A method for calculating the fracture conductivity of a fracturing fracture considering efficient placement of proppant

Abstract

The present application relates to the field of petroleum engineering, and particularly relates to a method and device for calculating the fracture conductivity of a fracturing fracture considering efficient placement of proppants, the method comprising the following steps: 1) considering the influence of the compressive stress in the proppant column on the fracture width, establishing a residual fracture width control equation; 2) establishing a fiber permeability calculation equation, and using the fiber permeability calculation equation and the proppant permeability to establish a proppant cluster permeability calculation equation; 3) comprehensively using the equations in steps 1) and 2) to obtain a channel fracturing effective fracture conductivity prediction equation, and using the fracture conductivity prediction equation to optimize the fracturing parameters. The present application provides a method for predicting the conductivity, which can realize the optimization of the fiber and proppant parameters under the condition of channel fracturing, obtain the effective proppant volume, and provide a reference for realizing the efficient placement of proppants.

Description

TECHNICAL FIELD

[0001] The application belongs to the technical field of oil and gas field development engineering, and particularly relates to a method for calculating the fracture conductivity of hydraulic fractures considering efficient placement of proppants. BACKGROUND

[0002] Hydraulic fracturing is a stimulation technique used in the oil and gas industry to enhance oil and gas recovery and mitigate near-wellbore damage. The technique involves initiating, extending, and opening fractures from the wellbore to the oil and gas bearing formation by pressurized fluid. Particles known as "proppants," including natural sand and synthetic materials, are pumped into the fractures along with the fracturing fluid. Once injection pressure is relieved, the combination of proppant particles, known as the proppant pack, serves a dual purpose of providing mechanical support and porous pathways for fluid flow within the fracture. In practical applications, several damage mechanisms tend to impair the permeability of the proppant pack, thereby affecting the effectiveness of the fracturing treatment. For example, fracturing gel residues and mineral precipitates tend to deposit in the pore space of the proppant pack, resulting in reduced porosity and permeability. Fine particles generated by localized rock and proppant pack breakdown under high confining stress also plug the pore space of the proppant pack. Attempts to mitigate the adverse effects of these damage mechanisms on fracture conductivity often result in increased costs of the fracturing treatment, and another cost-effective solution is to decouple the load-bearing task of the proppant pack from the task of providing fluid pathways. This decoupling can be achieved by placing proppants discontinuously in the fracture, thereby forming open pathways or voids between the proppant pillars, and microchannels for oil and gas flow in the proppant clusters after fiber degradation.

[0003] The technique of placing proppant non-uniformly is known as "channel fracturing", although the idea of discontinuous proppant placement was proposed in the early days of hydraulic fracturing, the technique has not been applied in practice until recently. This proppant placement is similar to the partial proppant single-layer placement often used in natural fracture stimulation. In this partially packed fracture, the fluid seeping into the fracture from the porous reservoir flows into the surrounding channels through the proppant column locally, and flows into the wellbore along the open channel network as a whole. Under this flow condition, the low permeability of the proppant packing layer does not seriously limit the overall conductivity of the fracture. The placement of discontinuous proppant can also save costs significantly, especially in the case of large-scale horizontal well fracturing operations. The "channel fracturing" technique includes injecting proppant-containing fluid into the fracture in short pulses and alternating with proppant-free fluid. During the entire operation, fibers or coagulating gels are added to mitigate the dispersion of the proppant pulses as they travel through the surface equipment, along the wellbore and within the fracture. During the injection phase, the relative duration of the proppant-containing pulse determines the volume fraction of the proppant-free channel network and the spacing between adjacent proppant columns. It is expected that an increase in proppant column spacing or channel volume fraction will be beneficial to some extent, as it will result in a greater increase in overall fracture conductivity. However, this trend cannot continue indefinitely, and excessive column spacing will result in excessive deformation of the channels, thereby reducing fracture conductivity. Therefore, there must be an optimal channel network volume fraction, i.e. an optimal spacing between proppant columns, that maximizes overall fracture conductivity. Therefore, in the related design of efficient proppant placement, how to maximize the effective conductivity of the partially packed fracture while reducing the amount of proppant used is a technical problem that needs to be solved in the field. SUMMARY

[0004] The present application aims to provide a method for calculating the conductivity of a fractured fracture considering efficient proppant placement.

[0005] To achieve the above-mentioned purpose, the technical scheme adopted by the present application is as follows: a method for calculating the conductivity of a fractured fracture considering efficient proppant placement, characterized in that it comprises the following steps:

[0006] 1) considering the effect of compressive stress within the proppant column on the fracture width, a residual fracture width control equation is established;

[0007] 2) a fiber permeability calculation equation is established, and a proppant cluster permeability calculation equation is established using the fiber permeability calculation equation and the proppant permeability;

[0008] 3) the equations in steps 1) and 2) are integrated to obtain a channel fracturing effective fracture conductivity prediction equation, and the fracture conductivity prediction equation is used for fracturing parameter optimization, wherein the effective fracture conductivity prediction equation is:

[0009]

[0010] where K eff is the effective fracture conductivity, b is the half-value of the proppant fracture width, K t is the proppant cluster permeability, and δ(x) is the residual fracture width.

[0011] Further, the residual fracture width control equation in step 1) is

[0012]

[0013] where K is the generalized Young's modulus, B y (ξ) is the dislocation density function, K is the kernel function, H is the Heaviside step function, σ0 is the formation closure pressure, σ p (x) is the compressive stress in the proppant column.

[0014] Further, the proppant cluster permeability calculation equation in step 2) is:

[0015]

[0016] where K t is the proppant cluster permeability; K p is the proppant column permeability; K f is the fiber permeability, K fi is the permeability of the fiber flow microchannel, n f is the fiber microchannel density, and θ is the angle.

[0017] Further, the permeability calculation method of the fiber flow microchannel is

[0018]

[0019] where b f is the fiber diameter, and φ is the porosity of the fiber flow channel.

[0020] In another aspect, the present application provides a device for calculating the fracture conductivity of a fracturing fracture considering efficient placement of proppants, characterized in that it comprises at least one processor and a memory communicatively connected to the processor; the memory stores instructions executable by the processor, and the instructions are executed by the at least one processor to enable the at least one processor to perform the calculation method of any one of the above.

[0021] In another aspect, the present application provides a computer readable storage medium having a computer program stored thereon, characterized in that the computer program, when executed by a processor, implements the steps of the calculation method of any one of the above.

[0022] In summary, the present application proposes a calculation method of fracture conductivity of a fracturing fracture considering efficient placement of proppants, the method of the present application can predict the conductivity of a propped fracture containing fibers under channel fracturing conditions, thereby providing a reference for improving the conductivity of channel fracturing fractures, reducing the amount of proppants and fibers, and realizing efficient placement of proppants. BRIEF DESCRIPTION OF DRAWINGS

[0023] Figure 1 A schematic diagram of a seepage channel for efficient placement of proppants;

[0024] Figure 2 A schematic diagram of a physical model in an embodiment of the present application;

[0025] Figure 3 Fracture width and error calculated at different discrete points in an embodiment of the present application;

[0026] Figure 4 Fracture width and error calculated at different discrete points in an embodiment of the present application;

[0027] Figure 5 Fracture conductivity change under partial filling in an embodiment of the present application;

[0028] Figure 6 Change of fracture residual width with closure pressure in an embodiment of the present application;

[0029] Figure 7 Change of effective percentage of proppants with closure pressure and Young's modulus in an embodiment of the present application;

[0030] Figure 8 Change of effective fracture conductivity with closure pressure in an embodiment of the present application. DETAILED DESCRIPTION

[0031] The present application will be described in detail below with reference to the accompanying drawings.

[0032] In order to make the purpose, technical scheme and advantages of the present application clearer and more apparent, the present application will be further described in detail below with reference to the accompanying drawings and embodiments. It should be understood that the specific embodiments described herein are only used to explain the present application and do not limit the present application.

[0033] In the "channel fracturing" technology, the proppant filling task and the fluid channel providing task are separated, the proppant is discontinuously placed in the fracture, thereby forming open channels or voids between the proppant columns, as shown in Figure 1 , wherein Figure 1 Part (a) of the figure depicts a partially filled fracture schematic diagram formed by the efficient placement technology, in the proppant cluster, micro-channels will also be formed for oil and gas flow after the fiber degrades, whereinFigure 1 (b) is a schematic diagram of the initial open fracture for the proppant injection stage.

[0034] To study the optimum value of the proppant column spacing (or volume fraction), the problem of the hydraulic fracture formed in a homogeneous, elastic and isotropic rock formation and partially filled with proppant particles is considered, as shown in Figure 1 (a), where the hydraulic fracture geometry is planar and the distribution of proppant in the fracture is irregular. For simplicity, the arrangement of proppant columns in the fracture is considered to be regular in the present invention, and a two-dimensional equivalent of the actual three-dimensional geometric problem is considered.

[0035] After making the above assumptions, the rock formation extends in two dimensions along the x-y plane, and the fracture is arranged along the x axis, as shown in Figure 2 (a). It is assumed that the proppant column width is 2b, the spacing between adjacent columns is 2a > 2b, and the spacing is uniform along the length 2L of the fracture. Since the fracture length is significantly greater than other characteristic dimensions involved in the model, i.e., the fracture length is much larger than other characteristic parameters, the geometry of the propped fracture can be idealized as periodic, with a unit cell as shown in Figure 2 (b). Figure 2 The column width spacing ratio a / b in b corresponds to the volume fraction of the proppant filling area in the actual fracture geometry (a). Figure 1 (a)). The fibers fill the proppant particles in the proppant clusters, and after the proppant is closed, the fibers communicate the various unconnected pores, forming fiber-guided microchannels, as shown in Figure 2 (c), Figure 2 (d).

[0036] In the present invention, it is assumed that the proppant column does not undergo lateral deformation and damage, but only longitudinal deformation. The compressive load on the proppant column causes the column height to decrease, accompanied by lateral expansion of the column width. In practice, the lateral expansion of the proppant column can reduce the gap between the proppant columns, redistribute the stress inside the proppant column, and in the present invention, this lateral expansion of the proppant column is ignored for simplicity of problem representation, and a simple uniaxial proppant consolidation empirical model is used, where the compressive stress σ p (x) is related to the proppant settling ratio λ, and the relationship is:

[0037]

[0038] where σ p (x) is the compressive stress in the proppant column, σ p0 is a dimensionless parameter, and α, β are dimensionless fitting parameters, and λ is the settling ratio.

[0039] It should be noted that the dimensionless parameter σ p0is a constant introduced to ensure that the above formula is dimensionally correct, and its unit is the same as the experimental stress σ p (x). For example, if the stress σ p (x) is measured in MPa, then σ p0 = 1 MPa. The settling ratio λ is the ratio of the change in the height of the proppant column to the original height, i.e.,

[0040]

[0041] where δ0is the initial height of the unloaded proppant column, and δ is the height of the proppant column under a certain pressure stress. The value of λ is in the interval (0, 1), and formula (1) correctly predicts that λ = 0 when σ p (x) = 0, and λ → 1 when σ p (x) → ∞.

[0042] In a preferred embodiment, the model can be corrected using experimental results, and the values of the fitting parameters can be obtained. In the experimental simulation, the initial height δ0of the proppant column is set to a certain value, and the proppant column is placed in a hydraulic machine equipped with a sensor for monitoring the distance between the load and the pressure head. The fitting parameters are obtained by applying different values of the pressure stress in different value ranges (e.g., 0-50 MPa).

[0043] It should be noted that the obtained values of the fitting parameters will vary greatly depending on the selection of the proppant, the presence or absence of additives (resin coating, fibers), the fluid saturation of the proppant column, and the type of applied load (uniaxial or triaxial), so it is particularly important to select experimental conditions that are very similar to in-situ conditions.

[0044] For the residual fracture width, the distributed dislocation technique (DDT) is selected to describe the fracture width problem, and the fracture width relationship is described by a dislocation density function, and the control equation for the residual fracture width is obtained as follows:

[0045]

[0046] where, is the generalized Young's modulus, which is defined as B y (ξ) is the dislocation density function, ξ is a parameter introduced in mathematical solution, H is the Heaviside step function, which takes 0 when b-x is greater than 1 and takes 1 when b-x is less than 1; K is the kernel function.

[0047]

[0048] In the formula, δ(x) is the fracture width; δ minThe width between the fracture faces corresponding to x = ±a, a is half of the distance between adjacent pillars, x is the lateral coordinate position parameter.

[0049] Setting parameter δ 1D Corresponding to the whole proppant filling, generally 0 < δ min < δ 1D Therefore, the minimum value of the fracture residual opening can be determined in advance:

[0050]

[0051] Where γ is the interval parameter, its range is (0, 1), so δ min The correct value of a is between two limits γ ∈ (0, 1). The value of a is selected by repeated experiments, so that the solution obtained satisfies the stress balance condition in the y direction:

[0052]

[0053] H is the Heaviside step function, σ0 is the formation closure pressure; a is half of the distance between adjacent pillars.

[0054] After the fracture is closed, the effective volume fraction V eff of the proppant actually providing proppant force can be calculated by the following formula:

[0055]

[0056] The effective volume fraction V eff can be used to calculate the amount of proppant corresponding to the actual proppant force, where the peak stress of the proppant filling area is σ p,pk = σ p (x = b).

[0057] For the proppant cluster, because it contains fibers, it plays the role of fiber flow guide. The fiber flow guide channel can be regarded as a series of dense microfracture systems, assuming that the fiber concentration and fiber addition meet the growth curve model:

[0058]

[0059] Where c is the fiber concentration, S, p, q are fitting parameters, and x is the fiber addition.

[0060] After knowing the fiber concentration, it can be calculated as:

[0061]

[0062] The fiber porosity is φ, V f is the fiber volume, and ρ is the fiber density, V pc is the volume of the proppant, and c is the fiber concentration.

[0063] n of dense microcracks f The number of groups is defined as:

[0064]

[0065] Furthermore, the permeability of the fiber-guided microchannels can be obtained as follows:

[0066]

[0067] Among them, b f The diameter of the fiber. Porosity of the fiber flow channel.

[0068] Therefore, the permeability of the support cluster containing fiber-guided channels can be expressed as:

[0069]

[0070] Among them, K t To support cluster penetration rate; K p It is the permeability of the support column, obtained through experimental testing; K f It is the fiber permeability, n f θ represents the fiber microchannel density and θ represents the angle.

[0071] Finally, the formula for calculating the effective fracture conductivity (13) can be obtained:

[0072]

[0073] Among them, K eff For effective crack conductivity, b is half the crack width of the supporting column, and K t To support the cluster permeability, δ(x) represents the residual crack width.

[0074] To verify the crack width calculation model of this invention, the following basic parameters were set as shown in Table 1: column spacing 2a and width 2b, initial crack opening δ0, lateral stress magnitude σ0, and generalized Young's modulus of rock. and the mechanical properties σ of the proppant-filled body p0 The values ​​of the parameters α, β, and γ remain constant throughout the calculation.

[0075] Table 1 Basic Parameters

[0076]

[0077] like Figure 3 As shown, the crack width and error were calculated under the condition of full proppant filling. The error between the calculated results and the theoretical calculation results is less than 10%. -4, which verifies the correctness of the fracture width model in the application.

[0078] Figure 4 The fracture width and error in the full proppant filling condition are calculated, and the calculation result shows that when the discrete points N used in the calculation is 100, the calculation requirement is basically met.

[0079] In order to verify the fracture conductivity calculation model of the application, the basic parameters are set as shown in Table 2: the proppant permeability K p and the microchannel permeability K f , the proppant permeability K p , which can be regarded as a constant (K f >> K p ), and the proppant density, fiber density and fiber microchannel density n f , channel width b f , angle θ and the like, the above parameter values remain unchanged in the whole calculation process.

[0080] Table 2 Basic parameters

[0081]

[0082] As shown in Figure 5 , in the case of partial proppant filling and no fiber flow guiding microchannel, the fracture conductivity is mainly affected by the filling degree. Along the development of the unit cell, the flow conductivity of the proppant filling area is far less than that of the non-filling curve, and the greater the proppant filling ratio, the greater the residual fracture opening, and the greater the fracture conductivity. The calculation result is basically consistent with the calculation result of Andrei et al., which illustrates the correctness of the calculation of the model. At the same time, according to the fiber microchannel calculation model proposed in this paper, it can be found that with the increase of the fiber limit concentration, the fracture conductivity increases exponentially, how to provide the limit concentration of the fiber in the proppant, without losing its overflow, fully forming small clusters, and the microchannel also plays an important role in the fracture conductivity.

[0083] Figure 6 The change law of the fracture residual width under different closure pressures is shown, and the calculation result shows that with the gradual increase of the proppant volume a / b, the fracture width gradually decreases, and the average width of the channel between the proppant clusters also decreases. At the same time, with the increase of the closure pressure, the fracture residual width decreases, and the average width of the channel decreases more rapidly.

[0084] Figure 7The change rule of the effective percentage of the proppant under different closure pressures is shown, and the results show that with the gradual increase of the proppant cluster spacing (a-b), the effective percentage of the proppant first decreases and then increases, and there is a minimum effective percentage; with the increase of the proppant cluster b, the minimum effective percentage increases; with the increase of the closure pressure, the minimum effective percentage increases; and with the increase of the formation Young's modulus, the minimum effective percentage decreases.

[0085] Figure 8 The change rule of the effective flow conductivity of the propped fracture under different closure pressures is shown, and the results show that with the gradual increase of the proppant cluster spacing (a-b), the effective flow conductivity of the fracture first increases and then decreases, and there is an optimal spacing; with the increase of the proppant cluster b, the optimal spacing decreases; with the increase of the closure pressure, the optimal spacing decreases; and with the increase of the formation Young's modulus, the optimal spacing increases.

[0086] It can be seen that the present application provides a calculation method of the fracture flow conductivity considering the high-efficiency placement of the proppant, can realize the optimization of the fiber and proppant parameters under the channel fracturing condition, and obtains the effective proppant volume, so as to provide a reference for realizing the high-efficiency placement technology of the proppant.

[0087] The above only describes the preferred embodiments of the present application and is not used to limit the present application, and any modification, equivalent replacement and improvement made within the spirit and principle of the present application should be included in the protection scope of the present application.

Claims

1. A method for calculating the conductivity of fracturing fractures considering efficient proppant placement, characterized in that, The method comprises the following steps: 1) establishing a residual fracture width control equation by considering the effect of compressive stress in the proppant column on the fracture width; 2) establishing a permeability calculation equation for the fiber flow microchannel, and using the fiber permeability calculation equation and the proppant permeability to establish a proppant cluster permeability calculation equation; 3) obtaining a prediction equation for the effective fracture conductivity of channel fracturing by comprehensively using the equations in steps 1) and 2), and using the prediction equation for the effective fracture conductivity to optimize the fracturing parameters, wherein the prediction equation for the effective fracture conductivity is: where K eff is the effective fracture conductivity, b is the half-value of the fracture width, K t is the permeability of the proppant pack, and δ(x) is the residual fracture width.

2. The method for calculating the fracture conductivity of the fracturing fracture considering the efficient placement of the proppant according to claim 1, wherein the residual fracture width control equation in step 1) is wherein B is the bulk modulus, E is the Young's modulus, and v is the Poisson's ratio. y (ξ) is the dislocation density function, ξ is a parameter introduced in the mathematical solution, K(x,ξ) is the kernel function, H(b-|x|) is the Heaviside step function, σ0 is the formation closure pressure, σ p (x) is the compressive stress within the proppant column, and a is half the spacing between adjacent columns.

3. The method for calculating the fracture conductivity of the fracturing fracture considering the efficient placement of the proppant according to claim 1, wherein the proppant cluster permeability calculation equation in step 2) is: wherein K t Ks is the support cluster permeability; K p Ks is the support cluster permeability; K f Kf is the fiber permeability, K fi Kf is the fiber permeability, K f Kf is the fiber permeability, K n is the fiber microchannel density, and θ is the angle.

4. The method for calculating the fracture conductivity of the fracturing fracture considering the efficient placement of the proppant according to claim 1, wherein the permeability calculation method for the fiber flow microchannel is wherein K fi is the permeability of the fiber flow microchannels, b f is the fiber diameter, is the porosity of the fiber flow channels.

5. A device for predicting the fracture conductivity of a hydraulic fracture considering the efficient placement of proppant, comprising: The method comprises the following modules: a residual fracture width prediction module, which establishes a residual fracture width control equation by considering the effect of compressive stress in the proppant column on the fracture width; a proppant cluster permeability prediction module, which predicts the proppant cluster permeability based on the permeability of the fiber flow microchannel and the proppant permeability; an effective fracture conductivity prediction module, which predicts the effective fracture conductivity of channel fracturing based on the residual fracture width prediction module and the proppant cluster permeability prediction module, and uses the prediction equation for the effective fracture conductivity to optimize the fracturing parameters, wherein the prediction method for the effective fracture conductivity is: where K eff is the effective fracture conductivity, b is the half-value of the fracture width, K t is the permeability of the proppant pack, and δ(x) is the residual fracture width.

6. A device for calculating the fracture conductivity of a hydraulic fracture considering the efficient placement of proppant, comprising: It comprises: at least one processor and a memory connected in communication with the processor; The memory stores instructions executable by the processor, and the instructions are executed by the at least one processor to enable the at least one processor to execute the calculation method of any one of claims 1-4.

7. A computer readable storage medium having stored thereon a computer program, characterized in that, The computer program is executed by the processor to implement the steps of the calculation method of any one of claims 1-4.

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