Well testing method for solving beaded interporous reservoirs

Abstract

The application relates to the technical field of well testing analysis methods, and is a well testing method for solving string-bead type fracture-cave type oil reservoirs. The method comprises the following steps: establishing a stratum seepage equation considering gravity effect, combining with Laplace transformation, and obtaining an analytic solution of well bottom pressure in final Laplace space. The fitting degree of the pressure solution obtained by the application with the double derivative curve of the measured well pressure solution is high, which indicates that the well bottom pressure solution data obtained according to the method of the application is close to the actual parameter data, so that the method of the application is used for pressure recovery data interpretation of the fracture-cave type oil reservoirs with string-bead type cave distribution.

Description

Technical Field

[0001] This invention relates to the field of well test analysis methods, and is a well test method for solving beaded fractured-vuggy reservoirs. Background Technology

[0002] Currently, carbonate reservoirs account for over 50% of the world's proven oil and gas reserves, with fractured-vuggy carbonate reservoirs making up 60% of that. Fractured-vuggy reservoirs possess complex pore structures, various fracture-vuggy connection methods, diverse flow mechanisms, and extremely strong stratigraphic heterogeneity, making their study a current focus in oil and gas reservoir development. Because fractured-vuggy reservoirs contain numerous fractures and caves of varying sizes, conventional research methods are unsuitable; therefore, new methods are needed to address their specific characteristics.

[0003] Interpreting pressure recovery data from fractured-vuggy reservoirs using existing well test models revealed inaccurate interpretations and poor curve fitting in some wells. Microseismic data from these wells showed a beaded pattern of karst caves within the formation. Therefore, it is necessary to develop a new beaded fractured-vuggy reservoir well test model suitable for interpreting pressure recovery data from fractured-vuggy reservoirs. Summary of the Invention

[0004] This invention provides a well testing method for solving the problem of fractured-vuggy reservoirs, overcoming the shortcomings of the prior art. It can effectively solve the problem that existing well testing models are not suitable for interpreting pressure recovery data of fractured-vuggy reservoirs.

[0005] The technical solution of this invention is achieved through the following measures: a well testing method for solving beaded fractured-vuggy reservoirs, comprising the following steps:

[0006] Step 1: Obtain the basic formation parameters of a certain well, and substitute these parameters into equation (1).

[0007] ① Equation (1) is the differential equation governing seepage in n regions, established based on the continuity equation and Darcy's law:

[0008]

[0009] ② The initial condition of the seepage control differential equation is: p(z,t=0)=p i (2)

[0010] ③The external boundary conditions of the seepage control differential equation are as follows:

[0011] Infinite boundary conditions:

[0012] p n (z→∞,t)=p i (3)

[0013] Closed boundary conditions:

[0014]

[0015] isobaric boundary conditions:

[0016] p n (z=z e ,t)=p i (5)

[0017] ④ When the pressure is equal everywhere in each cavern:

[0018]

[0019] ⑤ Let the storage coefficient of the karst cave be C. v Then there is a flow relationship at the cave:

[0020]

[0021] ⑥ The flow conditions at the wellbore are:

[0022]

[0023] In equations (1) to (8), p j This represents the pressure in the j-th region, j = 1, 2, 3, ..., n+1, where n is the number of caves; ρ is the fluid density; g is the acceleration due to gravity; and c is the pressure in the j-th region. f φ is the fluid compressibility coefficient; z is the height in the vertical direction; φ is the porosity; μ is the fluid viscosity; c t π is the overall compressibility coefficient; t is time; pi is the original formation pressure; z e h is the boundary height. l Let p be the height coordinates, l = 1, 2, 3, ..., 2n; vm The pressure in the cavern is m = 1, 2, 3, ..., n; r f Let C be the radius of the region. vm Let be the storage coefficient of the m-th karst cave; q be the production rate; B be the formation volume coefficient; and k be the formation permeability.

[0024] Step 2, dimensionless transformation of the mathematical model in Step 1 yields the following dimensionless mathematical model:

[0025]

[0026] The initial conditions for the dimensionless mathematical model are: p D (z D ,0)=0 (10)

[0027] Infinite boundary condition: pnD (z D →∞,t D )=0 (11)

[0028] Closed boundary conditions:

[0029] isobaric boundary condition: p nD (z D =z eD ,t D )=0 (13)

[0030] When the pressure is equal everywhere in every cavern:

[0031]

[0032] Let the reservoir coefficient of the karst cave be C. v Then there is a flow relationship at the cave:

[0033]

[0034] The flow conditions at the wellbore are:

[0035] Step 3: Perform a Laplace transform on the dimensionless equation from Step 2 to obtain the dimensionless equation in Laplace space:

[0036]

[0037]

[0038]

[0039]

[0040] Infinite boundary conditions:

[0041] Closed boundary conditions:

[0042] isobaric boundary conditions:

[0043] In equations (25) to (31), s is a Laplace variable, and the general solution of equation (25) is:

[0044]

[0045] In equation (32), c1, c2, c3, ..., c 2n+2 The coefficients are undetermined; the other coefficients are defined as follows:

[0046]

[0047] By combining equations (25) to (33) above, we obtain matrix equations under different boundary conditions. Solving the matrix equations yields the undetermined coefficients c1, c2, c3, ..., c. 2n+2 The matrix equations under different boundary conditions are as follows:

[0048] Infinite boundary conditions:

[0049]

[0050] Closed boundary conditions:

[0051]

[0052] isobaric boundary conditions:

[0053]

[0054] In equation (36),

[0055]

[0056] Step 4: Based on the undetermined coefficients obtained in Step 3, the dimensionless bottom-hole pressure solution in Laplace space can be obtained as follows:

[0057]

[0058] Considering the well reservoir and skin effect, the dimensionless bottom hole pressure solution in the Rado space is:

[0059]

[0060] In equation (39), S kin C is the epidermal coefficient. D The dimensionless wellbore storage coefficient is used to obtain the dimensionless bottom hole pressure solution in physical space through Stehfest inversion:

[0061]

[0062] In equation (40):

[0063]

[0064] The following are further optimizations and / or improvements to the above-mentioned technical solution:

[0065] In step 2 above, there is no dimensionless pressure.

[0066] Dimensionless Time

[0067] Dimensionless distance

[0068] Dimensionless wellbore storage coefficient

[0069] Dimensionless cave storage coefficient

[0070] Dimensionless gravity coefficient G D =2ρgc f ·r f (twenty two)

[0071] Dimensionless mobility ratio

[0072] Dimensionless storage ratio ω 1n =(φc t )1 / (φc t ) n (twenty four).

[0073] This invention targets fractured-vuggy reservoirs with beaded cavern distribution in the formation. The model used in the method considers gravity factors and establishes a mathematical model based on the continuity equation and Darcy's law. Simultaneously, the bottomhole pressure solution is obtained through Laplace transform and inverse Laplace numerical inversion. The obtained pressure solution shows a high degree of fit between the double derivative curves and the measured well pressure solution, indicating that the bottomhole pressure solution data obtained by the method according to this invention closely approximates the actual parameter data. This enables the method of this invention to be used for interpreting pressure recovery data in fractured-vuggy reservoirs with beaded cavern distribution. Attached Figure Description

[0074] Appendix Figure 1 This is a schematic diagram of the wellbore model region division of the present invention.

[0075] Appendix Figure 2 This is a double logarithmic curve of the bottom hole pressure and pressure derivative under three boundary conditions when the number of karst caves in the model of this invention is 1.

[0076] Appendix Figure 3 This is a double logarithmic curve of the bottom pressure and pressure derivative when the number of karst caves in the model of this invention is 2.

[0077] Appendix Figure 4 The measured well pressure and pressure derivative double logarithmic plot in the embodiment of the present invention.

[0078] Appendix Figure 5 A curve fitting diagram of the measured well pressure and pressure derivative in the embodiments of the present invention and the calculated pressure and pressure derivative of the present invention. Detailed Implementation

[0079] The present invention is not limited to the following embodiments, and the specific implementation can be determined according to the technical solution of the present invention and the actual situation.

[0080] The present invention will be further described below with reference to embodiments, and the suitability of the method described herein will be verified:

[0081] According to the method described in this invention, the double logarithmic curves of bottom hole pressure and pressure derivative for different numbers of karst caves are obtained (see figure). Figure 2 , Figure 3 .

[0082] Example: This well testing method for solving beaded fractured-vuggy reservoirs uses a wellbore model as follows. Figure 1 As shown in Table 1, the basic formation parameters for a specific well in the Shunbei area are selected.

[0083] A double logarithmic chart was plotted using the actual pressure recovery data measured from the well (see...). Figure 4 ).

[0084] The basic formation parameters of the well are input into step 1 of the method of this invention. Then, the parameters such as the volume of the karst cave are derived using the method described in this invention, thus obtaining the interpretation results, as shown in Table 2. Pressure and pressure derivative curves are then plotted based on the interpretation results (see Table 2). Figure 5 (Theoretical curve).

[0085] pass Figure 5 It can be seen that the double logarithmic curves of pressure and pressure derivative plotted according to the calculation results of the present invention basically coincide with the actual measured double logarithmic curves of pressure and pressure derivative, indicating that the two have a high degree of fit, thus indicating that the bottom hole pressure solution data obtained by the well test method of the present invention is close to the actual bottom hole parameter data.

[0086] The above technical features constitute the embodiments of the present invention, which have strong adaptability and implementation effect. Unnecessary technical features can be added or removed according to actual needs to meet the needs of different situations.

[0087] Table 1 Basic Formation Parameters Measured in Wells

[0088] parameter value unit Original formation pressure 80.21 MPa Wellbore radius 0.0746 m Porosity 0.1 fluid viscosity 0.00025 Pa·s Formation volume coefficient 1.99 Fluid compressibility 0.0029 <![CDATA[MPa -1 ]]> Mid-depth 7531 m fluid density 800.01 <![CDATA[kg / m 3 ]]>

[0089] Table 2 Explanation Results

[0090]

Claims

1. A well testing method for solving beaded fractured-vuggy reservoirs, characterized in that... The following steps: Step 1: Obtain the basic formation parameters of a certain well, and substitute these parameters into equation (1). ① Equation (1) is the differential equation governing seepage in n regions, established based on the continuity equation and Darcy's law: ② The initial condition of the seepage control differential equation is: p(z,t=0)=p i (2) ③The external boundary conditions of the seepage control differential equation are as follows: Infinite boundary conditions: p n (z→∞,t)=p i (3) Closed boundary conditions: isobaric boundary conditions: p n (z=z e ,t)=p i (5) ④ When the pressure is equal everywhere in each cavern: ⑤ Let the storage coefficient of the karst cave be C. v Then, a flow relationship exists at the cave: ⑥ The flow conditions at the wellbore are: In equations (1) to (8), p j This represents the pressure in the j-th region, j = 1, 2, 3, ..., n+1, where n is the number of caves; ρ is the fluid density; g is the acceleration due to gravity; and c is the pressure in the j-th region. f φ is the fluid compressibility coefficient; z is the height in the vertical direction; φ is the porosity; μ is the fluid viscosity; c t π is the overall compressibility coefficient; t is time; pi is the original formation pressure; z e h is the boundary height. l Let p be the height coordinates, l = 1, 2, 3, ..., 2n; vm The pressure in the cavern is m = 1, 2, 3, ..., n; r f Let C be the radius of the region. vm Let be the storage coefficient of the m-th karst cave; q be the production rate; B be the formation volume coefficient; and k be the formation permeability. Step 2: Dimensionless transformation of the mathematical model from Step 1 yields the following dimensionless mathematical model: The initial conditions for the dimensionless mathematical model are: p D (z D ,0)=0 (10) Infinite boundary condition: p nD (z D →∞,t D )=0 (11) Closed boundary conditions: isobaric boundary condition: p nD (z D =z eD ,t D )=0 (13) When the pressure is equal everywhere in every cavern: Let the reservoir coefficient of the karst cave be C. v Then, a flow relationship exists at the cave: The flow conditions at the wellbore are: Step 3: Perform a Laplace transform on the dimensionless equation from Step 2 to obtain the dimensionless equation in Laplace space: Infinite boundary conditions: Closed boundary conditions: isobaric boundary conditions: In equations (25) to (31), s is a Laplace variable, and the general solution of equation (25) is: In equation (32), c1, c2, c3, ..., c 2n+2 The coefficients are undetermined; the other coefficients are defined as follows: By combining equations (25) to (33) above, matrix equations under different boundary conditions are obtained. Solving the matrix equations yields the undetermined coefficients c1, c2, c3, ..., c. 2n+2 The matrix equations under different boundary conditions are as follows: Infinite boundary conditions: Closed boundary conditions: isobaric boundary conditions: In equation (36), Step 4: Based on the undetermined coefficients obtained in Step 3, the dimensionless bottom hole pressure solution in Laplace space is obtained as follows: Considering the well reservoir and skin effect, the dimensionless bottom hole pressure solution in the Rado space is: In equation (39), S kin C is the epidermal coefficient. D The dimensionless wellbore storage coefficient is used to obtain the dimensionless bottom hole pressure solution in physical space through Stehfest inversion: In equation (40):

2. The well testing method for solving beaded fractured-vuggy reservoirs according to claim 1, characterized in that... In step 2, Dimensionless pressure Dimensionless Time Dimensionless distance Dimensionless wellbore storage coefficient Dimensionless cave storage coefficient Dimensionless gravity coefficient G D =2ρgc f ·r f (twenty two) Dimensionless mobility ratio Dimensionless storage ratio ω 1n =(φc t )1 / (φc t ) n (twenty four).

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