Method for calculating well cleaning induced flow operation time of low-permeability gas well stratum

Abstract

The invention discloses a method for calculating well cleaning induced flow operation time of a low-permeability gas well stratum. The method comprises the steps that stratum parameters and a rock sample are obtained, a standard rock core is manufactured, and a compression coefficient and porosity are measured; obtaining the relationship between the flow velocity and the pressure gradient through a displacement experiment, fitting by adopting a piecewise function to obtain a critical pressure gradient when the flow velocity and the pressure gradient present a linear relationship, and deriving the mathematical relationship between the flow velocity and the pressure gradient to obtain the relationship between the permeability and the pressure gradient; dividing a stratum area around a target well into N radial grids, and drawing up a time sequence; calculating a coefficient matrix A, pseudo-pressure, a coefficient matrix B, pseudo-pressure distribution, real pressure distribution and pressure gradient distribution at the first moment; repeatedly and circularly calculating pressure gradients at other moments; and calculating the invasion depth of the working fluid to obtain the minimum time when the pressure gradient at the mud invasion depth is greater than the critical pressure gradient. Compared with a traditional evaluation method, the stratum well cleaning induced flow time calculation method is more accurate.

Description

Technical Field

[0001] The invention belongs to the technical field of oil and gas production, and particularly relates to a method for calculating the time of a well cleaning and blowout induction operation in a low-permeability gas well formation. Background Art

[0002] Low-permeability gas reservoirs have high capillary forces, making it easy for drilling and completion fluids to invade formation pores and create a water lock. Gas well cleanup and blowout induction are crucial for dislodging invading fluids and ensuring normal well production. Because the gas-water flow patterns in newly drilled formations are unknown, characterizing the transient flow of the induced blowout fluid is challenging, making it difficult to determine a suitable induced blowout schedule. This significantly impacts the initial well production and the accuracy of subsequent testing data. Therefore, a method for calculating the cleanup and blowout induction time in low-permeability gas wells was developed to provide a theoretical basis for developing a suitable testing schedule for low-permeability gas reservoirs. Summary of the Invention

[0003] To address these issues, the present invention provides a method for calculating the time required to induce a blowout during a well-clearing operation in a low-permeability gas well. This method uses laboratory core flooding experiments to determine the transient nonlinear flow characteristics of fluids during the well-clearing process. Using a non-steady-state seepage model, the method calculates the formation pressure gradient, thereby determining the time required to induce a blowout. This method is robust and more consistent with actual formation conditions, providing theoretical support for determining the time required to induce a blowout during a well-clearing operation in a low-permeability gas well.

[0004] The present invention provides a technical solution to solve the above technical problems: a method for calculating the time of a low-permeability gas well formation clean-up and blowout induction operation, comprising the following steps:

[0005] Obtain the thickness h and original formation pressure p of the target layer i , formation temperature T wb , core displacement test rock samples, make standard cores, carry out indoor core experiments to obtain the core compression coefficient C r , porosity φ parameter;

[0006] The relationship between flow velocity v and pressure gradient G is obtained through core flooding experiments;

[0007] The relationship between flow velocity v and pressure gradient G is fitted by piecewise function to obtain the critical pressure gradient G when flow velocity v and pressure gradient G present a linear relationship. c , the relationship between the flow velocity v and the pressure gradient G is derived by derivation;

[0008] The formation area around the target well r e Divide into N radial grids and formulate a time series;

[0009] Calculate the coefficient matrix A of the first moment in the time series;

[0010] Calculate the pseudo-pressure corresponding to the real pressure and the coefficient matrix B at the first moment in the time series;

[0011] Calculate the pseudo-pressure distribution at the first moment in the time series;

[0012] The function fits the relationship between the real pressure and the pseudo-pressure, and calculates the real pressure corresponding to the pseudo-pressure at the first moment in the time series;

[0013] Calculate the pressure gradient distribution at the first moment in the time series;

[0014] Repeat the cycle to calculate the pressure gradient at the remaining moments in the time series;

[0015] Calculate the working fluid invasion depth D using logging data and compare the pressure gradient G at the mud invasion depth D with the critical pressure gradient G c The reasonable time t for well cleaning and blowout induction operation when the pressure gradient at the mud invasion depth is greater than the critical pressure gradient is obtained. c .

[0016] A further technical solution is to obtain the layer thickness h through logging data, and the original formation pressure p i Obtained by downhole pressure gauge, formation temperature T wb Obtained from a downhole pressure gauge.

[0017] A further technical solution is that the core displacement test rock samples are obtained by downhole core drilling tools.

[0018] A further technical solution is that the core compression coefficient C r , porosity φ is obtained by testing experimental rock samples.

[0019] A further technical solution is that the relationship between the flow velocity v and the pressure gradient G is obtained through core displacement experiments.

[0020] A further technical solution is that the critical pressure gradient G c It is the minimum pressure gradient when the flow rate and pressure gradient show a linear relationship.

[0021] A further technical solution is that the calculation formula of the coefficient matrix A is:

[0022]

[0023] Where C is the wellbore storage coefficient, m 3 / MPa; Δx is the position difference between two adjacent grids, m; Δt is the difference between two adjacent time series, h; μ wb is the fluid viscosity at the bottom of the well, mPa·s; k is the permeability when the flow velocity and pressure gradient are linear, mD; h is the reservoir thickness, m; K2 is the dynamic permeability of the second grid, mD; rw is the well radius, m; φ is the porosity, dimensionless; is the gas compressibility coefficient at the second grid pressure, MPa -1 ; μ2 is the fluid viscosity at the second grid pressure, mPa·s; K i is the dynamic permeability of the ith grid, mD; C gi is the gas compressibility coefficient at the i-th grid pressure, MPa-1; μ i is the fluid viscosity at the i-th grid pressure, mPa·s; K N-1 is the dynamic permeability of the N-1th grid, mD; C g(N-1) is the gas compressibility coefficient at the N-2th grid pressure, MPa -1 ;μ N-1 is the fluid viscosity at the N-1th grid pressure, mPa·s; K N is the dynamic permeability of the Nth grid, mD; C gN is the gas compressibility coefficient at the Nth grid pressure, MPa -1 ;μ N is the fluid viscosity at the Nth grid pressure, mPa·s;

[0024] A further technical solution is that the pseudo-pressure calculation formula is:

[0025]

[0026] Where ψ is the pseudo pressure, MPa 2 / (mPa·s); p is the true pressure, MPa, μ is the gas viscosity at the true pressure, mPa·s; Z is the gas deviation factor at the true pressure.

[0027] A further technical solution is that the calculation formula of the coefficient matrix B is:

[0028]

[0029] Where q is the output, m is the 3 / d;T wb is the temperature at the bottom of the well, K; p sc is the pressure under standard conditions, MPa; T sc is the temperature under standard conditions, K; t is the time, hours; is the pseudo pressure at the bottom hole flow pressure at time n, MPa 2 / (mPa·s); is the pseudo pressure of the second grid at time n, MPa 2 / (mPa·s); is the pseudo pressure of the ith grid at time n, MPa 2 / (mPa·s); is the pseudo-pressure of the N-1th grid at time n; is the pseudo-pressure of the Nth grid at time n; ψ in is the pseudo pressure under the original formation pressure, MPa 2 / (mPa·s);

[0030] A further technical solution is that the calculation formula of the pseudo-pressure distribution is:

[0031] ψ=A -1 B=[ψ wf ψ2...ψ i ...ψ N-1 ψ N ] T

[0032] A further technical solution is that the relationship between the real pressure and the pseudo pressure can be expressed as:

[0033] p=f(ψ)=[p wf p2...p i ...p N-1 p N ] T

[0034] Where f(ψ) is a polynomial function of the pseudo-pressure ψ, p wf is the bottom hole pressure, MPa; p2 is the pressure of the second grid, MPa; p i is the pressure of the ith grid, MPa; p N-1 is the pressure of the N-1th grid, MPa; p N is the pressure of the Nth grid, MPa.

[0035] A further technical solution is that the pressure gradient distribution calculation formula is:

[0036]

[0037] Where G is the pressure gradient, MPa / m; G1 is the pressure gradient of the first grid, MPa / m; G2 is the pressure gradient of the second grid, MPa / m; G i is the pressure gradient of the ith grid, MPa / m; G N-1 is the pressure gradient of the N-1th grid, MPa / m; G N is the pressure gradient of the Nth grid, MPa / m; p i is the real pressure corresponding to the pseudo-pressure of the i-th grid, MPa; p i-1 is the real pressure corresponding to the pseudo-pressure of the i-1th grid, MPa; x iis the distance between the ith grid and the bottom of the well, m; x i-1 is the distance from the i-1th grid to the bottom of the well, m.

[0038] A further technical solution is to repeat the cycle calculation to calculate the coefficient matrix A, coefficient matrix B, pseudo-pressure distribution, pressure distribution, and pressure gradient distribution at the next moment in the time series until the last moment of the time series is calculated.

[0039] A further technical solution is that the reasonable time for the well cleaning and blowout induction operation is t c is the minimum time at which the pressure gradient at the mud invasion depth is greater than the critical pressure gradient

[0040] Beneficial effects of the present invention: The present invention provides a method for calculating the time required for well cleaning and blowout induction in low-permeability gas well formations. By fitting the results of indoor core displacement experiments with a piecewise function, the nonlinear relationship between fluid flow rate and pressure gradient is mathematically characterized, and the pressure gradient corresponding to the transition from nonlinear flow to linear flow is obtained. On this basis, a non-steady-state reservoir flow model that considers dynamic permeability is established, and the pressure gradient at the invasion depth is compared to determine the time required for well cleaning and blowout induction in low-permeability gas well formations. This method is reliable in principle, more consistent with actual formation conditions, and can provide theoretical support for determining the time required for well cleaning and blowout induction in low-permeability gas well formations. BRIEF DESCRIPTION OF THE DRAWINGS

[0041] Figure 1 Fitting the relationship between flow rate and pressure gradient to a piecewise function

[0042] Figure 2 Formation pressure gradient distribution at 0.12 hours DETAILED DESCRIPTION

[0043] The technical solution of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the embodiments described are only part of the embodiments of the invention, not all of them. Based on the embodiments of the present invention, all other embodiments obtained by ordinary technicians in this field without making any creative efforts are within the scope of protection of the present invention.

[0044] The method for calculating the time of a low-permeability gas well formation cleanup and blowout induction operation provided by the present invention comprises the following steps:

[0045] Step 1: Obtain the reservoir thickness h as 40m and the original formation pressure p from the well logging data. i The rock compression coefficient is 0.000435MPa. -1 , porosity is 10%.

[0046] Step 2: Obtain the relationship between flow velocity v and pressure gradient G through core flooding experiments;

[0047] Step 3: Use piecewise function to fit the relationship between flow velocity v and pressure gradient G, and obtain the critical pressure gradient G when flow velocity v and pressure gradient G show a linear relationship. c is 0.177MPa / m, such as Figure 1 As shown in the figure, the relationship between permeability and pressure gradient is derived by derivation of the mathematical relationship between flow velocity and pressure gradient; the relationship between flow velocity v and pressure gradient G is fitted by piecewise function as follows:

[0048]

[0049] Step 4: Divide the 200m stratigraphic area around the well into 200 radial grids and formulate a time series {0.0010.002...10...19.5 20};

[0050] Step 5. Calculate the coefficient matrix A at the first moment in the time series:

[0051]

[0052] Where C is the wellbore storage coefficient, m 3 / MPa; Δx is the position difference between two adjacent grids, m; Δt is the difference between two adjacent time series, h; μ wb is the fluid viscosity at the bottom of the well, mPa·s; k is the permeability when the flow velocity and pressure gradient are linear, mD; h is the reservoir thickness, m; K2 is the dynamic permeability of the second grid, mD; r w is the well radius, m; φ is the porosity, dimensionless; is the gas compressibility coefficient at the second grid pressure, MPa -1 ; μ2 is the fluid viscosity at the second grid pressure, mPa·s; K i is the dynamic permeability of the ith grid, mD; C gi is the gas compressibility coefficient at the i-th grid pressure, MPa-1; μ i is the fluid viscosity at the i-th grid pressure, mPa·s; K N-1 is the dynamic permeability of the N-1th grid, mD; C g(N-1) is the gas compressibility coefficient at the N-2th grid pressure, MPa -1 ;μ N-1 is the fluid viscosity at the N-1th grid pressure, mPa·s; K N is the dynamic permeability of the Nth grid, mD; C gN is the gas compressibility coefficient at the Nth grid pressure, MPa -1 ;μ Nis the fluid viscosity at the Nth grid pressure, mPa·s;

[0053] The coefficient matrix A at the first moment 0.001 hours is:

[0054]

[0055] Step 6: Calculate the pseudo-pressure corresponding to the real pressure and the coefficient matrix B at the first moment in the time series. The pseudo-pressure calculation formula is:

[0056]

[0057] Where ψ is the pseudo pressure, MPa 2 / (mPa·s); p is the true pressure, MPa, μ is the gas viscosity at the true pressure, mPa·s; Z is the gas deviation factor at the true pressure.

[0058] The calculation formula of the coefficient matrix B is:

[0059]

[0060] Where q is the output, m is the 3 / d;T wb is the temperature at the bottom of the well, K; p sc is the pressure under standard conditions, MPa; T sc is the temperature under standard conditions, K; t is the time, hours; is the pseudo pressure at the bottom hole flow pressure at time n, MPa 2 / (mPa·s); is the pseudo pressure of the second grid at time n, MPa 2 / (mPa·s); is the pseudo pressure of the ith grid at time n, MPa 2 / (mPa·s); is the pseudo-pressure of the N-1th grid at time n; is the pseudo-pressure of the Nth grid at time n; ψ in is the pseudo pressure under the original formation pressure, MPa 2 / (mPa·s);

[0061] The coefficient matrix B at the first moment 0.001 hours is:

[0062]

[0063] Step 7: Calculate the pseudo-pressure distribution ψ at the first moment in the time series. The calculation formula for the pseudo-pressure distribution is:

[0064] ψ=A -1 B=[ψwf ψ2...ψ i ...ψ N-1 ψ N ] T

[0065] The pseudo-pressure distribution at the first moment 0.001 hours is:

[0066] ψ=[88578.46 88580.06…88603.40…88603.40 88603.40] T

[0067] Step 8. Fit the function to the relationship between the real pressure and the pseudo-pressure, and calculate the real pressure corresponding to the pseudo-pressure at the first moment in the time series:

[0068] p=f(ψ)=[p wf p2…p i …p N-1 p N ] T

[0069] Where f(ψ) is a polynomial function of the pseudo-pressure ψ, p wf is the bottom hole pressure, MPa; p2 is the pressure of the second grid, MPa; p i is the pressure of the ith grid, MPa; p N-1 is the pressure of the N-1th grid, MPa; p N is the pressure of the Nth grid, MPa.

[0070] The pressure distribution at the first moment 0.001 hours is:

[0071] p = 1.51 × 10 -14 ×ψ 3 -2.9×10 -9 ×ψ 2 +0.00058×ψ+6.34

[0072] =[44.9104 44.9111…44.9206…44.9206 44.9206] T

[0073] Step 9. Calculate the pressure gradient distribution at the first moment in the time series:

[0074]

[0075] Where G is the pressure gradient, MPa / m; G1 is the pressure gradient of the first grid, MPa / m; G2 is the pressure gradient of the second grid, MPa / m; G iis the pressure gradient of the ith grid, MPa / m; G N-1 is the pressure gradient of the N-1th grid, MPa / m; G N is the pressure gradient of the Nth grid, MPa / m; p i is the real pressure corresponding to the pseudo-pressure of the i-th grid, MPa; p i-1 is the real pressure corresponding to the pseudo-pressure of the i-1th grid, MPa; x i is the distance between the ith grid and the bottom of the well, m; x i-1 is the distance from the i-1th grid to the bottom of the well, m.

[0076] The pressure gradient distribution at the first moment 0.001 hours is:

[0077] G=[2.70 2.58…0…0 0] T

[0078] Step 10: Repeat steps 5, 6, 7, 8, and 9 to calculate the pressure gradient distribution at the remaining moments of the time series.

[0079] Step 11: Use the logging data to calculate the working fluid invasion depth D, which is 0.97 meters. Compare the pressure gradient G at the mud invasion depth of 0.97 meters with the critical pressure gradient G. c The size of Figure 2 As shown in the figure, the minimum time for the pressure gradient at the mud invasion depth to be greater than the critical pressure gradient of 0.177 MPa / m is 0.12 hours, which is the reasonable time for well cleaning and blowout induction operation t c 0.12 hours.

[0080] The above description does not limit the present invention in any form. Although the present invention has been disclosed through the above embodiments, it is not intended to limit the present invention. Any technician familiar with the profession can use the technical content disclosed above to make some changes or modifications to equivalent embodiments without departing from the scope of the technical solution of the present invention. However, any simple modifications, equivalent changes and modifications made to the above embodiments based on the technical essence of the present invention without departing from the content of the technical solution of the present invention are still within the scope of the technical solution of the present invention.

Claims

1. A method for calculating the time of a low permeability gas well formation clean-up and blowout induction operation, characterized in that: The following steps are involved: Obtain the target layer's formation thickness h and original formation pressure p i , formation temperature T wb , core displacement test rock samples, make standard cores, carry out indoor core experiments to obtain the core compression coefficient C r , porosity φ parameter; The relationship between flow velocity v and pressure gradient G is obtained through core flooding experiments; The relationship between flow velocity v and pressure gradient G is fitted by piecewise function to obtain the critical pressure gradient G when flow velocity v and pressure gradient G present a linear relationship. c , the relationship between the flow velocity v and the pressure gradient G is derived by derivation; The formation area around the target well r e Divide into N radial grids and formulate a time series; Calculate the coefficient matrix A of the first moment in the time series; Calculate the pseudo-pressure corresponding to the real pressure and the coefficient matrix B at the first moment in the time series; Calculate the pseudo-pressure distribution ψ at the first moment in the time series; The function fits the relationship between the real pressure and the pseudo-pressure, and calculates the distribution of the real pressure p in the time series; Calculate the pressure gradient distribution at the first moment in the time series; Repeat the cycle to calculate the pressure gradient at the remaining moments in the time series; Calculate the working fluid invasion depth D using logging data and compare the pressure gradient G at the mud invasion depth D with the critical pressure gradient G c The reasonable time t for well cleaning and blowout induction operation when the pressure gradient at the mud invasion depth is greater than the critical pressure gradient is obtained. c .

2. The method for calculating the time of a low permeability gas well formation cleaning and blowout induction operation according to claim 1, wherein: The target layer thickness h is obtained through well logging data, and the original formation pressure p i Obtained by downhole pressure gauge, formation temperature T wb The core displacement test rock samples were obtained by downhole core drilling tools, and the core compression coefficient C r The porosity φ is obtained by testing the experimental rock samples, and the relationship between the flow velocity v and the pressure gradient G is obtained through core displacement experiments.

3. The method for calculating the time of a low permeability gas well formation cleaning and blowout induction operation according to claim 1, wherein: The critical pressure gradient G c It is the minimum pressure gradient when the flow rate and pressure gradient show a linear relationship.

4. The method for calculating the time of a low permeability gas well formation cleaning and blowout induction operation according to claim 1, wherein: The calculation formula of the coefficient matrix A is: Where C is the wellbore storage coefficient, m 3 / MPa; Δx is the position difference between two adjacent grids, m; Δt is the difference between two adjacent time series, h; μ wb is the fluid viscosity at the bottom of the well, mPa·s; k is the permeability when the flow velocity and pressure gradient are linear, mD; h is the reservoir thickness, m; K2 is the dynamic permeability of the second grid, mD; r w is the well radius, m; φ is the porosity, dimensionless; is the gas compressibility coefficient at the second grid pressure, MPa -1 ; μ2 is the fluid viscosity at the second grid pressure, mPa·s; K i is the dynamic permeability of the ith grid, mD; C gi is the gas compressibility coefficient at the i-th grid pressure, MPa-1; μ i is the fluid viscosity at the i-th grid pressure, mPa·s; K N-1 is the dynamic permeability of the N-1th grid, mD; C g(N-1) is the gas compressibility coefficient at the N-2th grid pressure, MPa -1 ;μ N-1 is the fluid viscosity at the N-1th grid pressure, mPa·s; K N is the dynamic permeability of the Nth grid, mD; C gN is the gas compressibility coefficient at the Nth grid pressure, MPa -1 ; μ N is the fluid viscosity at the Nth grid pressure, mPa·s.

5. The method for calculating the time of a low permeability gas well formation cleaning and blowout induction operation according to claim 1, wherein: The calculation formula of the coefficient matrix B is: Where q is the output, m is the 3 / d;T wb is the temperature at the bottom of the well, K; p sc is the pressure under standard conditions, MPa; T sc is the temperature under standard conditions, K; t is time, hours; is the pseudo pressure at the bottom hole flow pressure at time n, MPa 2 / (mPa·s); is the pseudo pressure of the second grid at time n, MPa 2 / (mPa·s); is the pseudo pressure of the ith grid at time n, MPa 2 / (mPa·s); is the pseudo-pressure of the N-1th grid at time n; is the pseudo-pressure of the Nth grid at time n; ψ in is the pseudo pressure under the original formation pressure, MPa 2 / (mPa·s); ψ is the pseudo pressure, and its calculation formula is MPa 2 / (mPa·s); p is the true pressure, MPa, μ is the gas viscosity at the true pressure, mPa·s; Z is the gas deviation factor at the true pressure.

6. The method for calculating the time of a low permeability gas well formation cleaning and blowout induction operation according to claim 1, wherein: The calculation formula of the pseudo-pressure distribution ψ is: ψ=A -1 B=[ψ wf ψ2 … ψ i … ψ N-1 ψ N ] T 7. The method for calculating the time of a low permeability gas well formation cleaning and blowout induction operation according to claim 1, wherein: The relationship between the real pressure p and the pseudo pressure can be expressed as: p=f(ψ)=[p wf p2 … p i … p N-1 p N ] T Where f(ψ) is a polynomial function of the pseudo-pressure ψ, p wf is the bottom hole pressure, MPa; p2 is the pressure of the second grid, MPa; p i is the pressure of the ith grid, MPa; p N-1 is the pressure of the N-1th grid, MPa; p N is the pressure of the Nth grid, MPa.

8. The method for calculating the time of a low permeability gas well formation cleaning and blowout induction operation according to claim 1 is characterized in that: The pressure gradient G distribution calculation formula is: Where G is the pressure gradient, MPa / m; G1 is the pressure gradient of the first grid, MPa / m; G2 is the pressure gradient of the second grid, MPa / m; G i is the pressure gradient of the ith grid, MPa / m; G N-1 is the pressure gradient of the N-1th grid, MPa / m; G N is the pressure gradient of the Nth grid, MPa / m; p i is the real pressure corresponding to the pseudo-pressure of the i-th grid, MPa; p i-1 is the real pressure corresponding to the pseudo-pressure of the i-1th grid, MPa; x i is the distance between the ith grid and the bottom of the well, m; x i-1 is the distance from the i-1th grid to the bottom of the well, m.

9. The method for calculating the time of a low permeability gas well formation clean-up and blowout induction operation according to claim 1, wherein: The repeated cycle calculation is to calculate the coefficient matrix A, coefficient matrix B, pseudo-pressure distribution, pressure distribution, and pressure gradient distribution at the next moment in the time series until the last moment of the time series is calculated.

10. The method for calculating the time of a low permeability gas well formation clean-up and blowout induction operation according to claim 1, wherein: The reasonable time for well cleaning and blowout induction operation is t c It is the minimum time that the pressure gradient at the mud invasion depth is greater than the critical pressure gradient.

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