellbore material balance equation to obtain the dimensionless pressure value under the downhole throttling condition, then draws a double logarithmic pressure derivative curve chart based on the dimensionless pressure value, simulates the variable well storage effect under different parameter combinations under the downhole throttling condition, then makes a normalized pseudo pressure difference and its derivative and the measured curve of the shut-in time based on the actual pressure recovery data under the throttling condition, and draws it on the double logarithmic pressure derivative curve chart, keeps the measured curve and the double logarithmic pressure derivative curve chart coincident, solves the relevant parameters of the variable well storage stage according to the fitting key points, describes the variable well storage effect caused by the downhole throttling of the gas well through the relevant parameters, and realizes the model establishment and simulation description and analysis of the variable well storage effect caused by the downhole throttling.

[0195] The present application establishes a corresponding simulation analysis method for the variable well storage effect under the downhole throttling condition, realizes the effective simulation of the variable well storage effect caused by the downhole throttling effect of the gas well, simulates the variable well storage effect in the early stage of pressure recovery, realizes the interpretation and analysis of the variable well storage phenomenon under the downhole throttling condition, and improves the reliability of the interpretation result; the simulation method of the present application is simple and fast, has high practicability, and has high reliability in describing the variable well storage effect, and the described variable well storage effect provides a favorable basis for the later gas field development.

[0196] The preferred embodiments of the present application are described in detail above, but the present application is not limited to the above-mentioned embodiments, and various changes can be made within the knowledge of those skilled in the art without departing from the purpose of the present application.

[0197] Many other changes and modifications can be made without departing from the concept and scope of the present application. It should be understood that the present application is not limited to the specific embodiments, and the scope of the present application is defined by the appended claims. The components and structures not described in detail in the present embodiment are common components and structures or common means in the industry, and are not described here.

Claims

1. A method for simulating the variable well reservoir effect caused by downhole throttling in gas wells, characterized in that, Includes the following steps: Step 1) Establish the dimensionless wellbore material balance equation under downhole throttling conditions to obtain the dimensionless pressure value under downhole throttling conditions; Step 2) Based on the dimensionless pressure value described in Step 1), plot a double logarithmic pressure derivative curve to simulate the variation characteristics of the reservoir effect under different parameter combinations under downhole throttling conditions; Step 3) Based on the actual pressure recovery data under throttling conditions, create a normalized pseudo-pressure difference and its derivative versus the measured curve of shut-in time, and plot it on the same chart as the double logarithmic pressure derivative curve described in Step 2), keeping the measured curve and the double logarithmic pressure derivative curve chart aligned. Solve for the relevant parameters of the variable well reservoir stage based on the fitting key points, and use these relevant parameters to describe the variable well reservoir effect caused by downhole throttling in the gas well.

2. The method for simulating the variable well reservoir effect caused by downhole throttling in a gas well according to claim 1, characterized in that, In step 1), the dimensionless wellbore material balance equation under downhole throttling conditions is established, wherein the dimensionless wellbore material balance equation is: in: - is the symbol for partial differentials; -Dimensionless pseudo-pressure; -Dimensionless pseudo-pressure difference; -Dimensionless distance; -Reservoir coefficient at the upper end of the throttle; -Reservoir coefficient at the lower end of the throttle; -Dimensionless throttle depth; -Dimensionless time; - Dimensionless time related to pressure difference changes.

3. The method for simulating the variable reservoir effect caused by downhole throttling in a gas well according to claim 1, characterized in that, Step 1) involves solving the dimensionless wellbore material balance equation using the Laplace transform, and then using the Stehfest method to calculate the Laplace space solution to obtain the dimensionless pressure value under downhole throttling conditions.

4. The method for simulating the variable well reservoir effect caused by downhole throttling in a gas well according to claim 1, characterized in that, In step 2), the double logarithmic pressure derivative curve chart includes pressure and pressure derivative charts under different dimensionless choke depth conditions, pressure and pressure derivative charts under different dimensionless time conditions related to the change of dimensionless pressure difference, pressure and pressure derivative charts under different wellbore storage coefficient ratios above and below the choke, and pressure and pressure derivative charts under different dimensionless pseudo-pressure difference conditions. The double logarithmic pressure derivative curve chart simulates the variation characteristics of the wellbore storage effect under different parameter combinations under downhole choke conditions.

5. The method for simulating the variable reservoir effect caused by downhole throttling in a gas well according to claim 4, characterized in that, The pressure and pressure derivative diagrams under different dimensionless choke depths, different dimensionless time conditions related to the change of dimensionless pressure difference, different ratios of wellbore storage coefficients above and below the choke, and different dimensionless pseudo-pressure differences can all reveal the changing trends of the initial and final wellbore storage coefficients.

6. The method for simulating the variable well reservoir effect caused by downhole throttling in a gas well according to claim 1, characterized in that, In step 3), the measured curve is plotted on the double logarithmic pressure derivative curve chart described in step 2). The double logarithmic pressure derivative curve chart chart that best matches the measured curve is found. The measured curve chart and the double logarithmic pressure derivative curve chart chart are kept in coincidence. Fitting points are selected, and nonlinear regression is used to obtain the relevant parameters of the variable well reservoir model. These relevant parameters are used to describe the variable well reservoir effect caused by downhole throttling in the gas well.

7. The method for simulating the variable well reservoir effect caused by downhole throttling in a gas well according to claim 6, characterized in that, The parameters related to the variable well reservoir model include the final wellbore reservoir coefficient, the initial wellbore reservoir coefficient value, and the variable well reservoir transition time. These parameters describe the variable well reservoir effect caused by downhole throttling in gas wells.

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