A method for predicting full-stage average formation pressure of gas reservoirs by constant volume gas drive

Abstract

This invention relates to a method for predicting the average formation pressure throughout the entire process of a constant-volume gas-driven gas reservoir. The method calculates the pseudo-pressure corresponding to the original formation pressure and the pseudo-pressure corresponding to the bottomhole flowing pressure at t=1; calculates the initial value of the pressure transition skin; obtains the deviation coefficient and gas viscosity corresponding to the bottomhole flowing pressure based on high-pressure physical property data, and calculates an approximate solution for the pressure transition skin; calculates the pseudo-average formation pressure; and calculates the average formation pressure. This invention establishes the full-stage productivity equation for constant-volume gas-driven gas reservoirs and proposes an approximate solution for the pressure transition skin, which can be used to calculate the average formation pressure throughout the entire process of constant-volume gas-driven gas reservoirs, providing important theoretical support for the full-stage dynamic analysis of constant-volume gas-driven gas reservoirs.

Description

Technical Field

[0001] This invention relates to the field of oil and gas field development technology, and specifically to a method for predicting the average formation pressure of a constant-volume gas-driven gas reservoir throughout all stages. Background Technology

[0002] The productivity equation reveals the physical and mathematical relationships between mean formation pressure, bottomhole flowing pressure, and gas production, and belongs to the fundamental theory in the field of gas field development. The physical model determines the scope of application. In establishing existing productivity equations, the physical model is usually set for a constant-volume gas-driven reservoir. Based on this, factors such as non-Darcy flow, skin coefficient, stress sensitivity, slip effect, starting pressure gradient, condensate oil, gas-water two-phase flow, and fractures are considered, and the corresponding parameters are modified. This allows for the establishment of productivity equations under different physical models, thus expanding the scope of application of the productivity equation.

[0003] The production regime determines the applicable stage. In establishing a one-dimensional capacity equation, the production regime is typically assumed to be constant output, corresponding to a stable production stage. Other capacity equations built upon this assumption do not consider changes in the production regime, and their applicable stage remains unchanged. Gas well production typically exhibits different stages such as stable production, variable production, and declining production. Establishing a unified capacity equation across all stages, thus broadening the applicable stage of capacity equations, is of great significance for the effective development of gas fields. Summary of the Invention

[0004] This invention aims to address the aforementioned problems by proposing a method for predicting the average formation pressure throughout the entire process of constant-volume gas-driven gas reservoirs.

[0005] The technical solution of this invention is as follows:

[0006] For horizontal, homogeneous, and constant-volume gas-driven reservoirs, the gas flow in the reservoir follows Darcy's law. Based on Darcy's equation, the boundary pressure p is established. e (t) and bottom hole flowing pressure p wf Equations between (t):

[0007] (1)

[0008] In the formula: ψ(p) e ) represents the quasi-boundary pressure, indicating the boundary pressure p. e (t) corresponds to the pseudo-pressure, in MPa 2 / mPa·s;

[0009] p e (t) represents the boundary pressure, in MPa;

[0010] t represents the production time, t≥0, d;

[0011] ψ(pwf ) represents the pseudo-bottom hole flowing pressure, and p represents the bottom hole flowing pressure. wf (t) corresponds to the pseudo-pressure, in MPa 2 / mPa·s;

[0012] p wf (t) represents the bottom hole flowing pressure, in MPa;

[0013] p sc Standard pressure, MPa;

[0014] Z sc The standard deviation coefficient is dimensionless.

[0015] T sc Standard temperature, K;

[0016] T is the reservoir temperature, in K;

[0017] K is the reservoir permeability, 10 -3 μm 2 ;

[0018] h is the reservoir thickness, in meters;

[0019] r e Let vent radius be m;

[0020] r w Let be the radius of the wellbore, in meters (m).

[0021] q sc (r,t) represents the gas volumetric flow rate at point t with radius r under standard ground conditions, in m. 3 / d;

[0022] r is any radius, r w ≤r≤r e , m.

[0023] For a constant-volume gas-driven gas reservoir, from any radius r to the venting radius r e The mass balance equation in the reservoir is:

[0024] (2)

[0025] In the formula: For any radius r to the vent radius r e The average formation pressure of the reservoir at time t, in MPa;

[0026] Z r (r,t) is The corresponding deviation coefficient is dimensionless.

[0027] p i The original formation pressure is expressed in MPa.

[0028] Z i The original formation pressure p i The corresponding deviation coefficient is dimensionless.

[0029] G(r) represents any radius r to the venting radius r. e The original geological reserves of the reservoir, m 3 ;

[0030] G p (r,t) represents any radius r to the venting radius r. e Cumulative wellhead gas production of the reservoir at time t, m 3 .

[0031] Wherein, any radius r to the vent radius r e The expression for the original geological reserves G(r) of the reservoir is:

[0032] (3)

[0033] In the formula: φ is the reservoir porosity, which is dimensionless;

[0034] S gi The original gas saturation of the reservoir is dimensionless.

[0035] Differentiate both sides of equation (2) with respect to t, and then substitute equation (3) into equation (2) to obtain:

[0036] (4)

[0037] When any radius r = wellbore radius r w Then, equation (4) becomes:

[0038] (5)

[0039] In the formula: q sc (t) represents the wellhead gas production at time t, in m 3 / d;

[0040] Let r be the radius of the wellbore. w To the vent radius r e The average formation pressure of the reservoir at time t, in MPa;

[0041] Z r (t) is The corresponding deviation coefficient is dimensionless.

[0042] Dividing both sides of equations (4) and (5) respectively, we derive:

[0043] (6)

[0044] Substituting equation (6) into equation (1), we obtain:

[0045] (7)

[0046] The definition of pseudo-pressure ψ(p) is:

[0047] (8)

[0048] In the formula: ψ(p) is the pseudo-pressure corresponding to pressure p, in MPa 2 / mPa·s;

[0049] p represents pressure, in MPa;

[0050] μ(p) is the gas viscosity corresponding to pressure p, in mPa·s;

[0051] Z(p) is the deviation coefficient corresponding to pressure p, which is dimensionless;

[0052] p0 is the reference pressure, and it is recommended to set p0=0, MPa;

[0053] Starting from equation (8), based on the additivity of the integration interval, the pseudo-pressures exist as follows:

[0054] (9)

[0055] In the formula: The pseudo-mean formation pressure represents the mean formation pressure. The corresponding pseudo-pressure, MPa 2 / mPa·s.

[0056] Definition of pressure conversion skin:

[0057] (10)

[0058] In the formula: The definition of the pressure conversion skin is dimensionless.

[0059] Substituting equations (9) and (10) into equation (7), we obtain the full-stage production capacity equation:

[0060] (11)

[0061] Since the integral term in equation (10) contains p e Several unknown parameters, such as (t), lead to It is difficult to solve directly, which makes it impossible to use the full-stage production capacity equation directly.

[0062] An approximate solution S for pressure-transforming skin is proposed. p (t):

[0063] (12)

[0064] in

[0065] (13)

[0066] In the formula: S p (t) is an approximate solution for the pressure conversion skin, which is dimensionless;

[0067] S p (i) represents the initial value of the pressure conversion skin, which is dimensionless;

[0068] Z wf (t) is p wf The deviation coefficient corresponding to (t) is dimensionless;

[0069] μ i The original formation pressure p i The corresponding gas viscosity, mPa·s;

[0070] μ wf (t) is p wf (t) corresponds to the gas viscosity in mPa·s;

[0071] t D For dimensionless production time, t D =t / 1, t D >0, dimensionless;

[0072] ψ(p i ) is p i The corresponding pseudo-pressure, MPa 2 / mPa·s;

[0073] ψ(p wf (1) is p wf (t=1) corresponding pseudo-pressure, MPa 2 / mPa·s;

[0074] q sc (1) is the wellhead gas production at t=1, m 3 / d.

[0075] Comparing the definition and approximate solution of the pressure conversion epidermis, it was found that the variation patterns of the approximate solution and the definition are generally similar, but there are slight differences in some local areas. The variation pattern of the definition is... The variation law of the approximate solution is determined by Z. wf (t), μ wf (t) and t DThe decision is made to use known parameters to replace the unknown parameters in the definition in the approximate solution, so that the production capacity equation for the whole stage can be independent of the material balance equation. Compared with the definition, the approximate solution has stronger operability.

[0076] The derivation of the full-stage capacity equation was not simplified in any way, and q was not required. sc (t) and p wf Since (t) remains constant, the full-stage production capacity equation is applicable to all stages of gas reservoir development, including various development stages such as constant production, variable production, and declining production.

[0077] By successively using equations (13), (12), and (11), the pseudo-average formation pressure can be calculated. Analysis of a large amount of experimental data on the physical properties of high-pressure natural gas revealed the following binomial relationship:

[0078] (14)

[0079] In the formula: a is μ(p)Z(p)-p 2 The curve is obtained using the first coefficient obtained through linear fitting;

[0080] b is μ(p)Z(p)-p 2 The curve uses the second coefficient obtained through linear fitting;

[0081] Substituting equation (14) into equation (8), we derive the expression for converting pressure into pseudo-pressure:

[0082] (15)

[0083] Let (15) be in The expression for converting pseudo-pressure into mean formation pressure is derived as follows:

[0084] (16)

[0085] In the formula: The mean formation pressure is expressed in MPa.

[0086] Using equation (16), the average formation pressure throughout the entire development stage of the gas reservoir can be obtained. .

[0087] The technical advantages of this invention are as follows:

[0088] This invention establishes the full-stage productivity equation for constant-volume gas-driven gas reservoirs and proposes an approximate solution for the pressure transition skin, which can be used to calculate the average formation pressure of constant-volume gas-driven gas reservoirs throughout the entire process, providing important theoretical support for the full-stage dynamic analysis of constant-volume gas-driven gas reservoirs. Attached Figure Description

[0089] Figure 1 This is a schematic diagram of the deviation coefficient and gas viscosity of the present invention.

[0090] Figure 2 The bottom flow pressure and wellhead gas production rate for production system 1.

[0091] Figure 3 For production system 2, the bottom hole flowing pressure and wellhead gas production are calculated. Detailed Implementation

[0092] A method for predicting the average formation pressure throughout the entire process of a constant-volume gas-driven gas reservoir is as follows:

[0093] Step 1: Calculate the original formation pressure p using equation (15). i The corresponding pseudo-pressure ψ(p) i Bottom hole flowing pressure p wf (t) at t=1 corresponding pseudo-pressure ψ(p) wf (1)); The initial value S of the pressure conversion skin is calculated by equation (13). p (i);

[0094] Step 2: Obtain the bottom hole flowing pressure p based on the high pressure physical property data. wf The deviation coefficient Z corresponding to (t) wf (t) and gas viscosity μ wf (t), the approximate solution S of the pressure conversion skin is obtained by equation (12). p (t);

[0095] Step 3: Calculate the pseudo-mean formation pressure using equation (11). ;

[0096] Step 4: Calculate the mean formation pressure using equation (16). .

[0097] Specific experimental examples

[0098] Numerical simulations are used to illustrate the calculation process and results of this invention. The basic calculation parameters used in the embodiments are shown in Table 1, and the deviation coefficients and gas viscosities used are shown in [Table 1]. Figure 1 To verify the reliability of this invention throughout the entire gas reservoir development process, a sufficiently long production time is required. Therefore, the production time t is set from 1 day to 30,000 days. At the same time, the entire process is also affected by different modes such as fixed production, decreasing production, increasing production, and decreasing production. Therefore, two gas well production systems are set: gas wells first set production and then decreasing production, and gas wells first increase production and then decreasing production.

[0099] Table 1 Basic Calculation Parameters

[0100]

[0101] (a) Production System 1: Gas wells first determine production and then gradually reduce it.

[0102] Based on the calculation requirements, output the bottom hole flowing pressure p. wf (t) and wellhead gas production q sc (t), see Figure 2 ;

[0103] Step 1: Calculate the original formation pressure p using equation (15). i The corresponding pseudo-pressure ψ(p) i and bottom hole flowing pressure p wf (t) at t=1 corresponding pseudo-pressure ψ(p) wf (1)); Calculated to obtain =8159.25;

[0104] The initial value S of the pressure conversion skin is calculated using equation (13). p (i) = 5.83;

[0105] Step 2: According to Figure 1 The data obtained from the wellbore bottom flowing pressure p wf The deviation coefficient Z corresponding to (t) wf (t) and gas viscosity μ wf (t), the approximate solution S of the pressure conversion skin is obtained by equation (12). p (t), the results are shown in Table 2;

[0106] Step 3: Calculate the pseudo-mean formation pressure using equation (11). The results are shown in Table 2;

[0107] Step 4: Calculate the mean formation pressure using equation (16). The results were compared with those of numerical simulation, as shown in Table 2, which demonstrates that the present invention has high accuracy for both the fixed production and reduction stages.

[0108] Table 2 Calculation process and results of Production System 1

[0109] .

[0110] (ii) Production System 2: Gas wells first determine production and then gradually reduce it.

[0111] Based on the calculation requirements, output the bottom hole flowing pressure p. wf (t) and wellhead gas production q sc (t), see Figure 3 ;

[0112] Step 1: Calculate the original formation pressure p using equation (15). i The corresponding pseudo-pressure ψ(p) iand bottom hole flowing pressure p wf (t) at t=1 corresponding pseudo-pressure ψ(p) wf (1)); Calculated to obtain = 299.01;

[0113] The initial value S of the pressure conversion skin is calculated using equation (13). p (i) = 6.41;

[0114] Step 2: According to Figure 1 The data obtained from the wellbore bottom flowing pressure p wf The deviation coefficient Z corresponding to (t) wf (t) and gas viscosity μ wf (t), the approximate solution S of the pressure conversion skin is obtained by equation (12). p (t), the results are shown in Table 3;

[0115] Step 3: Calculate the pseudo-mean formation pressure using equation (11). The results are shown in Table 3;

[0116] Table 3 Calculation process and results of production system 2

[0117] .

[0118] Step 4: Calculate the mean formation pressure using equation (16). The results were compared with those of numerical simulation, as shown in Table 3, demonstrating that the present invention has high accuracy for both the fixed production and reduction stages.

[0119] The calculation results of combined production system 1 and production system 2 show that the calculated average formation pressure for the entire stage has high accuracy under different production systems such as fixed production, decreasing production, increasing production, and decreasing production, indicating that the present invention is applicable to the entire stage of gas reservoir development.

Claims

1. A method for predicting the average formation pressure throughout the entire process of a constant-volume gas-driven gas reservoir, characterized in that: The method is as follows: Step 1: Calculate the initial values ​​of the pressure conversion skin. ; By using the following formula (15) (15) In the formula: For pressure The corresponding pseudo-pressure, MPa 2 / mPa·s; for The curve is obtained using the first coefficient obtained through linear fitting; for The curve uses the second coefficient obtained through linear fitting; Pressure, MPa; Reference pressure, MPa; For pressure The corresponding gas viscosity, mPa·s; For pressure The corresponding deviation coefficient is dimensionless. The original formation pressure was calculated. Corresponding pseudo-pressure Bottom hole flowing pressure exist Corresponding pseudo-pressure ; By using the following formula (13) (13) In the formula: The initial value of the pressure conversion skin is dimensionless; The standard deviation coefficient is dimensionless. Standard temperature, K; Standard pressure, MPa; For reservoir permeability, 10 -3 μm 2 ; Let be the reservoir thickness, in meters (m). Let K be the reservoir temperature. Original formation pressure The corresponding pseudo-pressure, MPa 2 / mPa·s; Bottom hole flowing pressure exist The corresponding pseudo-pressure, MPa 2 / mPa·s; for Wellhead gas production at time, m 3 / d; The initial value of the pressure conversion skin was calculated. ; Step 2: Calculate the approximate solution for the pressure conversion skin. ; Bottomhole flowing pressure was obtained based on high pressure physical property data. Corresponding deviation coefficient and gas viscosity , through the following formula (12) (12) In the formula: This is an approximate solution for the pressure conversion skin, and it is dimensionless. Bottom hole flowing pressure The corresponding deviation coefficient is dimensionless. Original formation pressure The corresponding deviation coefficient is dimensionless. Let vent radius be m; Let be the radius of the wellbore, in meters (m). Original formation pressure The corresponding gas viscosity, mPa·s; Bottom hole flowing pressure The corresponding gas viscosity, mPa·s; For dimensionless production time, Dimensionless; An approximate solution for the pressure conversion skin was obtained through calculation. ; Step 3: Calculate the pseudo-mean formation pressure ; By using the following formula (11) (11) In the formula: The pseudo-mean formation pressure represents the mean formation pressure. The corresponding pseudo-pressure, MPa 2 / mPa·s; The simulated bottom hole flowing pressure represents the bottom hole flowing pressure. The corresponding pseudo-pressure, MPa 2 / mPa·s; The bottom hole flowing pressure is in MPa. for Wellhead gas production at time, m 3 / d; The calculated pseudo-mean formation pressure ; Step 4: Calculate the mean formation pressure ; By using the following formula (16) (16) In the formula: The mean formation pressure is expressed in MPa. The mean formation pressure was calculated. .

2. The method for predicting the average formation pressure of a constant-volume gas-driven gas reservoir throughout all stages according to claim 1, characterized in that: The reference pressure is set to 0 MPa.

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