Fracturing fracture conductivity calculation method considering efficient laying of proppant

Abstract

The invention relates to the field of petroleum engineering, in particular to a fracturing fracture conductivity calculation method and device considering efficient laying of a proppant, and the method comprises the following steps: 1) considering the influence of the pressure stress in a proppant column on the fracture width, and establishing a residual fracture width control equation; 2) establishing a fiber permeability calculation equation, and establishing a support cluster permeability calculation equation by utilizing the fiber permeability calculation equation and the propping agent permeability; and (3) integrating the equations in the step (1) and the step (2) to obtain an effective fracture conductivity prediction equation for channel fracturing, and performing fracturing parameter optimization by utilizing the fracture conductivity prediction equation. The flow conductivity prediction method provided by the invention can realize optimization of fiber and proppant parameters under a channel fracturing condition, obtains the effective proppant volume, and provides reference for realizing a proppant efficient laying technology.

Description

Technical Field

[0001] The invention belongs to the technical field of oil and gas field development engineering, and in particular relates to a method for calculating the conductivity of a fracturing crack taking into account efficient proppant paving. Background Art

[0002] Hydraulic fracturing is a production stimulation technique used in the oil and gas industry to increase oil and gas recovery and mitigate near-wellbore damage. The technique involves initiating, extending, and opening fractures into hydrocarbon-bearing formations through the use of pressurized fluids from the wellbore. Particles called "proppants," including natural sands and synthetic materials, are pumped into the fractures along with the fracturing fluid. Once the injection pressure is relieved, the combination of proppant particles (called the proppant pack) performs the dual role of providing mechanical support and providing porous pathways for fluid flow within the fracture. In practice, there are several failure mechanisms that tend to damage the permeability of the proppant pack, thereby affecting the effectiveness of the fracturing treatment. For example, fracturing gel residues and mineral precipitates tend to settle in the pore spaces of the proppant pack, resulting in reduced porosity and permeability. Fine particles generated by localized crushing of the rock and proppant pack under high confining stresses can also block the pore spaces of the proppant pack. Attempts to mitigate the adverse effects of these damage mechanisms on fracture conductivity often result in increased fracturing treatment costs. Another cost-effective solution is to separate 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 channels or voids between the proppant pillars, and in proppant clusters, microchannels for oil and gas flow are formed after fiber degradation.

[0003] The technique of placing proppants unevenly is known as “channel fracturing,” and although the idea of ​​discontinuous proppant placement was proposed in the early days of hydraulic fracturing, the technique has only recently been put into practice. This type of proppant placement is similar to the partial proppant monolayer placement often used in natural fracture stimulation. In such partially packed fractures, fluids penetrating the fracture from a porous reservoir flow locally through proppant columns into the surrounding channels and generally along an open network of channels into the wellbore. Under such flow conditions, the low permeability of the proppant pack does not significantly limit the overall conductivity of the fracture. Discontinuous proppant placement can also result in significant cost savings, especially in the case of large horizontal well fracturing operations. The “channel fracturing” technique involves injecting short pulses of proppant-containing fluid into the fracture, alternating with proppant-free fluid. Fibers or coacervate gels are added throughout the operation to mitigate the dispersion of the proppant pulses as they propagate through the surface equipment, along the wellbore, and into the fracture. The relative duration of the proppant-containing pulses during the injection phase 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 is beneficial to a certain extent because it leads to a greater increase in overall fracture conductivity. However, this trend cannot continue indefinitely, and excessive column spacing will lead to excessive channel deformation, thereby reducing fracture conductivity. Therefore, there must be an optimal channel network volume fraction, that is, the optimal spacing between proppant columns, which maximizes the overall fracture conductivity. Therefore, when designing related efficient proppant placement, how to maximize the effective conductivity of partially filled fractures while reducing the amount of proppant used is a technical problem that needs to be solved in this field. Summary of the invention

[0004] The object of the present invention is to provide a method for calculating the conductivity of a hydraulic fracture taking into account the efficient placement of proppants.

[0005] In order to achieve the above object, the technical solution adopted by the present invention is: a method for calculating the conductivity of a hydraulic fracture taking into account the efficient placement of proppant, characterized in that it comprises the following steps:

[0006] 1) Considering the influence of compressive stress in the proppant column on the crack width, the residual crack width control equation is established;

[0007] 2) Establishing a fiber permeability calculation equation, and using the fiber permeability calculation equation and the proppant permeability calculation equation to establish a support cluster permeability calculation equation;

[0008] 3) Combining the equations in step 1) and step 2), the effective fracture conductivity prediction equation of channel fracturing is obtained, and the fracture conductivity prediction equation is used to optimize the fracturing parameters, wherein the effective fracture conductivity prediction equation is:

[0009]

[0010] Among them, K eff is the effective fracture conductivity, b is the half value of the support column slit width, K t is the support cluster permeability, and δ(x) is the residual fracture width.

[0011] Furthermore, the residual crack width control equation in step 1) is:

[0012]

[0013] in, 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, σ 0 is the formation closure pressure, σ p (x) is the compressive stress in the proppant column.

[0014] Furthermore, the calculation equation for the support cluster permeability in step 2) is:

[0015]

[0016] Among them, K t is the support cluster permeability; K p is the permeability of the supporting column; K f is the fiber permeability, K fi is the permeability of the fiber guide microchannel, n f is the fiber microchannel density, and θ is the angle.

[0017] Furthermore, the permeability calculation method of the fiber guide microchannel is:

[0018]

[0019] Among them, b f is the fiber diameter, is the porosity of the fiber flow-guiding channel.

[0020] On the other hand, the present invention provides a device for calculating the conductivity of a fracturing crack taking into account efficient proppant placement, characterized in that it includes: 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 at least one processor so that the at least one processor can execute any of the calculation methods described above.

[0021] On the other hand, the present invention provides a computer-readable storage medium having a computer program stored thereon, wherein the computer program, when executed by a processor, implements the steps of the computing method as described in any one of the above items.

[0022] In summary, the present invention proposes a method for calculating the conductivity of fracturing fractures taking into account the efficient placement of proppants. The method of the present invention can predict the conductivity of propped fractures 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 proppant placement technology. BRIEF DESCRIPTION OF THE DRAWINGS

[0023] Figure 1 Schematic diagram of the seepage channel of the proppant efficient laying technology;

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

[0025] Figure 3 The crack width and error calculated at different discrete points in the embodiment of the present invention;

[0026] Figure 4 The crack width and error calculated at different discrete points in the embodiment of the present invention;

[0027] Figure 5 The change of fracture conductivity under partial filling in the embodiment of the present invention;

[0028] Figure 6 is the variation of the residual width of the crack with the closing pressure in the embodiment of the present invention;

[0029] Figure 7 The effective percentage of the proppant varies with the closure pressure and Young's modulus in the embodiment of the present invention;

[0030] Figure 8 Graph showing the change of effective conductivity of the fracture with closing pressure in the embodiment of the present invention. DETAILED DESCRIPTION

[0031] The present invention will be described in detail below in conjunction with the accompanying drawings.

[0032] In order to make the purpose, technical solution and advantages of the present invention more clearly understood, the present invention is further described in detail below in conjunction with the accompanying drawings and embodiments. It should be understood that the specific embodiments described herein are only used to explain the present invention and are not used to limit the present invention.

[0033] In the "channel fracturing" technique, when the load-bearing task of the proppant pack is separated from the task of providing fluid channels, proppants are placed discontinuously in the fracture, thereby forming open channels or voids between the proppant columns, e.g. Figure 1 As shown, Figure 1Part (a) depicts a schematic diagram of partially filled fractures formed by efficient laying technology. In the proppant cluster, microchannels are formed after fiber degradation for oil and gas flow. Figure 1 (b) Schematic diagram of the initial crack opening during the proppant injection stage.

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

[0035] After making the above assumptions, if Figure 2 As shown in (a), the rock layer extends two-dimensionally along the xy plane, and the cracks are arranged along the x-axis. Assume that the width of the support column is 2b, the distance between adjacent columns is 2a>2b, and it is uniform along the crack length 2L. Since the crack length is significantly larger than other characteristic dimensions involved in the model, that is, the crack length is much larger than other characteristic parameters, the geometric shape of the support crack can be idealized as periodic, and its unit cell is as follows Figure 2 (b) as shown. Figure 2 The pillar width spacing ratio a / b in b corresponds to the volume fraction of the proppant-filled area in the actual fracture geometry ( Figure 1 (a)). The fibers are filled into the proppant particles in the proppant cluster. After the proppant is closed, the fibers communicate with each unconnected pore to form a fiber-guided microchannel, such as Figure 2 (c) Figure 2 (d) as shown.

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

[0037]

[0038] Among them, σ p (x) is the compressive stress in the proppant column, σ p0 is the dimension elimination parameter, α, β are dimensionless fitting parameters, and λ is the sedimentation ratio.

[0039] It should be noted that the dimension elimination parameter σ p0 is a constant, which is introduced to ensure that the above formula is dimensionally correct. Its unit is the same as the experimentally measured stress σ p (x) is the same. For example, stress σ is measured in MPa p (x), then σ p0 =1MPa. The sedimentation ratio λ is the ratio of the change in proppant column height to the original height, that is:

[0040]

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

[0042] In a preferred embodiment, the model can be calibrated using experimental results to obtain the values ​​of the fitting parameters. In the experimental simulation, the initial height δ of the proppant column is 0 Set to a certain value, the proppant column is placed in a hydraulic press equipped with a sensor to monitor the distance between the load and the pressure head. Different values ​​of compressive stress are used to obtain fitting parameters in different value ranges (e.g., 0 to 50 MPa).

[0043] It should be noted that the values ​​of the fitted parameters obtained can vary greatly depending on the choice of proppant, the presence or absence of additives (resin coatings, fibers), the fluid saturation of the proppant column, and the type of loading applied (uniaxial or triaxial), so it is particularly important to choose experimental conditions that are very similar to the in situ conditions.

[0044] For the residual crack width, the distributed dislocation technique (DDT) is used to describe the crack width problem. The relationship of the crack width is described by the dislocation density function, and the control equation of the residual crack width can be obtained as follows:

[0045]

[0046] in, is the generalized Young's modulus, which is defined under plane stress as B y (ξ) is the dislocation density function, ξ is the parameter introduced in the mathematical solution, H is the Heaviside step function, in H(bx), when bx is greater than 1, it is 0, and when bx is less than 1, it is 1; K is the kernel function.

[0047]

[0048] Where δ(x) is the crack width; δ min It corresponds to the width between the crack surfaces at x = ±a, where a is half of the spacing between adjacent columns and x is the transverse coordinate position parameter.

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

[0050]

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

[0052]

[0053] H is the Heaviside step function, σ 0 is the formation closure pressure; a is half of the distance between adjacent columns.

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

[0055]

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

[0057] For proppant clusters, since they contain fibers, they play the role of fiber diversion. The fiber diversion channel can be regarded as a series of dense micro-fracture systems, assuming that the fiber concentration and fiber addition satisfy the growth curve model:

[0058]

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

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

[0061]

[0062] is the fiber porosity, V f is the fiber volume, ρ is the fiber density, V p is the proppant volume and c is the fiber concentration.

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

[0064]

[0065] Furthermore, the permeability of the fiber flow-guiding microchannel can be obtained as:

[0066]

[0067] Among them, b f is the fiber diameter, is the porosity of the fiber flow-guiding channel.

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

[0069]

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

[0071] Finally, the calculation formula of effective fracture conductivity can be obtained:

[0072]

[0073] Among them, K eff is the effective fracture conductivity, b is the half value of the support column slit width, K t is the support cluster permeability, and δ(x) is the residual fracture width.

[0074] In order to verify the crack width calculation model of the present invention, the basic parameters are set as shown in Table 1: column spacing 2a and width 2b, initial crack opening δ 0 , lateral geostress magnitude σ 0 , Generalized Young's modulus of rock and mechanical properties of proppant filling bodyσ p0 , α, β and γ, the values ​​of the above parameters remain unchanged throughout the calculation process.

[0075] Table 1 Basic parameters

[0076]

[0077] like Figure 3 As shown in the figure, the fracture width and error under full proppant filling are calculated, and the error between the calculated result and the theoretical calculation result is less than 10 -4 , which verifies the correctness of the seam width model in this invention.

[0078] Figure 4 The fracture width and error under full proppant filling were calculated in the paper. The calculation results show that when the discrete points N used in the calculation are 100, the calculation requirements are basically met.

[0079] In order to verify the fracture conductivity calculation model of the present invention, basic parameters are set as shown in Table 2: proppant permeability K p and microchannel permeability K f , proppant permeability K p Can be regarded as a constant (K f >>K p ), as well as proppant density, fiber density and fiber microchannel density n f , channel width b f , angle θ, etc. The values ​​of the above parameters remain unchanged during the entire calculation process.

[0080] Table 2 Basic parameters

[0081]

[0082] like Figure 5 As shown in the figure, when the proppant is partially filled and there is no fiber conduction microchannel, the fracture conductivity is mainly affected by the filling degree. Along the unit cell development, the conductivity of the proppant-filled area is much smaller than the unfilled curve, and the larger the proppant filling ratio, the larger the residual fracture opening, and the greater the fracture conductivity. The calculation results are basically consistent with those of Andrei et al., which shows the correctness of the calculation of this 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 fiber in the proppant without overflowing and fully forming small clusters, and the microchannel also plays an important role in the fracture conductivity.

[0083] Figure 6 The variation law of the residual width of the fracture under different closing pressures is shown. The calculation results show that as the proppant volume a / b gradually increases, the fracture width gradually decreases, and the average channel width between the proppant clusters also decreases. At the same time, as the closing pressure increases, the residual width of the fracture decreases, and the average channel width decreases more rapidly.

[0084] Figure 7The variation law of proppant effective percentage under different closure pressures is shown. The results show that as the distance between proppant clusters (ab) gradually increases, the effective percentage of proppant decreases first and then increases, and there is a minimum effective percentage. As the proppant cluster b increases, the minimum effective percentage increases; as the closure pressure increases, the minimum effective percentage increases; as the Young's modulus of the formation increases, the minimum effective percentage decreases.

[0085] Figure 8 The variation law of effective conductivity of propped fractures under different closing pressures is shown. The results show that as the distance between proppant clusters (ab) gradually increases, the effective conductivity of fractures increases first and then decreases, and there is an optimal distance. As the number of proppant clusters b increases, the optimal distance decreases; as the closing pressure increases, the optimal distance decreases; as the Young's modulus of the formation increases, the optimal distance increases.

[0086] It can be seen that the present invention provides a method for calculating the conductivity of fracturing fractures taking into account the efficient placement of proppants, which can optimize the fiber and proppant parameters under channel fracturing conditions and obtain the effective proppant volume, thereby providing a reference for realizing the efficient placement technology of proppants.

[0087] The above description is only a preferred embodiment of the present invention and is not intended to limit the present invention. Any modifications, equivalent substitutions and improvements made within the spirit and principles of the present invention should be included in the protection scope of the present invention.

Claims

1. A method for calculating the conductivity of a hydraulic fracture taking into account efficient proppant placement, characterized in that: The following steps are involved: 1) Considering the influence of compressive stress in the proppant column on the crack width, the residual crack width control equation is established; 2) Establishing a fiber permeability calculation equation, and using the fiber permeability calculation equation and the proppant permeability calculation equation to establish a support cluster permeability calculation equation; 3) Combining the equations in step 1) and step 2), the effective fracture conductivity prediction equation for channel fracturing is obtained, and the fracture conductivity prediction equation is used to optimize the fracturing parameters, wherein the effective fracture conductivity prediction equation is: Among them, K eff is the effective fracture conductivity, b is the half value of the support column slit width, K t is the support cluster permeability, and δ(x) is the residual fracture width.

2. The method for calculating the conductivity of a hydraulic fracture considering efficient proppant placement according to claim 1, wherein the residual fracture width control equation in step 1) is: in, 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.

3. The method for calculating the conductivity of a hydraulic fracture taking into account efficient proppant placement according to claim 1, wherein the proppant cluster permeability calculation equation in step 2) is: in, K t is the support cluster permeability; K p is the permeability of the supporting column; K f is the fiber permeability, K fi is the permeability of the fiber guide microchannel, n f is the fiber microchannel density, and θ is the angle.

4. The method for calculating the conductivity of a fracturing fracture taking into account efficient proppant placement according to claim 1, wherein the permeability of the fiber guide microchannel is calculated as follows: in, b f is the fiber diameter, is the porosity of the fiber flow-guiding channel.

5. A device for predicting the conductivity of a hydraulic fracture taking into account efficient proppant placement, characterized in that: Includes the following modules: A residual crack width prediction module, wherein the residual crack width prediction module establishes a residual crack width control equation under the condition that the compressive stress in the proppant column affects the crack width; A support cluster permeability prediction module, wherein the support cluster permeability prediction module predicts the support cluster permeability based on the fiber permeability and the proppant permeability; The effective fracture conductivity prediction module predicts the effective fracture conductivity of channel fracturing based on the residual fracture width prediction module and the support cluster permeability prediction module, and optimizes the fracturing parameters using the fracture conductivity prediction equation. The effective fracture conductivity prediction method is as follows: Among them, K eff is the effective fracture conductivity, b is the half value of the support column slit width, K t is the support cluster permeability, and δ(x) is the residual fracture width.

6. A device for calculating the conductivity of a hydraulic fracture taking into account efficient proppant placement, characterized in that: include: at least one processor and a memory in communication with the processor; The memory stores instructions that can be executed by the processor, and the instructions are executed by at least one processor to enable the at least one processor to execute the computing method described in any one of claims 1 to 4.

7. A computer-readable storage medium having a computer program stored thereon, characterized in that: When the computer program is executed by a processor, the steps of the computing method according to any one of claims 1 to 4 are implemented.

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