Method for optimizing design of deep shale gas horizontal well with close cutting and non-uniform perforation

Abstract

The application discloses a deep shale gas horizontal well dense cutting fracturing non-uniform perforation optimization design method and relates to the technical field of shale gas development. The application is specially aimed at the deep shale gas horizontal well dense cutting fracturing non-uniform perforation process, and a deep shale horizontal well fracturing hydraulic fracture initiation and extension model, a single cluster perforation hole flow friction pressure drop model and a perforation hole number optimization model are established. Since the method fully considers the influence of the inter-crack stress interference effect on the extension of each cluster hydraulic fracture during the deep shale horizontal well dense cutting fracturing, the number of each cluster perforation hole in the non-uniform perforation is optimized and adjusted, the half length of each cluster hydraulic fracture is made to be consistent, the goal of synchronous extension of the fracture is achieved, and the problem that the number of cluster perforation holes in the deep shale gas horizontal well dense cutting fracturing non-uniform perforation process is mainly designed according to engineering experience is solved.

Description

TECHNICAL FIELD

[0001] The present application relates to the technical field of shale gas development, and particularly relates to a deep shale gas horizontal well dense cutting fracturing non-uniform perforation optimization design method. BACKGROUND

[0002] The shale gas reservoir has extremely low porosity and permeability, and is extremely difficult to exploit. At present, through horizontal well staged multi-cluster fracture network fracturing technology, commercial development of medium and shallow shale gas with a depth of 3500 meters or less has been realized, and gradually moves towards the deep shale gas field. The deep shale gas formation has characteristics of high temperature, high pressure and high stress, which is not conducive to the formation of fracture network. Therefore, by reducing the perforation cluster spacing during staged multi-cluster fracturing and reducing the hydraulic fracture spacing, the stress interference effect between fractures is fully utilized to promote the formation of fracture network. This process is called dense cutting fracturing technology. However, with the reduction of perforation cluster spacing and the increase of stress interference effect between fractures, the liquid inlet difference of each cluster perforation increases, and the extension behavior of mutual competition between hydraulic fractures of each cluster perforation occurs, that is, the hydraulic fracture extension of some perforation clusters is limited, while the hydraulic fracture extension of other perforation clusters is excessive, resulting in different lengths of hydraulic fractures of each cluster, which seriously affects the fracturing stimulation effect.

[0003] In the process of dense cutting fracturing of deep shale gas horizontal well, in order to promote the extension length of hydraulic fractures of each cluster to be consistent, it is necessary to ensure uniform liquid inlet of each cluster perforation, and a non-uniform perforation technology is proposed. This technology arranges different perforation hole numbers in each cluster perforation, and uses perforation friction to force the fracturing fluid to automatically branch and uniformly enter the hydraulic fractures of each cluster, so as to ensure uniform extension of the fractures.

[0004] At present, the non-uniform perforation technology has been widely used in the field of horizontal well fracturing, and the related research mainly focuses on the extension law of hydraulic fractures of each cluster and the influence of perforation hole number on fracture extension. However, at present, the perforation hole number in the non-uniform perforation process mainly relies on engineering experience for general design. SUMMARY

[0005] The present application aims to solve the problem that in the current non-uniform perforation process of deep shale gas horizontal well dense cutting fracturing, the perforation hole number of each cluster mainly relies on engineering experience for general design. The present application provides a deep shale gas horizontal well dense cutting fracturing non-uniform perforation optimization design method, which fully considers the influence of stress interference effect between fractures on the extension of hydraulic fractures of each cluster during deep shale gas horizontal well dense cutting fracturing, and then optimizes and adjusts the perforation hole number of each cluster, promotes the extension half-length of hydraulic fractures of each cluster to be consistent, realizes the goal of "controlling the length and promoting the short, synchronous extension", and provides technical support and effective tools for efficient development of shale gas.

[0006] The technical scheme of the present application is as follows:

[0007] The method comprises the following steps.

[0008] Step S1: according to the pump injection rate, the perforation cluster number and the perforation hole diameter of the target deep shale horizontal well, the minimum critical perforation hole number of a single cluster is determined by using a single cluster perforation hole flow friction pressure drop model.

[0009] Step S2: according to the design parameters of the target deep shale horizontal well and the minimum critical perforation hole number of a single cluster, the hydraulic fracture extension half-length and the hydraulic fracture half-length variation coefficient of each cluster are determined by using a deep shale horizontal well dense multi-cluster hydraulic fracture extension model.

[0010] Step S3: according to the hydraulic fracture extension half-length of each cluster, the perforation hole number optimization model is used to adjust the perforation hole number of each cluster so that the number distribution is no longer uniform.

[0011] Step S4: according to the adjusted perforation hole number of each cluster, the hydraulic fracture extension half-length and the hydraulic fracture half-length variation coefficient of each cluster under the non-uniform perforation condition are determined by using the deep shale horizontal well dense multi-cluster hydraulic fracture extension model.

[0012] Step S5: the perforation hole number optimization model is used again to adjust the perforation hole number of each cluster until the hydraulic fracture extension half-length of each cluster is basically consistent, and the optimal value of the perforation hole number of each cluster is output, and a hydraulic fracture extension space distribution map of each cluster is drawn.

[0013] Further, the detailed steps of step S1 are as follows:

[0014] Step S11: the pump injection rate, the perforation cluster number and the perforation hole diameter of the target deep shale horizontal well are obtained.

[0015] Step S12: a single cluster perforation hole flow friction pressure drop model is established by using fluid mechanics theory.

[0016] Step S13: according to the pump injection rate, the perforation cluster number and the perforation hole diameter, the perforation hole friction pressure drop under different single cluster perforation hole numbers is calculated by using the single cluster perforation hole flow friction pressure drop model.

[0017] Step S14: the perforation hole friction pressure drop curve with the single cluster perforation hole number is drawn according to the perforation hole friction pressure drop under different single cluster perforation hole numbers.

[0018] Step S15: a single cluster perforation hole flow friction pressure drop threshold is preset, and the minimum critical perforation hole number of a single cluster is determined under the condition that the single cluster perforation hole flow friction pressure drop is less than the threshold.

[0019] Further, the detailed steps of step S2 are as follows:

[0020] Step S21: Obtain the design parameters of the target deep shale horizontal well, including formation parameters, fracturing parameters and perforation parameters;

[0021] Step S22: Establish a deep shale horizontal well multi-cluster hydraulic fracture extension model with tight cutting and fracturing by using rock mechanics theory, fluid mechanics theory and fluid-structure coupling theory;

[0022] Step S23: Simulate the extension behavior of each cluster of hydraulic fractures under uniform perforation conditions by using the deep shale horizontal well multi-cluster hydraulic fracture extension model with tight cutting and fracturing, and determine the extension half-length of each cluster of hydraulic fractures and the hydraulic fracture half-length variation coefficient.

[0023] Further, the detailed steps of step S3 are:

[0024] Step S31: Establish a perforation hole number optimization model;

[0025] Step S32: By comparing the current extension half-length of each cluster of hydraulic fractures with the average extension half-length, use the perforation hole number optimization model to increase the number of perforation holes in the cluster with shorter current hydraulic fracture extension half-length, so that the number of perforation holes in each cluster is no longer uniform.

[0026] Further, the detailed steps of step S4 are:

[0027] According to the adjusted number of perforation holes in each cluster, simulate the extension behavior of each cluster of hydraulic fractures under non-uniform perforation conditions by using the deep shale horizontal well multi-cluster hydraulic fracture extension model with tight cutting and fracturing, and determine the extension half-length of each cluster of hydraulic fractures and the hydraulic fracture half-length variation coefficient.

[0028] Further, the detailed steps of step S5 are:

[0029] Step S51: Pre-set a hydraulic fracture half-length variation coefficient threshold;

[0030] If the hydraulic fracture half-length variation coefficient is greater than the threshold, the perforation hole number optimization model is used again to adjust the number of perforation holes in each cluster;

[0031] If the hydraulic fracture half-length variation coefficient is less than or equal to the threshold, it is determined that the adjustment of the number of perforation holes in each cluster is complete, and the optimal value is reached. The optimal value of the number of perforation holes in each cluster is output, and the spatial distribution map of the extension of each cluster of hydraulic fractures is drawn.

[0032] Further, the single-cluster perforation hole flow friction pressure drop model comprises:

[0033]

[0034] In the formula:

[0035] Δpcl q is the flow friction pressure drop of single cluster perforation hole; q cl q is the fluid flow of single cluster perforation hole; n pf n is the number of perforation holes; d pf d is the inner diameter of perforation hole; α pf α is the hole flow coefficient; ρ is the density of fracturing fluid.

[0036] Further, the deep shale horizontal well multi-cluster hydraulic fracture extension model with close-cuts includes: a material balance equation, an intra-fracture fluid pressure drop equation, a fracturing fluid filtration equation, a fracture width equation, a fracture discrete element stress-strain balance equation, a fracture discrete element coordinate conversion equation, a fracture height equation, a multi-cluster hydraulic fracture flow distribution equation, a multi-cluster hydraulic fracture extension boundary condition and initial condition equation, and a multi-cluster hydraulic fracture extension half-length variation coefficient equation.

[0037] Further, the material balance equation is as follows:

[0038]

[0039] In the formula:

[0040] q is the intra-fracture flow;

[0041] s is the fracture length direction coordinate;

[0042] t is time;

[0043] h f is the fracture height;

[0044] w f is the fracture opening;

[0045] q L is the fracturing fluid filtration velocity;

[0046] The intra-fracture fluid pressure drop equation is as follows:

[0047]

[0048] In the formula:

[0049] p is the intra-fracture pressure;

[0050] μ is the liquid viscosity;

[0051] The fracturing fluid filtration equation is as follows:

[0052]

[0053] In the formula:

[0054] C L is the formation filtration coefficient;

[0055] τ is the start-up filtration time;

[0056] Crack width equation:

[0057] wf(s) = (Dn)j

[0058] where:

[0059] (D n ) j is the corresponding crack j element normal displacement at crack length s;

[0060] The crack discrete element stress-strain equilibrium equation is as follows:

[0061]

[0062] where:

[0063]

[0064]

[0065]

[0066]

[0067] where:

[0068] (σ t ) i is the shear stress experienced by the crack i element in the local coordinate system;

[0069] (σ n ) i is the normal stress experienced by the crack i element in the local coordinate system;

[0070] (D n ) j is the normal displacement of the crack j element;

[0071] (D t ) j is the tangential displacement of the crack j element;

[0072] (A tt ) ij is the tangential stress component caused by the tangential displacement discontinuity of the crack j element on the crack i element;

[0073] (A tn ) ij is the normal stress component caused by the tangential displacement discontinuity of the crack j element on the crack i element;

[0074] (A nt ) ijthe tangential stress component caused by the normal displacement discontinuity of the fracture j element on the fracture i element;

[0075] (A nn ) ij the normal stress component caused by the normal displacement discontinuity of the fracture j element on the fracture i element;

[0076] E is the Young's modulus of the rock;

[0077] ν is the Poisson's ratio of the formation;

[0078] n j is the cosine value of the angle between the global coordinate y axis and the local coordinate ζ axis of the fracture j element;

[0079] l j is the cosine value of the angle between the global coordinate x axis and the local coordinate ξ axis of the fracture j element;

[0080] F3~F6 are partial derivative equations of the Papkovitch function;

[0081] fracture discrete element coordinate conversion equation:

[0082]

[0083] in the formula:

[0084] ζ ij and ξ ij are local coordinate values;

[0085] x i is the x axis coordinate value of the center of the fracture i element under the global coordinate;

[0086] x j is the x axis coordinate value of the center of the fracture j element under the global coordinate;

[0087] y i is the y axis coordinate value of the center of the fracture i element under the global coordinate;

[0088] y j is the y axis coordinate value of the center of the fracture j element under the global coordinate;

[0089] fracture height equation:

[0090]

[0091] in the formula:

[0092] K Ic is the fracture toughness of the shale; σ c is the closure stress of the formation;

[0093] flow distribution equation of each cluster of hydraulic fractures:

[0094]

[0095] wherein:

[0096]

[0097]

[0098] wherein:

[0099] p heel is the pressure at the end of the horizontal well;

[0100] p fi,i is the pressure at the tip of the i-th cluster of hydraulic fractures;

[0101] Δp cl,i is the frictional pressure drop at the i-th cluster of perforations;

[0102] Δp w,j is the pressure drop of fluid flow in the j-th section of horizontal well;

[0103] p i | s＝0 is the pressure at the coordinate s = 0 along the length of the i-th cluster of hydraulic fractures;

[0104] σ hmin is the minimum horizontal principal stress of the formation;

[0105] n pf,i is the number of perforations in the i-th cluster;

[0106] μ is the viscosity of the fracturing fluid;

[0107] L w,j is the length of the j-th section of horizontal well;

[0108] q w,j is the flow rate of the j-th section of horizontal well;

[0109] q cl,i is the flow rate of fluid from the i-th cluster of perforations;

[0110] d w is the diameter of the horizontal wellbore;

[0111] The subscript i represents the number of each cluster of fractures; the subscript j represents the number of each section of horizontal well;

[0112] The extended boundary condition and initial condition equation of each cluster of hydraulic fractures:

[0113]

[0114] wherein:

[0115] L f is the half-length of the fracture;

[0116] The equation of the variation coefficient of the hydraulic fracture extension half-length of each cluster is:

[0117]

[0118] In the formula:

[0119] μ f is the average value of the hydraulic fracture half-length of each cluster;

[0120] σ f is the standard deviation value of the hydraulic fracture half-length of each cluster;

[0121] χ f is the variation coefficient of the hydraulic fracture half-length of each cluster;

[0122] Further, the perforation hole number optimization model comprises:

[0123]

[0124] In the formula:

[0125] is the i-th cluster perforation hole number after optimization; is the i-th cluster perforation hole number before optimization.

[0126] Compared with the prior art, the present application has the beneficial effects that:

[0127] The optimization design method for non-uniform perforation in dense-cut fracturing of deep shale gas horizontal wells includes the following steps: Step S1: Based on the pumping rate, number of perforation clusters, and orifice inner diameter of the target deep shale horizontal well dense-cut fracturing design, determine the minimum critical number of perforations per cluster using a single-cluster perforation flow friction pressure drop model; Step S2: Based on the design parameters of the target deep shale horizontal well, combined with the minimum critical number of perforations per cluster, utilize the multi-cluster hydraulic fracture extension method of dense-cut fracturing in deep shale horizontal wells. The model is used to determine the half-length extension of hydraulic fractures in each cluster and the coefficient of variation of the half-length extension; Step S3: Based on the half-length extension of hydraulic fractures in each cluster, the number of perforations in each cluster is adjusted using the perforation number optimization model to make its distribution non-uniform; Step S4: Based on the adjusted number of perforations in each cluster, the multi-cluster hydraulic fracture extension model of deep shale horizontal well dense cutting fracturing is used to determine the half-length extension of hydraulic fractures in each cluster and the coefficient of variation of the half-length extension of hydraulic fractures under non-uniform perforation conditions; Step S5: Again... This method utilizes an optimization model for the number of perforations to adjust the number of perforations in each cluster until the half-length of hydraulic fracture extension in each cluster is essentially the same. The optimal value for the number of perforations in each cluster is output, and a spatial distribution map of the hydraulic fracture extension in each cluster is plotted. Specifically designed for the non-uniform perforation process in deep shale gas horizontal wells with close-cut fracturing, this method establishes a hydraulic fracture initiation and extension model, a single-cluster perforation flow friction pressure drop model, and a perforation number optimization model. This leads to the proposed optimization design method for non-uniform perforation in deep shale gas horizontal wells with close-cut fracturing. Because this method fully considers the influence of inter-fracture stress interference on the extension of each cluster of hydraulic fractures during close-cut fracturing in deep shale gas horizontal wells, it optimizes and adjusts the number of perforations in each cluster of non-uniform perforations, promoting a more consistent half-length of hydraulic fracture extension in each cluster, achieving the goal of "suppressing long fractures and promoting short fractures, with synchronous extension." This solves the problem that the number of perforations in clusters in the non-uniform perforation process of deep shale gas horizontal wells with close-cut fracturing mainly relies on general engineering experience for design. Attached Figure Description

[0128] Figure 1 Numerical calculation flowchart for the optimized design method of non-uniform perforation for dense cutting fracturing in deep shale gas horizontal wells;

[0129] Figure 2 This is a graph showing the variation of perforation friction with the number of perforations in a single cluster in Example 2.

[0130] Figure 3 This is a spatial distribution diagram of the extension of each cluster of hydraulic fractures before the optimization of the number of perforations in the target well in Example 2 (uniform perforation process);

[0131] Figure 4 This is a spatial distribution diagram of the extension of hydraulic fractures in each cluster after the number of perforations in the target well is optimized (non-uniform perforation process) in Example 2. Detailed Implementation

[0132] It should be noted that the relational terms, such as first and second, and the like are used solely to distinguish one from another entity or action, without necessarily requiring or implying any such actual relationship or order between such entities or actions. Moreover, the terms "comprises", "comprising", or any other variations thereof, are intended to cover a non-exclusive inclusion, such that a process, method, article, or apparatus that comprises a list of elements does not include only those elements but can include other elements not expressly listed or inherent to such process, method, article, or apparatus. An element proceeded by "comprises... a" does not, without more constraints, exclude the existence of additional identical elements in the process, method, article, or apparatus that comprises the element.

[0133] The features and characteristics of the present application will be further described below in connection with the embodiments.

[0134] Embodiment One

[0135] At present, the non-uniform perforation technology has been widely used in the field of horizontal well fracturing, and the related research mainly focuses on the extension law of each cluster of hydraulic fractures, and the influence of the number of perforation holes on the extension of the fractures. However, at present, the number of cluster perforation holes in the non-uniform perforation process is mainly designed according to engineering experience.

[0136] The embodiment aims at the above problems, and provides a deep shale gas horizontal well multi-fracturing non-uniform perforation optimization design method, which fully considers the influence of the stress interference effect between fractures on the extension of each cluster of hydraulic fractures when the deep shale horizontal well is multi-fractured, and then optimizes and adjusts the number of perforation holes of each cluster of non-uniform perforation, so as to make the extension half-length of each cluster of hydraulic fractures consistent, realize the goal of "controlling the length and promoting the shortness, and synchronous extension", and provide technical support and effective tools for efficient development of shale gas.

[0137] Please refer to Figure 1 , a deep shale gas horizontal well multi-fracturing non-uniform perforation optimization design method, which specifically comprises the following steps:

[0138] Step S1: according to the pump injection displacement, the number of perforation clusters, and the inner diameter of the perforation hole of the target deep shale horizontal well multi-fracturing design, a single cluster perforation hole flow friction pressure drop model is used to determine the minimum critical number of perforation holes of the single cluster perforation.

[0139] In the embodiment, specifically, the single cluster perforation hole flow friction pressure drop model comprises:

[0140]

[0141] Wherein:

[0142]

[0143] wherein:

[0144] Δp cl is the flow friction pressure drop of single cluster perforation hole, unit: Pa;

[0145] q cl is the fluid flow of single cluster perforation hole, unit: m 3 / s;

[0146] n pf is the number of perforation holes, unit: pieces;

[0147] d pf is the inner diameter of perforation hole, unit: m;

[0148] α pf is the hole flow coefficient, generally 0.8, dimensionless;

[0149] ρ is the density of fracturing fluid, unit: kg / m 3 ;

[0150] Q T is the injection flow of fracturing pump, unit: m 3 / s;

[0151] N cl is the number of perforation clusters, unit: clusters;

[0152] In the embodiment, specifically, the detailed steps of the step S1 are:

[0153] Step S11: obtaining the pump injection flow, the number of perforation clusters and the inner diameter of perforation hole of the target deep shale horizontal well close to the cutting fracturing design;

[0154] Step S12: using the fluid mechanics theory to establish a single cluster perforation hole flow friction pressure drop model;

[0155] Step S13: according to the pump injection flow, the number of perforation clusters and the inner diameter of perforation hole, using the single cluster perforation hole flow friction pressure drop model, the perforation hole friction pressure drops under different numbers of single cluster perforation holes are calculated respectively; that is, using (Formula 1) and (Formula 2) to calculate the perforation hole friction pressure drops under different numbers of single cluster perforation holes; preferably, using (Formula 1) and (Formula 2) to calculate the perforation hole friction pressure drops under the numbers of single cluster perforation holes of 1 cluster to 48 clusters respectively;

[0156] Step S14: according to the perforation hole friction pressure drops under different numbers of single cluster perforation holes, a curve of the perforation hole friction changing with the number of single cluster perforation holes is drawn;

[0157] Step S15: preset a single cluster perforation hole flow friction pressure drop threshold, and determine the minimum critical number of perforation holes of the single cluster perforation hole under the condition that the single cluster perforation hole flow friction pressure drop is less than the threshold; preferably, the threshold is set to 0.5 MPa; that is, the minimum critical number of perforation holes of the single cluster perforation hole is determined under the condition that the single cluster perforation hole flow friction pressure drop is less than 0.5 MPa.

[0158] Step S2: according to the design parameters of the target deep shale horizontal well, in combination with the minimum critical number of perforation holes of the single cluster perforation hole, the half length of each cluster hydraulic fracture and the hydraulic fracture half length variation coefficient are determined by using the deep shale horizontal well multi-cluster hydraulic fracture extension model with close cutting and fracturing.

[0159] In the embodiment, specifically, the deep shale horizontal well multi-cluster hydraulic fracture extension model with close cutting and fracturing includes: a material balance equation, a fracture fluid pressure drop equation, a fracturing fluid filtration equation, a fracture width equation, a fracture discrete element stress-strain balance equation, a fracture discrete element coordinate conversion equation, a fracture height equation, a cluster hydraulic fracture flow distribution equation, a cluster hydraulic fracture extension boundary condition and initial condition equation, and a cluster hydraulic fracture extension half length variation coefficient equation.

[0160] Wherein:

[0161] The material balance equation is:

[0162]

[0163] In the formula:

[0164] q is the fracture flow rate, unit: m 3 / s;

[0165] s is the fracture length direction coordinate, unit: m;

[0166] t is time, unit: s;

[0167] h f is the fracture height, unit: m;

[0168] w f is the fracture opening, unit: m;

[0169] q L is the fracturing fluid filtration velocity, unit: m / s;

[0170] The fracture fluid pressure drop equation is:

[0171]

[0172] In the formula:

[0173] p is the fracture pressure, unit: Pa;

[0174] μ is the liquid viscosity, unit: Pa-s;

[0175] Fracturing fluid filtration equation:

[0176]

[0177] In the formula:

[0178] C L is the formation filtration coefficient, unit: m / s 0.5 ;

[0179] τ is the initial filtration time, unit: s;

[0180] Fracture width equation:

[0181] w f (s) = (D n ) j (Formula 6)

[0182] In the formula:

[0183] (D n ) j is the corresponding normal displacement of the fracture j element at the fracture length s, unit: m;

[0184] Fracture discrete element stress-strain equilibrium equation:

[0185]

[0186] Where:

[0187]

[0188]

[0189]

[0190]

[0191] In the formula:

[0192] (σ t ) i is the shear stress of the fracture i element in the local coordinate system, unit: Pa;

[0193] (σ n ) i is the normal stress of the fracture i element in the local coordinate system, unit: Pa;

[0194] (D n ) j is the normal displacement of the fracture j element, unit: m;

[0195] (D t ) j is the tangential displacement of the crack j element, unit: m;

[0196] (A tt ) ij is the tangential stress component caused by the tangential displacement discontinuity of the crack j element on the crack i element;

[0197] (A tn ) ij is the normal stress component caused by the tangential displacement discontinuity of the crack j element on the crack i element;

[0198] (A nt ) ij is the tangential stress component caused by the normal displacement discontinuity of the crack j element on the crack i element;

[0199] (A nn ) ij is the normal stress component caused by the normal displacement discontinuity of the crack j element on the crack i element;

[0200] E is the Young's modulus of rock, unit: Pa;

[0201] ν is the Poisson's ratio of stratum, dimensionless;

[0202] n j is the cosine value of the angle between the global coordinate y axis and the local coordinate ζ axis of the crack j element, dimensionless;

[0203] l j is the cosine value of the angle between the global coordinate x axis and the local coordinate ξ axis of the crack j element, dimensionless;

[0204] F3~F6 are partial derivative equations of Papkovitch function;

[0205] Coordinate conversion equation of crack discrete element:

[0206]

[0207] In the formula:

[0208] ζ ij and ξ ij are local coordinate values, unit: m;

[0209] x i is the x axis coordinate value of the center of the crack i element under the global coordinate, unit: m;

[0210] x j is the x axis coordinate value of the center of the crack j element under the global coordinate, unit: m;

[0211] y iThis represents the y-axis coordinate of the center of crack element i in global coordinates, in meters (m).

[0212] y j This represents the y-axis coordinate of the center of crack element j in global coordinates, in meters.

[0213] Crack height equation:

[0214]

[0215] In the formula:

[0216] K Ic Shale fracture toughness, unit: Pa·m 0.5 ;σ c Formation closure stress, unit: Pa.

[0217] Flow distribution equations for each cluster of hydraulic fractures:

[0218]

[0219] in:

[0220]

[0221]

[0222] In the formula:

[0223] p heel This refers to the pressure at the heel of a horizontal well, in Pa.

[0224] p fi,i The pressure at the opening of the i-th hydraulic fracture cluster, in Pa;

[0225] Δp cl,i The frictional pressure drop at the orifice of the i-th cluster of perforations, in Pa;

[0226] Δp w,j The pressure drop of fluid flow within the j-th horizontal well section is expressed in Pa.

[0227] p i | s＝0 The pressure at coordinate s = 0 along the length of the i-th hydraulic fracture cluster is the inlet pressure of the i-th hydraulic fracture cluster, in Pa.

[0228] σ hmin The minimum horizontal principal stress of the formation, in Pa;

[0229] n pf,i The number of apertures in the i-th cluster, in units of 1;

[0230] μ is the viscosity of the fracturing fluid, in Pa·s;

[0231] L w,j Lj is the length of the jth section of horizontal well, unit: m;

[0232] q w,j qj is the flow rate of the jth section of horizontal well, unit: m 3 / s;

[0233] q cl,i qi is the fluid flow rate of the i th cluster of perforation, i.e. the flow rate allocated by the i th cluster of hydraulic fracture, unit: m 3 / s;

[0234] d w d is the diameter of horizontal wellbore, unit: m;

[0235] The subscript i represents the number of each cluster of fracture; the subscript j represents the number of each section of horizontal well;

[0236] The extension boundary condition equation and the initial condition equation of each cluster of hydraulic fracture are as follows:

[0237]

[0238] In the formula:

[0239] L f L is the half length of fracture, unit: m;

[0240] The half length variation coefficient equation of each cluster of hydraulic fracture is as follows:

[0241]

[0242] In the formula:

[0243] μ f μ is the average value of the half length of each cluster of hydraulic fracture, unit: m;

[0244] σ f σ is the standard deviation value of the half length of each cluster of hydraulic fracture, unit: m;

[0245] χ f χ is the variation coefficient of the half length of each cluster of hydraulic fracture, dimensionless;

[0246] Further, in the embodiment, the detailed steps of step S2 are as follows:

[0247] Step S21: obtaining the design parameters of the target deep shale horizontal well; preferably, the design parameters include formation parameters (maximum horizontal principal stress of formation, minimum horizontal principal stress of formation, rock Young's modulus, rock Poisson's ratio, reservoir rock fracture toughness, formation filtration coefficient), fracturing parameters (fracturing discharge, fracturing fluid volume, pumping time, fracturing pipe string inner diameter, fracturing fluid viscosity) and perforation parameters (cluster spacing, cluster number, perforation hole number, perforation hole inner diameter).

[0248] Step S22: a deep shale horizontal well dense cutting and fracturing multi-cluster hydraulic fracture extension model is established by using rock mechanics theory, fluid mechanics theory and fluid-structure coupling theory;

[0249] Step S23: the extension behavior of each cluster of hydraulic fractures under the condition of uniform perforation is simulated by using the deep shale horizontal well dense cutting and fracturing multi-cluster hydraulic fracture extension model, and the extension half-length of each cluster of hydraulic fractures and the hydraulic fracture half-length variation coefficient are determined; that is, the detailed steps of the step S23 are: the (Formula 1) to (Formula 16) are solved simultaneously, (Formula 17) is combined, the material balance equation and the fracture fluid pressure drop equation are solved by using the finite difference method, the fracture discrete element stress-strain balance equation is solved by using the boundary element method, the cluster hydraulic fracture flow distribution equation is solved by using the Newton iteration method, the geometric parameters in the extension process of each cluster of hydraulic fractures are calculated, including: the half-length of each cluster of hydraulic fractures, the fracture width, the fracture height, and the flow distribution obtained by each cluster of hydraulic fractures, and the (Formula 18) is combined to output the extension half-length of each cluster of hydraulic fractures and the hydraulic fracture half-length variation coefficient data after fracturing.

[0250] Step S3: according to the extension half-length of each cluster of hydraulic fractures, the perforation hole number optimization model is used to adjust the number of perforation holes in each cluster, so that the number distribution is no longer uniform;

[0251] In this embodiment, specifically, the perforation hole number optimization model includes:

[0252]

[0253] In the formula:

[0254] is the number of perforation holes in the i th cluster after optimization, unit: pieces;

[0255] is the number of perforation holes in the i th cluster before optimization, unit: pieces;

[0256] In this embodiment, specifically, the detailed steps of the step S3 are:

[0257] Step S31: a perforation hole number optimization model is established;

[0258] Step S32: by comparing the extension half-length of each cluster of hydraulic fractures with the average extension half-length, the perforation hole number optimization model is used, that is, (Formula 19) is used to optimize the number of perforation holes in each cluster, that is, the number of perforation holes in the cluster with shorter hydraulic fracture extension half-length is increased, so that the number of perforation holes in each cluster is no longer uniformly distributed.

[0259] Step S4: according to the adjusted number of perforation holes of each cluster, using the multi-cluster hydraulic fracture extension model of deep shale horizontal well dense cutting fracturing, the hydraulic fracture extension half-length of each cluster and the hydraulic fracture half-length variation coefficient under the condition of non-uniform perforation are determined;

[0260] In this embodiment, the detailed steps of step S4 are specifically:

[0261] According to the adjusted number of perforation holes of each cluster, using the multi-cluster hydraulic fracture extension model of deep shale horizontal well dense cutting fracturing, the hydraulic fracture extension behavior of each cluster under the condition of non-uniform perforation is simulated, and the hydraulic fracture extension half-length of each cluster and the hydraulic fracture half-length variation coefficient are determined; that is, the adjusted number of perforation holes of each cluster is substituted into formula (15), the multi-cluster hydraulic fracture extension model of deep shale horizontal well dense cutting fracturing is used to simulate the hydraulic fracture extension behavior of each cluster under the condition of non-uniform perforation, and the hydraulic fracture extension half-length of each cluster and the hydraulic fracture half-length variation coefficient are determined.

[0262] Step S5: the number of perforation holes of each cluster is adjusted repeatedly again using the perforation hole number optimization model until the hydraulic fracture extension half-length of each cluster is basically consistent, the optimal value of the number of perforation holes of each cluster is output, and the spatial distribution map of the hydraulic fracture extension of each cluster is drawn;

[0263] In this embodiment, the detailed steps of step S5 are specifically:

[0264] Step S51: a hydraulic fracture half-length variation coefficient threshold is preset; preferably, the threshold is set to 0.05;

[0265] If the hydraulic fracture half-length variation coefficient is greater than the threshold, the number of perforation holes of each cluster is adjusted again using the perforation hole number optimization model; that is, if the hydraulic fracture half-length variation coefficient is greater than 0.05, the number of perforation holes of each cluster is adjusted again using the perforation hole number optimization model;

[0266] If the hydraulic fracture half-length variation coefficient is less than or equal to the threshold, it is determined that the number of perforation holes of each cluster is adjusted and optimal; and the optimal value of the number of perforation holes of each cluster is output, and the spatial distribution map of the hydraulic fracture extension of each cluster is drawn; that is, if the hydraulic fracture half-length variation coefficient is less than or equal to 0.05, it is determined that the number of perforation holes of each cluster is adjusted and optimal.

[0267] The method is specially for the deep shale gas horizontal well dense cutting fracturing non-uniform perforation process, establishes a deep shale gas horizontal well fracturing hydraulic fracture initiation and extension model, a single cluster perforation hole flow friction pressure drop model, a perforation hole number optimization model, and thus proposes a deep shale gas horizontal well dense cutting fracturing non-uniform perforation optimization design method.

[0268] Embodiment two

[0269] Embodiment two is an embodiment of the application of the deep shale gas horizontal well dense cutting fracturing non-uniform perforation optimization design method proposed in embodiment one to a deep shale horizontal well.

[0270] Please refer to Figures 1-3 ,

[0271] The formation parameters, fracturing parameters and perforation parameters of a certain deep shale horizontal well are shown in Table 1.

[0272] Table 1 Deep shale horizontal well dense cutting fracturing design parameter table

[0273]

[0274]

[0275] First, a single cluster perforation hole flow friction pressure drop model is established by using fluid mechanics theory, and the minimum critical hole number of a single cluster perforation is determined by combining the single cluster perforation hole flow friction pressure drop model:

[0276] The specific steps are: ① input the pump injection displacement, perforation cluster number and hole inner diameter of the target deep shale horizontal well dense cutting fracturing design; ② use (formula 1) ~ (formula 2) to calculate the hole friction pressure drop under the condition that the single cluster perforation number is 1 cluster ~ 48 clusters, and draw the hole friction curve changing with the single cluster perforation number, as shown in Figure 2 The minimum critical hole number of a single cluster perforation is determined to be 12 under the condition that the single cluster perforation hole flow friction pressure drop is less than 0.5 MPa.

[0277] Subsequently, a deep shale horizontal well dense cutting fracturing multi-cluster hydraulic fracture extension model is established by using rock mechanics theory, fluid mechanics theory and fluid-structure coupling theory, and the extension of each cluster hydraulic fracture is calculated by combining the deep shale horizontal well dense cutting fracturing multi-cluster hydraulic fracture extension model:

[0278] The specific steps are: ① setting the number of perforation holes of each cluster to 12; ② combining (Formula 1) to (Formula 16) with the boundary condition and initial condition equation (Formula 17) of each cluster hydraulic fracture extension; ③ solving the material balance equation and the in-fracture fluid pressure drop equation by using the finite difference method; ④ solving the stress-strain balance equation of the fracture discrete unit by using the boundary element method; ⑤ solving the flow distribution equation of each cluster hydraulic fracture by using the Newton iteration method, and calculating the geometric parameters in the extension process of each cluster hydraulic fracture, including: the half length of each cluster hydraulic fracture, the fracture width, the fracture height, and the flow distribution of each cluster hydraulic fracture; ⑥ outputting the extended half length of each cluster hydraulic fracture and the hydraulic fracture half length variation coefficient data after fracturing.

[0279] Subsequently, a perforation hole number optimization model is established, and the current perforation hole number of each cluster is repeatedly adjusted in combination with the perforation hole number optimization model to finally calculate the optimal value of the perforation hole number of each cluster:

[0280] The specific steps are: ① comparing the extended half length of each cluster hydraulic fracture with the average extended half length, and optimizing the current perforation hole number of each cluster by using (Formula 19), that is, increasing the perforation hole number of the cluster with a shorter extended half length of the hydraulic fracture; ② substituting the adjusted perforation hole number of each cluster into (Formula 15), and simulating the extension behavior of each cluster hydraulic fracture under the condition of non-uniform perforation by using the deep shale horizontal well multi-cluster hydraulic fracture extension model to determine the extended half length of each cluster hydraulic fracture and the hydraulic fracture half length variation coefficient; ③ if the hydraulic fracture half length variation coefficient is greater than 0.05, the perforation hole number optimization model is used again to optimize the hole number, and the perforation hole number of each cluster is repeatedly adjusted; if the hydraulic fracture half length variation coefficient is less than or equal to 0.05, the perforation hole number of each cluster is adjusted and the optimal value is reached.

[0281] Finally, the numerical calculation flowchart of the deep shale gas horizontal well multi-cluster hydraulic fracturing non-uniform perforation optimization design method as shown in Figure 1 is used to carry out example calculation, and according to the calculation results, the optimal value of the perforation hole number of each cluster in the multi-cluster hydraulic fracturing non-uniform perforation process of the target well (as shown in Table 2), the spatial distribution diagram of the extended hydraulic fracture of each cluster before the perforation hole number optimization of the target well (uniform perforation process) (as shown in Figure 3 ), and the spatial distribution diagram of the extended hydraulic fracture of each cluster after the perforation hole number optimization of the target well (non-uniform perforation process) (as shown in Figure 4 ) are output.

[0282] Table 2 Optimal value of perforation hole number of each cluster in multi-cluster hydraulic fracturing non-uniform perforation process of target well

[0283]

[0284] The above embodiments only express the specific implementation of the present application, which is described in more detail and specifically, but cannot be understood as a limitation to the protection scope of the present application. It should be noted that for those skilled in the art, without departing from the technical concept of the present application, a number of modifications and improvements can be made, which are all within the protection scope of the present application.

Claims

1. A method for optimizing the design of non-uniform perforation in deep shale gas horizontal wells through dense fracturing, characterized in that... Includes the following steps: Step S1: Based on the pumping flow rate, number of perforation clusters, and inner diameter of the target deep shale horizontal well dense cutting fracturing design, determine the minimum critical number of perforations for a single perforation cluster using the single perforation flow friction pressure drop model. Step S2: Based on the design parameters of the target deep shale horizontal well and the minimum critical number of perforations in a single cluster, use the deep shale horizontal well dense cutting fracturing multi-cluster hydraulic fracture extension model to determine the half-length of each cluster of hydraulic fractures and the coefficient of variation of the half-length of the hydraulic fractures. Step S3: Based on the half-length of hydraulic fracture extension in each cluster, use the perforation number optimization model to adjust the number of perforations in each cluster so that their distribution is no longer uniform. Step S4: Based on the adjusted number of perforations in each cluster, use the deep shale horizontal well dense cutting fracturing multi-cluster hydraulic fracture extension model to determine the half-length of hydraulic fracture extension and the coefficient of variation of hydraulic fracture half-length under non-uniform perforation conditions. Step S5: Utilize the perforation number optimization model again to adjust the number of perforations in each cluster until the half-length of hydraulic fracture extension in each cluster is basically the same. Output the optimal value of the number of perforations in each cluster and draw the spatial distribution map of the hydraulic fracture extension in each cluster.

2. The method for optimizing the design of non-uniform perforation in deep shale gas horizontal wells with dense cutting fracturing according to claim 1, characterized in that, The detailed steps of step S1 are as follows: Step S11: Obtain the pump injection rate, number of perforation clusters, and perforation inner diameter of the target deep shale horizontal well dense cutting fracturing design; Step S12: Using fluid mechanics theory, establish a flow friction and pressure drop model for a single cluster of perforations. Step S13: Based on the pumping flow rate, number of perforation clusters, and orifice inner diameter, use the single-cluster perforation flow friction pressure drop model to calculate the orifice friction pressure drop under different single-cluster perforation numbers. Step S14: Based on the pressure drop of the perforation friction under different numbers of perforations per cluster, plot the curve of perforation friction as a function of the number of perforations per cluster. Step S15: Preset a threshold for flow friction pressure drop in a single cluster of perforations. Determine the minimum critical number of perforations for a single cluster of perforations based on the condition that the flow friction pressure drop in a single cluster of perforations is less than the threshold.

3. The method for optimizing the design of non-uniform perforation in deep shale gas horizontal wells with dense cutting fracturing according to claim 1, characterized in that, The detailed steps of step S2 are as follows: Step S21: Obtain the design parameters of the target deep shale horizontal well, including formation parameters, fracturing parameters, and perforation parameters; Step S22: Using rock mechanics theory, fluid mechanics theory, and fluid-structure interaction theory, establish a model for the extension of multiple hydraulic fractures in deep shale horizontal wells through close cutting and fracturing. Step S23: Using a deep shale horizontal well dense cutting fracturing multi-cluster hydraulic fracture extension model, simulate the extension behavior of each cluster of hydraulic fractures under uniform perforation conditions, and determine the half-length extension of each cluster of hydraulic fractures and the coefficient of variation of the half-length extension of the hydraulic fractures.

4. The method for optimizing the design of non-uniform perforation in deep shale gas horizontal wells with dense cutting fracturing according to claim 1, characterized in that, The detailed steps of step S3 are as follows: Step S31: Establish an optimization model for the number of perforations; Step S32: By comparing the current extended half length of each hydraulic fracture cluster with the average extended half length, the number of perforation holes in clusters with shorter extended half lengths of hydraulic fractures is increased using the perforation hole number optimization model, so that the distribution of the number of perforation holes in each cluster is no longer uniform.

5. The method for optimizing the design of non-uniform perforation in dense-cut fracturing of deep shale gas horizontal wells according to claim 1, characterized in that, The detailed steps of step S4 are as follows: Based on the adjusted number of perforations in each cluster, the hydraulic fracture extension model of multiple clusters under non-uniform perforation conditions was simulated using a deep shale horizontal well dense cutting fracturing model. The half-length of each cluster of hydraulic fractures and the coefficient of variation of the half-length of the hydraulic fractures were then determined.

6. The method for optimizing the design of non-uniform perforation in deep shale gas horizontal wells with dense cutting fracturing according to claim 1, characterized in that, The detailed steps of step S5 are as follows: Step S51: Preset the threshold for the half-length variation coefficient of hydraulic fracture; If the coefficient of variation of the hydraulic fracture half-length is greater than the threshold, the number of holes in each cluster of holes is adjusted again using the hole number optimization model. If the coefficient of variation of the half-length of the hydraulic fracture is less than or equal to the threshold, it is determined that the number of perforations in each cluster has been adjusted and has reached the optimal value; and the optimal value of the number of perforations in each cluster is output, and the spatial distribution map of the extension of each cluster of hydraulic fractures is drawn.

7. The method for optimizing the design of non-uniform perforation in deep shale gas horizontal wells with dense cutting fracturing according to claim 1, characterized in that, The single-cluster perforation orifice flow friction pressure drop model includes: In the formula: Δp cl For the flow friction and pressure drop of a single cluster of perforations; q cl n is the fluid flow rate at a single cluster of perforations; pf d represents the number of perforations; pf α is the inner diameter of the perforation hole; pf ρ is the orifice flow rate coefficient; ρ is the fracturing fluid density.

8. The method for optimizing the design of non-uniform perforation in deep shale gas horizontal wells with dense cutting fracturing according to claim 1, characterized in that, The deep shale horizontal well dense cutting fracturing multi-cluster hydraulic fracture extension model includes: material balance equation, intra-fracture fluid pressure drop equation, fracturing fluid loss equation, fracture width equation, fracture discrete element stress-strain balance equation, fracture discrete element coordinate transformation equation, fracture height equation, flow distribution equation for each cluster of hydraulic fractures, boundary and initial conditions equations for each cluster of hydraulic fractures, and half-length variation coefficient equation for each cluster of hydraulic fractures.

9. The method for optimizing the design of non-uniform perforation in deep shale gas horizontal wells with dense cutting fracturing according to claim 8, characterized in that, The mass balance equation is as follows: In the formula: q represents the flow rate within the crack; s represents the crack length direction coordinate; t represents time; h represents the flow rate within the crack. f w is the crack height. f q represents the crack aperture; L This refers to the fracturing fluid loss rate. The equation for the pressure drop of the fluid inside the crevice is as follows: In the formula: p is the pressure inside the crack; μ is the viscosity of the liquid. The fracturing fluid loss equation is as follows: In the formula: C L τ is the formation filtration coefficient; τ is the initiation time of filtration. Crack width equation: wf(s)=(Dn)j In the formula: (D n ) j Let be the normal displacement of the crack element j at crack length s; the stress-strain equilibrium equation for the discrete crack element is as follows: in: In the formula: (σ t ) i Let σ be the shear stress experienced by crack element i in the local coordinate system; n ) i Let D be the normal stress experienced by crack element i in the local coordinate system; n ) j D is the normal displacement of the crack element j; t ) j Let A be the tangential displacement of crack element j; (A) tt ) ij The tangential stress component caused by the tangential displacement discontinuity of crack element j on crack element i; (A tn ) ij The normal force component caused by the tangential displacement discontinuity of crack element j on crack element i; (A nt ) ij The tangential stress component caused by the discontinuity of the normal displacement of crack element j on crack element i; (A nn ) ij The normal force component caused by the discontinuity of normal displacement in fracture element j on fracture element i; E is the Young's modulus of the rock; ν is the Poisson's ratio of the formation; n j The cosine of the angle between the global y-axis and the local ζ-axis of the crack element j; j F3 represents the cosine of the angle between the global x-axis and the local ξ-axis of the crack element j; F3 to F6 are the partial derivative equations of the Papkovitch function. Coordinate transformation equation for crack discrete element: In the formula: ζ ij and ξ ij These are local coordinate values; x i x represents the x-axis coordinate of the center of crack element i in global coordinates; j The x-axis coordinate of the center of crack element j in global coordinates; y i The y-axis coordinate of the center of crack element i in global coordinates; y j This represents the y-axis coordinate of the center of crack element j in global coordinates. Crack height equation: In the formula: K Ic For shale fracture toughness; σ c This refers to the formation closure stress; Flow distribution equations for each cluster of hydraulic fractures: in: In the formula: p heel For horizontal wellhead pressure; p fi,i Δp represents the pressure at the opening of the i-th hydraulic fracture cluster; cl,i Δp is the frictional pressure drop at the orifice of the i-th cluster of apertures; w,j p represents the pressure drop of fluid flow within the j-th horizontal well section. i | s＝0 σ represents the pressure at the coordinate s = 0 along the length direction of the i-th hydraulic fracture cluster; hmin The minimum horizontal principal stress of the formation; n pf,i The number of perforations in the i-th cluster; μ is the viscosity of the fracturing fluid; L w,j q is the length of the j-th horizontal well segment; w,j Let q be the flow rate of the j-th horizontal well segment; cl,i d represents the fluid flow rate at the i-th cluster of perforations; w The diameter of the horizontal wellbore; subscript i indicates the number of each cluster of fractures; subscript j indicates the number of each horizontal well section. Boundary conditions and initial condition equations for the extension of hydraulic fractures in each cluster: In the formula: L f The length of the crack is half its length; Equations for the coefficient of variation of the half-length of hydraulic fractures in each cluster: In the formula: μ f σ is the average half-length of the hydraulic fractures in each cluster; f χ represents the standard deviation of the half-length of each cluster of hydraulic fractures; f denoted as the half-length variation coefficient of each cluster of hydraulic fractures.

10. The method for optimizing the design of non-uniform perforation in deep shale gas horizontal wells with dense fracturing according to claim 1, characterized in that, The perforation hole number optimization model includes: In the formula: To optimize the number of apertures in the i-th cluster; To optimize the number of apertures in the i-th cluster.

Images