Fracture-vug type gas reservoir well testing model with shaft connected with large karst cave and establishing method and application of fracture-vug type gas reservoir well testing model

Abstract

The invention discloses a fracture-vug type gas reservoir well testing model with a shaft connected with a large karst cave and an establishing method and application of the fracture-vug type gas reservoir well testing model. The method comprises the following steps: selecting proper gas reservoir parameters to establish a fracture-vug type gas reservoir well testing model for connecting a shaft with a large karst cave according to a physical model for connecting the shaft with the large karst cave; according to the gas reservoir characteristics, an energy equation between the shaft and the large karst cave is established, the energy equation considers pressure loss at the joint of the large karst cave and the shaft, and the actual geological condition is better met. The novel fracture-vuggy gas reservoir well test interpretation method using the fracture-vuggy gas reservoir well test model comprises the following steps: performing solution and numerical inversion according to the fracture-vuggy gas reservoir well test model to obtain a real space bottom hole pressure solution; a real space bottom hole pressure value is obtained by utilizing the real space bottom hole pressure solution and combining the gas reservoir parameter actual value; and fitting the real space bottom hole pressure value with the actually measured bottom hole pressure data to obtain parameters such as the volume of the large karst cave. The karst cave volume of the gas reservoir can be explained more accurately by using the gas reservoir type well testing model.

Description

Technical Field

[0001] The present invention belongs to the technical field of unconventional oil and gas reservoir development, and relates to a fracture-cavity gas reservoir well testing model suitable for a wellbore of a large-scale karst cave connected to a large karst cave, and a method for establishing and applying the model (i.e., a new method for well testing interpretation of fracture-cavity carbonate gas reservoirs that uses the fracture-cavity gas reservoir well testing model to obtain parameters such as the cave volume, storage ratio, crossflow coefficient, etc. of the fracture-cavity gas reservoir through pressure recovery well testing). Background Art

[0002] Fracture-cavity carbonate gas reservoirs occupy an important position in the production of oil and gas resources in the world. In recent years, the exploration and development of fracture-cavity carbonate gas reservoirs in China has shown a rapid development trend, especially in the Tarim, Ordos and Sichuan Basins. The pore structure of fracture-cavity carbonate gas reservoirs (referred to as fracture-cavity gas reservoirs) is very complex, including matrix, fractures and large caves. Fractures are the main flow channels, while matrix and large caves are the main storage spaces. The types of connections between matrix, fractures and caves are diverse and have strong heterogeneity. Fracture-cavity carbonate gas reservoirs (i.e., fracture-cavity gas reservoirs) can be divided into two types: one is a fracture-cavity gas reservoir with small-scale caves, the diameter of which is between millimeters and centimeters. Researchers use triple medium models to study this type of fracture-cavity gas reservoir with small-scale caves. The other is a fracture-cavity gas reservoir with large-scale caves (referred to as large caves), the diameter of which is between several meters and tens of meters. This type of large-scale karst fracture-cave gas reservoir is widely distributed in western China, especially in Xinjiang.

[0003] In recent years, scholars have begun to study the impact of large-scale caves on fracture-cave carbonate oil and gas reservoirs. Zhang Fuxiang et al. considered the caves as high-permeability areas and established a well test model for fracture-cave oil reservoirs drilled in large-scale caves. Liu Hong et al. proposed that caves can be considered as equipotential bodies to establish a well test model. Gao et al. considered the filling effect of the caves and used the Barree-Conway method to solve the non-Darcy flow of fluids in the caves. Peng Chaoyang et al. used a discrete medium network, regarded the caves as zero-dimensional models, and established two well test models for oil and water in fracture-cave oil reservoirs. The above studies are all based on the study of fracture-cave oil reservoirs in large-scale caves. Nowadays, there are few studies on fracture-cave gas reservoirs in large-scale caves. Fracture-cave gas reservoirs in large-scale caves have been discovered in Shunbei area of ​​my country. This type of gas reservoir has an extremely deep burial depth and high temperature and high pressure in the reservoir. During the drilling process, engineers discovered that the drill pipe was empty and a large amount of mud was leaking. Combined with seismic data, they found that the well had entered a large cave (i.e. a large-scale cave) during the drilling process. Figure 1 This is the seismic profile when drilling into a large cave.

[0004] The existing technology can be summarized into the following two types:

[0005] 1. Conventional sandstone well testing is an important means to understand reservoir dynamics. Its purpose is to evaluate the production dynamics of oil and gas wells or reservoirs and obtain formation parameters through the test data of oil and gas wells. Pressure recovery well testing is the most commonly used method in well testing. However, the traditional well testing model is not suitable for fracture-cavity oil and gas reservoirs. It cannot provide cave-related parameters and reserve data. For fracture-cavity gas reservoirs, its application significance is very small.

[0006] 2. Well testing of fracture-cavity oil reservoirs: The well testing interpretation method for the fluid in the reservoir is oil, which can obtain the cave and fracture parameters of fracture-cavity oil reservoirs. However, in fracture-cavity gas reservoirs, the fluid is gas, which is highly compressible, and its volume coefficient and fluid viscosity are greatly affected by pressure. Therefore, the well testing model of fracture-cavity oil reservoirs is not applicable to fracture-cavity gas reservoirs, so the well testing model of fracture-cavity gas reservoirs must be re-established.

[0007] In summary, when a well is drilled in a large-scale cave and the wellbore is connected to the large-scale cave, the gas flow in the large-scale cave no longer follows Darcy's law. Therefore, the traditional triple medium model applicable to fracture-cave gas reservoirs in small-scale caves cannot accurately describe its flow characteristics. Especially when the wellbore is connected to a large-scale cave, the gas flow is more complicated. Therefore, it is necessary to establish a fracture-cave gas reservoir well test model applicable to large-scale caves (large caves) (that is, a fracture-cave gas reservoir well test model in which a well is drilled in a large cave and the wellbore is connected to the large cave). However, there is currently no such well test model for fracture-cave gas reservoirs in which the wellbore is connected to a large cave and is applicable to large-scale caves. Summary of the invention

[0008] The technical problem to be solved by the present invention is that the existing fracture-cave oil reservoir well test model applicable to large-scale karst caves and the existing triple medium model applicable to fracture-cave gas reservoirs in small-scale karst caves are not applicable to fracture-cave gas reservoirs in large-scale karst caves. The present invention aims to provide a fracture-cave gas reservoir well test model applicable to large-scale karst caves, in which a wellbore is connected to a large karst cave, and a method for establishing the same, and also provides an application method of the fracture-cave gas reservoir well test model in which a wellbore is connected to a large karst cave, that is, a new method for interpreting mean well test of fracture-cave gas reservoirs when large-scale karst caves exist.

[0009] The present invention can establish a fracture-cavity gas reservoir well test model when a wellbore is connected to a large cave (i.e., a large-scale cave). The present invention can establish a corresponding fracture-cavity gas reservoir well test interpretation model for the situation where the wellbore is connected to the large cave, and obtain parameters such as the volume of the large cave, storage ratio, wellbore storage coefficient, crossflow coefficient, wellbore skin coefficient and permeability through data interpretation.

[0010] The technical solution adopted by the present invention to solve the above technical problems is as follows:

[0011] 1. A fracture-cavity gas reservoir well testing model in which a wellbore is connected to a large karst cave, the fracture-cavity gas reservoir well testing model comprising the following five formulas:

[0012]

[0013] The physical meanings of the five formulas in the above fracture-cavity gas reservoir well testing model are:

[0014] The first formula: the seepage equation of the fracture system;

[0015] The second formula: the seepage equation of the matrix system;

[0016] The third formula: through the wellbore skin factor S w Corrected bottom hole pressure;

[0017] The fourth formula: The total natural gas production calculation formula, the total production is composed of the four parts on the right side of the equation;

[0018] The fifth formula is the energy equation between the wellbore and the large cave; the meaning of each parameter is: ψ wD is the dimensionless bottom hole pseudo pressure, ψ cD is the dimensionless cave pseudo-pressure; ψ fD is the dimensionless fracture pseudo-pressure, ψ mD is the dimensionless matrix pseudo-pressure, λ is the cross-flow coefficient, ω is the storage capacity ratio, S w Wellbore skin factor, C wD is the dimensionless wellbore storage coefficient, C cD is the dimensionless cave reservoir coefficient, h D is the dimensionless height, ξ is the cave coefficient, η is the pressure propagation coefficient, r D is the dimensionless radius, r cD is the dimensionless cave radius, t D is the dimensionless time and t is the time.

[0019] 2. A method for establishing a well testing model of a fracture-cavity gas reservoir in which a wellbore is connected to a large karst cave, the method comprising the following steps:

[0020] Step 1: Establish a physical model of the wellbore connected to the large cave;

[0021] Step 2: According to the physical model of the wellbore connected to the large cave, appropriate gas reservoir parameters are selected to establish a fracture-cave gas reservoir well test model in which the wellbore is connected to the large cave.

[0022] 3. The method for establishing a fracture-cave gas reservoir well test model in which the wellbore is connected to a large cave, wherein the physical model in which the wellbore is connected to the large cave includes an internal physical model and an external physical model; the internal physical model includes a wellbore whose outlet end is located on the ground surface and a large-scale large cave connected to the other end of the wellbore, and the large cave is simulated by a large cylinder, and the two have heights h1 and h2 respectively; the external physical model includes a matrix and fractures.

[0023] 4. The method for establishing a fracture-cave gas reservoir well test model in which the wellbore is connected to a large cave takes into account the pressure fluctuations of a large amount of gas stored in the large cave and the wellbore in the internal physical model, and also takes into account the local energy loss generated when the gas enters the wellbore from the large cave.

[0024] 5. The method for establishing the well test model of the fracture-cavity gas reservoir in which the wellbore is connected to the large cave adopts a dual-porosity medium model to describe the flow of gas in the external physical model, and at the same time, introduces pseudo-pressure instead of pressure.

[0025] 6. The method for establishing a fracture-cavity gas reservoir well test model in which the wellbore is connected to a large cave, wherein the gas reservoir parameters include: wellbore radius, porosity, comprehensive compression coefficient, initial pressure, formation thickness and gas reservoir temperature.

[0026] 7. The method for establishing the well test model of the fracture-cavity gas reservoir in which the wellbore is connected to the large cave is to derive the physical model of the wellbore connected to the large cave according to the derivation method after considering the internal physical model and the external physical model, and to establish a new mathematical model according to the derivation formula, which is the well test model of the fracture-cavity gas reservoir in which the wellbore is connected to the large cave;

[0027] In the derivation process, an energy equation between the wellbore and the large cave is established according to the gas reservoir characteristics, and the energy equation between the wellbore and the large cave takes into account the pressure loss at the connection between the large cave and the wellbore;

[0028] The energy equation between the wellbore and the large cave is: (This is dimensionalized, and the pseudo-pressure is converted into pressure)

[0029]

[0030] In the above formula, the meaning of each parameter is:

[0031] p w represents the bottom hole pressure, p c represents the pressure inside the cave, r w represents the wellbore radius, d c represents the diameter of the cave, v0 represents the initial velocity of the gas, χ represents the speed of pressure wave propagation, C c represents the cave storage coefficient, and t represents time.

[0032] 8. An application method of the fracture-cavity gas reservoir well test model in which the wellbore is connected to a large karst cave, that is, a new method for interpreting fracture-cavity gas reservoir well test using the fracture-cavity gas reservoir well test model in which the wellbore is connected to a large karst cave, the method comprising the following steps:

[0033] Step 1: According to the fracture-cave gas reservoir well test model in which the wellbore is connected to the large cave, solving and numerical inversion are performed to obtain the real space bottom hole pressure solution;

[0034] Step 2: using the real space bottom hole pressure solution and combining it with the actual value of the gas reservoir parameter, obtain the real space bottom hole pressure value (that is, substituting the actual value of the gas reservoir parameter into the real space bottom hole pressure solution formula for calculation to obtain the real space bottom hole pressure value);

[0035] Step 3: Fit the real space bottom hole pressure value and the measured bottom hole pressure data (pressure recovery data of fracture-cavity gas reservoir) using the plate fitting method to obtain parameters such as cave volume, storage ratio and permeability of the large cave.

[0036] 9. The application method of the fracture-cave gas reservoir well testing model of the large-scale karst cave, the step 1 comprises:

[0037] Step 1.1, using Laplace transform to solve the well test model and obtain a dimensionless bottom hole pseudo-pressure solution function in Laplace space;

[0038] Step 1.2: Using the Stehfest numerical inversion technique, perform numerical inversion on the Laplace space bottom hole pressure solution function to obtain the real space bottom hole pressure solution.

[0039] 10. The application method of the fracture-cave gas reservoir well test model of the large-scale karst cave, in the step 1.1, the well test model is subjected to Laplace transformation to obtain a dimensionless bottom hole pseudo-pressure solution function in Laplace space under infinite formation boundary conditions:

[0040]

[0041] in:

[0042]

[0043]

[0044]

[0045]

[0046]

[0047]

[0048]

[0049]

[0050]

[0051]

[0052]

[0053] s is the Laplace variable; K0, K1, I0 and I1 are Bessel functions.

[0054] Beneficial effects of the present invention:

[0055] The present invention establishes a fracture-cavity gas reservoir well testing model when the wellbore is connected to a large cave (i.e., a large-scale cave). The fracture-cavity gas reservoir well testing model proposes an energy equation (Formula 5) between the wellbore and the large cave based on the gas reservoir characteristics. The energy equation takes into account the pressure loss at the connection between the large cave and the wellbore, which is more in line with actual geological conditions.

[0056] At the same time, the fracture-cavity gas reservoir well testing model takes into account the compressibility of gas and introduces the definition of pseudo-pressure, so that the volume of large caves in fracture-cavity gas wells can be obtained through data interpretation using the fracture-cavity gas reservoir well testing interpretation model. At the same time, parameters such as storage volume ratio, wellbore storage coefficient, crossflow coefficient, wellbore skin coefficient and permeability are more accurate.

[0057] The present invention establishes a new method for interpreting well testing of fracture-cavity gas reservoirs when large-scale karst caves exist. By actually measuring the pressure recovery data of fracture-cavity gas reservoirs, the large karst cave and fracture parameters are obtained through the plate fitting method to evaluate the production dynamics of the gas reservoir. The present invention can accurately interpret the well testing data when the wellbore is connected to the large-scale karst cave, which has important guiding significance for the development of fracture-cavity carbonate gas reservoirs.

[0058] The new method for interpreting fracture-cavity gas reservoir well test of the present invention provides a matching interpretation method for calculating reservoir parameters and reserves of fracture-cavity gas reservoirs. The method can directly interpret the volume of large caves in fracture-cavity gas reservoirs and provide technical support for the formulation of oilfield development plans. The present invention has two major advantages: (1) The model is simple and easy to solve. An analytical solution can be given in Laplace space, and the analytical solution does not involve the calculation of complex functions, so the calculation speed is fast; (2) The interpretation result after fitting can directly give the size of the cave volume, which can be conveniently used to calculate the reserves of a single well. BRIEF DESCRIPTION OF THE DRAWINGS

[0059] Figure 1 It is a seismic profile when drilling into a large cave;

[0060] Figure 2 It is a schematic diagram of the physical model of the present invention;

[0061] Figure 3 is a graph of pressure and pressure derivative in Example 2 of the present invention;

[0062] Figure 4 It is a double logarithmic curve fitting diagram in Example 2 of the present invention. DETAILED DESCRIPTION

[0063] In order to make the purpose, technical solution and advantages of the present invention clearer, the technical solution of the present invention will be clearly and completely described below in combination with specific embodiments and drawings. Obviously, the described embodiments are only part of the embodiments of the present invention, not all of the embodiments. Based on the embodiments described in the present invention, all embodiments obtained by ordinary technicians in this field without creative work are within the scope of protection of the present invention.

[0064] Example 1

[0065] The present embodiment provides a method for establishing a fracture-cavity gas reservoir well testing model in which a wellbore is connected to a large karst cave, and the method comprises the following steps:

[0066] Step 1: Establish a physical model of the wellbore connected to the large cave;

[0067] The physical model of the wellbore connected to the large cave is divided into two parts, namely the internal physical model and the external physical model. The internal physical model includes the wellbore with the outlet located on the ground surface and the large-scale large cave connected to the other end of the wellbore. The large cave is simulated by a large cylinder, and the two have heights h1 and h2 respectively; the external physical model includes the matrix and fractures. Figure 2 shown.

[0068] Situation of the internal physical model: In the internal physical model, a large amount of gas is stored in large caves and wellbores, forming a high-pressure fluid storage space; when the well is opened for production, the compressibility of the fluid and the pipe wall will cause pressure fluctuations; at the same time, local energy loss will occur when the gas enters the wellbore from the large cave.

[0069] Case of external physical model: In the external physical model, a dual-porosity medium model is used to describe the gas flow. It is assumed that the gas only enters the wellbore through the fractures, and the gas directly entering the wellbore from the matrix can be ignored.

[0070] Step 2: According to the physical model of the wellbore connected to the large cave, select appropriate gas reservoir parameters and establish a fracture-cave gas reservoir well test model in which the wellbore is connected to the large cave.

[0071] According to the physical model of the wellbore connected to the large cave described above, after considering the situations of the internal physical model and the external physical model described above, the deduction is carried out according to the deduction method described below. According to the deduction process and deduction equation (calculation formula), a new well testing model (mathematical model) is established, which is the fracture-cavity type gas reservoir well testing model in which the wellbore is connected to the large cave.

[0072] The derivation method and derivation process are as follows:

[0073] First, the internal physical model is studied. In the process of natural gas entering the wellbore from the large cave and then flowing in the wellbore, the continuity equation and momentum equation need to be satisfied. In this process, the present invention only considers the flow in the vertical direction. A large amount of natural gas is stored in the large cave and the wellbore, forming a high-pressure fluid storage space. When the well is opened, the compressibility of the fluid and the pipe wall will cause pressure fluctuations.

[0074] When natural gas enters the wellbore from the large cave and then flows vertically in the wellbore, it must satisfy the following continuity equation and momentum equation:

[0075] Continuity equation

[0076] Combining the continuity equation and the momentum equation

[0077] In the above formula, t is time, s; ρ is gas density, kg / m 3 ; v is the gas velocity, m / s; r w is the wellbore radius, m; f is the friction coefficient, dimensionless; z is the gas compressibility coefficient, dimensionless.

[0078] For the fluid element, equation (3) can be written by the law of conservation of mass:

[0079]

[0080] N is the cross-sectional area of ​​the fluid element.

[0081] Expanding equation (3) yields equation (4):

[0082]

[0083] Equation (4) can be simplified to equation (5):

[0084]

[0085] Due to the large pressure changes, the wellbore will also deform. Its deformation is determined by the wall thickness, wellbore radius and elastic modulus of the tubing material. When the pressure changes, the relationship between its radial deformation and pressure is equation (6):

[0086]

[0087] In the above formula, r w is the wellbore radius, m; e is the pipe wall thickness, m; E w is the elastic modulus of the tubing, MPa.

[0088] From the tubing area formula, we can get equation (7):

[0089]

[0090] Combining equation (6) and equation (7), we can get equation (8):

[0091]

[0092] Converting the density term to a function of pressure and combining equation (5) and equation (8) yields equation (9):

[0093]

[0094] Here, define a variable:

[0095]

[0096] In the above formula, χ is the speed of pressure wave propagation, m / s; E f is the gas bulk modulus, MPa.

[0097] Combining equation (9) and equation (10), we can get equation (11):

[0098]

[0099] Combining equation (1), equation (2), and equation (11), we can finally get equation (13):

[0100]

[0101] When gas flows in a large cave, the gas flow velocity is very slow. According to actual data, it is about 1×10-4m / s to 1×10-3m / s. The friction term is related to the second power of the gas flow velocity. Therefore, the friction term is very small and is ignored here.

[0102] The relationship between the cave storage coefficient and the gas flow velocity is:

[0103]

[0104] Therefore, equation (12) can be rewritten as:

[0105]

[0106] The solution of equation (14) is:

[0107]

[0108] Where v0 is the initial gas flow velocity, m / s.

[0109] The gas flow velocity at the junction of the large cave and the wellbore is:

[0110]

[0111] The cross-sectional area of ​​the large cave is much larger than that of the wellbore, and the connection between the two is like a contraction tube. When the gas enters the wellbore from the large cave, the speed will increase rapidly, and the pressure of the gas will decrease. At this time, some gas will form vortices near the tube wall, and these vortices will consume energy. The energy equation from the large cave to the wellbore is:

[0112]

[0113] In the above formula, p c is the cave pressure, MPa; p w is the bottom hole pressure, MPa; h j is the local loss, m.

[0114] Local loss of shrink tube h j The empirical formula is:

[0115]

[0116] In the above formula, A w is the wellbore cross-sectional area, m 2 ; A c is the cross-sectional area of ​​the cave, m 2 .

[0117] Combining equation (16), equation (17) and equation (18), we can obtain equation (19), which is the wellbore energy equation (the energy equation between the wellbore and the large cave):

[0118]

[0119] In the above formula, the meaning of each parameter is:

[0120] p w represents the bottom hole pressure, p c represents the pressure inside the cave, r w represents the wellbore radius, d c represents the diameter of the cave, v0 represents the initial velocity of the gas, χ represents the speed of pressure wave propagation, C c represents the cave storage coefficient, and t represents time.

[0121] The biggest difference between the gas reservoir type well testing model of the present invention and the existing oil reservoir type well testing model is that the present invention establishes an energy equation between the wellbore and the large cave based on the gas reservoir characteristics, and the present invention takes into account the pressure loss at the connection between the large cave and the wellbore, which is more in line with actual geological conditions.

[0122] For the external physical model, the present invention adopts a dual-porous medium model to describe the flow of gas, and at the same time, introduces pseudo-pressure to replace pressure.

[0123]

[0124] In the above formula, the meaning of each parameter is:

[0125] ψ is the pseudo-pressure, p is the pressure, μ is the gas viscosity, and Z is the compressibility factor.

[0126] The equation is as follows:

[0127] The following is the seepage equation of the dual medium model.

[0128]

[0129]

[0130] In the above formula, the meaning of each parameter is:

[0131] k f is the fracture permeability, k m is the matrix permeability, ψ f is the fracture pseudo-pressure, ψ m is the matrix pseudo pressure, α is the cross-flow coefficient, μ is the gas viscosity, φ f is the fracture porosity, φ m is the matrix porosity, c f is the crack compression coefficient, c m is the matrix compressibility coefficient, t is the time, and r is the radius.

[0132] When the gas approaches the wellbore, an inertial-turbulent effect occurs, which causes an additional pressure drop. In well testing, the total skin factor is introduced to describe this pressure drop.

[0133] S w =s w +D′q sc (25)

[0134] In the above formula, S w is the total skin factor, dimensionless; s w is the true skin factor, dimensionless; q sc is the wellhead production, m 3 / s, D′ is the turbulence coefficient, s / m 3 .

[0135] The bottom hole pressure can be expressed as:

[0136]

[0137] In the above formula, the meaning of each parameter is:

[0138] ψ f is the pseudo-pressure of the fluid in the fracture, ψ w is the pseudo pressure of the fluid in the wellbore, S w is the wellbore skin factor, r w is the wellbore radius.

[0139] The gas state equation is:

[0140]

[0141] In the above formula, the meaning of each parameter is:

[0142] p is the gas pressure, ρ is the gas density, z is the gas compressibility coefficient, T is the gas temperature, R is the gas universal constant, and M is the gas molecular weight.

[0143] The total natural gas production q under formation conditions is:

[0144]

[0145] In the above formula, q is the total natural gas production under formation conditions, m 3 / s; B g is the formation volume coefficient, dimensionless; p sc is the pressure under standard conditions, which is 0.101MPa; T sc is the temperature under standard conditions, which is 288.16K.

[0146] The total natural gas production q under formation conditions consists of four parts: (1) wellbore storage; (2) cave storage; (3) gas flowing into the wellbore from fractures; (4) gas flowing into the cave from fractures. Its expression is as follows:

[0147]

[0148] In the above formula, the meaning of each parameter is:

[0149] q sc is the gas production under standard conditions, T is the temperature of the gas, T sc is the gas temperature under standard conditions, μ is the gas viscosity, p sc is the gas pressure under standard conditions, ψ is the pseudo pressure, C is the reservoir coefficient, ψ wis the pseudo-wellbore pressure, ψ c is the cave pseudo-pressure, ψ f is the fracture pseudo-pressure, C w is the wellbore storage coefficient, C c is the cave storage coefficient, r w is the wellbore radius, r c is the radius of the cave, r f is the fracture radius, r is the radius variable, t is the time variable, h1 is the wellbore height, h2 is the cave height, and k is the permeability. (Subscript w represents wellbore, subscript c represents cave, and subscript f represents fracture).

[0150] Formula (27) is the total natural gas production equation under formation conditions. Originally, both sides of formula (27) have -zμ / 2p. Therefore, both sides of the equation are divided by -zμ / 2p. In this way, formula (26) is converted into the left side of formula (27).

[0151] According to the derivation process and derivation equation (calculation formula), a new well testing model (mathematical model) is established, which is the fracture-cavity type gas reservoir well testing model in which the wellbore is connected to the large karst cave.

[0152] The final established fracture-cavity gas reservoir well test model in which the wellbore is connected to a large karst cave is:

[0153]

[0154] The physical meanings of the five formulas in the above fracture-cavity gas reservoir well testing model are:

[0155] The first formula: the seepage equation of the fracture system;

[0156] The second formula: the seepage equation of the matrix system;

[0157] The third formula: through the wellbore skin coefficient S w Corrected bottom hole pressure;

[0158] The fourth formula: The total natural gas production calculation formula, the total production is composed of the four parts on the right side of the equation;

[0159] The fifth formula: the energy equation between the wellbore and the large cave;

[0160] The meaning of each parameter is: wD is the dimensionless bottom hole pseudo pressure, ψ fD is the dimensionless fracture pseudo-pressure, ψ mD is the dimensionless matrix pseudo-pressure, λ is the cross-flow coefficient, ω is the storage capacity ratio, S w Wellbore skin factor, C wD is the dimensionless wellbore storage coefficient, C cD is the dimensionless cave reservoir coefficient, h Dis the dimensionless height, ξ is the cave coefficient, η is the pressure propagation coefficient, and t is the time.

[0161] in:

[0162]

[0163]

[0164] The meanings and units of the parameters in the formula are shown in Table 1, and the meanings of the subscripts in the parameters are shown in Table 2.

[0165] Table 1 Meaning of parameters and their units

[0166]

[0167]

[0168] Table 2 Meaning of the subscripts in the parameters

[0169]

[0170]

[0171] The gas reservoir type well test model in which the wellbore is connected to the large karst cave established in the present invention has the following two advantages:

[0172] (1) When modeling, the present invention establishes an energy equation (the fifth formula) between the wellbore and the large cave based on the characteristics of the gas reservoir. The energy equation takes into account the pressure loss at the connection between the large cave and the wellbore. This model is later used to explain the cave volume of the gas reservoir, which is more in line with the actual geological conditions.

[0173] When gas enters the wellbore from the large cave, the gas velocity suddenly increases, and according to the energy equation, the gas pressure will decrease. If the energy equation is not considered, the gas pressure calculated by the model will be too high, and the well test results will be inaccurate. Therefore, it is more in line with the actual situation to establish an energy equation between the wellbore and the large cave.

[0174] (2) The karst cave volume of the gas reservoir interpreted by the gas reservoir type well testing model of the present invention is more accurate than the karst cave volume of the gas reservoir interpreted by the existing oil reservoir type well testing model in the prior art.

[0175] The fracture-cavity gas reservoir well testing model of the present invention takes into account the compressibility of gas and introduces the definition of pseudo-pressure, so that the volume of large caves in fracture-cavity gas wells can be obtained through data interpretation using the fracture-cavity gas reservoir well testing interpretation model. At the same time, parameters such as storage volume ratio, wellbore storage coefficient, crossflow coefficient, wellbore skin coefficient and permeability are more accurate.

[0176] Crude oil is a slightly compressible fluid, while gas is a compressible fluid. There is a big difference in the compressibility of the two. When gas enters the wellbore from the cave, due to its compressibility, the energy equation of gas must be corrected by a correction factor compared to crude oil. Therefore, the reservoir-type well testing model cannot accurately explain the fracture-cavity gas reservoir. The present invention establishes a gas reservoir-type well testing model based on the gas reservoir characteristics. The third formula in the gas reservoir-type well testing model is to use the wellbore skin coefficient S w Corrected bottom hole pressure; that is, in the present invention, the energy equation of the gas is added with a correction factor, namely the wellbore skin factor S w , making the cave volume of the gas reservoir interpreted by the gas reservoir-type well testing model more accurate.

[0177] Example 2

[0178] This embodiment analyzes the well test pressure recovery data of a well in Shunbei area to obtain the well test curve of the well, which is an application of the fracture-cavity gas reservoir well test model established in Embodiment 1 in which the wellbore is connected to a large cave.

[0179] This embodiment uses the fracture-cavity gas reservoir well test model established in Example 1, in which the wellbore is connected to a large cave, to perform a new method for interpreting fracture-cavity gas reservoir well test, including the following steps:

[0180] Step 1, obtaining a real space bottom hole pressure solution according to a fracture-cave gas reservoir well test model in which the wellbore is connected to a large cave;

[0181] This step 1 includes:

[0182] Step 1.1, solve the well test model using Laplace transform to obtain the dimensionless bottom hole pseudo-pressure solution function in Laplace space:

[0183]

[0184] in:

[0185]

[0186]

[0187]

[0188]

[0189]

[0190]

[0191]

[0192]

[0193]

[0194]

[0195]

[0196] s is the Laplace variable; K0, K1, I0 and I1 are Bessel functions.

[0197] Step 1.2: using the Stehfest numerical inversion technique, the real space bottom hole pressure solution (formula) is obtained from the Laplace space bottom hole pressure solution function.

[0198] Step 2: using the real space bottom hole pressure solution and combining it with the actual value of the gas reservoir parameter, obtain the real space bottom hole pressure value (that is, substituting the actual value of the gas reservoir parameter into the real space bottom hole pressure solution formula for calculation to obtain the real space bottom hole pressure value);

[0199] The actual values ​​of basic gas reservoir parameters of this well example are shown in Table 1.

[0200] Table 1 Basic parameters of the example well (actual values ​​of gas reservoir parameters)

[0201]

[0202] Step 3: Fit the real space bottom hole pressure value and the measured bottom hole pressure data (pressure recovery data of fracture-cavity gas reservoir) using the plate fitting method to obtain parameters such as cave volume, storage ratio, wellbore storage coefficient, crossflow coefficient, wellbore skin coefficient and permeability of the large cave.

[0203] By writing a calculation program based on the previous steps 1 and 2, we can obtain the bottom hole pressure (real space bottom hole pressure value) and the derivative dimensionless double logarithmic graph when there is a large cave in the formation and the external formation is a dual medium, such as Figure 3 shown. Figure 3 The curve in the upper middle part is the pressure curve, and the curve in the lower part is the pressure derivative curve.

[0204] During the actual well test, the well test pressure recovery data, that is, the measured bottom hole pressure data, is obtained, and the actual pressure recovery curve is drawn from it; by taking the derivative of the actual pressure recovery curve, a double logarithmic curve of pressure and derivative is drawn, and Figure 3 The given chart is fitted. After fitting, the double logarithmic pressure and derivative fitting chart of this well case is obtained, as shown in Figure 4 shown.

[0205] according to Figure 4The fitting diagram of the large cave is used to obtain the parameters such as the cave volume, storage ratio, wellbore storage coefficient, crossflow coefficient, wellbore skin coefficient and permeability.

[0206] 1. Cave volume calculation process:

[0207] In the above, two parameters are defined, the pressure propagation coefficient η and the cave coefficient ξ.

[0208] in

[0209] (1) First, the pressure propagation coefficient η is obtained by curve fitting, and then the cave diameter d is inferred from η. c .

[0210]

[0211] (2) Through curve fitting, the value of the cave coefficient ξ is obtained, and then the cave height h2 is inferred from ξ.

[0212]

[0213] (3) Cave volume calculation formula:

[0214] Second, the storage capacity ratio and cross-flow coefficient are directly obtained through curve fitting.

[0215] 3. Permeability calculation process:

[0216] (1) Obtain the pressure fitting value p through curve fitting M and time fitting value t M .

[0217] (2) Known formula:

[0218]

[0219] q is the wellhead gas production, B g is the gas volume coefficient, h1, h2 are the heights, and μ is the gas viscosity. These parameters are known, so the permeability can be calculated:

[0220]

[0221] 4. Calculation formula of wellbore storage coefficient:

[0222]

[0223] 5. Skin coefficient calculation process: Obtaining parameters through curve fitting The value of .

[0224] Then the skin factor is calculated by the following formula

[0225]

[0226] At this time, the parameters and C w Known.

[0227] Table 2 gives the interpretation results of this well case.

[0228] Table 2 Interpretation results of example wells

[0229]

Claims

1. A fracture-cavity gas reservoir well testing model in which a wellbore is connected to a large karst cave, characterized in that: The fracture-cavity gas reservoir well testing model includes the following five formulas: The physical meanings of the five formulas in the above fracture-cavity gas reservoir well testing model are: The first formula: the seepage equation of the fracture system; The second formula: the seepage equation of the matrix system; The third formula: through the wellbore skin factor S w Corrected bottom hole pressure; The fourth formula: The total natural gas production calculation formula, the total production is composed of the four parts on the right side of the equation; The fifth formula: the energy equation between the wellbore and the large cave; The meaning of each parameter is: wD is the dimensionless bottom hole pseudo pressure, ψ cD is the dimensionless cave pseudo-pressure; ψ fD is the dimensionless fracture pseudo-pressure, ψ mD is the dimensionless matrix pseudo-pressure, λ is the cross-flow coefficient, ω is the storage capacity ratio, S w Wellbore skin factor, C wD is the dimensionless wellbore storage coefficient, C cD is the dimensionless cave reservoir coefficient, h D is the dimensionless height, ξ is the cave coefficient, η is the pressure propagation coefficient, r D is the dimensionless radius, r cD is the dimensionless cave radius, t D is the dimensionless time and t is the time.

2. A method for establishing a fracture-cavity gas reservoir well testing model in which a wellbore is connected to a large cave as claimed in claim 1, characterized in that: The method comprises the following steps: Step 1: Establish a physical model of the wellbore connected to the large cave; Step 2: According to the physical model of the wellbore connected to the large cave, appropriate gas reservoir parameters are selected to establish a fracture-cave gas reservoir well test model in which the wellbore is connected to the large cave.

3. The method for establishing a fracture-cavity gas reservoir well test model in which a wellbore is connected to a large cave as claimed in claim 2, characterized in that: The physical model of the wellbore connected to the large cave includes an internal physical model and an external physical model; the internal physical model includes a wellbore with an outlet end located on the ground surface and a large-scale large cave connected to the other end of the wellbore, and the large cave is simulated by a large cylinder, and the two have heights h1 and h2 respectively; the external physical model includes a matrix and cracks.

4. The method for establishing a fracture-cavity gas reservoir well testing model in which a wellbore is connected to a large karst cave as claimed in claim 3, characterized in that: In the internal physical model, the pressure fluctuation of a large amount of gas stored in large caves and wellbores is considered, and the local energy loss generated when the gas enters the wellbore from the large cave is considered.

5. The method for establishing a fracture-cavity gas reservoir well testing model in which a wellbore is connected to a large cave as claimed in claim 4, characterized in that: In the external physical model, a dual-pore medium model is used to describe the flow of gas, and pseudo-pressure is introduced to replace pressure.

6. The method for establishing a fracture-cavity gas reservoir well test model in which a wellbore is connected to a large cave as claimed in claim 5, characterized in that: The gas reservoir parameters include: wellbore radius, porosity, comprehensive compression coefficient, initial pressure, formation thickness and gas reservoir temperature.

7. The method for establishing a fracture-cavity gas reservoir well testing model in which a wellbore is connected to a large karst cave as claimed in claim 6, characterized in that: According to the physical model of the wellbore connected to the large cave, after considering the situations of the internal physical model and the external physical model, a new mathematical model is established according to the derivation method, that is, the fracture-cave gas reservoir well test model of the wellbore connected to the large cave; In the derivation process, an energy equation between the wellbore and the large cave is established according to the gas reservoir characteristics, and the energy equation between the wellbore and the large cave takes into account the pressure loss at the connection between the large cave and the wellbore; The energy equation between the wellbore and the large cave is: In the above formula, the meaning of each parameter is: p w represents the bottom hole pressure, p c represents the pressure inside the cave, r w represents the wellbore radius, d c represents the diameter of the cave, v0 represents the initial velocity of the gas, χ represents the speed of pressure wave propagation, C c represents the cave storage coefficient, and t represents time.

8. An application method of the fracture-cavity gas reservoir well test model in which the wellbore is connected to a large karst cave, i.e., a new method for interpreting fracture-cavity gas reservoir well test using the fracture-cavity gas reservoir well test model in which the wellbore is connected to a large karst cave as described in claim 1, characterized in that: The method comprises the following steps: Step 1: According to the fracture-cave gas reservoir well test model in which the wellbore is connected to the large cave, solving and numerical inversion are performed to obtain the real space bottom hole pressure solution; Step 2: using the real space bottom hole pressure solution and combining it with the actual value of the gas reservoir parameter to obtain the real space bottom hole pressure value; Step 3: Fit the real space bottom hole pressure value and the measured bottom hole pressure data using the plate fitting method to obtain the cave volume, storage ratio and permeability parameters of the large cave.

9. The application method of the fracture-cavity gas reservoir well testing model in which the wellbore is connected to a large karst cave as claimed in claim 8, characterized in that: The step 1 comprises: Step 1.1, using Laplace transform to solve the well test model and obtain a dimensionless bottom hole pseudo-pressure solution function in Laplace space; Step 1.2: using the Stehfest numerical inversion technique, numerically invert the Laplace space bottom hole pressure solution function to obtain the real space bottom hole pressure solution.

10. The application method of the fracture-cavity gas reservoir well testing model in which the wellbore is connected to a large karst cave as claimed in claim 9, characterized in that: In step 1.1, the well test model is subjected to Laplace transformation to obtain a dimensionless bottom hole pseudo-pressure solution function in Laplace space under infinite formation boundary conditions: in: s is the Laplace variable; K0, K1, I0 and I1 are Bessel functions.

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