A method for determining the location of pressure breakthrough points in shale gas wells

Abstract

The present invention relates to a method for determining the position of a pressure-channeling point in a shale gas well, comprising the following steps: S1, establishing a physical model: establishing a two-phase seepage physical model of a dual-medium multi-stage fracturing horizontal well in a shale gas reservoir; S2, establishing a mathematical model: including a fracture two-phase flow equation, a matrix equation, initial conditions, and boundary conditions; S3, solving a point source pressure response expression: deriving a point source pressure response expression through a point source function method, Laplace transformation, and orthogonal transformation; S4, solving the bottom hole flow pressure of the pressure-channeling well: establishing a group of pressure response equations using the superposition principle, and obtaining the bottom hole flow pressure in real space through numerical inversion calculation; S5, determining the pressure-channeling parameters: drawing a pressure-channeling chart, and fitting the measured bottom hole flow pressure with the chart to determine the pressure-channeling liquid volume and the position of the pressure-channeling point. The present invention provides a method for determining the position of a pressure-channeling point in a shale gas well, which is used to solve the problem that the position of the pressure-channeling point is unknown.

Description

Technical Field

[0001] The present invention relates to the technical field of shale gas development, and in particular to a method for determining the position of a pressure breakthrough point in a shale gas well. Background Art

[0002] When fracturing unconventional gas reservoirs in wells on the same platform, the fracturing cracks or natural cracks in adjacent wells may be connected, resulting in well-to-well pressure channeling, especially for adjacent wells with close distances between platforms. The possibility of pressure channeling increases. The fracturing fluid in the fracturing well enters the production well through the fracture communication, resulting in an increase in the bottom flow pressure of the production well and a decrease in gas production, which reduces the development effect of the platform.

[0003] At present, there are few studies on pressure channeling by domestic and foreign scholars. Most of the studies are simple evaluations of the pressure channeling degree and recovery speed of the production data of the pressure channeling wells, and the establishment of numerical models to study the crack propagation between the fracturing wells and production wells. However, numerical simulations require the establishment of precise models and are too complicated. Currently, there is no research that clearly defines the location of the pressure channeling point.

[0004] The factors affecting pressure channeling were analyzed, and a method for determining the location of the pressure channeling point in shale gas wells was proposed, which can provide an important basis for evaluating the degree of pressure channeling between wells, determining the amount of pressure channeling fluid, the location of the pressure channeling point, and the subsequent fracturing construction and production measures of fracturing wells and production wells. Summary of the invention

[0005] The purpose of the present invention is to address the problem of unknown location of the fracturing point due to the crosstalk of fracturing fluid between the fracturing well and the production well, and to provide a method for determining the location of the crosstalk point in a shale gas well for subsequent fracturing construction in the fracturing well and guidance of the drainage of fracturing fluid in the production well.

[0006] The present invention provides a method for determining the location of a shale gas well pressure breakthrough point, the main steps of which are:

[0007] S1. Establish physical model: Establish a two-phase seepage physical model for dual-medium multi-stage fracturing horizontal wells in shale gas reservoirs:

[0008] The following hypothesis is proposed:

[0009] (1) Shale reservoirs are dual-medium reservoirs, namely, matrix desorption diffusion system and fracture Darcy flow system;

[0010] (2) Gas-water two-phase flow exists in the fracture system, and the water saturation and gas saturation remain unchanged at a certain time in the early stage of production of the gas well;

[0011] (3) Shale gas reservoirs are closed at the top and bottom and have infinite boundaries in the horizontal direction;

[0012] (4) The reservoir is penetrated by multiple non-deformable hydraulic fractures with equal spacing between the hydraulic fractures;

[0013] (5) The fluid has infinite conductivity and isothermal flow in both the hydraulic fracture and the wellbore;

[0014] (6) Ignore the effects of gravity and capillary forces;

[0015] S2. Establish mathematical model: including fracture two-phase flow equation, matrix equation, initial conditions, boundary conditions:

[0016] Matrix gas phase equation:

[0017]

[0018] Where: m is the matrix density, kg / m 3 ; S g is the gas phase saturation, 1; t is the time, h; φ m is the matrix porosity, 1; q mm is the desorption diffusion capacity of shale matrix interstitial, kg / (m 3 s);

[0019] Matrix water phase equation:

[0020]

[0021] Where: S w is the water phase saturation, 1;

[0022] Fracture gas phase equation:

[0023]

[0024] Where: g is the gas phase density, kg / m 3 ;k f is the crack permeability, μm 2 ;k frg is the relative permeability of fracture gas phase, 1; p f is the crack pressure, MPa; μ g is the gas phase viscosity, mPa·s; q m is the total desorption and diffusion capacity of the system in the hydraulic fracture, kg / (m 3 .s);φ f is the fracture porosity, 1;

[0025] Fracture water phase equation:

[0026]

[0027] Where: wis the water phase density, kg / m 3 ;k frw is the relative permeability of fracture water phase, 1; μ w is the viscosity of the water phase, mPa·s;

[0028] The fracture gas phase equation and fracture water phase equation are added together to obtain the hydraulic fracture two-phase flow equation. The gas-water two-phase pseudo-pressure function is introduced and simplified according to the seepage mechanics principle:

[0029] Two-phase pseudo-pressure function:

[0030]

[0031] Where: m (p) is the two-phase pseudo pressure, kg / (s·m 3 );

[0032] Hydraulic fracture two-phase flow equation:

[0033]

[0034] Where:

[0035] c t =ρ g0 C g S g +ρ w0 C w S w

[0036] Where: m (pf) is the two-phase pseudo pressure of the fracture, kg / (s·m 3 );c t is the air-water flow parameter group, kg / (m 3 MPa); ρ g0 , w0 are the gas phase density and gas phase density at the initial state, kg / m 3 ; C g , C w are respectively the gas phase compressibility coefficient and the water phase compressibility coefficient, MPa -1 ;

[0037] Pseudo-pressure form of the two-phase flow equation for hydraulic fractures:

[0038]

[0039] Where:

[0040]

[0041] Where: η f is the two-phase fracture flow parameter group, s -1;

[0042] The matrix flow equation can also be combined by the above simplification method and the two-phase pseudo-pressure function can be introduced, so the matrix equation becomes:

[0043]

[0044] Where:

[0045]

[0046] Where: m ( p m) is the pseudo pressure of two-phase fracture, kg / (s·m 3 );η m is the two-phase matrix flow parameter group, s -1 ;

[0047] Introduce dimensionless variables:

[0048] The dimensionless two-phase pseudo-pressure is:

[0049]

[0050] Where: h is the thickness of shale gas reservoir, m; q t is the characteristic mass flow rate of gas and water phases, kg / s; m i is the two-phase pseudo pressure under initial conditions, kg / (s·m 3 );

[0051] The dimensionless time is:

[0052]

[0053] Where: L is the length of the horizontal well, m;

[0054] The dimensionless fracture pseudo-pressure difference is:

[0055] Δm Df =m Di -m Df

[0056] The dimensionless fracture pseudo-pressure difference is:

[0057] Δm Dm =m Di -m Dm

[0058] The pseudo-steady-state diffusion parameter group is:

[0059]

[0060] Where: p sc is the formation pressure under standard conditions, MPa; T is the formation temperature, K; Tsc is the formation temperature under standard conditions, K; q sc is the mass flow rate under standard conditions, kg / s; p i is the original formation pressure, MPa;

[0061] The non-steady-state diffusion parameter group is:

[0062]

[0063] The two-phase flow equation and matrix flow equation of hydraulic fracture are dimensionless:

[0064]

[0065] Where:

[0066] The two-phase storage capacity ratio is:

[0067]

[0068] The crossflow coefficient is:

[0069]

[0070] Where: D is the matrix diffusion coefficient, m 2 / s;ρ sc is the gas density under standard conditions, kg / m 3 ;

[0071] Dirac trigonometric functions are introduced to locate dimensionless production point sources in three-dimensional Cartesian coordinates:

[0072]

[0073] Where: q D is the dimensionless output of the point source, kg / s; q g ,q w are respectively the gas volume flow rate and the water volume flow rate, m 3 / s; B g is the gas volume coefficient, 1;

[0074] The two-phase flow equation of hydraulic fracture becomes as follows:

[0075]

[0076] Laplace transformation of the dimensionless fracture and matrix seepage equations:

[0077]

[0078] Where: are the dimensionless pseudo-pressure difference of two-phase fracture and two-phase matrix after Laplace transformation; s is the Laplace variable;

[0079] For the diffusion quantity q on the surface of natural microcracks in two-phase flow mf It can be divided into two categories: quasi-steady-state diffusion and non-steady-state diffusion:

[0080] (1) Quasi-steady-state diffusion:

[0081] The expression of quasi-steady-state diffusion term is:

[0082]

[0083] Where: G is the geometric factor of the spherical matrix block, 1; R is the radius of the spherical matrix block of the shale gas reservoir, m; V a and V are the gas equilibrium concentration in the pseudo-steady-state diffusion and the gas equilibrium concentration in the hydraulic fracture, respectively. 3 / m 3 ;

[0084] V a and V vary with time, we have:

[0085]

[0086] Where: c m is the gas mass density, kg / m 3 ;

[0087] Introduce dimensionless variables:

[0088] The dimensionless gas equilibrium concentration is:

[0089] V aD =V a -V i

[0090] Where: V i is the gas equilibrium concentration in the hydraulic fracture under the initial condition, m 3 / m 3 ;

[0091] The dimensionless fracture gas equilibrium concentration is:

[0092] V D =VV i

[0093] The dimensionless gas mass density is:

[0094]

[0095] Where: c i is the gas mass density under initial conditions, kg / m 3 ;

[0096] The dimensionless quasi-steady-state diffusion term expression is:

[0097]

[0098] Laplace variation:

[0099]

[0100] Where:

[0101]

[0102] Introducing the Langmuir isotherm adsorption law:

[0103]

[0104] Where: V m is the Langmuir isotherm adsorption constant, m 3 / t;p L is the Langmuir pressure, MPa; substituting it into the dimensionless gas equilibrium concentration expression and performing Laplace transformation, we get:

[0105]

[0106] Introducing the desorption coefficient α:

[0107]

[0108] Substituting in, we get:

[0109]

[0110] because:

[0111]

[0112] Substituting and simplifying, we get:

[0113]

[0114] The total desorption and diffusion amount of the system in the hydraulic fracture q m = Desorption and diffusion of shale matrix interstitial space q mm + Diffusion amount on the surface of natural microcrack wall q mf :

[0115] q m =q mm +q mf

[0116] Substituting into the matrix and fracture two-phase seepage equation:

[0117]

[0118] Where:

[0119]

[0120] (2) Non-steady-state diffusion:

[0121] The expression of non-steady-state diffusion term is:

[0122]

[0123] Introducing Fick's second law, we have:

[0124]

[0125] Where: r m is the radial radius of the spherical matrix system, m;

[0126] The dimensionless matrix block radius is:

[0127]

[0128] The non-steady-state diffusion term expression is dimensionless:

[0129]

[0130] Unsteady-state desorption solution conditions:

[0131] Initial conditions:

[0132]

[0133] Boundary conditions:

[0134]

[0135] According to the solution conditions, we can get:

[0136]

[0137] According to the definition of hyperbolic function, the above formula can be written as follows:

[0138]

[0139] Introducing the Langmuir isotherm adsorption law and the desorption factor α, we obtain:

[0140]

[0141] You can get:

[0142]

[0143] The total desorption and diffusion amount of the system in the hydraulic fracture q m = Desorption and diffusion of shale matrix interstitial space q mm + Diffusion amount on the surface of natural microcrack wall q mf :

[0144] q m =q mm +q mf

[0145] Substituting into the matrix and fracture two-phase seepage equation:

[0146]

[0147] Where:

[0148]

[0149] The fractured horizontal well is closed at the top and bottom and has infinite boundaries in the horizontal direction, so the following solution conditions apply: Initial conditions:

[0150] P f (x,y,z,t) t＝0 =P i

[0151] Internal boundary conditions:

[0152]

[0153] External boundary conditions:

[0154]

[0155] Introducing the pseudo-pressure function and dimensionless definition:

[0156] The dimensionless x, y, and z coordinate values ​​are:

[0157]

[0158] get:

[0159] Dimensionless initial conditions:

[0160]

[0161] Internal boundary conditions:

[0162]

[0163] External boundary conditions:

[0164]

[0165] S3. Solve the point source pressure response expression: The point source pressure response expression is derived through the point source function method, Laplace transform, and orthogonal transform:

[0166] Introducing the eigenvalue method, for closed top and bottom and infinite horizontal boundaries, the characteristic equation group is in the following form:

[0167]

[0168] Obtain the eigenvalues ​​and eigenfunctions of the characteristic equations in the x, y, and z directions:

[0169] Three-dimensional eigenvalues:

[0170]

[0171] n=1,2,3…

[0172] β=1,2,3…

[0173] γ=1,2,3…

[0174] Three-dimensional characteristic function:

[0175]

[0176] Through the complete orthogonal system equations, we can get the complete orthogonality expressions in the x, y, and z directions, and finally get the three-dimensional complete orthogonality equation:

[0177]

[0178] The Laplace dimensionless pseudo-pressure expression under the orthogonal transformation is subjected to the orthogonal inverse transformation:

[0179]

[0180] Where: (x Di ,y Di , z Di ) is the dimensionless coordinate of the crack source point; (x D ,y D , z D ) are dimensionless coordinates of the observation point;

[0181] S4. Solve the bottom hole flow pressure of the pressure channeling well: Use the superposition principle to establish the pressure response equation group, and obtain the bottom hole flow pressure in real space through numerical inversion calculation:

[0182] The types of fracturing interference include the following: First, although no obvious interference characteristics are formed during the fracturing process, the pore seepage in the matrix causes short-term abnormal pressure characteristics in the production well; second, it is believed that the injection of water induces the opening of natural fractures, and the natural fractures are regarded as high-permeability networks, which connect the horizontal well fractures to form interference; third, it is believed that due to the influence of geological characteristics, hydraulic fractures form longer single-wing seam characteristics, which leads to longer expansion of artificial fractures and connects with the artificial fractures of adjacent wells, resulting in pressure interference; due to the seepage channels between the matrix, the interference between wells is very limited in unconventional reservoirs under low permeability conditions. Therefore, the view that the communication of natural fractures and artificial fractures leads to the interference between wells and causes pressure interference is recognized by most people. This view believes that the pressure channel point source is located on the fracture;

[0183] The fracturing well starts fracturing. At T1, pressure channeling occurs between the fracturing well and the production well. The fracturing well communicates with the production well through the fractures. The fracturing fluid enters the production well through the fracture channel, and the bottom flow pressure of the production well increases. At T2, the fracturing well is shut down, and the bottom flow pressure of the production well decreases. Assume that the mass flow rate of the injection of the pressure channeling fluid is q p The coordinate where the fracture channel extends and intersects the fracture of the production well is (x p ,y p , z p ), in Laplace transform, there is a property called "time delay theorem" or "time translation theorem", the time delay will be converted into an exponential factor in the transform domain, the pressure point on the production well fracture is regarded as a discrete center point, the dimensionless pseudo-pressure response expression of the pressure point to the observation point is:

[0184]

[0185] Where: T 1D is the dimensionless compression time, 1; q pD is the dimensionless pressure-blowup liquid injection mass flow rate, 1;

[0186] Discretize the nf hydraulic fractures along the x-axis, and equally separate the left and right wings of each hydraulic fracture into n units. Then, each fracture is discretized into 2n units. Di is the endpoint coordinate of the ith discrete unit, x dDi is the midpoint coordinate of the ith discrete unit. The surface source pressure response of the fracture microelement is obtained by performing the zx fracture surface integral on the point source pressure response. When pressure channeling occurs, the formation includes the microelement on the fracture and the pressure channeling point source. By using the superposition principle, the dimensionless pseudo-pressure expression for fixed-rate production in the Laplace space of the pressure channeling well can be obtained:

[0187]

[0188] Based on the assumption of infinite conductivity, the pressure at any position inside the hydraulic fracture is the same as that at any position of the horizontal wellbore:

[0189]

[0190] Taking i and j over all the micro-elements of the fracture, 2n×n f sets of equations can be constructed. The gas well production is a known quantity, and the cumulative production equation of the micro-element section is constructed:

[0191]

[0192] When the production well is not fractured (t < T1), the following calculation matrix can be obtained:

[0193]

[0194] When the production well is in the fracturing stage (T1 ≤ t < T2), the following calculation matrix can be obtained:

[0195]

[0196] When the production well is in the post-fracturing stage (t ≥ T2), the following calculation matrix can be obtained:

[0197]

[0198] Considering the effects of skin effect and wellbore storage effect:

[0199]

[0200] In the formula: C D is the dimensionless wellbore storage coefficient, 1; S k is the skin factor, 1;

[0201] According to the equations of the three stages of the production well, the solutions of the bottom-hole flowing pressure in the Laplace space at different stages are solved, and then the Stehfest numerical inversion method is used to transform the solutions in the Laplace space into the solutions in the real space, and dimensionalized into the bottom-hole flowing pressure P wf :

[0202]

[0203] In the formula: i is a natural number greater than 0; N is an even number greater than 0; s i is the Laplace space variable; V i is the weight coefficient; f(s i ) is the inversion function;

[0204] S5. Determine the fracturing parameters: Draw the fracturing chart, fit the measured bottom-hole flowing pressure with the chart, and the fracturing liquid volume and the position of the fracturing point can be determined:

[0205] The bottom hole pressure curve of the pressure channeling well can be obtained from the model in S4. According to the measured pressure data, the reservoir parameters are first determined by fitting the partial curve before the pressure channeling. Then, the parameter interpretation results obtained by fitting are input into the model for fitting the pressure data after the pressure channeling occurs. The injection rate of the pressure channeling fluid and the coordinates of the pressure channeling points can be determined.

[0206] Compared with the prior art, the present invention has the following beneficial effects: (1) it reasonably explains the change in bottom hole flow pressure after the production well is hydraulically pumped; (2) it determines the position coordinates of the hydraulic pumping point, providing guidance for the drainage process of the production well; (3) it determines the amount of fracturing fluid injected into the production well, which can be used as an evaluation method for the degree of hydraulic pumping between wells. BRIEF DESCRIPTION OF THE DRAWINGS

[0207] In order to more clearly illustrate the embodiments of the present invention or the technical solutions in the prior art, the drawings required for use in the embodiments or the description of the prior art are briefly introduced below.

[0208] In the attached picture:

[0209] Figure 1 The present invention provides a flow chart of a method for determining the location of a pressure breakthrough point in a shale gas well.

[0210] Figure 2 It is a schematic diagram of the pressure-channeling point on the staged fracturing horizontal well of the present invention.

[0211] Figure 3 It is a pressure and pressure derivative chart of the pressure channeling well of the present invention. DETAILED DESCRIPTION

[0212] The present invention is described in detail below in conjunction with specific embodiments. It should be noted that the following embodiments are only further descriptions of the present invention, but the protection scope of the present invention is not limited to the following embodiments.

[0213] The present invention provides a method comprising the following steps:

[0214] S1. Establish physical model: Establish a two-phase seepage physical model for dual-medium multi-stage fracturing horizontal wells in shale gas reservoirs:

[0215] The following hypothesis is proposed:

[0216] (1) Shale reservoirs are dual-medium reservoirs, namely, matrix desorption diffusion system and fracture Darcy flow system;

[0217] (2) Gas-water two-phase flow exists in the fracture system, and the water saturation and gas saturation remain unchanged at a certain time in the early stage of production of the gas well;

[0218] (3) Shale gas reservoirs are closed at the top and bottom and have infinite boundaries in the horizontal direction;

[0219] (4) The reservoir is penetrated by multiple non-deformable hydraulic fractures with equal spacing between the hydraulic fractures;

[0220] (5) The fluid has infinite conductivity and isothermal flow in both the hydraulic fracture and the wellbore;

[0221] (6) Ignore the effects of gravity and capillary forces;

[0222] S2. Establish mathematical model: including fracture two-phase flow equation, matrix equation, initial conditions, boundary conditions:

[0223] Matrix gas phase equation:

[0224]

[0225] Where: m is the matrix density, kg / m 3 ; S g is the gas phase saturation, 1; t is the time, h; φ m is the matrix porosity, 1; q mm is the desorption diffusion capacity of shale matrix interstitial, kg / (m 3 s);

[0226] Matrix water phase equation:

[0227]

[0228] Where: S w is the water phase saturation, 1;

[0229] Fracture gas phase equation:

[0230]

[0231] Where: g is the gas phase density, kg / m 3 ;k f is the crack permeability, μm 2 ;k frg is the relative permeability of fracture gas phase, 1; p f is the crack pressure, MPa; μ g is the gas phase viscosity, mPa·s; q m is the total desorption and diffusion capacity of the system in the hydraulic fracture, kg / (m 3 .s);φ f is the fracture porosity, 1;

[0232] Fracture water phase equation:

[0233]

[0234] Where: w is the water phase density, kg / m 3 ;k frw is the relative permeability of fracture water phase, 1; μ w is the viscosity of the water phase, mPa·s;

[0235] The fracture gas phase equation and fracture water phase equation are added together to obtain the hydraulic fracture two-phase flow equation. The gas-water two-phase pseudo-pressure function is introduced and simplified according to the seepage mechanics principle:

[0236] Two-phase pseudo-pressure function:

[0237]

[0238] Where: m (p) is the two-phase pseudo pressure, kg / (s·m 3 );

[0239] Hydraulic fracture two-phase flow equation:

[0240]

[0241] Where:

[0242] c t =ρ g0 C g S g +ρ w0 C w S w

[0243] Where: m (pf) is the two-phase pseudo pressure of the fracture, kg / (s·m 3 );c t is the air-water flow parameter group, kg / (m 3 MPa); ρ g0 , w0 are the gas phase density and gas phase density at the initial state, kg / m 3 ; C g , C w are respectively the gas phase compressibility coefficient and the water phase compressibility coefficient, MPa -1 ;

[0244] Pseudo-pressure form of the two-phase flow equation for hydraulic fractures:

[0245]

[0246] Where:

[0247]

[0248] Where: η fis the two-phase fracture flow parameter group, s -1 ;

[0249] The matrix flow equation can also be combined by the above simplification method and the two-phase pseudo-pressure function can be introduced, so the matrix equation becomes:

[0250]

[0251] Where:

[0252]

[0253] Where: m ( p m) is the pseudo pressure of two-phase fracture, kg / (s·m 3 );η m is the two-phase matrix flow parameter group, s -1 ;

[0254] Introduce dimensionless variables:

[0255] The dimensionless two-phase pseudo-pressure is:

[0256]

[0257] Where: h is the thickness of shale gas reservoir, m; q t is the characteristic mass flow rate of gas and water phases, kg / s; m i is the two-phase pseudo pressure under initial conditions, kg / (s·m 3 );

[0258] The dimensionless time is:

[0259]

[0260] Where: L is the length of the horizontal well, m;

[0261] The dimensionless fracture pseudo-pressure difference is:

[0262] Δm Df =m Di -m Df

[0263] The dimensionless fracture pseudo-pressure difference is:

[0264] Δm Dm =m Di -m Dm

[0265] The pseudo-steady-state diffusion parameter group is:

[0266]

[0267] Where: p scis the formation pressure under standard conditions, MPa; T is the formation temperature, K; T sc is the formation temperature under standard conditions, K; q sc is the mass flow rate under standard conditions, kg / s; p i is the original formation pressure, MPa;

[0268] The non-steady-state diffusion parameter group is:

[0269]

[0270] The two-phase flow equation and matrix flow equation of hydraulic fracture are dimensionless:

[0271]

[0272] Where:

[0273] The two-phase storage capacity ratio is:

[0274]

[0275] The crossflow coefficient is:

[0276]

[0277] Where: D is the matrix diffusion coefficient, m 2 / s;ρ sc is the gas density under standard conditions, kg / m 3 ;

[0278] Dirac trigonometric functions are introduced to locate dimensionless production point sources in three-dimensional Cartesian coordinates:

[0279]

[0280] Where: q D is the dimensionless output of the point source, kg / s; q g ,q w are respectively the gas volume flow rate and the water volume flow rate, m 3 / s; B g is the gas volume coefficient, 1;

[0281] The two-phase flow equation of hydraulic fracture becomes as follows:

[0282]

[0283] Laplace transformation of the dimensionless fracture and matrix seepage equations:

[0284]

[0285] Where: are the dimensionless pseudo-pressure difference of two-phase fracture and two-phase matrix after Laplace transformation; s is the Laplace variable;

[0286] For the diffusion quantity q on the surface of natural microcracks in two-phase flow mf It can be divided into two categories: quasi-steady-state diffusion and non-steady-state diffusion:

[0287] (1) Quasi-steady-state diffusion:

[0288] The expression of quasi-steady-state diffusion term is:

[0289]

[0290] Where: G is the geometric factor of the spherical matrix block, 1; R is the radius of the spherical matrix block of the shale gas reservoir, m; V a and V are the gas equilibrium concentration in the pseudo-steady-state diffusion and the gas equilibrium concentration in the hydraulic fracture, respectively. 3 / m 3 ;

[0291] V a and V vary with time, we have:

[0292]

[0293] Where: c m is the gas mass density, kg / m 3 ;

[0294] Introduce dimensionless variables:

[0295] The dimensionless gas equilibrium concentration is:

[0296] V aD =V a -V i

[0297] Where: V i is the gas equilibrium concentration in the hydraulic fracture under the initial condition, m 3 / m 3 ;

[0298] The dimensionless fracture gas equilibrium concentration is:

[0299] V D =VV i

[0300] The dimensionless gas mass density is:

[0301]

[0302] Where: c i is the gas mass density under initial conditions, kg / m 3 ;

[0303] The dimensionless quasi-steady-state diffusion term expression is:

[0304]

[0305] Laplace variation:

[0306]

[0307] Where:

[0308]

[0309] Introducing the Langmuir isotherm adsorption law:

[0310]

[0311] Where: V m is the Langmuir isotherm adsorption constant, m 3 / t;p L is the Langmuir pressure, MPa; substitute it into the dimensionless gas equilibrium concentration expression and perform Laplace transformation to obtain:

[0312]

[0313] Introducing the desorption coefficient α:

[0314]

[0315] Substituting in, we get:

[0316]

[0317] because:

[0318]

[0319] Substituting and simplifying, we get:

[0320]

[0321] The total desorption and diffusion amount of the system in the hydraulic fracture q m = Desorption and diffusion of shale matrix interstitial space q mm + Diffusion amount on the surface of natural microcrack wall q mf :

[0322] q m =q mm +q mf

[0323] Substituting into the matrix and fracture two-phase seepage equation:

[0324]

[0325] Where:

[0326]

[0327] (2) Non-steady-state diffusion:

[0328] The expression of non-steady-state diffusion term is:

[0329]

[0330] Introducing Fick's second law, we have:

[0331]

[0332] Where: r m is the radial radius of the spherical matrix system, m;

[0333] The dimensionless matrix block radius is:

[0334]

[0335] The non-steady-state diffusion term expression is dimensionless:

[0336]

[0337] Unsteady-state desorption solution conditions:

[0338] Initial conditions:

[0339]

[0340] Boundary conditions:

[0341]

[0342] According to the solution conditions, we can get:

[0343]

[0344] According to the definition of hyperbolic function, the above formula can be written as follows:

[0345]

[0346] Introducing the Langmuir isotherm adsorption law and the desorption factor α, we obtain:

[0347]

[0348] You can get:

[0349]

[0350] The total desorption and diffusion amount of the system in the hydraulic fracture q m = Desorption and diffusion of shale matrix interstitial space q mm + Diffusion amount on the surface of natural microcrack wall q mf :

[0351] q m =q mm +q mf

[0352] Substituting into the matrix and fracture two-phase seepage equation:

[0353]

[0354] Where:

[0355]

[0356] The fractured horizontal well is closed at the top and bottom and has infinite boundaries in the horizontal direction, so the following solution conditions apply: Initial conditions:

[0357] P f (x,y,z,t) t＝0 =P i

[0358] Internal boundary conditions:

[0359]

[0360] External boundary conditions:

[0361]

[0362] Introducing the pseudo-pressure function and dimensionless definition:

[0363] The dimensionless x, y, and z coordinate values ​​are:

[0364]

[0365] get:

[0366] Dimensionless initial conditions:

[0367]

[0368] Internal boundary conditions:

[0369]

[0370] External boundary conditions:

[0371]

[0372] S3. Solve the point source pressure response expression: The point source pressure response expression is derived through the point source function method, Laplace transform, and orthogonal transform:

[0373] Introducing the eigenvalue method, for closed top and bottom and infinite horizontal boundaries, the characteristic equation group is in the following form:

[0374]

[0375] Obtain the eigenvalues ​​and eigenfunctions of the characteristic equations in the x, y, and z directions:

[0376] Three-dimensional eigenvalues:

[0377]

[0378] n=1,2,3…

[0379] β=1,2,3…

[0380] γ=1,2,3…

[0381] Three-dimensional characteristic function:

[0382]

[0383] Through the complete orthogonal system equations, we can get the complete orthogonality expressions in the x, y, and z directions, and finally get the three-dimensional complete orthogonality equation:

[0384]

[0385] The Laplace dimensionless pseudo-pressure expression under the orthogonal transformation is subjected to the orthogonal inverse transformation:

[0386]

[0387] Where: (x Di ,y Di , z Di ) is the dimensionless coordinate of the crack source point; (x D ,y D , z D ) is the dimensionless coordinate of the observation point;

[0388] S4. Solution of bottom flow pressure of pressure channeling well: Use the superposition principle to establish the pressure response equation group, and obtain the bottom flow pressure in real space through numerical inversion calculation:

[0389] The types of fracturing interference include the following: First, although no obvious interference characteristics are formed during the fracturing process, the pore seepage in the matrix causes short-term abnormal pressure characteristics in the production well; second, it is believed that the injection of water induces the opening of natural fractures, and the natural fractures are regarded as high-permeability networks, which connect the horizontal well fractures to form interference; third, it is believed that due to the influence of geological characteristics, hydraulic fractures form longer single-wing seam characteristics, which leads to longer expansion of artificial fractures and connects with the artificial fractures of adjacent wells, resulting in pressure interference; due to the seepage channels between the matrix, the interference between wells is very limited in unconventional reservoirs under low permeability conditions. Therefore, the view that the communication of natural fractures and artificial fractures leads to the interference between wells and causes pressure interference is recognized by most people. This view believes that the pressure channel point source is located on the fracture;

[0390] The fracturing well starts fracturing. At T1, pressure channeling occurs between the fracturing well and the production well. The fracturing well communicates with the production well through the fractures. The fracturing fluid enters the production well through the fracture channel, and the bottom flow pressure of the production well increases. At T2, the fracturing well is shut down, and the bottom flow pressure of the production well decreases. Assume that the mass flow rate of the injection of the pressure channeling fluid is q p The coordinate where the fracture channel extends and intersects the fracture of the production well is (x p ,y p , z p ), the location of the pressure point on the crack is as follows Figure 2 As shown in the figure, in Laplace transform, there is a property called "time delay theorem" or "time translation theorem". The time delay will be converted into an exponential factor in the transform domain. The pressure point on the production well fracture is regarded as a discrete center point. The dimensionless pseudo-pressure response expression of the pressure point to the observation point is:

[0391]

[0392] Where: T 1D is the dimensionless compression time, 1; q pD is the dimensionless pressure-blowup liquid injection mass flow rate, 1;

[0393] Discretize the nf hydraulic fractures along the x-axis, and equally separate the left and right wings of each hydraulic fracture into n units. Then, each fracture is discretized into 2n units. Di is the endpoint coordinate of the ith discrete unit, x dDi is the midpoint coordinate of the ith discrete unit. The surface source pressure response of the fracture microelement is obtained by performing the zx fracture surface integral on the point source pressure response. When pressure channeling occurs, the formation includes the microelement on the fracture and the pressure channeling point source. By using the superposition principle, the dimensionless pseudo-pressure expression for fixed-rate production in the Laplace space of the pressure channeling well can be obtained:

[0394]

[0395] Based on the assumption of infinite conductivity, the pressure at any position inside the hydraulic fracture is the same as that at any position of the horizontal wellbore:

[0396]

[0397] Taking i and j over all the micro-elements of the fracture, 2n×n f equations can be constructed. The gas well production is a known quantity, and the cumulative production equation of the micro-element section is constructed:

[0398]

[0399] When the production well is not fractured (t < T1), the following calculation matrix can be obtained:

[0400]

[0401] When the production well is in the fracturing stage (T1 ≤ t < T2), the following calculation matrix can be obtained:

[0402]

[0403] When the production well is in the stage after the fracturing ends (t ≥ T2), the following calculation matrix can be obtained:

[0404]

[0405] Considering the effects of skin effect and wellbore storage effect:

[0406]

[0407] In the formula: C D is the dimensionless wellbore storage coefficient, 1; S k is the skin factor, 1;

[0408] According to the equations of the three stages of the production well, the solutions of the bottom-hole flowing pressure in the Laplace space at different stages are solved, and then the Stehfest numerical inversion method is used to transform the Laplace space solution into the solution in the real space, and it is dimensionalized to become the bottom-hole flowing pressure P wf :

[0409]

[0410] In the formula: i is a natural number greater than 0; N is an even number greater than 0; s i is the Laplace space variable; V i is the weight coefficient; f(s i ) is the inversion function;

[0411] S5. Determine the fracturing parameters: Draw the fracturing chart, fit the measured bottom-hole flowing pressure with the chart, and the fracturing liquid volume and the position of the fracturing point can be determined:

[0412] According to the model in S4, different injection speeds and position coordinates of pressure-channeling points are set to combine parameters, and the pressure and pressure derivative graphs are drawn as follows: Figure 3 As shown, the chart can be fitted with the measured flow pressure data of the pressure channeling well. First, the partial curve before the pressure channeling is fitted to determine the reservoir parameters, and then the parameter interpretation results obtained by fitting are input into the model for fitting the flow pressure data after the pressure channeling occurs. The injection rate of the pressure channeling liquid and the coordinates of the pressure channeling points can be determined.

[0413] The principle of the establishment method involved in the present invention is as follows: firstly, a two-phase seepage physical model of a shale gas reservoir dual-medium multi-stage fractured horizontal well is established, and then a corresponding seepage mathematical model is established. The seepage mathematical model includes a fracture two-phase flow equation, a matrix equation, an initial condition, and a boundary condition. The point source pressure response expression is derived by using a point source function method, Laplace transformation, orthogonal transformation and other methods. The pressure response equation group at different stages of the production well is established by using the superposition principle. By solving the equation group, a dimensionless bottom hole flow pressure in Laplace space can be obtained. The bottom hole flow pressure in real space is obtained by numerical inversion. The pressure channeling liquid volume and the position of the pressure channeling point can be obtained by fitting with the measured bottom hole flow pressure.

[0414] The above describes the specific embodiments of the present invention. It should be understood that the present invention is not limited to the above specific embodiments, and those skilled in the art may make various modifications or variations within the scope of the claims, which will not affect the essence of the present invention.

Claims

1. A method for determining the location of a shale gas well pressure breakthrough point, characterized in that: The steps include: S1. Establish physical model: Establish a two-phase seepage physical model for dual-medium multi-stage fracturing horizontal wells in shale gas reservoirs: The following hypothesis is proposed: (1) Shale reservoirs are dual-medium reservoirs, namely, matrix desorption diffusion system and fracture Darcy flow system; (2) Gas-water two-phase flow exists in the fracture system, and the water saturation and gas saturation remain unchanged at a certain time in the early stage of production of the gas well; (3) Shale gas reservoirs are closed at the top and bottom and have infinite boundaries in the horizontal direction; (4) The reservoir is penetrated by multiple non-deformable hydraulic fractures with equal spacing between the hydraulic fractures; (5) The fluid has infinite conductivity and isothermal flow in both the hydraulic fracture and the wellbore; (6) Ignore the effects of gravity and capillary forces; S2. Establish mathematical model: including fracture two-phase flow equation, matrix equation, initial conditions, boundary conditions: Matrix gas phase equation: Where: m is the matrix density, kg / m 3 ; S g is the gas phase saturation, 1; t is time, h; φ m is the matrix porosity, 1; q mm is the desorption and diffusion capacity of shale matrix pores, kg / (m 3 s); Matrix water phase equation: Where: S w is the water phase saturation, 1; Fracture gas phase equation: Where: g is the gas phase density, kg / m 3 ;k f is the crack permeability, μm 2 ;k frg is the relative permeability of fracture gas phase, 1; p f is the crack pressure, MPa; μ g is the gas phase viscosity, mPa·s; q m is the total desorption and diffusion capacity of the system in the hydraulic fracture, kg / (m 3 .s);φ f is the fracture porosity, 1; Fracture water phase equation: Where: w is the water phase density, kg / m 3 ;k frw is the relative permeability of fracture water phase, 1; μ w is the viscosity of the water phase, mPa·s; The fracture gas phase equation and fracture water phase equation are added together to obtain the hydraulic fracture two-phase flow equation. The gas-water two-phase pseudo-pressure function is introduced and simplified according to the seepage mechanics principle: Two-phase pseudo-pressure function: Where: m(p) is the two-phase pseudo pressure, kg / (s·m 3 ); Two-phase flow equation of hydraulic fracture: The right side is simplified by the principle of seepage mechanics: Where: c t =ρ g0 C g S g +r w0 C w S w Where: m(p f ) is the two-phase pseudo pressure of the fracture, kg / (s·m 3 );c t is the air-water flow parameter group, kg / (m 3 MPa); ρ g0 , w0 are the gas phase density and water phase density at the initial state, kg / m 3 ; C g , C w are respectively the gas phase compressibility coefficient and the water phase compressibility coefficient, MPa -1 ; Pseudo-pressure form of the two-phase flow equation for hydraulic fractures: Where: Where: η f is the two-phase fracture flow parameter group, s -1 ; The matrix equation can also be combined by the above simplification method and the two-phase pseudo-pressure function can be introduced, so the matrix equation becomes: Where: Where: m(p m ) is the matrix two-phase pseudo pressure, kg / (s·m 3 );η m is the two-phase matrix flow parameter group, s -1 ; Introduce dimensionless variables: The dimensionless two-phase pseudo-pressure is: Where: h is the thickness of shale gas reservoir, m; q t is the characteristic mass flow rate of gas and water phases, kg / s; m i is the two-phase pseudo pressure under initial conditions, kg / (s·m 3 ); The dimensionless time is: Where: L is the length of the horizontal well, m; The dimensionless fracture pseudo-pressure difference is: Δm Df =m Di -m Df The dimensionless matrix pseudo-pressure difference is: Δm Dm =m Di -m Dm The pseudo-steady-state diffusion parameter group is: Where: p sc is the formation pressure under standard conditions, MPa; T is the formation temperature, K; T sc is the formation temperature under standard conditions, K; q sc is the mass flow rate under standard conditions, kg / s; p i is the original formation pressure, MPa; The non-steady-state diffusion parameter group is: The two-phase flow equation and matrix flow equation of hydraulic fracture are dimensionless: Where: The two-phase storage capacity ratio is: The crossflow coefficient is: Where: D is the matrix diffusion coefficient, m 2 / s;ρ sc is the gas density under standard conditions, kg / m 3 ; Dirac trigonometric functions are introduced to locate dimensionless production point sources in three-dimensional Cartesian coordinates: Where: q D is the dimensionless output of the point source, kg / s; q g ,q w are respectively the gas volume flow rate and the water volume flow rate, m 3 / s; B g is the gas volume coefficient, 1; The two-phase flow equation of hydraulic fracture becomes as follows: Laplace transformation of the dimensionless fracture and matrix seepage equations: Where: are the dimensionless pseudo-pressure difference of two-phase fracture and two-phase matrix after Laplace transformation; s is the Laplace variable; For the diffusion quantity q on the surface of natural microcracks in two-phase flow mf It can be divided into two categories: quasi-steady-state diffusion and non-steady-state diffusion: (1) Quasi-steady-state diffusion: The expression of quasi-steady-state diffusion term is: Where: G is the geometric factor of the spherical matrix block, 1; R is the radius of the spherical matrix block of the shale gas reservoir, m; V a and V are the gas equilibrium concentration in the pseudo-steady-state diffusion and the gas equilibrium concentration in the hydraulic fracture, respectively. 3 / m 3 ; V a and V vary with time, we have: Where: c m is the gas mass density, kg / m 3 ; Introduce dimensionless variables: The dimensionless gas equilibrium concentration is: V aD =V a -V i Where: V i is the gas equilibrium concentration in the hydraulic fracture under the initial condition, m 3 / m 3 ; The dimensionless fracture gas equilibrium concentration is: V D =VV i The dimensionless gas mass density is: Where: c i is the gas mass density under initial conditions, kg / m 3 ; The dimensionless quasi-steady-state diffusion term expression is: Laplace variation: Where: Introducing the Langmuir isotherm adsorption law: Where: V m is the Langmuir isotherm adsorption constant, m 3 / t;p L is the Langmuir pressure, MPa; Substituting into the dimensionless gas equilibrium concentration expression and performing Laplace transformation, we obtain: Introducing the desorption coefficient α: Substituting in, we get: because: Substituting and simplifying, we get: The total desorption and diffusion amount of the system in the hydraulic fracture q m = Desorption and diffusion of shale matrix interstitial space q mm + Diffusion amount on the surface of natural microcrack wall q mf : q m =q mm +q mf Substituting into the matrix and fracture two-phase seepage equation: Where: (2) Non-steady-state diffusion: The expression of non-steady-state diffusion term is: Introducing Fick's second law, we have: Where: r m is the radial radius of the spherical matrix system, m; The dimensionless matrix block radius is: The non-steady-state diffusion term expression is dimensionless: Unsteady-state desorption solution conditions: Initial conditions: Boundary conditions: According to the solution conditions, we can get: According to the definition of hyperbolic function, the above formula can be written as follows: Introducing the Langmuir isotherm adsorption law and the desorption factor α, we obtain: You can get: The total desorption and diffusion amount of the system in the hydraulic fracture q m = Desorption and diffusion of shale matrix interstitial space q mm + Diffusion amount on the surface of natural microcrack wall q mf : q m =q mm +q mf Substituting into the matrix and fracture two-phase seepage equation: Where: The fractured horizontal well is closed at the top and bottom and has an infinite boundary in the horizontal direction. Thus, the following definite solution conditions are obtained: Initial condition: P f (x,y,z,t) t＝0 =P i Inner boundary condition: Outer boundary condition: Introduce the pseudo-pressure function and dimensionless definition: The dimensionless coordinate values in the x, y, and z directions are: Obtain: Dimensionless initial condition: Inner boundary condition: Outer boundary condition: S3. Solve the point-source pressure response expression: Through the point-source function method, Laplace transform, and orthogonal transformation, the point-source pressure response expression is derived: Introduce the eigenvalue method. For the case of a well closed at the top and bottom and with an infinite boundary in the horizontal direction, its characteristic equation set is in the following form: Obtain the eigenvalues and eigenfunctions of the characteristic equation set in the x, y, and z directions: Three-dimensional eigenvalues: n＝1，2，3… β∈(-∞,∞) γ ∈ (-∞, ∞) Three-dimensional eigenfunction: Through the complete orthogonal system equation, the complete orthogonality expressions in the x, y, and z directions can be obtained. Finally, the three-dimensional complete orthogonality equation is obtained: The Laplace dimensionless pseudo-pressure expression in the case of orthogonal transformation is inversely orthogonally transformed: Where: (x Di ,y Di , z Di ) is the dimensionless coordinate of the crack source point; (x D ,y D , z D ) is the dimensionless coordinate of the observation point; S4. Solve the bottom-hole flowing pressure of the fractured and channeled well: Use the superposition principle to establish a pressure response equation set, and through numerical inversion calculation, obtain the bottom-hole flowing pressure in real space: The types of fracturing and channeling include the following categories: First, during the fracturing process of the fractured well, although no obvious channeling characteristics are formed, through pore seepage in the matrix, it causes short-term pressure anomaly characteristics in the production well; Second, it is considered that the injection water induces the opening of natural fractures, regards the natural fractures as a high-permeability network, and connects with the fracturing fractures of the horizontal well to form channeling; Third, it is considered that affected by geological characteristics, the hydraulic fracture forms a long single-wing fracture characteristic, resulting in a long extension of the artificial fracture and connection with the artificial fractures of adjacent wells, leading to fracturing and channeling; Since the inter-well interference caused by the seepage channels between matrices is very limited in unconventional reservoirs under low-permeability conditions, the statement that the communication of natural fractures and the connection of artificial fractures cause inter-well interference and fracturing and channeling is recognized by most people. This statement believes that the fracturing and channeling point source is located on the fracturing fracture; The fracturing well starts fracturing. At T1, pressure channeling occurs between the fracturing well and the production well. The fracturing well communicates with the production well through the fractures. The fracturing fluid enters the production well through the fracture channel, and the bottom flow pressure of the production well increases. At T2, the fracturing well is shut down, and the bottom flow pressure of the production well decreases. Assume that the mass flow rate of the injection of the pressure channeling fluid is q p The coordinate where the fracture channel extends and intersects the fracture of the production well is (x p ,y p , z p ), in Laplace transform, there is a property called "time delay theorem" or "time translation theorem", the time delay will be converted into an exponential factor in the transform domain, the pressure point on the production well fracture is regarded as a discrete center point, the dimensionless pseudo-pressure response expression of the pressure point to the observation point is: Where: T 1D is the dimensionless compression time, 1; q pD is the dimensionless pressure-blowup liquid injection mass flow rate, 1; For f The hydraulic fractures are discretized along the x-axis direction, and the left and right wings of each hydraulic fracture are equally separated into n units. Then each fracture is discretized into 2n units. Di is the endpoint coordinate of the ith discrete unit, x dDi is the midpoint coordinate of the ith discrete unit. The surface source pressure response of the fracture microelement is obtained by performing the zx fracture surface integral on the point source pressure response. When pressure channeling occurs, the formation includes the microelement on the fracture and the pressure channeling point source. By using the superposition principle, the dimensionless pseudo-pressure expression for fixed-rate production in the Laplace space of the pressure channeling well can be obtained: Based on the assumption of infinite conductivity, the pressure at any position inside the hydraulic fracture and any position of the horizontal wellbore is the same: By taking i and j to cover all the infinitesimal elements in the crack, we can construct 2n×n f The gas well production is a known quantity, and the cumulative production equation of the microelement segment is constructed: When the production well is not fractured and channeled (t < T1), the following calculation matrix can be obtained: When the production well is in the fracturing and channeling stage (T1 ≤ t < T2), the following calculation matrix can be obtained: When the production well is in the stage after the fracturing and channeling ends (t ≥ T2), the following calculation matrix can be obtained: Considering the influence of skin effect and wellbore storage effect: Where: C D is the dimensionless wellbore storage coefficient, 1; S k is the skin factor, 1; According to the equations of the three stages of the production well, the solutions of the bottom hole pressure in different stages in Laplace space are solved, and then the Stehfest numerical inversion method is used to transform the Laplace space solution into the real space solution, which is dimensionally converted into the bottom hole pressure P wf : Where: i is a natural number greater than 0; N is an even number greater than 0; s i is the Laplace space variable; V i is the weight coefficient; f(s i ) is the inversion function; S5. Determine the fracturing and channeling parameters: Draw the fracturing and channeling chart, fit the measured bottom-hole flowing pressure with the chart, and the fracturing and channeling liquid volume and the position of the fracturing and channeling point can be determined: From the model in S4, the bottom-hole flowing pressure curve chart of the fractured and channeled well can be obtained. According to the measured flowing pressure data, first fit the curve before fracturing and channeling to determine the reservoir parameters, and then input the parameter interpretation results obtained by fitting into the model for fitting the flowing pressure data after fracturing and channeling, and the injection rate of the fracturing and channeling liquid volume and the fracturing and channeling point coordinates can be determined.

Images