A method for calculating the three-dimensional propagation morphology of multi-cluster fractures in horizontal wells

Abstract

The present invention discloses a method for calculating the three-dimensional expansion morphology of multi-cluster hydraulic fracturing cracks in a horizontal well segment. The method comprises: obtaining formation parameters, hydraulic fracturing construction parameters, and engineering parameters; establishing a full three-dimensional model of multi-cluster hydraulic fracturing cracks in a horizontal well segment under induced stress interference, wherein the full three-dimensional plane model of multi-cluster hydraulic fracturing cracks in a horizontal well segment under induced stress interference comprises a full three-dimensional plane model of multi-cluster hydraulic fracturing cracks and an induced stress model; and determining the three-dimensional expansion morphology of the target cracks under induced stress interference based on the formation parameters, hydraulic fracturing construction parameters, engineering parameters, and the full three-dimensional plane model of multi-cluster hydraulic fracturing cracks in a horizontal well segment under induced stress interference. The present invention constructs a new full three-dimensional plane model that takes into account the bilinear flow of the cracks, so that the calculation results are more consistent with the actual crack expansion morphology; and takes into account the influence of induced stress on the expansion morphology of multiple cracks, so that the expansion morphology of multiple cracks calculated by this method is more consistent with the actual underground crack extension situation.

Description

Technical Field

[0001] The present invention relates to the technical field of unconventional oil and gas reservoir transformation, and in particular to a method for calculating three-dimensional expansion of staged multi-cluster fracturing cracks in a horizontal well. Background Art

[0002] Shale gas, a type of unconventional natural gas, is abundant and, compared to other fossil fuels, is low-carbon and environmentally friendly. Horizontal well staged multi-cluster fracturing is a key tool for unconventional oil and gas production. Multi-fracture propagation connects natural fractures and bedding, and, through induced stresses, alters the formation stress field, causing fractures to branch and form complex networks within the reservoir, thereby increasing oil and gas production. Characterizing the three-dimensional propagation morphology of fractures is crucial for fracturing operation design, including proppant dosage and fracture conductivity prediction.

[0003] Currently, scholars at home and abroad have constructed different two-dimensional models, pseudo-three-dimensional models, and full three-dimensional models under different preconditions. Among them, the two-dimensional model has a simple structure and is easy to calculate, but the two-dimensional morphology of the fracture is significantly different from the actual three-dimensional extension of the fracture. Although the pseudo-three-dimensional model takes into account the three-dimensional extension of the fracture, the flow of liquid within the fracture is still one-dimensional. The full three-dimensional model can model the three-dimensional extension of the fracture and the two-dimensional flow of liquid within the fracture, but its calculation is complex and difficult to promote and apply. Summary of the Invention

[0004] In view of this, the present invention provides a method for calculating the three-dimensional expansion morphology of multi-cluster hydraulic fracturing cracks in horizontal wells, which can solve the technical problems in the existing technology that the fracture morphology used in the two-dimensional model is quite different from the actual morphology due to its simple structure, and the full three-dimensional model needs to consider the calculation complexity caused by the two-dimensional flow of liquid in the fracture.

[0005] In order to solve the above technical problems, the present invention provides a method for calculating the three-dimensional expansion morphology of multi-cluster hydraulic fracturing cracks in a horizontal well, comprising:

[0006] Obtain formation parameters, fracturing operation parameters and engineering parameters;

[0007] Establishing a full three-dimensional model of multi-cluster hydraulic fractures in a horizontal well under induced stress interference, wherein the full three-dimensional plane model of multi-cluster hydraulic fractures in a horizontal well under induced stress interference includes a full three-dimensional plane model of multi-cluster hydraulic fractures and an induced stress model;

[0008] Determining the initial three-dimensional fracture expansion morphology of the multi-cluster fractures in the horizontal well segment according to the formation parameters, the fracturing operation parameters, the engineering parameters and the full three-dimensional model of the multi-cluster fracture plane;

[0009] determining an in-situ stress field under induced stress interference based on the three-dimensional propagation morphology of the initial crack and the induced stress model, and determining a stress intensity factor of the in-situ stress field under induced stress interference;

[0010] updating the formation parameters, fracturing operation parameters and engineering parameters according to the in-situ stress field under the induced stress interference;

[0011] The updated formation parameters, fracturing operation parameters, engineering parameters and stress intensity factors are input into the full three-dimensional model of the multi-cluster fracture plane to calculate the three-dimensional extension morphology of the target fracture under induced stress interference.

[0012] In some possible implementations, the multi-cluster hydraulic fracture plane full 3D model includes: multiple single-cluster fracture plane full 3D models, and the formation parameters, construction parameters, and engineering parameters each include formation parameters, construction parameters, and engineering parameters of multiple single clusters; determining the initial fracture 3D propagation morphology of the multi-cluster fractures in the horizontal well segment based on the formation parameters, hydraulic fracture construction parameters, engineering parameters, and the multi-cluster hydraulic fracture plane full 3D model includes:

[0013] Inputting the formation parameters, construction parameters and engineering parameters of the plurality of single clusters into the corresponding single cluster fracture plane full three-dimensional model to obtain the corresponding fracture three-dimensional model expansion morphology of the plurality of single clusters;

[0014] The expansion forms of the three-dimensional fracture models of the plurality of single clusters together constitute the initial three-dimensional fracture expansion form of the multi-stage multi-cluster fractures in the multi-horizontal wells.

[0015] In some possible implementations, the multi-cluster hydraulic fracture plane full 3D model further includes a first PKN model, and the single-cluster fracture plane full 3D model includes a second PKN model; and inputting the formation parameters, hydraulic fracturing operation parameters, and engineering parameters of the multiple single-cluster fracture plane full 3D models into the corresponding single-cluster fracture plane full 3D models to obtain the corresponding multiple single-cluster fracture 3D model expansion forms includes:

[0016] Determining the fracture heights at the wellbore of the plurality of corresponding single cluster fractures according to the formation parameters, fracturing operation parameters, engineering parameters, and the corresponding single cluster fracture full three-dimensional model;

[0017] Determining the sublinear flow direction along-line fracture widths of the plurality of corresponding single-cluster fractures according to the formation parameters, fracturing operation parameters, engineering parameters, and the corresponding single-cluster fracture full three-dimensional model;

[0018] Inputting the fracture heights of the plurality of single clusters at the wellbore into the second PKN model to obtain the maximum single-wing fracture length and the maximum single-wing fracture width of the plurality of single cluster fractures;

[0019] According to the maximum single-wing crack length and maximum crack width of the plurality of single-cluster cracks and the corresponding full three-dimensional model of the single-cluster cracks, the crack width, displacement and pressure drop along the main linear flow length direction of the plurality of corresponding single clusters are calculated;

[0020] According to the plurality of single clusters of fracture widths, displacements and pressure drops along the main linear flow length directions and the corresponding single cluster fracture full three-dimensional models, all fracture heights and fracture widths along the fracture height directions of the plurality of corresponding single clusters are calculated;

[0021] Calculating the three-dimensional volumes of multiple single-cluster fractures based on all fracture heights in the length direction and fracture widths along the fracture height direction of the multiple corresponding single-cluster fractures, and comparing the three-dimensional volumes of the multiple single-cluster fractures with the fracture volumes of the corresponding single-cluster fractures calculated by the second PKN model;

[0022] If the volume error between the two is less than the first threshold, the three-dimensional expansion form of a single crack with a symmetrical double-wing crack is obtained. Otherwise, the single-wing length of the crack is changed and input into the corresponding single-cluster crack plane full three-dimensional model for calculation until the error is less than the first threshold, and then the three-dimensional expansion forms of single cracks corresponding to multiple single clusters are obtained.

[0023] In some possible implementations, the three-dimensional volume of the fracture is obtained by accumulating all fracture heights in the fracture length direction and all fracture widths along the fracture height direction of the plurality of single clusters, including:

[0024] According to all the fracture heights and fracture widths along the fracture height direction of the plurality of single-cluster fractures, the three-dimensional volume of each point on the corresponding single-cluster fracture length is determined, and the corresponding three-dimensional volumes are accumulated to obtain the three-dimensional volume of the corresponding fracture.

[0025] In some possible implementations, determining the in-situ stress field under induced stress interference based on the initial crack three-dimensional propagation morphology and the induced stress model, and determining the stress intensity factor of the in-situ stress field under induced stress interference include:

[0026] The induced stress of each crack is calculated based on the three-dimensional expansion morphology of the multiple clusters of cracks and the induced stress calculation formula;

[0027] The induced stress of each crack is superimposed to obtain the in-situ stress field under the influence of the induced force;

[0028] The stress intensity factor of the in-situ stress field under the influence of the induced stress is determined according to the in-situ stress field under the influence of the induced stress.

[0029] In some possible implementations, the induced stress of each crack is calculated based on the three-dimensional extension morphology of the multiple clusters of cracks and the induced stress calculation formula, including:

[0030] Determining, based on the three-dimensional expansion morphology of the multiple clusters of cracks, the angle at which each crack deviates from a preset point from the crack lower tip, the crack center, and the crack upper tip, as well as the distance from the preset point to the crack lower tip, the crack center, and the crack upper tip;

[0031] The induced stress generated by each crack on the preset point in the direction of minimum horizontal principal stress, vertical stress and maximum principal stress is determined based on the angle of the preset point away from the lower tip of the crack, the center of the crack and the upper tip of the crack, the distance from the preset point to the lower tip of the crack, the center of the crack and the upper tip of the crack, and the induced stress formula.

[0032] In some possible implementations, the induced stress of each crack is superimposed to obtain the in situ stress field under the influence of the induced force, including:

[0033] The induced stress generated by each crack in the direction of the minimum horizontal principal stress of the preset point, the induced stress generated in the vertical stress direction and the induced stress generated in the direction of the maximum horizontal principal stress are calculated by a superposition calculation formula to determine the superposition induced stress of each crack in the direction of the minimum horizontal principal stress, the vertical stress direction and the maximum horizontal principal stress direction of the preset point.

[0034] In some possible implementations, determining the stress intensity factor of the in-situ stress field under the influence of the induced stress according to the in-situ stress field under the influence of the induced stress includes:

[0035] updating the formation parameters, fracturing operation parameters and engineering parameters according to the in-situ stress field under the influence of the induced stress;

[0036] The stress intensity factor is determined based on the updated formation parameters, fracturing operation parameters and engineering parameters.

[0037] In some possible implementations, updating the formation parameters, fracturing operation parameters, and engineering parameters based on the in-situ stress field under the induced stress interference includes:

[0038] determining a minimum horizontal stress and a maximum horizontal stress according to the in situ stress field;

[0039] The fracture length, fracture width and fracture height under the interference of the in-situ stress field are determined according to the maximum horizontal stress and the minimum horizontal stress to obtain updated formation parameters, fracturing operation parameters and engineering parameters.

[0040] In some possible implementations, the updated formation parameters, fracturing operation parameters, engineering parameters, and stress intensity factors are input into a full three-dimensional model of a multi-cluster fracture plane to calculate a three-dimensional fracture propagation morphology under induced stress interference, including:

[0041] Determining the turning angle of the crack along the extension direction according to the stress intensity factor and the crack deflection angle equation;

[0042] The updated formation parameters, fracturing operation parameters, engineering parameters and the turning angle of the fracture extension direction are input into the full three-dimensional model of the multi-cluster fracture plane to calculate the three-dimensional extension morphology of the fracture under the induced stress interference.

[0043] Compared with the existing technology, the present invention establishes a new planar full 3D fracture propagation model. It uses a full 3D model of multi-cluster hydraulic fracturing fractures to obtain the initial 3D fracture extension shape. It uses an induced stress model to determine the in-situ stress field under induced stress interference. Based on the in-situ stress field under induced stress interference, the stress-affected formation parameters, hydraulic fracturing operation parameters, and engineering parameters are updated to obtain the target 3D fracture extension shape under induced stress interference. The planar full 3D fracture propagation model of the present invention considers the 3D extension shape of the fracture and the bilinear flow within the fracture, and extends it to the simultaneous initiation of multiple segments and multiple clusters of fractures in horizontal wells. It considers the influence of induced stress on the extension shape of multiple fractures. The calculation is simple and easy to promote, and it can be used to guide and improve the optimization design of staged multi-cluster hydraulic fracturing operation in horizontal wells of shale gas reservoirs. BRIEF DESCRIPTION OF THE DRAWINGS

[0044] Figure 1 A flowchart of an embodiment of a method for calculating the three-dimensional expansion morphology of multi-cluster hydraulic fractures in a horizontal well provided by the present invention;

[0045] Figure 2 A schematic diagram of an embodiment of the present invention for discrete solution of the width of a sublinear flow gap in the height direction;

[0046] Figure 3 A schematic diagram of an embodiment of the present invention for discrete solution of the main linear flow gap width along the length direction;

[0047] Figure 4 This is a schematic diagram of an embodiment of the superposition calculation of induced stress generated by multiple cracks on a preset point provided by the present invention. DETAILED DESCRIPTION

[0048] The preferred embodiments of the present invention will be described in detail below in conjunction with the accompanying drawings, wherein the accompanying drawings constitute a part of this application and are used together with the embodiments of the present invention to illustrate the principles of the present invention, and are not used to limit the scope of the present invention.

[0049] Before describing the embodiments, the following definitions are given for the relevant terms: a horizontal well is a well with an inclination angle of at or near 90° and a wellbore drilled in a horizontal direction for a certain length, and is used for oil field exploitation; staged fracturing of a horizontal well refers to a section of about 50m to 100m; a cluster: each section is perforated in 2-4 places, each perforation section is 1-1.5m, and the middle interval is 6-20m. This perforation method is called a cluster; a full three-dimensional model of the fracture plane: a three-dimensional model that calculates and simulates the length, width, and height of the fracture, as well as the two-dimensional flow of the fluid in the fracture in the length and width directions; main linear flow: the flow of fluid in the fracture along the length direction is called main linear flow; sub-linear flow: the flow of fluid in the fracture along the height direction is called sub-linear flow.

[0050] like Figure 1 , which is a flow chart of an embodiment of a method for calculating the three-dimensional expansion morphology of multi-cluster hydraulic fracturing cracks in a horizontal well provided by the present invention, comprising the following steps:

[0051] Step S101: Acquire formation parameters, fracturing operation parameters, and engineering parameters;

[0052] Step S102: establishing a full three-dimensional model of multi-cluster hydraulic fractures in a horizontal well under induced stress interference, wherein the full three-dimensional plane model of multi-cluster hydraulic fractures in a horizontal well under induced stress interference includes a full three-dimensional plane model of multi-cluster hydraulic fractures and an induced stress model;

[0053] Step S103: determining the initial three-dimensional fracture expansion morphology of the multi-cluster fractures in the horizontal well segment according to the formation parameters, fracturing operation parameters, engineering parameters and the full three-dimensional model of the multi-cluster fracture plane;

[0054] Step S104: determining the in-situ stress field under the induced stress interference according to the initial three-dimensional crack extension morphology and the induced stress model, and determining the stress intensity factor of the in-situ stress field under the induced stress interference;

[0055] Step S105: updating the formation parameters, fracturing operation parameters and engineering parameters according to the in-situ stress field under the induced stress interference;

[0056] Step S106: inputting the updated formation parameters, fracturing operation parameters, engineering parameters and stress intensity factors into the multi-cluster fracture plane full 3D model to calculate the target fracture 3D propagation morphology under induced stress interference.

[0057] It should be noted that the formation parameters are: elastic modulus, Poisson's ratio, fracture toughness of the upper barrier layer, fracture toughness of the reservoir, fracture toughness of the lower barrier layer, minimum horizontal principal stress of the upper barrier layer, minimum horizontal principal stress of the reservoir, maximum horizontal principal stress of the reservoir, minimum horizontal principal stress of the lower barrier layer, filtration coefficient, and ground stress gradient; fracturing construction parameters are: displacement and fracturing fluid viscosity; and engineering parameters are: vertical pressure drop and fluid gravity gradient.

[0058] It should also be noted that, considering that there will be induced stress between multiple clusters of fractures, and the induced stress will change the expansion morphology of multiple clusters of fractures, the embodiment of the present invention establishes a full three-dimensional model of horizontal well segmented multi-cluster fracturing fractures under induced stress interference to truly simulate the three-dimensional expansion morphology of horizontal well segmented multi-cluster fracturing fractures.

[0059] It should be further explained that the induced stress between multiple clusters of fractures will affect the formation parameters, fracturing operation parameters, and engineering parameters and change their actual values. Therefore, it is necessary to update the formation parameters, fracturing operation parameters, and engineering parameters according to the in situ stress field under the interference of the induced stress in order to accurately reflect the three-dimensional expansion morphology of the actual multi-cluster fractures in the horizontal well segment.

[0060] Compared with the existing technology, the present invention establishes a new planar full 3D fracture propagation model. It uses a full 3D model of multi-cluster hydraulic fracturing fractures to obtain the initial 3D fracture extension shape. It uses an induced stress model to determine the in-situ stress field under induced stress interference. Based on the in-situ stress field under induced stress interference, the stress-affected formation parameters, hydraulic fracturing operation parameters, and engineering parameters are updated to obtain the target 3D fracture extension shape under induced stress interference. The planar full 3D fracture propagation model of the present invention considers the 3D extension shape of the fracture and the bilinear flow within the fracture, and extends it to the simultaneous initiation of multiple segments and multiple clusters of fractures in horizontal wells. It considers the influence of induced stress on the extension shape of multiple fractures. The calculation is simple and easy to promote, and it can be used to guide and improve the optimization design of staged multi-cluster hydraulic fracturing operation in horizontal wells of shale gas reservoirs.

[0061] In some possible implementations, the multi-cluster hydraulic fracture plane full 3D model includes: multiple single-cluster fracture plane full 3D models, and the formation parameters, construction parameters, and engineering parameters each include formation parameters, construction parameters, and engineering parameters of multiple single clusters; determining the initial fracture 3D propagation morphology of the multi-cluster fractures in the horizontal well segment based on the formation parameters, hydraulic fracture construction parameters, engineering parameters, and the multi-cluster hydraulic fracture plane full 3D model includes:

[0062] Inputting the formation parameters, construction parameters and engineering parameters of the plurality of single clusters into the corresponding single cluster fracture plane full three-dimensional model to obtain the corresponding fracture three-dimensional model expansion morphology of the plurality of single clusters;

[0063] The expansion forms of the three-dimensional fracture models of the plurality of single clusters together constitute the initial three-dimensional fracture expansion form of the multi-stage multi-cluster fractures in the multi-horizontal wells.

[0064] It should be noted that the full three-dimensional plane model of a single cluster of cracks is established by deducing the crack length, crack height and crack width of the cracks and the crack penetration situation.

[0065] The multi-cluster hydraulic fracture plane full three-dimensional model is composed of multiple single-cluster fracture plane full three-dimensional models.

[0066] In some possible implementations, the multi-cluster hydraulic fracture plane full 3D model further includes a first PKN model, and the single-cluster fracture plane full 3D model includes a second PKN model; and inputting the formation parameters, hydraulic fracturing operation parameters, and engineering parameters of the multiple single-cluster fracture plane full 3D models into the corresponding single-cluster fracture plane full 3D models to obtain the corresponding multiple single-cluster fracture 3D model expansion morphologies includes:

[0067] Determining the fracture heights at the wellbore of the plurality of corresponding single cluster fractures according to the formation parameters, fracturing operation parameters, engineering parameters, and the corresponding single cluster fracture full three-dimensional model;

[0068] Determining the sublinear flow direction along-line fracture widths of the plurality of corresponding single-cluster fractures according to the formation parameters, fracturing operation parameters, engineering parameters, and the corresponding single-cluster fracture full three-dimensional model;

[0069] Inputting the fracture heights of the plurality of single clusters at the wellbore into the second PKN model to obtain the maximum single-wing fracture length and the maximum single-wing fracture width of the plurality of single cluster fractures;

[0070] According to the maximum single-wing crack length and maximum crack width of the plurality of single-cluster cracks and the corresponding full three-dimensional model of the single-cluster cracks, the crack width, displacement and pressure drop along the main linear flow length direction of the plurality of corresponding single clusters are calculated;

[0071] According to the plurality of single clusters of fracture widths, displacements and pressure drops along the main linear flow length directions and the corresponding single cluster fracture full three-dimensional models, all fracture heights and fracture widths along the fracture height directions of the plurality of corresponding single clusters are calculated;

[0072] Calculating the three-dimensional volumes of multiple single-cluster fractures based on all fracture heights in the length direction and fracture widths along the fracture height direction of the multiple corresponding single-cluster fractures, and comparing the three-dimensional volumes of the multiple single-cluster fractures with the fracture volumes of the corresponding single-cluster fractures calculated by the second PKN model;

[0073] If the volume error between the two is less than the first threshold, the three-dimensional expansion form of a single crack with a symmetrical double-wing crack is obtained. Otherwise, the single-wing length of the crack is changed and input into the corresponding single-cluster crack plane full three-dimensional model for calculation until the error is less than the first threshold, and then the three-dimensional expansion forms of single cracks corresponding to multiple single clusters are obtained.

[0074] It should be noted that the first PKN model and the second PKN model are essentially the same. The PKN model is a two-dimensional hydraulic fracturing model proposed by Perkins and Kern in 1961. Later, Norgren modified, developed and improved the continuity equation based on the consideration of fluid loss in 1972, forming the current PKN model.

[0075] It should be noted that the three-dimensional expansion morphology of a single fracture is described by the fracture length, fracture width, fracture width along the fracture height direction, fracture width along the main linear flow length direction, and fracture width along the secondary linear flow direction.

[0076] In some embodiments of the present invention, a full three-dimensional model of a single-cluster fracture plane includes: Equations (1), (2), (3), (4), and (5), where the pressure through the fracture is equal to the fracture toughness of the formation, thereby obtaining the following equation:

[0077]

[0078]

[0079]

[0080]

[0081] K u =K 1IC (4)

[0082] K d =K 3IC (5)

[0083] Where: K 1IC is the fracture toughness of the upper interlayer, MPa·m 0.5 ;K 2IC is the reservoir fracture toughness, MPa·m 0.5 ;K 3IC is the fracture toughness of the lower interlayer, MPa·m 0.5 ;K u is the stress intensity factor at the crack tip, MPa·m 0.5 ;K d is the stress intensity factor at the crack tip, MPa·m 0.5; d1 is the height of the fracture above the fracture, m; d2 is the height of the fracture below the fracture, m; h is the half height of the reservoir, m; σ up is the minimum horizontal principal stress of the upper interlayer, MPa; σ mid is the minimum horizontal principal stress of the reservoir, MPa; σ down is the minimum horizontal principal stress of the lower interlayer, MPa; g v is the vertical pressure drop; g s is the ground stress gradient, MPa / m; g p is the fluid gravity gradient.

[0084] In a specific embodiment, the height of the crack at the wellbore can be calculated by the above formulas (1), (2), (3), (4), and (5). Generally speaking, during the calculation process, the height of the crack at the wellbore is divided into two cases according to the different formation conditions, namely, the crack penetrates the layer and the crack does not penetrate the layer. If the crack penetrates the layer, the crack height is calculated by combining formulas (1), (2), (3), and (5). If the crack does not penetrate the layer, the crack height is calculated using formula (3).

[0085] In some embodiments of the present invention, a discrete solution method can be used to calculate the width of the secondary flow crack along the direction of the layer. For details, please refer to Figure 2 , which is a schematic diagram of the discrete solution of the width of the sublinear flow fracture along the height direction. c01k ~W c02k is the width of the sublinear flow crack along the direction of the height, k 011 ~k 01j With k 021 ~k 02j The distance from the preset point in the crack height direction to the crack center, d 01 The height of the upper compartment seam, d 02 The lower compartment seam height is H 01 and H 02 is the half height of the crack, h 01 and h 02 is the reservoir half-height, and s is the distance between the fracture center and the flow pressure center.

[0086] In a specific embodiment, the sublinear flow direction along-line fracture widths of multiple single-cluster fractures may be determined based on formation parameters, fracturing operation parameters, engineering parameters, and corresponding full 3D models of single-cluster fractures.

[0087] In a specific embodiment, the full three-dimensional model of a single-cluster fracture plane also includes the following formulas: Formula (6), Formula (7), Formula (8), Formula (9), Formula (10), Formula (11), Formula (12), Formula (13), Formula (14) and Formula (15). Through the influence of stress on fracture width, the following formula is obtained:

[0088] W(k)=W1(k)-W2(k)-W3(k)+W4(k) h1≤h,h2≤h (6)

[0089] W(k)=W1(k)-W2(k)-W3(k)+W4(k)-W5(k) h1>h,h2≤h (7)

[0090] W(k)=W1(k)-W2(k)-W3(k)+W4(k)-W6(k) h1≤h,h2>h (8)

[0091] W(k)=W1(k)-W2(k)-W3(k)+W4(k)-W5(k)-W6(k) h1>h,h2>h (9)

[0092]

[0093]

[0094]

[0095]

[0096]

[0097]

[0098]

[0099] Where: h is the reservoir half height, m; H is the fracture half height, m; σ up is the minimum horizontal principal stress of the upper interlayer, MPa; σ mid is the minimum horizontal principal stress of the reservoir, MPa; σ down is the minimum horizontal principal stress of the lower interlayer, MPa; g v is the vertical pressure drop; g s is the ground stress gradient, MPa / m; g p is the fluid gravity gradient; s is the distance between the fracture center and the flow pressure center, in m; k is the distance from the preset point in the fracture height direction to the fracture center, in m; E is the elastic modulus, in MPa; v is the Poisson's ratio, h1 is the upper half of the fracture height, h2 is the lower half of the fracture height, W1 is the effect of net pressure on the fracture width, W2 is the fracture width affected by the flow pressure drop, W3 is the fracture width affected by the fluid gravity pressure drop, W4 is the fracture width affected by the stress difference between the preset point in the fracture height direction and the center point, W5 is the fracture width affected by the stress difference between the upper barrier layer and the reservoir, and W6 is the fracture width affected by the stress difference between the lower barrier layer and the reservoir.

[0100] According to the different situations of longitudinal crack expansion, the calculation method of the crack width along the crack height direction will be determined according to the crack penetration situation. If the crack does not penetrate the upper and lower layers, use formula (6) for calculation; if the upper half of the crack height penetrates the layers but the lower half does not, use formula (7) for calculation; if the upper half of the crack height does not penetrate the layers but the lower half does, use formula (8) for calculation; if both the upper and lower half of the crack height penetrate the layers, use formula (9) for calculation.

[0101] In a specific embodiment, the single-cluster fracture plane full three-dimensional model further includes a second PKN model, wherein the second PKN model includes equations (16) to (21).

[0102] The fracture heights of the multiple single clusters at the wellbore are input into the PKN model to obtain the maximum single-wing fracture length and fracture width of the multiple single cluster fractures. The detailed steps are as follows:

[0103] Assume a W max Substitute the geological parameters and construction parameters into equations (16) to (21) to obtain a new W max , the new W max Continue to substitute into formula (16) to formula (21) until W calculated by formula (21) is max With the previous W max The error is <0.0001%, then W is calculated max and L f The maximum single-wing crack length and width. W max and L f The calculation formulas for the maximum single-wing crack length and crack width are as follows:

[0104]

[0105]

[0106]

[0107]

[0108]

[0109]

[0110] Where: H is the half height of the crack, m; E is the elastic modulus, MPa; v is the Poisson's ratio; erfc(x) is the x error compensation function; q is the displacement, m 3 / min; μ is the fracturing fluid viscosity, Pa·s; c is the filtration coefficient, m / min 0.5 ; t is construction time, min; W max is the maximum crack width, m; L f is the length of a single wing of the crack, m.

[0111] In some embodiments of the present invention, a discrete solution method can be used to calculate the main linear flow crack length direction crack width, please refer to the details. Figure 3 , which is a schematic diagram of the discrete solution of the crack width along the length direction of the main linear flow crack. i L is the distance between the preset point in the fracture length direction and the wellbore, f is the length of the single wing of the crack, W loi (x i ) is the seam length direction x i The slit width at Δp 1-i Preset point x for the seam length direction i with x i-1 The pressure difference between net,i is x i with x i-1 The net pressure drop between i is the preset point.

[0112] In a specific embodiment, the along-the-line crack width, displacement and along-the-line pressure drop of multiple single clusters in the main linear flow length direction can be calculated based on the maximum single-wing crack length, maximum single-wing crack width and the corresponding full three-dimensional model of the multiple single cluster cracks.

[0113] In a specific embodiment, the full three-dimensional model of a single cluster fracture plane also includes equations (22) to (27). The following formula is obtained by the relationship between the maximum single wing fracture length, the maximum single wing fracture width, the fracture width along the main linear flow length direction, the displacement, and the pressure drop along the fracture:

[0114]

[0115]

[0116]

[0117]

[0118]

[0119]

[0120] Where: h is the reservoir half height, m; E is the elastic modulus, MPa; v is the Poisson's ratio; x i is the distance between the preset point in the fracture length direction and the wellbore, m; q(x i ) is the seam length direction x i Flow rate at, m 3 / s;W loi (x i ) is the seam length direction x i The width of the slit at m; W lop,i is the seam length direction xi with x i-1 The average fracture width, m; μ is the viscosity of the fracturing fluid, Pa·s; c is the filtration coefficient, m / min 0.5 ;W max is the maximum crack width, m; L f is the length of a single crack wing, m; Δp 1-i Preset point x for the seam length direction i with x i-1 Pressure difference between, MPa; q i is x i Flow rate at point, m 3 / s; Δx oj,j-1 is x i and x i-1 The distance between them, m; K f is the crack permeability, μm 2 ;Δp net,i is x i with x i-1 Net pressure drop between, MPa; p net is x i Net pressure drop between the pipe and the seam, MPa.

[0121] All fracture heights and fracture widths along the fracture height directions of the plurality of single-cluster fractures are calculated based on the fracture widths, displacements, and pressure drops along the plurality of single-cluster main linear flow length directions and the corresponding full three-dimensional model of the single-cluster fractures, including:

[0122] According to the width, displacement and pressure drop along the length direction of multiple single cluster main linear flow, calculate the x i The seam height at the location and the seam width along the seam height direction.

[0123] The three-dimensional volumes of multiple single-cluster cracks are calculated based on all the crack heights in the length direction and the crack widths along the crack height direction of the multiple single-cluster cracks, and the three-dimensional volumes of the multiple single-cluster cracks are compared with the crack volumes of the corresponding single clusters calculated by the PKN model. If the volume error between the two is less than a first threshold, the three-dimensional expansion morphology of the single crack of the symmetrical double-wing crack is obtained. Otherwise, the single-wing length of the crack is changed and input into the corresponding single-cluster crack plane full three-dimensional model for calculation until the error is less than the first threshold, so as to obtain the three-dimensional expansion morphology of the single crack corresponding to the multiple single clusters.

[0124] It can be understood that the layer penetration refers to fractures that are hydraulically fractured to the upper and lower layers, and the PKN model is a PKN model that takes Cater fluid loss into consideration.

[0125] In the embodiment of the present invention, the main linear flow and sub-linear flow of a single cluster of fractures are taken into consideration, and the obtained three-dimensional model is more in line with the actual situation.

[0126] In some possible implementations, the three-dimensional volume of the fracture is obtained by calculating and accumulating all fracture heights in the fracture length direction and all fracture widths along the fracture height direction of the plurality of single clusters, including:

[0127] According to all the fracture heights and fracture widths along the fracture height direction of the plurality of single-cluster fractures, the three-dimensional volume of each point on the corresponding single-cluster fracture length is determined, and the corresponding three-dimensional volumes are accumulated to obtain the three-dimensional volume of the corresponding fracture.

[0128] In some possible implementations, determining the in-situ stress field under induced stress interference based on the initial three-dimensional crack propagation morphology and the induced stress model, and determining the stress intensity factor of the in-situ stress field under the induced stress interference include:

[0129] The induced stress of each crack is calculated based on the three-dimensional expansion morphology of the multiple clusters of cracks and the induced stress calculation formula.

[0130] The induced stress of each crack is superimposed to obtain the in-situ stress field under the influence of the induced force;

[0131] The stress intensity factor of the in-situ stress field under the influence of the induced stress is determined according to the in-situ stress field under the influence of the induced stress.

[0132] The induced stress of each crack is calculated based on the three-dimensional expansion morphology of the multiple clusters of cracks and the induced stress calculation formula:

[0133] In this embodiment of the present invention, the induced stress generated by each fracture alters the current stress field distribution, which in turn affects the fracture propagation morphology. The present invention calculates the induced stress generated by each fracture separately and superimposes the induced stresses generated by each fracture to obtain the in-situ stress field, i.e., the in-situ stress field, representing the effect of multiple fractures on the in-situ stress field.

[0134] In some possible implementations, the induced stress of each crack is calculated based on the three-dimensional extension morphology of the multiple clusters of cracks and the induced stress calculation formula, including:

[0135] Determining, based on the three-dimensional expansion morphology of the multiple clusters of cracks, the angle of each crack relative to a preset point, the deviation of the crack lower tip, the crack center, and the crack upper tip, and the distance of a certain point from the crack lower tip, the crack center, and the crack upper tip;

[0136] The induced stress generated by each crack on the preset point in the direction of minimum horizontal principal stress, vertical stress and maximum principal stress is determined based on the angle of the preset point away from the lower tip of the crack, the center of the crack and the upper tip of the crack, the distance of a certain point from the lower tip of the crack, the center of the crack and the upper tip of the crack, and the induced stress equation.

[0137] In some possible implementations, the induced stresses generated by multiple cracks on the preset point are superimposed, and the induced stresses generated by each crack on the preset point in the direction of minimum horizontal principal stress, vertical stress, and maximum principal stress are calculated. Figure 4 Among them, Figure 4 ,θ (n-1),1 is the angle of the preset point away from the lower tip of the crack, θ (n-2),2 is the angle of the preset point away from the crack center, θ (n-3),3 The angle at which the preset point deviates from the tip of the crack.

[0138] In some possible implementations, the induced stress of each crack is calculated based on the three-dimensional expansion morphology of the multiple clusters of cracks and the induced stress calculation formula, where the induced stress formula is:

[0139]

[0140]

[0141] σ x =v(σ y +σ z ) (30)

[0142] in:

[0143]

[0144]

[0145]

[0146]

[0147]

[0148]

[0149] Where: H is the half height of the crack, m; v is the Poisson's ratio; p net is the net pressure, MPa; y and z are the horizontal and vertical coordinates of the preset point respectively; σ y is the induced stress generated by the crack at the preset point in the direction of the minimum horizontal principal stress, MPa; σ z is the induced stress generated by the crack on the preset point in the vertical stress direction, MPa; σ xis the induced stress generated by the crack on the preset point in the direction of the maximum principal stress, MPa; θ1 is the angle of the preset point away from the lower tip of the crack; θ2 is the angle of the preset point away from the center of the crack; θ3 is the angle of the preset point away from the upper tip of the crack; L1 is the distance from the preset point to the lower tip of the crack, m; L2 is the distance from the preset point to the center of the crack, m; L3 is the distance from the preset point to the upper tip of the crack, m.

[0150] The embodiment of the present invention calculates and determines the induced stress generated by each crack on a preset point in the direction of minimum horizontal principal stress, vertical stress and maximum principal stress by using an induced stress calculation formula.

[0151] In some possible implementations, determining the stress intensity factor of the in-situ stress field under the influence of the induced stress according to the in-situ stress field includes:

[0152] updating the formation parameters, fracturing operation parameters and engineering parameters according to the in-situ stress field under the influence of the induced stress;

[0153] The stress intensity factor is determined based on the updated formation parameters, fracturing operation parameters and engineering parameters.

[0154] According to the updated formation parameters, fracturing operation parameters and engineering parameters, a stress intensity factor can be determined. A change in the stress intensity factor causes a change in the deflection angle of the fracture extension direction.

[0155] It can be understood that the preset point is any point on the crack that is arbitrarily selected.

[0156] In some possible implementations, updating the formation parameters, fracturing operation parameters, and engineering parameters according to the in-situ stress field under the induced stress interference includes:

[0157] determining a minimum horizontal stress and a maximum horizontal stress according to the in situ stress field;

[0158] The fracture length, fracture width and fracture height under the interference of the in-situ stress field are determined according to the maximum horizontal stress and the minimum horizontal stress to obtain updated formation parameters, fracturing operation parameters and engineering parameters.

[0159] In some possible implementations, the updated formation parameters, fracturing operation parameters, engineering parameters, and stress intensity factors are input into a full three-dimensional model of a multi-cluster fracture plane to calculate a three-dimensional fracture propagation morphology under induced stress interference, including:

[0160] Determining the turning angle of the crack along the extension direction according to the stress intensity factor and the crack deflection angle equation;

[0161] The updated formation parameters, fracturing operation parameters, engineering parameters and the turning angle of the fracture extension direction are input into the full three-dimensional model of the multi-cluster fracture plane to calculate the three-dimensional extension morphology of the fracture under the induced stress interference.

[0162] The crack deflection angle formula is:

[0163]

[0164] Where: θ is the crack turning angle; τ is the stress intensity factor, MPa.

[0165] The stress intensity factor is input into the deflection angle equation of the crack to determine the deflection angle of the crack extension direction, so that the three-dimensional expansion morphology of the crack under the induced stress interference is more in line with the actual situation and reflects the initiation of the horizontal well hydraulic fracturing crack.

[0166] The technical solution of the present invention is specifically aimed at the complex mechanical behavior of the initiation and extension of multiple clusters of cracks during the horizontal well fracturing process, and proposes a new planar full three-dimensional crack extension model, and establishes a full three-dimensional model of horizontal well segmented multi-cluster fracturing cracks under induced stress interference. The full three-dimensional model of horizontal well segmented multi-cluster fracturing cracks under induced stress interference takes into account the three-dimensional extension morphology of the cracks and the bilinear flow in the cracks, and extends it to multiple segments and multiple clusters of horizontal well cracks. Taking into account the influence of induced stress on the expansion morphology of multiple cracks, the three-dimensional expansion morphology of horizontal well segmented multi-cluster fracturing cracks can be accurately and simply calculated, which can better guide and improve the optimization design of horizontal well segmented multi-cluster fracturing construction in shale gas reservoirs.

Claims

1. A method for calculating the three-dimensional expansion morphology of multi-cluster hydraulic fracturing in a horizontal well, characterized by: include: Obtain formation parameters, fracturing operation parameters and engineering parameters; Establishing a full three-dimensional model of a horizontal well segmented multi-cluster hydraulic fracture plane under induced stress interference, wherein the full three-dimensional model of a horizontal well segmented multi-cluster hydraulic fracture plane under induced stress interference includes a full three-dimensional model of a multi-cluster hydraulic fracture plane and an induced stress model, the full three-dimensional model of a multi-cluster hydraulic fracture plane includes: a plurality of single-cluster hydraulic fracture plane full three-dimensional models, and the formation parameters, hydraulic fracturing operation parameters, and engineering parameters all include the formation parameters, hydraulic fracturing operation parameters, and engineering parameters of a plurality of single clusters; Inputting the formation parameters, fracturing operation parameters, and engineering parameters of the multiple single clusters into the corresponding single cluster fracture plane full 3D model to obtain corresponding multiple single cluster fracture 3D model expansion morphologies, wherein the multiple single cluster fracture 3D model expansion morphologies together constitute the initial fracture 3D expansion morphologies of the horizontal well segmented multi-cluster fractures; determining an in-situ stress field under induced stress interference based on the three-dimensional propagation morphology of the initial crack and the induced stress model, and determining a stress intensity factor of the in-situ stress field under induced stress interference; updating the formation parameters, fracturing operation parameters and engineering parameters according to the in-situ stress field under the induced stress interference; The updated formation parameters, fracturing operation parameters, engineering parameters and stress intensity factors are input into the full three-dimensional model of the multi-cluster fracturing fracture plane to calculate the three-dimensional propagation morphology of the target fracture under the induced stress interference; The multi-cluster hydraulic fracture plane full 3D model also includes a first PKN model, and the single-cluster fracture plane full 3D model includes a second PKN model; the formation parameters, hydraulic fracturing operation parameters, and engineering parameters of the multiple single clusters are respectively input into the corresponding single-cluster fracture plane full 3D models to obtain the corresponding multiple single-cluster fracture 3D model expansion forms, including: Determining the fracture heights at the wellbore of the plurality of corresponding single cluster fractures according to the formation parameters, fracturing operation parameters, engineering parameters of the plurality of single cluster fractures, and the corresponding single cluster fracture plane full three-dimensional model; Determining the sublinear flow direction along-line fracture widths of the plurality of corresponding single-cluster fractures according to the formation parameters, fracturing operation parameters, engineering parameters, and the corresponding single-cluster fracture plane full three-dimensional model; Inputting the fracture heights of the plurality of single clusters at the wellbore into the second PKN model to obtain the maximum single-wing fracture length and the maximum single-wing fracture width of the plurality of single cluster fractures; According to the maximum single-wing crack length and maximum single-wing crack width of the plurality of single-cluster cracks and the corresponding single-cluster crack plane full three-dimensional model, the along-line crack width, displacement and along-line pressure drop of the plurality of corresponding single clusters in the main linear flow length direction are calculated; According to the plurality of single clusters of fracture widths, displacements and pressure drops along the main linear flow length direction and the corresponding single cluster fracture plane full three-dimensional model, all fracture heights and fracture widths along the fracture height direction of the plurality of corresponding single clusters are calculated; Calculating the three-dimensional volumes of multiple single-cluster fractures based on all fracture heights in the length direction and fracture widths along the fracture height direction of the multiple corresponding single-cluster fractures, and comparing the three-dimensional volumes of the multiple single-cluster fractures with the fracture volumes of the corresponding single-cluster fractures calculated by the second PKN model; If the volume error between the two is less than the first threshold, the three-dimensional expansion form of a single crack with a symmetrical double-wing crack is obtained. Otherwise, the single-wing length of the crack is changed and input into the corresponding single-cluster crack plane full three-dimensional model for calculation until the error is less than the first threshold, and then the three-dimensional expansion forms of single cracks corresponding to multiple single clusters are obtained.

2. The method for calculating the three-dimensional expansion morphology of multi-cluster hydraulic fracturing in a horizontal well according to claim 1, characterized in that: The three-dimensional volume of the fracture is obtained by calculating and accumulating all fracture heights in the fracture length direction and the fracture widths along the fracture height direction of the plurality of single clusters, including: According to all the fracture heights and fracture widths along the fracture height direction of the plurality of single-cluster fractures, the three-dimensional volume of each point on the corresponding single-cluster fracture length is determined, and the corresponding three-dimensional volumes are accumulated to obtain the three-dimensional volume of the corresponding fracture.

3. The method for calculating the three-dimensional expansion morphology of multi-cluster hydraulic fracturing in a horizontal well according to claim 1, characterized in that: Determining the in-situ stress field under the induced stress interference according to the three-dimensional propagation morphology of the initial crack and the induced stress model, and determining the stress intensity factor of the in-situ stress field under the induced stress interference, including: The induced stress of each crack is calculated based on the three-dimensional expansion morphology of the multiple clusters of cracks and the induced stress calculation formula; Superimposing the induced stress of each crack to obtain the in-situ stress field under the influence of the induced stress; The stress intensity factor of the in-situ stress field under the influence of the induced stress is determined according to the in-situ stress field under the influence of the induced stress.

4. The method for calculating the three-dimensional expansion morphology of multi-cluster hydraulic fracturing in a horizontal well according to claim 3, characterized in that: The induced stress of each crack is calculated based on the three-dimensional expansion morphology of the multiple clusters of cracks and the induced stress calculation formula, including: Determining, based on the three-dimensional expansion morphology of the multiple clusters of cracks, the angle at which each crack deviates from a preset point from the crack lower tip, the crack center, and the crack upper tip, as well as the distance from the preset point to the crack lower tip, the crack center, and the crack upper tip; The induced stress generated by each crack on the preset point in the direction of minimum horizontal principal stress, vertical stress and maximum principal stress is determined based on the angle of the preset point away from the lower tip of the crack, the center of the crack and the upper tip of the crack, the distance from the preset point to the lower tip of the crack, the center of the crack and the upper tip of the crack, and the induced stress formula.

5. The method for calculating the three-dimensional expansion morphology of multi-cluster hydraulic fracturing in a horizontal well according to claim 3, characterized in that: The induced stress of each crack is superimposed to obtain the in situ stress field under the influence of the induced force, including: The induced stress generated by each crack in the direction of the minimum horizontal principal stress of the preset point, the induced stress generated in the vertical stress direction and the induced stress generated in the direction of the maximum horizontal principal stress are calculated by a superposition calculation formula to determine the superimposed induced stress of each crack in the direction of the minimum horizontal principal stress, the vertical stress direction and the maximum horizontal principal stress direction of the preset point.

6. The method for calculating the three-dimensional expansion morphology of multi-cluster hydraulic fracturing in a horizontal well according to claim 3, characterized in that: Determining the stress intensity factor of the in-situ stress field under the influence of the induced stress according to the in-situ stress field, including: updating the formation parameters, fracturing operation parameters and engineering parameters according to the in-situ stress field under the influence of the induced stress; The stress intensity factor is determined based on the updated formation parameters, fracturing operation parameters and engineering parameters.

7. The method for calculating the three-dimensional expansion morphology of multi-cluster hydraulic fracturing in a horizontal well according to claim 1, characterized in that: The formation parameters, fracturing operation parameters and engineering parameters are updated according to the in-situ stress field under the induced stress interference, including: determining a minimum horizontal stress and a maximum horizontal stress according to the in situ stress field; The fracture length, fracture width and fracture height under the interference of the in-situ stress field are determined according to the maximum horizontal stress and the minimum horizontal stress to obtain updated formation parameters, fracturing operation parameters and engineering parameters.

8. The method for calculating the three-dimensional expansion morphology of multi-cluster hydraulic fracturing in a horizontal well according to claim 1, characterized in that: The updated formation parameters, fracturing operation parameters, engineering parameters and stress intensity factors are input into the full three-dimensional model of the multi-cluster fracturing fracture plane to calculate the three-dimensional fracture propagation morphology under the induced stress interference, including: Determining the turning angle of the crack extension direction according to the stress intensity factor and the crack deflection angle equation; The updated formation parameters, fracturing operation parameters, engineering parameters and the turning angle of the fracture extension direction are input into the full three-dimensional model of the multi-cluster fracture plane to calculate the three-dimensional extension morphology of the fracture under the induced stress interference.

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