Method for predicting production and recoverable reserves of fractured horizontal well in deep shale gas

Abstract

The application discloses a kind of deep shale gas fracturing horizontal well production and recoverable reserves prediction method, mainly including constructing matrix system gas seepage equation and hydraulic fracture gas seepage equation, two seepage equations are combined to build productivity equation, the total production Q of a unit time of the predicted well is obtained by adding the production of multiple hydraulic fractures gt According to the total production time when abandoned, the recoverable reserves EUR is calculated by adding calculation. Fully consider the high temperature and high pressure in deep shale gas, the effect of gas adsorption, matrix system permeability and high closure stress on hydraulic fracture, and build the productivity calculation equation after quantifying each effect, greatly improve the accuracy and reliability of its prediction method, which can provide important theoretical basis for deep shale gas development plan, fracturing optimization design and effect evaluation.

Description

TECHNICAL FIELD

[0001] The application belongs to the technical field of shale gas development, and particularly relates to a deep shale gas fracturing horizontal well production and recoverable reserves prediction method. BACKGROUND

[0002] The shale gas resources in Sichuan Basin and its periphery are quite rich, and are the main battlefield of shale gas development in China at present. In the south of Sichuan, more than 80% of the shale gas resources are buried in deep reservoirs above 3500 m, and the deep marine shale gas production has the condition of building a capacity of more than 30 billion cubic meters, and is the main body of shale gas production growth in the future. At present, the shale gas development technology for the middle and shallow layers is relatively mature, but for the deep shale gas, due to the influence of high temperature, high pressure and high stress environment of the reservoir, the stress sensitivity mechanism of shale gas adsorption, mass transfer diffusion and fracture is significantly different from that of the middle and shallow layers, which directly makes the current conventional shale gas production model no longer applicable.

[0003] Domestic and foreign scholars have established shale gas production models by describing the shale gas percolation mechanism. The existing production models mainly consider the multiple pore medium characteristics of shale gas reservoirs, the multiple transport mechanism of micro-nano pores, the stress sensitivity of adsorbed gas and fractures. For the multiple pore medium model, it mainly includes a double medium model based on matrix-fracture, a three medium model of organic matter, inorganic matter and fracture, and a four medium model of organic matter, matrix pore, natural fracture and discrete large-scale artificial fracture, and the mass transfer between multiple pore media is characterized by a channeling term; the gas transmission in matrix nano-pores is mainly based on Knudsen diffusion, surface diffusion and slip effect.

[0004] In addition, the pore cross-section type (slit, circle and ellipse), stress sensitivity, organic matrix shrinkage, water film thickness, real gas effect and adsorption layer also have certain influence on gas transmission. At present, domestic and foreign scholars have established apparent permeability models of organic matter pores, inorganic matter pores and micro-fractures to characterize the gas transmission mechanism and micro-scale effect. However, the established apparent permeability model ignores the influence of nano-pore confinement effect on gas transmission under high temperature and high pressure in deep layers, so it is difficult to accurately characterize the mass transfer diffusion mechanism of deep shale gas. Shale gas mainly exists in the form of adsorbed gas and free gas in shale reservoirs, and the current shale gas production model mainly uses the Langmuir isotherm adsorption model to describe the shale gas adsorption rule under different pressures, and some scholars also use the BET (Brunauer-Emmett-Teller) isotherm adsorption model based on multi-layer adsorption. However, relevant experimental studies show that under high temperature and high pressure conditions, the adsorption amount of shale gas decreases with the increase of pressure, so neither the Langmuir adsorption nor the BET adsorption model can accurately describe the shale gas adsorption rule under high temperature and high pressure in deep layers.

[0005] And the fracture stress sensitivity in shale gas production process is an important factor affecting shale gas productivity, scholars at home and abroad have carried out a large number of stress sensitivity experiments on propped hydraulic fractures and natural fractures. The change rule of hydraulic fracture conductivity with closure stress under different proppant particle size, proppant type and sanding concentration is revealed. The stress sensitivity model of the fracture is established by power function or exponential function. The current shale gas productivity model mainly considers the influence of stress sensitivity of the fracture on productivity, but ignores the influence of fracture creep on permeability under high closure stress.

[0006] In summary, the current productivity model based on the flow mechanism of shale gas is difficult to accurately predict the production performance and the ultimate recoverable reserves (EUR) of deep shale gas. It is urgent to propose a prediction method suitable for the production and EUR of deep shale gas fractured horizontal wells, which can provide a theoretical basis for the development plan, fracturing optimization design and effect evaluation of deep shale gas. SUMMARY

[0007] Therefore, the present application provides a deep shale gas fractured horizontal well production and recoverable reserves prediction method to solve the problem that the existing prediction method ignores the influence of high temperature and high pressure on shale gas adsorption and the influence of fracture creep on permeability under high closure stress, that is, the accuracy and reliability of the existing prediction method are poor for deep shale gas.

[0008] The technical scheme is as follows:

[0009] A deep shale gas fractured horizontal well production and recoverable reserves prediction method, which comprises the following steps:

[0010] S1, based on the micropore filling adsorption model, an adsorption model of deep shale gas is constructed;

[0011] S2, based on the difference between shale organic matter and inorganic matter pore morphology and gas transmission mechanism, a unified matrix total apparent permeability model is established, and the matrix apparent permeability model at least includes real gas effect and confinement effect influencing factors;

[0012] S3, based on the Kelvin viscoelastic deformation model, a single hydraulic fracture deformation model and a conductivity model are constructed;

[0013] S4, according to the shale gas adsorption model in step S1 and the matrix total apparent permeability model in step S2, a matrix system gas seepage equation in shale gas production process is established;

[0014] According to the single fracture deformation model and the conductivity model in step S3, a hydraulic fracture gas seepage equation is established;

[0015] S5, constructing the production of a single hydraulic fracture according to the matrix system gas seepage equation and the hydraulic fracture gas seepage equation Q well a calculation model;

[0016] S6, the number of the predicted well hydraulic fractures is n , n is an integer greater than or equal to 1, and the production of multiple hydraulic fractures is summed to obtain the total production of the predicted well per unit time Q gt ;

[0017] S7, according to the predetermined abandoned single production of the predicted well Q gto , the total production time when it reaches the abandoned single production is calculated Q gto t all , all Q gt in the total production time are summed to obtain the recoverable reserves EUR of the well.

[0018] Using the above scheme, first, a special shale gas adsorption model is constructed for deep shale gas, second, the influence factors of real gas effect and limited effect under high temperature and high pressure are introduced when establishing the matrix system gas seepage equation, and the hydraulic fracture gas seepage equation considering the influence of hydraulic fracture creep is combined, so that the finally established production calculation model takes into account the special environment of deep shale gas on shale gas adsorption and the change factors of hydraulic fracture, and is more in line with the actual situation downhole, which is beneficial to improve the accuracy and reliability of the prediction results, and provides a theoretical basis for the development plan of deep shale gas, the optimization design and effect evaluation of fracturing.

[0019] As preferred: the step S2 further includes slip flow, Knudsen diffusion, and matrix stress sensitivity and water film influence factors. The transmission of gas in nanopores usually includes slip flow and Knudsen diffusion, at the same time, the matrix stress sensitivity and the thickness of the water film will affect the transmission of gas, and the above factors are included in this step, which is beneficial to improve the accuracy of the total apparent permeability model of the matrix, and makes it more in line with the actual situation downhole.

[0020] As preferred: in the step S2, first, the characterization of the influence factors is performed respectively for the circular pores and slit pores included in the matrix pores, second, the respective apparent permeability is constructed according to Darcy's law, and finally, the total apparent permeability model of the matrix is constructed according to the organic matter content. Using the above scheme, different pore cross-section types are characterized respectively, and finally summed according to the proportion, which is also more in line with the actual situation downhole, and is beneficial to further improve the calculation accuracy of the total apparent permeability of the matrix. ​

[0021] As preferred: the deformation amount of the single hydraulic fracture in step S3 further comprises an effective closure stress P C The embedding amount of the fracture proppant under the action of the closure stress PE And the elastic deformation amount Δ PD By adopting the above scheme, the proppant will be elastically deformed or partially embedded with the matrix under the action of the closure stress, both changes will affect the actual conductivity of the hydraulic fracture, therefore, the consideration is introduced here, and the calculation accuracy of the fracture conductivity can be improved.

[0022] As preferred: the fracture parameters including n The fracture parameters are preset values, which are obtained by inferring the well history or the hydraulic fracturing process data of other production wells in the block, the actual production of the prediction well, the reservoir and the preset fracture parameters are brought into the numerical calculation model of step S5 to calculate the bottom hole flowing pressure, and the bottom hole flowing pressure is compared with the actual bottom hole flowing pressure, the fracture parameters are adjusted, and the actual bottom hole flowing pressure is fitted, so that the calculated bottom hole flowing pressure and the actual bottom hole flowing pressure are consistent, and the new fracture parameters are determined;

[0023] The new fracture parameters and the reservoir parameters are brought into the numerical calculation model to determine the actual hydraulic fracture and the reservoir pore pressure distribution, and the total production of the prediction well per unit time is calculated Q gt And the recoverable reserves EUR.

[0024] After the preset data is calculated and then fitted with the known actual data, the preset data can be infinitely close to the true value of the parameter, so that more accurate calculation parameters are provided for calculation, that is, the accuracy and authenticity of the calculation result are improved.

[0025] As preferred: in step S4, the finite difference method is adopted to discretize the gas seepage equation of the matrix system and the gas seepage equation of the hydraulic fracture to establish the productivity numerical calculation equation group.

[0026] Compared with the prior art, the beneficial effects of the present application are:

[0027] By adopting the deep shale gas fracturing horizontal well production and recoverable reserves prediction method provided by the present application, various influence effects of high temperature and high pressure on gas adsorption, matrix system permeability and high closure stress hydraulic fracture in deep shale gas are fully considered, and the productivity calculation equation is constructed after quantifying each effect, so that the accuracy and reliability of the prediction method are greatly improved, and important theoretical basis can be provided for the development plan compilation, fracturing optimization design and effect evaluation of deep shale gas. BRIEF DESCRIPTION OF DRAWINGS

[0028] Fig. 1 The flowchart of the present application is shown in the figure;

[0029] Fig. 2 is a schematic diagram of the comparison between the actual bottom-hole flowing pressure and the fitted bottom-hole flowing pressure;

[0030] Fig. 3 is a schematic diagram of the comparison between the fitted production and the actual production;

[0031] Fig. 4 is a schematic diagram of the predicted well production Q gt and the recoverable reserves EUR prediction. DETAILED DESCRIPTION

[0032] The present application will be further described below in conjunction with the accompanying drawings.

[0033] Reference Figs. 1 to 3 The deep shale gas fracturing horizontal well production and recoverable reserves prediction method shown mainly comprises the following steps, step S1, based on the micropore filling adsorption model, an adsorption model of deep shale gas is constructed.

[0034] Step S2, based on the differences in shale organic matter and inorganic matter pore morphology and gas transmission mechanism, a unified matrix total apparent permeability model is established, and the matrix apparent permeability model at least includes real gas effect and confinement effect influencing factors.

[0035] Step S3, based on the Kelvin viscoelastic deformation model, a single hydraulic fracture deformation model and a conductivity model are constructed.

[0036] Step S4, according to the shale gas adsorption model in step S1 and the matrix total apparent permeability model in step S2, a matrix system gas seepage equation in the shale gas production process is established; according to the single fracture deformation model and the conductivity model in step S3, a hydraulic fracture gas seepage equation is established;

[0037] Step S5, according to the matrix system gas seepage equation and the hydraulic fracture gas seepage equation, a single hydraulic fracture production Q well calculation model is constructed.

[0038] Step S6, the number of the predicted well hydraulic fractures is n , n an integer greater than or equal to 1, the production of multiple hydraulic fractures is summed to obtain the total production of the predicted well per unit time Q gt ;

[0039] Step S7, according to the pre-set abandoned single production of the predicted well Q gto , the total production time when it reaches the abandoned single production Q gto is calculated.t all The total production time is the sum of all Q gt The EUR of the well is obtained by adding up the recoverable reserves of all

[0040] The following is the specific implementation of step S1. Through laboratory experiments, it is found that with the increase of test pressure, the shale gas adsorption capacity first increases and then decreases. This is because the experimental test adsorption gas capacity under high pressure is excess adsorption capacity. Therefore, based on the Dubinin-Astakhov adsorption model of micropore filling, the excess adsorption capacity of deep shale gas can be expressed as follows:

[0041] (1)

[0042] And the excess adsorption capacity and the absolute adsorption capacity satisfy the following relationship:

[0043] (2)

[0044] Therefore, the absolute adsorption capacity of shale gas can be expressed as:

[0045] (3)

[0046] In the formula: M g is the molar mass of the gas, and the value is 16 g / mol; V 微孔 represents the volume of the adsorbed phase methane of micropore filling, and the value is 0.00981 cm 3 / g; p ad represents the adsorbed phase methane density, and the value is 0.399 g / cm 3 ; p g represents the free phase methane density (kg / m 3 ), E represents the adsorption characteristic energy, 7399.8 J / mol; V ex represents the excess adsorption capacity, cm 3 / g; V ab represents the absolute adsorption capacity, cm 3 / g; V std represents the volume of the gas under standard conditions, and the value is 0.0224 m 3 / mol; R represents the universal gas constant, and the value is 8.314 J / (mol.K); T represents the adsorption test temperature, K; kis a parameter related to the adsorption system, and has a value of 5.93, a dimensionless quantity; q is a constant related to the non-homogeneity of the adsorbent surface, and has a value of 1.61, a dimensionless quantity.

[0047] The shale matrix system mainly contains organic matter pores and inorganic matter pores. The storage and transport mechanisms of gas in the two types of pores are different. The organic matter pores mainly store adsorbed gas and free gas, while the inorganic matrix pores mainly store free gas, and the primary bound water is adsorbed on the inorganic pore wall surface in the form of a water film. The gas transport in nanopores is mainly divided into slip flow and Knudsen diffusion, in addition, the pore cross-section type, real gas effect, confinement effect, stress sensitivity and water film thickness will have a certain influence on gas transport.

[0048] Therefore, when the total apparent permeability model of the matrix is implemented, the application not only introduces the influence of the real gas effect and the confinement effect, but also characterizes the different transport modes of slip flow and Knudsen diffusion, as well as the pore cross-section, stress sensitivity and water film thickness which have an influence on the transport. Based on the field emission scanning electron microscope experiment, the applicant found that the organic matter pores in shale pores are mostly circular or elliptical, while the inorganic matter pores are generally slit-shaped. Therefore, considering the differences in the morphologies of organic matter and inorganic matter pores and the gas transport mechanism, a unified matrix apparent permeability model is established to describe the gas transport mechanism in deep shale matrix.

[0049] S2.1 First, the influence of real gas effect and confinement effect is analyzed

[0050] For deep shale reservoirs with high temperature and high pressure, the interaction between gas molecules and the influence of the volume of gas molecules on gas transport in nanopores cannot be ignored, that is, the real gas effect. The influence of this real gas effect on gas transport can be characterized by the gas deviation factor, gas viscosity and average molecular free path. The gas deviation factor and viscosity are expressed by the following two formulas:

[0051] (4)

[0052] (5)

[0053] Wherein:

[0054] (6)

[0055] (7)

[0056] The fitting coefficients for calculating viscosity in formula (5) are shown in Table 1, and the fitting coefficients in formula (6) are shown in Table 2. P ccFor different cross-sectional pores, the formula (9) and formula (11) are used for calculation respectively, and the formula (7) is calculated by different T cc For different cross-sectional pores, the formula (8) and formula (10) are used for calculation respectively, and the formula (7) is calculated by different P cc And T cc The gas deviation factor Z and the gas viscosity m g .

[0057] Table 1 Gas viscosity calculation fitting parameter table

[0058] ;

[0059] In the formula: Z Z represents the gas deviation factor, a dimensionless quantity; P P represents the reservoir pore pressure, MPa; T T represents the reservoir temperature, K; P pr is the gas contrast pressure, a dimensionless quantity; T pr is the gas contrast temperature, a dimensionless quantity; T cc Tc represents the gas critical temperature considering the confinement effect, K; P cc Pc represents the gas critical pressure considering the confinement effect, MPa

[0060] When the nanometer pore size is less than a certain value, the influence of the confinement effect on gas transmission under high temperature and high pressure conditions is more prominent. Affected by the confinement effect, the critical pressure and temperature of the gas will change. For circular pores, the gas critical temperature and pressure considering the influence of the confinement effect can be expressed as:

[0061] (8)

[0062] (9)

[0063] For slit-shaped pores, the gas critical temperature and pressure affected by the nanometer pore confinement effect are expressed as:

[0064] (10)

[0065] (11)

[0066] In the formula: D D represents the pore diameter of the circular pore, nm; h effeffective opening of slit-shaped pore, nm; σ represents the Leonard-Jones parameter, which is taken as 0.28 nm in this paper, d a represents the thickness of adsorption layer, nm; P cb represents the critical pressure of gas, which is taken as 4.59 MPa; T cb represents the critical temperature of gas, which is taken as 190.4 K.

[0067] The mean free path of real gas is defined as:

[0068] (12)

[0069] wherein: l r represents the mean free path of real gas, m. Knudsen number is an important parameter to judge the flow state of gas, so the Knudsen numbers in circular and rectangular slit-shaped pores are defined as:

[0070] (13)

[0071] (14)

[0072] wherein: Kn r represents the Knudsen numbers of real gas in two kinds of cross-section pores, dimensionless; r and h represents the pore radius and the opening of slit-shaped pore, nm, respectively.

[0073] S2.2 Transport analysis for slip flow

[0074] The mass flow rates of real gas in circular and rectangular cross-section nanometer pores in slip flow are respectively represented as:

[0075] (15)

[0076] (16)

[0077] wherein

[0078] (17)

[0079] (18)

[0080] wherein: α o is Kn r the dilute effective stress coefficient when the pore radius is infinite, taken as 1.19, dimensionless.α 1 and β The constants are fitting constants, with values ​​of 4 and 0.4 respectively, and are dimensionless. J cvs This represents the mass flow rate of real gas slip flow, in kg / (m³). 2 ·s); α r It is the rare-effect coefficient of an ideal gas, a dimensionless quantity; b It is the gas slip constant, with a value of -1, and is dimensionless. J rvs This represents the mass flow rate of gas slippage flow through the slit orifice, in kg / m³. 2 .s, α This represents the rare effect coefficient, a dimensionless quantity. A ( z — The influence coefficient of shape factor on slip flow, a dimensionless quantity; z The aspect ratio of the slit is a dimensionless quantity.

[0081] S2.3 Analysis of Knudsen diffusion transport

[0082] The Knudsen diffusion mass flow rates of real gases in circular and rectangular cross-section nanopores are expressed as follows:

[0083] (19)

[0084] (20)

[0085] in

[0086] (twenty one)

[0087] In the formula: B ( z ) represents the influence coefficient of the slit orifice shape factor on the Knudsen diffusion flow, a dimensionless quantity. Where: Jc kn and Jr kn These represent the Knudsen diffusion mass flow rates in circular and rectangular cross-section nanopores, respectively, in kg / (m³). 2 ·s); d This represents the ratio of the molecular diameter to the local pore diameter, with a value of 0.5, and is dimensionless. D f This represents the fractal dimension of the pore wall, with a value of 2.5, and is dimensionless. C g The gas compressibility factor is 1 / MPa. w The width of the slit opening is expressed in meters (m).

[0088] S2.4 Analysis of the influence of matrix stress sensitivity and water film thickness

[0089] Considering the influence of stress sensitivity on matrix pore size, the effective pore size of the circular and rectangular cross-section pores is:

[0090] (22)

[0091] (23)

[0092] In the formula: K ( p ) represents the matrix permeability considering stress sensitivity, mD; h str f ( p ) represents the matrix porosity considering stress sensitivity, dimensionless; r ef

[0093] wherein the matrix porosity and permeability stress sensitivity are expressed by the following two formulas:

[0094] (24)

[0095] (25)

[0096] In the formula: K i p i f i f and h respectively represent the stress sensitivity coefficients of the matrix permeability and porosity, MPa -1 .

[0097] Considering the influence of inorganic pore surface adsorbed water on the opening, the effective opening of the slit pore is:

[0098] (26)

[0099] In the formula: S w h ef

[0100] S2.5 Construction of matrix apparent permeability ​​​​​​​

[0101] The total mass flow in the matrix pore includes the slip flow and Knudsen diffusion mass flow in the organic pore and inorganic pore, and the slip flow and Knudsen diffusion flow are superimposed based on the weight coefficient proposed by Wu Keliu et al. to obtain the total mass flow, respectively as follows:

[0102] (27)

[0103] (28)

[0104] The contribution coefficients of the slip flow and Knudsen diffusion flow in the circular cross-section pore are respectively as follows:

[0105] (29)

[0106] (30)

[0107] The contribution coefficients of the slip flow and Knudsen diffusion mass flow in the rectangular slit pore are respectively as follows:

[0108] (31)

[0109] (32)

[0110] In the formulae, the contribution coefficient of the slip flow is a dimensionless quantity, and the contribution coefficient of the Knudsen diffusion flow is a dimensionless quantity. In the formulae, the contribution coefficient of the slip flow is a dimensionless quantity, and the contribution coefficient of the Knudsen diffusion flow is a dimensionless quantity. f slip f k w vs w k

[0111] The apparent permeability is used to describe the multiple transmission mechanism of the gas in the matrix, and according to the definition of the apparent permeability, the apparent permeability of the gas flow in the organic pore and inorganic pore can be expressed as follows:

[0112] (33)

[0113] (34)

[0114] It should be noted that in the calculation of formula (33) and formula (34), it is necessary to pay attention to the corresponding circular cross-section pore and rectangular slit pore, respectively, so that the gas deviation factor Z, gas viscosity m g , and real gas Knudsen number are substituted.​​​​Kn r The parameters should be calculated according to the corresponding formula in the foregoing.

[0115] The total apparent permeability of the matrix is:

[0116] (35)

[0117] In the formula: y represents the content of organic matter, a dimensionless quantity.

[0118] The analysis of step S3 is implemented as follows: in the production process of a shale gas well, in addition to the creep of the hydraulic fracture affected by the high closure stress and the increasing effective closure stress, the proppant also undergoes embedding and deformation and viscoelastic deformation of the fracture, the hydraulic fracture width decreases, the propped fracture permeability decreases, and finally the hydraulic fracture conductivity decreases. Based on data analysis, it can be known that the propped hydraulic fracture permeability can be characterized by an exponential decreasing function:

[0119] (36)

[0120] In the formula: k fi represents the initial hydraulic fracture permeability, D; d f represents the stress sensitivity coefficient of the shale hydraulic fracture, MPa -1 ; P c represents the current effective closure stress, MPa.

[0121] Referring to the analytical formula derived by Cuo and Liu (2012), the proppant deformation and embedding amount under the action of the effective closure stress P c are respectively:

[0122] (37)

[0123] (38)

[0124] In the formula: APE and APD represent the proppant embedding and elastic deformation, m; D av represents the average particle size of the proppant, mm; v 1 and v 2 represent the Poisson's ratios of the proppant and the shale respectively, take the value of 0.22, a dimensionless quantity; E 1 and E 2 represent the elastic moduli of the proppant and the shale respectively, take the value of 30 GPa.

[0125] The hydraulic fracture creep deformation is represented by the classical Kelvin viscoelastic deformation model, expressed as:

[0126] (39)

[0127] In the formula, m represents the deformation amount caused by fracture creep; e t 1 represents the shear model of the proppant, MPa; G 1 represents the production time, d; t 2 represents the Kelvin body elastic modulus, MPa; E 2 represents the viscosity coefficient of the Kelvin body, MPa.h. h

[0128] The total deformation amount of the hydraulic fracture is expressed as:

[0129] (40)

[0130] The hydraulic fracture conductivity affected by stress sensitivity and creep is expressed as:

[0131] (41)

[0132] In the formula, m represents the deformation amount caused by fracture creep; W f = W fi - AW

[0133] W f represents the current width of the hydraulic fracture, mm; W fi represents the initial width of the hydraulic fracture, F c represents the hydraulic fracture conductivity, D.cm.

[0134] The specific implementation of steps S4 and S5 is as follows

[0135] According to the high-temperature and high-pressure adsorption model of deep shale gas, the microscale effects such as real gas effect, confinement effect, slip flow, Knudsen diffusion, stress sensitivity and water film thickness are considered, that is, combined with formula (3) and formula (35), the gas seepage equation (i.e., mass conservation equation) of the matrix system in the shale gas production process is established:

[0136] (42)

[0137] In the formula, m represents the deformation amount caused by fracture creep; K tmap represents the apparent permeability of the matrix system, mD; P m ​​Pm, MPa; m g viscosity of gas, mPa·s; f m total porosity of matrix, dimensionless; t time, day; V ab amount of adsorbed gas per unit volume of matrix, (kg / m 3 ); p g density of gas, kg / m 3 ; W mf mass exchange term between matrix and fracture, kg / (d); Ax and Ay grid block size along the Cartesian coordinate system x and y direction, m; V b volume of matrix grid block, m 3 ; h f fracture height, m.

[0138] Considering the deformation of hydraulic fracture and the stress sensitivity of permeability, the gas seepage equation in the hydraulic fracture is established:

[0139] (43)

[0140] In the formula: K f fracture permeability (μm 2 ), f f fracture porosity, dimensionless. Q well mass flow rate of artificial fracture into the wellbore, i.e. production term, for the horizontal well model:

[0141] (44)

[0142] In the formula: W f hydraulic fracture width (m); P wf bottom hole flowing pressure (MPa); r e equivalent well radius, m; r w well radius (m), P f hydraulic fracture pressure (MPa).

[0143] Total production of shale gas well per unit time Q gt The sum of production of each fracture, i.e.:

[0144] (45)

[0145] In the formula: Q gt Total production of gas well (m 3 / d); n The number of fracture strips, which is an integer greater than or equal to 1.

[0146] In the specific implementation of the present application, finite difference method is used to discretize the matrix system gas seepage equation (i.e. formula 42) to obtain the following:

[0147] (46)

[0148] The conductivity is used to express formula (46) to obtain the matrix difference equation:

[0149] (47)

[0150] The coefficients in formula (47) are defined as follows:

[0151]

[0152] Therefore, formula (47) can be expressed as:

[0153] (48)

[0154] The formula represents the pressure field distribution of the matrix system.

[0155] Similarly, the difference equation of the hydraulic fracture system seepage mathematical model in the shale gas production equation group, i.e. formula (43), is:

[0156] (49)

[0157] The formula represents the pressure field distribution of the hydraulic fracture.

[0158] The conductivity in formula (49) is defined as:

[0159]

[0160] In the formula: A x, A y are respectively x , y Grid cross-sectional area in x, y directions, m2; At Time step, d; Vb is the volume of the grid block, in m3; Ax , Ay The grid blocks are respectively in x and y Dimension in direction, meters; T The conductivity is expressed as kg / (MPa·d).

[0161] Typically, during initial calculations, including n All fracture parameters are preset values, which are inferred from the well history or hydraulic fracturing process data of other production wells in the block. The actual production of the predicted well, the reservoir and the preset fracture parameters are substituted into the numerical calculation model in step S5 to calculate the bottom hole flowing pressure, and the calculated bottom hole flowing pressure is compared with the actual bottom hole flowing pressure. The fracture parameters are adjusted and fitted with the actual bottom hole flowing pressure so that the calculated bottom hole flowing pressure is consistent with the actual bottom hole flowing pressure, and new fracture parameters are determined.

[0162] By incorporating the new fracture and reservoir parameters into the numerical calculation model, i.e., formulas (48) and (49), and determining the actual hydraulic fracture and reservoir pore pressure distribution, the production rate at different production times can be calculated. Q gt .

[0163] On the other hand, as production time increases, the bottom hole flowing pressure... P wf It will decrease accordingly, the same At Within a time period Q gt This will also decrease accordingly. Based on the block well history, this application pre-sets a minimum output per abandoned block. Q gto That is, the predicted well Q gt Reaching or falling below Q gto When this time, it indicates that the well has reached the critical point of abandonment, and it can be considered that there is no longer any need to mine the well. From the start of production to the production rate of... Q gto The time is recorded as t all Regarding time t all All inside Q gt The total recoverable quantity (EUR) of the predicted well can be obtained by summing the results.

[0164] refer to Figs. 1 to 3 The prediction process for the production and recoverable reserves of a certain XX shale gas well using the deep shale gas fracturing horizontal well production and recoverable reserves prediction method of this application is as follows. The calculation process is completed by computer programming:

[0165] The fracture and reservoir parameters of the well are shown in Table 2 and Table 3, and the hydraulic fracture number is preset to 160 (20 segments, 8 clusters per segment), the fracture height is 10 m, and the fracture conductivity is calculated to be 0.2 D·cm. The general abandoned single yield of the well site in the block is 2000 m Q gto 3。

[0166] Table 2 Fracture parameters of XX well of Yuxi deep shale gas

[0167] ;

[0168] Table 3 Reservoir parameters of XX well of Yuxi deep shale gas

[0169] ;

[0170] The actual yield of the shale gas well, the reservoir and fracture parameters are brought into the numerical calculation model, the bottom hole flowing pressure is calculated by formula (45) P wf , and the actual bottom hole flowing pressure and the calculated bottom hole flowing pressure are compared as shown in Fig. 2 , the history yield fitting graph Fig. 3 and the bottom hole flowing pressure comparison Fig. 1 are determined, the fracture parameters (fracture number, length or conductivity) are adjusted to make the calculated bottom hole flowing pressure and the actual bottom hole flowing pressure consistent, and the new fracture parameters are determined as shown in Table 4.

[0171] Table 4 Fracture fitting parameters of XX well of Yuxi deep shale gas

[0172] ;

[0173] The new fracture parameters and the reservoir parameters are brought into the productivity equation set, the hydraulic fracture and matrix pore pressure equation set are coupled to solve, the hydraulic fracture and reservoir pore pressure distribution are determined, the yield at different production times is calculated, and the relationship between the abandoned single yield and the EUR is Q gto 3确定总的生产时间约为 7200d, and the yield and the EUR are shown in Fig. 4 , so the recoverable reserves EUR of the well is predicted to be about 70 million cubic meters.

[0174] Finally, it should be noted that the above description is only for the preferred embodiments of the present application, and those skilled in the art can make various similar expressions under the inspiration of the present application without violating the purpose and claims of the present application, and such changes fall within the protection scope of the present application.​​

Claims

1. A method for predicting the production and recoverable reserves of fracturing horizontal wells in deep shale gas formations, characterized in that, Includes the following steps: S1, Based on the micropore filling adsorption model, an adsorption model for deep shale gas is constructed; S2. Based on the differences in pore morphology and gas transport mechanism between organic and inorganic shale, a unified model of total apparent permeability of the matrix is ​​established. The apparent permeability model includes the influence factors of real gas effect and confinement effect. S3, based on the Kelvin viscoelastic deformation model, constructs a deformation model and a conductivity model for a single hydraulic crack; S4. Based on the shale gas adsorption model in step S1 and the total apparent permeability model of the matrix in step S2, establish the gas flow equation of the matrix system during shale gas production. ； In the formula: K tmap This represents the apparent permeability of the matrix system; P m Formation pressure; μ g Indicates gas viscosity; φ m Indicates the total porosity of the matrix; t Indicates time; V ab This indicates the amount of adsorbed gas per unit volume of matrix. ρ g Indicates gas density; W mf This represents the mass exchange term between the matrix and the fracturing fracture. Δx and Δy They represent the coordinates along the Cartesian coordinate system. x and y Grid block size in the direction; V b Indicates the volume of the matrix grid block; h f Indicates the crack height; x Represents the Cartesian coordinate system x Directional distance value; y Represents the Cartesian coordinate system y Directional distance value; Based on the deformation model and conductivity model of a single hydraulic fracture in step S3, establish the gas seepage equation for the hydraulic fracture. ； In the formula: K f Indicates the permeability of the crack; φ f Indicates the porosity of the fracturing fracture; Q well This represents the mass flow rate, or production, of artificially created fractures into the wellbore. W f This indicates the current width of the hydraulic fracture; P f This refers to the hydraulic fracture pressure. V bf Indicates the volume of the hydraulic fracture mesh; S5, Construct the production capacity of a single hydraulic fracture based on the gas flow equation of the matrix system and the gas flow equation of the hydraulic fracture. Q well Computational model; S6, the number of hydraulic fractures in the well to be predicted is... n , n The total production per unit time of the well to be predicted is obtained by summing the production of multiple hydraulic fractures, which are integers greater than or equal to 1. Q gt ; S7, based on the preset abandoned single-unit production of the well to be predicted. Q gto Calculate its output to reach that waste unit. Q gto Total production time t all All of the total production time Q gt The recoverable reserves (EUR) of the well are obtained by summing them up.

2. The method for predicting production and recoverable reserves of deep shale gas fractured horizontal wells according to claim 1, characterized in that: Step S2 also includes slip flow, Knudsen diffusion, matrix stress sensitivity, and water film influence factors.

3. The method for predicting production and recoverable reserves of deep shale gas fractured horizontal wells according to claim 1 or 2, characterized in that: In step S2, firstly, the influencing factors of the circular pores and slit pores included in the matrix pores are characterized, then the apparent permeability is constructed according to Darcy's law, and finally, the apparent permeability model of the matrix is ​​constructed according to the organic matter content.

4. The method for predicting production and recoverable reserves of deep shale gas fractured horizontal wells according to claim 1, characterized in that: The deformation in the deformation model of a single hydraulic fracture in step S3 also includes the effective closure stress. P C The embedding amount Δ of the crack proppant under action PE and elastic deformation Δ PD .

5. The method for predicting production and recoverable reserves of deep shale gas fractured horizontal wells according to claim 4, characterized in that: include n The fracture parameters are preset values, which are inferred from the well history or hydraulic fracturing process data of other production wells in the block where the fracture is located. The actual production, reservoir and preset fracture parameters of the well to be predicted are substituted into the numerical calculation model in step S5 to calculate the bottom hole flowing pressure, and it is compared with the actual bottom hole flowing pressure. The fracture parameters are adjusted and fitted with the actual bottom hole flowing pressure so that the calculated bottom hole flowing pressure is consistent with the actual bottom hole flowing pressure, and new fracture parameters are determined. By incorporating the new fracture and reservoir parameters into the numerical model, the actual hydraulic fracture and reservoir pore pressure distribution are determined, and then the total production per unit time of the well to be predicted is calculated. Q gt And recoverable reserves in EUR.

6. The method for predicting production and recoverable reserves of deep shale gas fractured horizontal wells according to claim 1, characterized in that: In step S4, the finite difference method is used to discretize the gas seepage equation of the matrix system and the gas seepage equation of the hydraulic fracture to establish a set of numerical calculation equations for production capacity.

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