Optimization design method and system for hydraulic fracturing slug dosage based on frog leap algorithm

Abstract

The present application relates to the technical fields of hydraulic fracturing slug dosage design, in order to solve the problems of complex calculation process and long time in slug dosage design, the present application provides a kind of optimization design method of hydraulic fracturing slug dosage based on frog leap algorithm, according to the fitness function of constraint condition and optimization target, constraint condition includes slug dosage constraint condition;Optimization variable is continuously iterated and optimized according to the fitness function by using frog leap algorithm, and optimization variable includes the slug fracturing fluid dosage of each section, until the convergence condition is met, so as to search the global optimal solution in the feasible region of slug fracturing fluid dosage.It also provides a system for implementing the method of the present application, including feasible region setting module, optimization variable setting module, constraint condition setting module, fitness function setting module and optimal solution search module.The frog leap algorithm used in the present application is easy to program and realize, and the calculation speed is fast, the optimization ability is strong, and the efficiency of slug dosage optimization design is guaranteed.

Description

Technical Field

[0001] This invention relates to a method for designing the amount of proppant slug used in hydraulic fracturing slug technology, which is mainly used for hydraulic fracturing production enhancement technology in unconventional reservoirs such as shale oil and gas reservoirs and tight sandstone reservoirs. Background Technology

[0002] Deep shale gas has enormous development potential. However, in hydraulic fracturing operations of deep shale gas wells, the increased closure pressure, enhanced rock plasticity, high construction pressure, sensitivity to sand intrusion, and difficulty in proppant addition make traditional continuous proppant addition methods unsuitable for deep shale gas hydraulic fracturing operations. A multi-stage proppant addition method should be adopted during the proppant-carrying fluid stage. This involves using a stepped proppant addition method (stepped proppant addition refers to gradually increasing the proppant ratio in increments) and alternating injection of proppant-carrying fluid and displacement fluid. After one liquid slug is pumped in, the next proppant slug is pumped in only after the construction pressure stabilizes. For example, gradually increasing the proppant ratio in increments of 1% to 2% reduces the risk of proppant transport and settling, increases the proppant-carrying efficiency of the fracturing fluid, reduces the sensitivity of the shale gas reservoir to high proppant ratios, and improves the uniformity of proppant placement during hydraulic fracturing.

[0003] In the design process of multi-stage slug hydraulic fracturing, it is necessary to determine the usage range of fracturing fluid and proppant in a single well based on cost and construction objectives, optimize the dosage of proppant-carrying fluid, displacement fluid, and proppant in each slug under different dosages, and then use fracturing simulation software to select a reasonable total dosage of fracturing fluid and proppant and the dosage of slugs in a single well. However, when optimizing the dosage of proppant-carrying fluid, displacement fluid, and proppant in each slug under different total fluid and proppant volumes, existing methods mainly employ trial-and-error methods, which usually rely on the experience of designers. This process is complex and time-consuming, which is particularly problematic in the design of special process parameters such as long horizontal slug fracturing and intermediate acid injection fracturing. This severely restricts the optimized design of hydraulic fracturing in deep shale gas wells. Therefore, there is an urgent need for a calculation method that can further optimize the dosage of proppant-carrying fluid and displacement fluid, as well as the proppant-fluid ratio, based on the designed fracturing fluid volume and total proppant dosage.

[0004] Chinese patent (CN103605874A) discloses a dimensionless coefficient fracturing optimization design method. The method involves determining the required dimensionless oil and gas production index (EPI) using dimensionless parameter design and a fracturing model; and determining the actual achievable EPI using the original construction parameters, reservoir parameters, drilling and logging data from adjacent wells in the fracturing zone. If the designed target EPI matches the actual achievable EPI, the required fracture parameters and construction design parameters are determined using the designed target EPI and the required proppant coefficient Nprop. If they do not match, the optimization of dimensionless characteristic parameters is repeated until a match is found with the actual achievable EPI.

[0005] Chinese Patent (CN103912247A) discloses a multi-stage slug injection process for horizontal gas wells, including a pre-flush fluid injection stage, a sand-mixing fluid injection stage, and a displacement fluid injection stage. The pre-flush fluid injection stage includes the following steps: 1) During horizontal well construction, when injecting the designed volume of pre-flush fluid, inject fracturing fluid of one tubing volume and the first slug; 2) After the first slug enters the formation, observe the oil pressure changes. When the first slug is fully in the formation and the oil pressure tends to stabilize, inject the second slug; 3) After the second slug enters the formation, observe the oil pressure changes. When the second slug is fully in the formation and the oil pressure tends to stabilize, inject the third slug. This invention features a novel process. By injecting multiple slugs of different particle sizes, it better polishes the perforation holes, reduces near-wellbore contamination, improves construction quality, and lowers construction risks.

[0006] Chinese patent (CN104533371A) discloses an asymmetric three-dimensional fracturing method for horizontal wells. The method is characterized by: after casing cementing or open-hole completion, the boundaries of the horizontal section of the horizontal well's seepage units are determined, dividing the horizontal reservoir into several independent seepage unit combinations, which serve as the basis for the distribution and combination of artificial fractures along the wellbore direction; within each independent seepage unit, the length and height of artificial fractures are calculated and designed based on the planar distribution and longitudinal stacking characteristics of the sand bodies, thereby achieving full control over the reserves.

[0007] Chinese Patent (CN106593394A) discloses a step-by-step sand addition method for shale gas fracturing. (1) Pump the pre-filled fluid into the wellbore to create a fracture in the formation; (2) Pump the first sand addition slug to add sand in a step-by-step manner; (3) Pump the first liquid slug. If the pressure shows a gradual increase, it indicates that the pressure change is slow and there is room to increase the sand ratio. Proceed to step (4); If the pressure indicates that it is not advisable to increase the sand ratio at this stage, it is necessary to further pump fracturing fluid to create a fracture. Proceed to step (1); (4) Pump the second sand addition slug to add sand in a step-by-step manner; (5) Pump the second liquid slug and observe the pressure change trend after the sand addition slugs with different sand ratios enter the formation; (6) Repeat steps (4) to (5) 15-20 times, specifically to achieve the sand addition amount required by the fracturing design, to complete the sand addition at each stage, and finally pump the displacement fluid to complete the entire fracturing operation.

[0008] Chinese Patent (CN105201484A) discloses a method for selecting the optimal fracturing section and optimizing construction parameters in a vertical well. The method includes the following steps: (1) establishing a calculation method for fracture initiation and dynamic propagation coupled with seepage-stress-fracture damage; (2) initially selecting the fracturing section based on the formation stratification and reservoir properties of the oil and gas reservoir; (3) establishing a reservoir hydraulic fracturing model and selecting the optimal fracturing parameters for the first layer based on the propagation of hydraulic fractures within the reservoir; (4) calculating the fracture morphology of the upper section using the fracturing parameters of the first layer; (5) calculating the fracture morphology of the upper section under different interlayer thicknesses based on the criterion of non-interconnection between upper and lower layer fractures, and determining the interlayer thickness that can prevent interconnection between upper and lower layer fractures; (6) determining the final fracturing section and optimizing the construction parameters of the upper section. This invention takes into account the stress interference of the first fracture to the later fracture during vertical well fracturing, and avoids the interconnection of hydraulic fractures between upper and lower sections, so as to maximize the production capacity of each section. However, this invention is mainly for vertical well fracturing and cannot be used in the design of deep horizontal well fracturing.

[0009] Chinese patent (CN106555577A) provides a novel method for optimizing the conductivity of network fractures. This method can determine the required conductivity of proppant-supported main fractures and proppant-free self-supporting fractures within a network fracture structure, thus providing guidance for fracturing optimization design and forming a highly efficient supported fracture network to improve fracturing performance in shale gas and tight oil and gas reservoirs. This method primarily optimizes complex network fractures by equating them to simpler fracture bodies based on the principle of hydroelectric similarity. First, the reservoirs connected by the fracture network are equating to high-permeability zones, and the permeability of these zones is optimized using optimal production. Then, based on the principle of hydroelectric similarity, the equivalent fracture permeability is optimized. Finally, the conductivity of ceramsite-supported main fractures and self-supporting branch fractures within the network fracture structure is optimized separately, thereby providing guidance for fracturing optimization design.

[0010] None of the aforementioned patent documents disclose how to optimize the slug usage design for hydraulic fracturing of horizontal wells. Summary of the Invention

[0011] The purpose of this invention is to provide an optimized design method for the amount of slugs used in hydraulic fracturing based on the frog-leap algorithm, which aims to solve the problems of complex calculation process and long time in the traditional hydraulic fracturing design of slug quantity design.

[0012] This invention is achieved through the following technical solution: an optimization design method for hydraulic fracturing slug usage based on the frog-leapfrog algorithm. A fitness function is established based on constraints and optimization objectives, including slug usage constraints. The frog-leapfrog algorithm iteratively optimizes the optimization variables, including the fracturing fluid usage of each slug, according to the fitness function, until convergence conditions are met, thereby finding the globally optimal solution within the feasible domain of slug fracturing fluid usage.

[0013] Furthermore, a feasible solution for the amount of fracturing fluid pumped into a single slug is determined. The feasible solution refers to the combination of the allowable amount of proppant-carrying fluid and the allowable amount of displacement fluid. All feasible solutions are numbered to obtain the feasible region.

[0014] The constraints include the slug dosage constraint, which includes: 1) the total fracturing fluid dosage and the total proppant dosage constraint; 2) the proppant dosage trend constraint with the number of slugs; and 3) the slug sand-to-fluid ratio constraint.

[0015] Establish a fitness function and take avoiding sand blockage as the optimization objective: based on the maximum difference in the amount of proppant used by adjacent slugs, and introduce constraints including the slug usage constraint.

[0016] Set optimization variables: {ζ1,......,ζ} i ,......,ζ n ,c1,Δc2,......,Δc i ,......Δc n};

[0017] Where n represents the total number of slugs, ζ i The fracturing fluid quantity of the i-th slug segment is represented by the feasible solution number; the feasible solutions for fracturing fluid quantities of different slug segments may be the same or different; c1 represents the sand-to-fluid ratio of the first slug segment; Δc i This represents the difference in the sand-to-liquid ratio between the i-th segment and the (i-1)-th segment;

[0018] The frog-jumping algorithm iteratively optimizes the optimization variables based on the fitness function until the convergence condition is met, thereby finding the global optimal solution within the feasible region.

[0019] Furthermore, the constraints also include special process constraints, namely, constraints on the amount of slug-carrying fluid, the amount of slug-displaced fluid, and the slug-fluid ratio under special fracturing process conditions.

[0020] Furthermore, the special process constraints are introduced into the fitness function through a judgment function.

[0021] Furthermore, the constraints are incorporated into the fitness function through a penalty function.

[0022] Furthermore, the constraints on the total amount of fracturing fluid and proppant are as follows: both the total amount of fracturing fluid and the total amount of proppant must be within the designed allowable range.

[0023] Furthermore, the constraint on the trend of slug proppant usage with the number of slugs is as follows: the amount of proppant used in the slugs must increase with the increase of the number of slugs, that is, the amount of proppant used in the previous slug is not greater than the amount of proppant used in the next slug.

[0024] Furthermore, the slug sand-to-liquid ratio constraint condition is: the difference in sand-to-liquid ratio between two adjacent slug segments is less than the maximum allowable difference in sand-to-liquid ratio between two adjacent slug segments.

[0025] Furthermore, the special process constraints include a sand-to-liquid ratio of no more than 5% in the first section of the slug proppant to prevent sand blockage and the need for a long slug with a volume greater than 1.5 to 2 wellbore volumes in the middle section for temporary plugging.

[0026] Furthermore, the expression for the fitness function is as follows:

[0027]

[0028] In the formula, ΔV si V represents the difference in the amount of slug proppant used between the i-th and (i-1)-th slug segments, where i = 2, ..., n; λ represents the penalty function coefficient; V s V represents the total amount of proppant used. max V represents the maximum permissible amount of proppant used. nin Δc represents the minimum allowable amount of total proppant. i Δc represents the difference in the sand-to-liquid ratio between the i-th segment and the (i-1)-th segment. max This indicates the maximum permissible difference in the sand-to-liquid ratio between two adjacent slug sections; F 判断 F is a judgment function for special process constraints. If the special process constraints are satisfied, then... 判断 =0, if the special process constraints are not met, F 判断 =-1.

[0029] Furthermore, the permissible value of the sand-carrying fluid volume of a single slug is calculated based on the wellbore volume. Then, the permissible value of the displacement fluid volume corresponding to the sand-carrying fluid volume of each slug is calculated based on actual experience. Finally, the combination of the permissible value of the sand-carrying fluid and the permissible value of the displacement fluid of a single slug is obtained by brute force enumeration. This combination represents the feasible solution. All feasible solutions are numbered to obtain the feasible region.

[0030] This invention also provides an optimization design system for hydraulic fracturing slug usage based on the frog-leap algorithm, used to implement the optimization design method for hydraulic fracturing slug usage based on the frog-leap algorithm of this invention, and includes the following functional modules:

[0031] A feasible region setting module is used to number the feasible solutions to obtain the feasible region;

[0032] An optimization variable setting module is used to set the optimization variables;

[0033] A constraint setting module is used to set the constraints;

[0034] A fitness function setting module is used to set the fitness function;

[0035] The optimal solution search module is used to iteratively optimize the optimization variables using the frog leaping algorithm based on the fitness function until the convergence condition is met, thereby searching for the global optimal solution within the feasible domain of slug fracturing fluid usage.

[0036] Compared with the prior art, the beneficial effects of the present invention include:

[0037] 1. This invention uses the fracturing fluid dosage of each slug as the optimization variable. Based on constraints and optimization objectives, a fitness function is established, forming an optimization model that is easy to solve using the leapfrog algorithm. This allows the leapfrog algorithm to search for the global optimum within the feasible region, overcoming the shortcomings of existing technologies that use trial-and-error algorithms to design slug dosage, resulting in complex calculations and long computation times. Furthermore, the optimization objective can be customized as needed.

[0038] 2. This invention adopts the frog-jumping algorithm, which is easy to program and implement. The algorithm is simple in concept, requires few parameters to be adjusted, has a fast calculation speed, and has a strong global search optimization capability. This avoids the limitations of traditional experience-based slug quantity design, which is complex and time-consuming, and ensures the efficiency of hydraulic fracturing slug quantity optimization design.

[0039] 3. The optimization model provided by this invention can further optimize the slug sand-liquid ratio based on the slug usage constraint to meet the optimization objective of avoiding sand blockage.

[0040] 4. This invention also fully considers the special construction process requirements such as gel slugs and long slugs in fracturing design, providing an effective basis for the next step of optimizing the geometry of fracturing fractures. Attached Figure Description

[0041] Figure 1 A flowchart for optimizing the amount of plug used in hydraulic fracturing.

[0042] Figure 2 The graph shows the optimization process of the fitness function in Example 2. Detailed Implementation

[0043] The present invention will now be described in further detail with reference to the accompanying drawings:

[0044] The purpose of this invention is to provide an optimization design method for slug usage in hydraulic fracturing based on the frog-leapfrog algorithm. A fitness function is established based on constraints and optimization objectives, including slug usage constraints. The frog-leapfrog algorithm iteratively optimizes the optimization variables, including the fracturing fluid usage of each slug, according to the fitness function until a convergence condition is met, thereby finding the globally optimal solution within the feasible region of the slug fracturing fluid usage. This aims to solve the problems of complex and time-consuming calculation processes in traditional hydraulic fracturing design for slug usage.

[0045] The method of the present invention is implemented through a corresponding optimization design system, which includes the following functional modules:

[0046] A feasible region setting module is used to number the feasible solutions to obtain the feasible region;

[0047] An optimization variable setting module is used to set the optimization variables;

[0048] A constraint setting module is used to set the constraints;

[0049] A fitness function setting module is used to set the fitness function;

[0050] The optimal solution search module is used to iteratively optimize the optimization variables using the frog leaping algorithm based on the fitness function until the convergence condition is met, thereby searching for the global optimal solution within the feasible domain of slug fracturing fluid usage.

[0051] Example 1

[0052] This embodiment is for general hydraulic fracturing construction process, that is, it does not involve special processes.

[0053] Specifically, Example 1 is implemented as follows: Figure 1 As shown, a method for optimizing the design of hydraulic fracturing slug usage based on the frog-leapfrog algorithm is presented. This method includes:

[0054] A feasible solution is determined for the amount of fracturing fluid pumped into a single slug pump. The feasible solution is a combination of the allowable amount of proppant-carrying fluid and the allowable amount of displacement fluid. All feasible solutions are numbered to obtain the feasible region.

[0055] Specifically, the allowable value of the sand-carrying fluid volume of a single slug is calculated based on the wellbore volume. Then, the allowable value of the displacement fluid volume corresponding to the sand-carrying fluid volume of each slug is calculated based on actual experience. Then, the combination of the allowable value of the sand-carrying fluid and the allowable value of the displacement fluid of a single slug is obtained by brute force enumeration. This combination is the feasible solution. All feasible solutions are numbered to obtain the feasible region.

[0056] Define the constraints, including slug usage constraints. The slug usage constraints include:

[0057] 1) Constraints on total fracturing fluid and proppant usage: Both the total fracturing fluid and proppant usage must be within the allowable range of the design.

[0058] 2) Constraints on the trend of slug proppant usage with the number of slugs: To prevent sand plugging during fracturing, the amount of proppant used in the slugs must increase with the number of slugs, that is, the amount of proppant used in the previous slug should not be greater than the amount of proppant used in the next slug.

[0059] 3) Slug sand-to-liquid ratio constraint: In order to prevent sand plugging during fracturing, the difference in sand-to-liquid ratio between two adjacent slugs is less than the maximum allowable difference in sand-to-liquid ratio between two adjacent slugs.

[0060] Establish a fitness function: mainly to avoid sand blockage and facilitate on-site construction, the increase in the amount of proppant used in each slug should be as small as possible. Therefore, the maximum value of the difference in the amount of proppant used in adjacent slugs is used as the basis, and constraints including the aforementioned slug usage constraint are introduced.

[0061] The expression for the fitness function is as follows:

[0062]

[0063] In the formula, ΔV si V represents the difference in the amount of slug proppant used between the i-th and (i-1)-th slug segments, where i = 2, ..., n; λ represents the penalty function coefficient; V s V represents the total amount of proppant used. max V represents the maximum permissible amount of proppant used. nin Δc represents the minimum allowable amount of total proppant. i Δc represents the difference in the sand-to-liquid ratio between the i-th segment and the (i-1)-th segment. max This represents the maximum permissible difference in the sand-to-liquid ratio between two adjacent slug sections.

[0064] Set optimization variables: {ζ1,......,ζ} i ,......,ζ n ,c1,Δc2,......,Δc i ,......Δc n};

[0065] Where n represents the total number of slugs, ζ i The fracturing fluid quantity of the i-th slug segment is represented by the feasible solution number; the feasible solutions for fracturing fluid quantities of different slug segments may be the same or different; c1 represents the sand-to-fluid ratio of the first slug segment; Δc iThis represents the difference in the sand-liquid ratio between the i-th segment and the (i-1)-th segment; to facilitate the optimization of the results for on-site construction, the sand-liquid ratio is taken as an integer.

[0066] The frog-leapfrog algorithm iteratively optimizes the optimization variables based on the fitness function, while the optimization variables must satisfy the total fracturing fluid consumption constraint, until the convergence condition is met, thereby searching for the global optimal solution within the feasible region.

[0067] refer to Figure 1 As shown below, the process of solving the frog leaping algorithm will be explained in detail.

[0068] ① Initialize the population and set the parameters of the frog jumping algorithm: including the total number of frogs F, the number of subgroups N, the number of frog groups M, and satisfying F=M×N, the maximum number of searches within the frog group, the maximum number of global loops, the maximum and minimum values ​​of fracturing fluid usage within the feasible region, and initialize the parameters in the frog group through a random function.

[0069] ② Calculate and sort the fitness value of each frog (frog corresponding to the optimization variable): Substitute the value of the optimization variable generated in each iteration (the difference between the feasible solution of fracturing fluid dosage and the sand-fluid ratio) into the fitness function to calculate the fitness value of each frog in the population, and sort the fitness values ​​of the frogs in ascending order.

[0070] ③ Divide the frog population into groups according to the sorting results: put the first frog into the first group, the second frog into the second group, ... and the (M+1)th frog into the first group, that is, put the n1×M+n2 (n1=1,2,……,N-1,n1=1,2,……,M) into the n2th group.

[0071] ④ According to the rules of the frog leaping algorithm, update the worst solution in the population, that is, update the worst frog p in the population. wl Update.

[0072] ⑤ If the convergence condition is met, output the global optimal solution as the optimized design result of the hydraulic fracturing slug usage; if the convergence condition is not met, recalculate the fitness values ​​of all frogs in the population according to the fitness function and sort them, then go to step ③.

[0073] Specifically, in step ④, the worst-performing frog p in the population... wl The steps to perform the update include:

[0074] Step 4.1: Let p be the position of the best frog in the population. bl The worst-case frog position is updated, where the update strategy for the n-dimensional variable of the worst-case frog position is as follows:

[0075] p new =p wl+rand×(p bl -p wl (1)

[0076]

[0077] p new =min[ub,p] new (3)

[0078] p new =max[lb,p new (4)

[0079] In the formula, rand is a random function with a range of [0,1]; [x] is a floor function with a value not exceeding the largest integer x; u b The upper bound of the n-dimensional variable representing the worst-case frog position; l b This represents the lower bound of the n-dimensional variable representing the worst-case frog position.

[0080] Step 4.2: If the fitness value of the worst-performing frog position after the update is lower than that of the original worst-performing frog position, then replace the original worst-performing frog with the frog at the updated position and go to step ④; otherwise, use the globally optimal frog p. bw Update the worst frog in the population p wl ;

[0081] Step 4.3: If the fitness value of the worst frog position after the update is lower than the fitness value of the original worst frog, then replace the original worst frog with the frog at the updated position and go to step 4.4; otherwise, randomly generate a feasible solution within the feasible region to replace the worst frog.

[0082] Step 4.4: If the number of searches within the population reaches the maximum allowed number of searches within the population, then the search ends; otherwise, the fitness function is used to calculate the fitness value of each frog in the population and sort them in ascending order, then proceed to step 4.1.

[0083] Example 2

[0084] This embodiment targets a special fracturing process. The only difference from Embodiment 1 is the addition of specific process constraints, namely, constraints on the proppant volume, displacement fluid volume, and proppant-to-fluid ratio under these special fracturing conditions. For example, the proppant-to-fluid ratio in the first slug segment should not exceed 5% to prevent sand blockage. Additionally, a long slug with a volume greater than 1.5 to 2 wellbore volumes is needed for temporary plugging in the middle section of the well. The amount of this proppant is considered part of the total fracturing fluid usage.

[0085] Due to the addition of special process constraints, the corresponding expression for the fitness function is as follows:

[0086]

[0087] In the formula, ΔV si V represents the difference in the amount of slug proppant used between the i-th and (i-1)-th slug segments, where i = 2, ..., n; λ represents the penalty function coefficient; V s V represents the total amount of proppant used. max V represents the maximum permissible amount of proppant used. nin Δc represents the minimum allowable amount of total proppant. i Δc represents the difference in the sand-to-liquid ratio between the i-th segment and the (i-1)-th segment. max This indicates the maximum permissible difference in the sand-to-liquid ratio between two adjacent slug sections; F 判断 F is a judgment function for special process constraints. If the special process constraints are satisfied, then... 判断 =0, if the special process constraints are not met, F 判断 =-1.

[0088] To better illustrate the beneficial effects of the present invention, specific examples are provided below.

[0089] The method described in Example 2 was used to optimize the amount of proppant-carrying fluid slug used in hydraulic fracturing of XX shale gas wells, involving a total fracturing fluid volume of 690m³. 3 The total amount of proppant used is 33-34m. 3 The design specifies a total of 6 slug sections. To avoid sand blockage, the sand-to-fluid ratio (c1) of the first slug section should not exceed 4%, and the maximum sand-to-fluid ratio should not exceed 14%. To increase the lateral stimulation volume during shale gas well fracturing, a long slug section of gel fluid, equivalent to 1.5 wellbore volumes (80m³), needs to be installed in the middle. 3 ).

[0090] The computational parameters of the frog leapfrog algorithm are: population size of 40, number of individuals in the population of 40, and convergence conditions: maximum number of searches in the population of 25 and maximum number of searches globally of 100.

[0091] To facilitate subsequent design optimization, the allowable value of the sand-carrying fluid volume of the slugs was calculated based on the wellbore volume, and then the allowable value of the displacement fluid volume corresponding to the sand-carrying fluid volume of each slug was calculated based on actual experience. The results are shown in Table 1.

[0092] Table 1 Combination of Plugging Sand Fluid and Displacement Fluid Volumes

[0093]

[0094]

[0095] Using the brute-force enumeration method, there are 48 feasible solutions for the combination of slug-carrying fluid and displacement fluid. The different combinations are numbered, and the results are shown in Table 2.

[0096] Table 2. Numbering of Sectional Plugging Sand Fluid and Displacement Fluid Volume Groups

[0097]

[0098]

[0099] Therefore, the variables for optimization are identified as follows:

[0100] {ζ1,ζ2,ζ3,ζ4,ζ5,ζ6,c1,Δc2,Δc3,Δc4,Δc5,Δc6} (5)

[0101] In the formula, ξ i The combination number of the carrying fluid and displacement fluid in the i-th slug is denoted by ; c1 is the sand-to-fluid ratio of the first slug, %; Δc i It represents the difference in the sand-liquid ratio between the i-th slug and the (i-1)-th slug.

[0102] According to the design requirements, the following process constraints must be met in the design:

[0103]

[0104] V2, V3, and V4 refer to the amount of fracturing fluid used in the second, third, and fourth slugs, respectively.

[0105] Therefore, the fitness function is established as follows:

[0106] f = max(ΔV) si )+λ×(max((V s -V max ),0)+max((V min -V s ),0)

[0107] +∑max(ΔV s ,0)+∑max(Δc i -Δc max ,0)+ (7)

[0108] ∑max(c1-4,0)+∑max(max(c i )-14,0))

[0109] The following example, using a feasible solution within the domain during the iteration process, illustrates the calculation process of the fitness function.

[0110] A feasible solution within the domain is: {20,20,19,20,19,19,2,1,1,1,1,1}. Based on Table 2, the volume of sand-carrying fluid and displacement fluid for each slug can be obtained. Based on the feasible solution and the sand slug data within the slugs (including the number of slugs and the length of each slug), the sand-to-fluid ratio for each slug can be obtained. Therefore, the pump sequence corresponding to the feasible solution can be derived, as shown in Table 3.

[0111] Table 3. Slug Fracturing Fluid Usage

[0112]

[0113] Substituting it into equation (8), we can obtain the fitness value of the feasible solution calculated by the fitness function.

[0114] Building upon this, we continue searching for the global optimum using the frog-leaping algorithm. The optimization process of the fitness function is as follows: Figure 2 As shown, after 100 global maximum searches, the fitness tends to stabilize and remains at 2.3, and the corresponding pump sequence is shown in Table 4. The optimization results are shown in the figure.

[0115] Table 4. Slug Fracturing Fluid Dosage

[0116]

[0117]

[0118] The above technical solution is only one embodiment of the present invention. For those skilled in the art, based on the principles disclosed in the present invention, it is easy to make various types of improvements or modifications, and not limited to the technical solutions described in the specific embodiments of the present invention. Therefore, the foregoing description is only a preferred option and is not restrictive.

Claims

1. An optimization design method for the amount of hydraulic fracturing slugs based on the frog-leapfrog algorithm, characterized in that, Includes the following steps: A feasible solution is determined for the amount of fracturing fluid pumped into a single slug. The feasible solution is a combination of the allowable amount of proppant-carrying fluid and the allowable amount of displacement fluid for a single slug. All feasible solutions are numbered to obtain the feasible region. The constraints include the slug usage constraint, which includes: 1) the total fracturing fluid usage and total proppant usage constraint; 2) the proppant usage trend with the number of slugs constraint; and 3) the slug sand-to-fluid ratio constraint. A fitness function is established based on constraints and an optimization objective, with sand blockage as the optimization objective: the maximum difference in proppant usage between adjacent slugs is used as the basis, and constraints including the slug usage constraint are introduced; the constraints are incorporated into the fitness function through a penalty function, and the expression of the fitness function is as follows: ； In the formula, Indicates the first Section and the The difference in the amount of proppant used in the segment plugs ; Indicates the coefficients of the penalty function; This indicates the total amount of proppant used. This indicates the maximum permissible amount of proppant used. This indicates the minimum permissible amount of total proppant. Indicates the first Section and the The difference in the ratio of sand to liquid in each segment of the plug. This represents the maximum permissible difference in the sand-to-liquid ratio between two adjacent slug sections; This is a judgment function for special process constraints. If the special process constraints are satisfied, ... If the special process constraints are not met, ; Set optimization variables: The optimization variables include the amount of fracturing fluid used in each slug plug segment; in, Indicates the total number of blocks. Indicates the first The feasible solution number for the fracturing fluid dosage of different slugs; the feasible solutions for the fracturing fluid dosage of different slugs may be the same or different. This indicates the sand-to-liquid ratio of the first slug. Indicates the first Section and the The difference in the ratio of sand to liquid in each segment; The frog-leapfrog algorithm iteratively optimizes the optimization variables based on the fitness function until the convergence condition is met, thereby finding the global optimal solution within the feasible domain of slug fracturing fluid usage.

2. The method for optimizing the design of hydraulic fracturing slug usage based on the frog-leapfrog algorithm according to claim 1, characterized in that, The constraints also include special process constraints, namely, constraints on the amount of slug-carrying fluid, the amount of slug-displaced fluid, and the slug-fluid ratio under special fracturing process conditions.

3. The method for optimizing the design of hydraulic fracturing slug usage based on the frog-leapfrog algorithm according to claim 2, characterized in that, The special process constraints are introduced into the fitness function through a decision function.

4. The method for optimizing the design of hydraulic fracturing slug usage based on the frog-leapfrog algorithm according to claim 2, characterized in that, Constraints on total fracturing fluid and proppant usage: Both total fracturing fluid and total proppant usage must be within the allowable range specified in the design.

5. The method for optimizing the design of hydraulic fracturing slug usage based on the frog-leapfrog algorithm according to claim 2, characterized in that, Segment proppant usage trend constraint with increasing segment number: The amount of proppant used in a segment must increase with the increase of the number of segments, that is, the amount of proppant used in the previous segment is not greater than the amount of proppant used in the next segment.

6. The method for optimizing the design of hydraulic fracturing slug usage based on the frog-leapfrog algorithm according to claim 2, characterized in that, Slug sand-liquid ratio constraint: The difference in sand-liquid ratio between two adjacent slug segments is less than the maximum allowable difference in sand-liquid ratio between two adjacent slug segments.

7. The method for optimizing the design of hydraulic fracturing slug usage based on the frog-leapfrog algorithm according to claim 2, characterized in that, The special process constraints include a sand-to-liquid ratio of no more than 5% in the first slug proppant section to prevent sand blockage, and the need for a long slug with a volume greater than 1.5 to 2 wellbore volumes in the middle section for temporary plugging.

8. The method for optimizing the design of hydraulic fracturing slug usage based on the frog-leapfrog algorithm according to claim 1, characterized in that, The permissible value of the sand-carrying fluid volume of a single slug is calculated based on the wellbore volume. Then, the permissible value of the displacement fluid volume corresponding to the sand-carrying fluid volume of each slug is calculated based on actual experience. Finally, the combination of the permissible value of the sand-carrying fluid and the permissible value of the displacement fluid of a single slug is obtained by brute force enumeration. This combination represents the feasible solution. All feasible solutions are numbered to obtain the feasible region.

9. An optimization design system for hydraulic fracturing slug usage based on the frog-leapfrog algorithm, characterized in that, This method is used to implement the optimized design method for hydraulic fracturing slug usage based on the frog-leap algorithm as described in any one of claims 1 to 8, and includes the following functional modules: The feasible region setting module is used to number the feasible solutions to obtain the feasible region. The feasible solution refers to the combination of the allowable amount of sand-carrying fluid and the allowable amount of displacement fluid for a single slug. An optimization variable setting module is used to set the optimization variables; A constraint setting module is used to set the constraints; A fitness function setting module is used to set the fitness function; The optimal solution search module is used to iteratively optimize the optimization variables using the frog leaping algorithm based on the fitness function until the convergence condition is met, thereby searching for the global optimal solution within the feasible domain of slug fracturing fluid usage.

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