A method for predicting the decline fraction of a constant volume closed gas well

Abstract

The present application relates to a kind of constant volume closed gas well production decline fraction prediction method, the pseudo average formation pressure of non-declining production time, the pseudo bottom hole flowing pressure of non-declining production time, pseudo original formation pressure, p wf (1) The pseudo bottom hole flowing pressure ψ (p wf (1)) of non-declining production time + decline production time is calculated;The initial value of pressure conversion skin is calculated;Initial decline component is calculated;Decline component of non-declining production time + decline production time is calculated;Production decline fraction is calculated.The present application establishes a kind of method for predicting the production decline fraction of constant volume closed gas well, considers the influence of different bottom hole flowing pressure on gas well production decline, and the prediction result does not exist polygeny, has strong application value for gas field development.

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 production decline fraction of a constant-volume closed gas well. Background Technology

[0002] Research on oil and gas well production decline began in 1945. By statistically analyzing oil well production decline curve data, ARPS proposed the definition of decline rate, leading to three decline models: exponential decline, hyperbolic decline, and harmonic decline. Based on this, years of research have resulted in various decline models, including power-law exponential decline, extended exponential decline, logistic growth, linear decline, generalized decline, power function decline, generalized exponential production, and rational formula-based production decline. In practical applications, gas well production decline often satisfies multiple decline models simultaneously, leading to multiple solutions in the prediction results. A possible reason for this phenomenon is that the decline model does not include bottomhole flowing pressure.

[0003] When gas flows in a reservoir, it usually follows Darcy's law of permeability. If we assume that the reservoir's porosity, permeability, saturation, and other physical properties do not change with production, the gas well production is mainly determined by the pressure difference between the average formation pressure and the bottom-hole flowing pressure. Based on Darcy's law, establishing a fractional prediction method for the production decline of a constant-volume closed gas well is of great value for gas field development. Summary of the Invention

[0004] The present invention aims to address the above-mentioned problems by proposing a fractional prediction method for the production decline of a constant-volume closed gas well.

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

[0006] For a constant-volume closed gas well, using Darcy's equation and the mass balance equation, and considering the change in average formation pressure with the pressure drop funnel, the full-stage production capacity equation can be derived:

[0007]

[0008] In the formula: The pseudo-mean formation pressure at time t, in MPa 2 / mPa·s; Let be the average formation pressure at time t, in MPa;

[0009] ψ(p wf (t) represents the pseudo-bottomhole flowing pressure at time t, in MPa. 2 / mPa·s;p wf (t) represents the bottom hole flowing pressure at time t, in MPa;

[0010] p sc Standard pressure, MPa;

[0011] Zsc The standard deviation coefficient is dimensionless.

[0012] T sc Standard temperature, K;

[0013] T is the reservoir temperature, in K;

[0014] K is the reservoir permeability, 10 -3 μm 2 ;

[0015] h is the reservoir thickness, in meters;

[0016] q sc (t) represents the wellhead gas production at time t, in m 3 / d;

[0017] r e Let vent radius be m;

[0018] r w Let be the radius of the wellbore, in meters (m).

[0019] S p (t) represents the pressure change at time t, dimensionless.

[0020] The definition of pseudo-pressure ψ(p) is:

[0021]

[0022] In the formula: ψ(p) is the pseudo-pressure corresponding to pressure p, in MPa 2 / mPa·s;

[0023] p represents pressure, in MPa;

[0024] p0 is the reference pressure, with a value of p0 = 0, MPa;

[0025] μ(p) is the gas viscosity corresponding to pressure p, in mPa·s;

[0026] Z(p) is the deviation coefficient corresponding to pressure p, which is dimensionless;

[0027] The derivation of equation (1) is not simplified in any way, and it does not require the gas well to maintain a constant production or pressure. Therefore, equation (1) is applicable to the entire production stage of a gas well. Based on equation (1), the relationship between gas well production and pressure can be obtained:

[0028]

[0029] Equation (3) is a variation of equation (1). Since equation (1) applies to all stages of gas well production, equation (3) also applies to all stages of gas well production, including different production systems such as constant production, variable production, and declining production. Among all stages of gas well production, the declining stage lasts the longest. The essence of the declining phenomenon is that the bottom hole pressure no longer has room to decrease, and the gas well can only start production with constant bottom hole pressure. Decreasing production is fundamentally different from production with reduced output.

[0030] To distinguish the decreasing phase from the other phases, let:

[0031] t = t B +t D (4)

[0032] In the formula: t is the production time, d;

[0033] t B d represents the decreasing start time, and also the non-decreasing end time.

[0034] t D To reduce production time, t D ≥0, d;

[0035] Substituting equation (4) into equation (3), we get:

[0036]

[0037] In the formula: q sc (t B +t D ) for t B +t D Wellhead gas production at time, m 3 / d;

[0038] For t B +t D The pseudo-mean formation pressure at that time, MPa 2 / mPa·s;

[0039] For t B +t D The average formation pressure at that time, in MPa;

[0040] ψ(p wf (t B +t D )) is t B +t D Simulated bottom hole flowing pressure at the time, MPa 2 / mPa·s;

[0041] p wf (t B+t D ) for t B +t D Bottom hole flowing pressure at that time, MPa;

[0042] S p (t B +t D ) for t B +t D Pressure changes over time on the skin, dimensionless.

[0043] The decline rate D(t) is defined as the fraction of output decrease per unit time:

[0044]

[0045] In the formula: D(t) is the rate of decrease at time t, d -1 ;

[0046] Substituting equation (5) into equation (6), we obtain:

[0047]

[0048] In equation (7), since p wf (t B +t D ) and S p (t B +t D The existence of ) makes it difficult to solve the derivative term directly, so it is difficult to calculate the decline rate D(t) using equation (7).

[0049] Referring to the definition of the decline rate D(t), an expression for the fractional decline in output is proposed:

[0050]

[0051] In the formula: D p (t D ) for t D The product decline fraction, 0 ≤ D p (t D )≤1, dimensionless;

[0052] q sc (t B ) for t B Wellhead gas production at time, m 3 / d.

[0053] When the gas well just begins to decline, the decline time t D =0, t = decreasing start time t B Substituting into equation (5), we get:

[0054]

[0055] In the formula: For t B The pseudo-mean formation pressure at that time, MPa 2 / mPa·s;

[0056] For t B The average formation pressure at that time, in MPa;

[0057] ψ(p wf (t B )) is t B Simulated bottom hole flowing pressure at the time, MPa 2 / mPa·s;

[0058] p wf (t B ) for t B Bottom hole flowing pressure at that time, MPa;

[0059] S p (t B ) for t B Pressure changes over time on the skin, dimensionless.

[0060] When a gas well enters the declining production phase, the bottom hole flowing pressure remains constant, i.e., p wf (t B ) = p wf (t B +t D Substituting equations (5) and (9) into equation (8), we obtain:

[0061]

[0062] The derivation of equation (10) was not simplified in any way, but the vent radius r e The parameters are usually unknown. To improve the feasibility of applying equation (10), an independent approximate solution for the pressure conversion skin is proposed:

[0063]

[0064] in

[0065]

[0066] In the formula: S p (t) represents the pressure change at time t, dimensionless;

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

[0068] μ i The original formation pressure pi The corresponding gas viscosity, mPa·s;

[0069] μ wf (t) represents the bottom hole flowing pressure p at time t. wf (t) corresponds to the gas viscosity in mPa·s;

[0070] t D For dimensionless production time, t D =t / 1,t D >0, dimensionless;

[0071] ψ(p i () represents the pseudo-original formation pressure, in MPa 2 / mPa·s;

[0072] p i The original formation pressure is expressed in MPa.

[0073] ψ(p wf (1) is p wf (1) Simulated bottom hole flowing pressure, MPa 2 / mPa·s;

[0074] p wf (1) is the bottom hole pressure at t=1, in MPa;

[0075] q sc (1) is the wellhead gas production at t=1, m 3 / d.

[0076] Substituting equations (11) and (12) into equation (10), we obtain:

[0077]

[0078] Where: μ wf (t B ) for t B Bottom-hole flowing pressure p wf (t B The corresponding gas viscosity, mPa·s;

[0079] t B D For t B The corresponding dimensionless production time, (t) B ) D =t B / 1, (t B ) D >0, dimensionless;

[0080] μ wf (t B +t D ) for tB +t D Bottom-hole flowing pressure p wf (t B +t D The corresponding gas viscosity, mPa·s;

[0081] t B D +t D D For t B +t D The corresponding dimensionless production time, t B D +t D D =t B / 1+t D / 1,t B D +t D D >0, dimensionless;

[0082] When a gas well enters the declining production phase, the bottom hole flowing pressure remains constant, i.e., μ. wf (t B )=μ wf (t B +t D ),make:

[0083]

[0084]

[0085] In the formula: d(t) B ) represents the initial decreasing component, i.e., t B Decreasing component at time, MPa 2 / mPa·s;

[0086] d(t B +t D ) for t B +t D Decreasing component at time, MPa 2 / mPa·s.

[0087] Substituting equations (14) and (15) into equation (13), we obtain the product decline fraction D. p (t D The formula for calculating ) is:

[0088]

[0089] Using equation (16), the different decreasing production times t can be calculated. D The fraction of decreasing output at time D p(t D ).

[0090] The technical advantages of this invention are as follows:

[0091] This invention establishes a method for predicting the production decline fraction of a constant-volume closed gas well. It considers the influence of different bottom hole flowing pressures on the production decline of the gas well, and the prediction results do not have multiple solutions. It has strong application value for gas field development. Attached Figure Description

[0092] Figure 1 The wellhead gas production and bottom hole flowing pressure are the parameters of this invention.

[0093] Figure 2 This is a comparison of the calculation results of the embodiments of the present invention. Detailed Implementation

[0094] A fractional method for predicting the production decline of a constant-volume closed gas well is as follows:

[0095] Step 1: Calculate t using formula (2) B The pseudo-mean formation pressure at time t B Simulated bottom hole pressure ψ(p) wf (t B )), pseudo-original formation pressure ψ(p) i ), p wf (1) The pseudo-bottom flow pressure ψ(p) wf (1)) and t B +t D The pseudo-mean formation pressure at time

[0096] Step 2: Calculate the initial value S of the pressure conversion skin using formula (12). p (i);

[0097] Step 3: Calculate the initial decreasing component d(t) using formula (14). B );

[0098] Step 4: Calculate t using formula (15) B +t D The decreasing component d(t) at time B +t D );

[0099] Step 5: Calculate the product decline fraction D using formula (16). p (t D ).

[0100] Example

[0101] The example is a numerical simulation of a gas well. The basic parameters are shown in Table 1, and the wellhead gas production q is... sc (t) and bottom hole pressure p wf The variation of (t) with production time t is shown in the figure. Figure 1 The gas wells are in constant production from t=1 to 599 days, and at p=600 to 30000 days. wf Production begins to decrease when (t) = 5 MPa, therefore p wf (t B =5MPa.

[0102] Table 1 Basic parameters of the embodiment

[0103]

[0104] A fractional method for predicting the production decline of a constant-volume closed gas well is as follows:

[0105] Step 1: Calculate using formula (2)

[0106] ψ(p wf (t B = 1757.67 MPa 2 / mPa·s、ψ(p i = 44892.22MPa 2 / mPa·s、ψ(p wf (1))=35645.18MPa 2 / mPa·s;

[0107] With t B +t D The changes have occurred, and the calculation results are shown in Table 2;

[0108] Step 2: Calculate the initial value S of the pressure conversion skin using formula (12). p (i) = 6.56;

[0109] Step 3: Calculate the initial decreasing component d(t) using formula (14). B = 3717.58 MPa 2 / mPa·s;

[0110] Step 4: Calculate t using formula (15) B +t D The decreasing component d(t) at time B +t D The calculation results are shown in Table 2;

[0111] Step 5: Calculate the product decline fraction D using formula (16). p (t DThe calculation results are shown in Table 2;

[0112] Table 2 shows the calculation process and results of the embodiments.

[0113]

[0114] The calculation results of this invention are compared with the results of the numerical model, see... Figure 2 As can be seen, when gas wells produce in a manner that first determines production and then decreases it, the calculation results of this invention show the same trend as the numerical model results, and at the same time, they show high accuracy, indicating that the calculation results of this invention are reliable and suitable for production decline fraction prediction.

Claims

1. A method for predicting the production decline fraction of a constant-volume closed gas well, characterized in that: The method is as follows: Step 1: Calculate the pseudo-pressure ψ(p); The decrease start time t is calculated. B Corresponding pseudo-mean formation pressure and simulated bottom hole flowing pressure pseudo-original formation pressure ψ(p) i ), p wf (1) The pseudo-bottom flow pressure ψ(p) wf (1)) and t B +t D The pseudo-mean formation pressure at time Step 2: Calculate the initial value S of the pressure conversion skin. p (i); By using the following formula (12) In the formula: S p (i) represents the initial value of the pressure conversion skin, which is dimensionless; Z sc The standard deviation coefficient is dimensionless. T sc Standard temperature, K; p sc Standard pressure, MPa; K is the reservoir permeability, 10 -3 μm 2 ; h is the reservoir thickness, in meters; T is the reservoir temperature, in K; ψ(p i () represents the pseudo-original formation pressure, in MPa 2 / mPa·s; p i The original formation pressure is expressed in MPa. ψ(p wf (1) is p wf (1) Simulated bottom hole flowing pressure, MPa 2 / mPa·s; p wf (1) is the bottom hole pressure at t=1, in MPa; q sc (1) is the wellhead gas production at t=1, m 3 / d; The initial value S of the pressure conversion skin was calculated. p (i); Step 3: Calculate the initial decreasing component d(t) B ); By using the following formula (14) In the formula: d(t) B ) represents the initial decreasing component, i.e., t B Decreasing component at time, MPa 2 / mPa·s; t B d represents the decreasing start time, and also the non-decreasing end time. For t B The pseudo-mean formation pressure at that time, MPa 2 / mPa·s; For t B The average formation pressure at that time, in MPa; ψ(p wf (t B )) is t B Simulated bottom hole flowing pressure at the time, MPa 2 / mPa·s; p wf (t B ) for t B Bottom hole flowing pressure at that time, MPa; μ i For p i The corresponding gas viscosity, mPa·s; μ wf (t B ) for t B Bottom-hole flowing pressure p wf (t B The corresponding gas viscosity, mPa·s; t B D For t B The corresponding dimensionless production time, (t) B ) D =t B / 1, (t B ) D >0, dimensionless; The initial decreasing component d(t) is calculated. B ); Step 4: Calculate t B +t D The decreasing component d(t) at time B +t D ); By using the following formula (15) In the formula: d(t) B +t D ) for t B +t D Decreasing component at time, MPa 2 / mPa·s; t D To reduce production time, t D ≥0, d; For t B +t D The pseudo-mean formation pressure at that time, MPa 2 / mPa·s; For t B +t D The average formation pressure at that time, in MPa; μ wf (t B +t D ) for t B +t D Bottom-hole flowing pressure p wf (t B +t D The corresponding gas viscosity, mPa·s; t B D +t D D For t B +t D The corresponding dimensionless production time, t B D +t D D =t B / 1+t D / 1,t B D +t D D >0, dimensionless; Calculate t B +t D The decreasing component d(t) at time B +t D ); Step 5: Calculate the product decline fraction D p (t D ) By using the following formula (16) In the formula: D p (t D ) for t D The product decline fraction, 0 ≤ D p (t D )≤1, dimensionless; The product decline fraction D was calculated. p (t D ).

2. The method for predicting the production decline fraction of a constant-volume closed gas well according to claim 1, characterized in that: In step 1, the pseudo-pressure ψ(p) By using the following formula (2) In the formula: ψ(p) is the pseudo-pressure corresponding to pressure p, in MPa 2 / mPa·s; p represents pressure, in MPa; p0 is the reference pressure, in MPa; μ(p) is the gas viscosity corresponding to pressure p, in mPa·s; Z(p) is the deviation coefficient corresponding to pressure p, which is dimensionless; The decrease start time t is calculated. B Corresponding pseudo-mean formation pressure and the pseudo-bottom flow pressure ψ(p) wf ( tB )), pseudo-original formation pressure ψ(p) i ), p wf (1) The pseudo-bottom flow pressure ψ(p) wf (1)) and t B +t D The pseudo-mean formation pressure at time 3. The method for predicting the production decline fraction of a constant-volume closed gas well according to claim 2, characterized in that: The method is as follows: the reference pressure p0 is taken as 0 MPa.

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