Multi-particle-size proppant conveying numerical simulation method based on group balance model

Abstract

The invention relates to a multi-particle-size proppant conveying numerical simulation method based on a group equilibrium model. The method comprises the following steps: establishing a solid-liquid multiphase flow mathematical model capable of describing particle size-speed distribution of proppant particles in combination with the group equilibrium model and a two-fluid model; closing the constructed solid-liquid multiphase flow mathematical model by adopting a moment integral method, establishing a discrete numerical model, and implanting the discrete numerical model into an open source code library OpenFOAM; taking a certain amount of proppant samples for particle size screen analysis, and counting the proportion of the proppant in each particle size section in the total screen analysis sample as an analog input parameter; an engineering scale fracture grid model is established based on a structured grid subdivision method, and proppant conveying numerical simulation is carried out after boundaries of the grid model and a numerical model are defined and initial values are assigned to the grid model and the numerical model. According to the method, the distribution characteristics of the proppant particles with different particle sizes and movement speeds are described by introducing the group equilibrium equation, the polydispersity characteristic of the proppant particles in dense solid-liquid multiphase flow is captured, and the calculation precision and the calculation efficiency are improved.

Description

Technical Field

[0001] The invention relates to the field of oil and gas field development engineering, and in particular to a multi-particle size proppant transportation numerical simulation method based on a population balance model. Background Art

[0002] During hydraulic fracturing, a large amount of proppant particles are mixed with fracturing fluid and injected into the formation fracture system. Under the action of high-pressure fluid flow, the proppant undergoes dynamic processes such as suspension migration and sedimentation accumulation, and finally forms a diverse spatial distribution pattern in the fracture, thereby maintaining the fracture open state and optimizing the oil and gas flow path and efficiency. Therefore, the proppant delivery link is directly related to the fracturing construction effect and oil and gas field production. The proppant entering the fracture has a distinct particle size distribution feature (such as 40 to 70 mesh or 70 to 140 mesh distribution, etc.). These particles of different particle sizes are closely mixed with the fracturing fluid, together forming a complex dense solid-liquid multiphase flow system. This system is a typical polydisperse system in fluid mechanics, and the diverse particle size distribution of particles further increases the complexity and dynamic behavior of the system.

[0003] Through indoor experiments, the transport behavior of multi-size proppants in narrow spaces can be intuitively explored, but the experimental equipment is often limited by its physical size in length and height, the experimental observation range and recording process are limited, and the experimental results are difficult to extrapolate. Therefore, indoor experimental research is not suitable for in-depth analysis of the long-distance migration and sedimentation laws of proppants in engineering-scale fractures. Methods represented by cutting-edge numerical technologies such as computational fluid dynamics-discrete element coupling method and multiphase particle grid method have shown excellent ability in capturing the fine characteristics of proppant particle size distribution and can track the movement trajectory of particles or particle clusters in complex flow environments. However, due to the inherent characteristics of their algorithm design, there are limitations when using them to deal with large-scale systems or extreme simulation scales. The Euler method based on the continuous medium assumption describes the transport process of proppant in fractures through the spatiotemporal evolution characteristics of solid phase particle concentration. It is particularly suitable for efficiently analyzing the flow and distribution laws of proppant in engineering-scale fractures, and provides a strong theoretical support and analysis tool for fracturing pump design and optimization. However, at present, such methods cannot capture the particle size distribution characteristics of proppant well, affecting the reliability of simulation results.

[0004] The population equilibrium model is used to describe the flow, aggregation, breakage and even phase change of macroscopic particles with different particle properties (such as particle size, velocity, etc.). It is widely used in the simulation of gas-liquid (such as bubbly flow) or gas-solid (such as fluidized bed) multiphase flow. However, it has not yet been fully introduced and applied to dense solid-liquid multiphase flow systems and polydisperse systems that specifically focus on particle agglomeration phenomena. Summary of the invention

[0005] In order to overcome the problems in the prior art, the present invention provides a numerical simulation method for multi-size proppant transport based on a population equilibrium model. To achieve the above purpose, the present invention provides the following scheme:

[0006] A method for numerically simulating the transport of multi-size proppants based on a population equilibrium model comprises the following steps:

[0007] S1. Combine the population equilibrium model and the two-fluid model to establish a solid-liquid multiphase flow mathematical model that can describe the proppant particle size-velocity distribution;

[0008] S2, using the moment integration method to close the solid-liquid multiphase flow mathematical model constructed in step S1, establish a discrete numerical model and embed it into the open source code library OpenFOAM;

[0009] S3, taking a certain amount of proppant sample for particle size screening, and calculating the proportion of proppant in each particle size segment in the total screening sample as the simulation input parameter;

[0010] S4. An engineering-scale fracture grid model is established based on the structured grid generation method. After defining the boundaries and assigning initial values ​​to the grid model and numerical model, a numerical simulation of proppant transport is performed.

[0011] A further technical solution is that the population equilibrium equation (PBE equation) in step S1 does not consider the particle aggregation, fragmentation and phase change process, and its expression is as follows:

[0012]

[0013] Where: n d is the particle number distribution function; ξ is the set of particle attributes (such as particle size d, velocity v, etc.); t is time; U d is the average velocity of the particle phase; G d is the drift rate.

[0014] A further technical solution is that the population equilibrium equation (PBE equation) in step S1 only considers two attribute variables, namely, the particle size and the velocity of the proppant, and assumes that particles of the same particle size have the same velocity, then the particle number distribution function n d Expressed as particle size-velocity joint distribution function f d , which is expressed as follows:

[0015]

[0016] Where: x is the position vector of a particle; v is the velocity of a particle; δ is the Dirac function; there are N integration nodes, and the proportion of particles at the p node to the total particles is w p , d is the particle size of a certain particle, d p is the particle size at node p.

[0017] A further technical solution is that the solid phase friction viscosity closed model in the TFM in step S1 takes into account the wet particle stacking cohesion, and its expression is as follows:

[0018]

[0019] Where: μ d,f is the solid friction viscosity; p d,f is the solid phase pressure; p d,c is the critical solid phase pressure; is the internal friction angle of the particles, which is 28.5°; S d is the solid phase shear rate; Θ is the particle temperature; n is the yield surface shape factor; c is the wet particle stacking cohesion, which is 2 kPa.

[0020] A further technical solution is that in step S2, the moment integral method is used to obtain the joint distribution function f d The k- and k+1-order moment balance equations are expressed as follows:

[0021]

[0022] Where k represents the kth order; U is the particle velocity.

[0023] A further technical solution is that the drag force between the solid and liquid phases in step S2 is obtained by summing the drag forces of each integration node, and its expression is as follows:

[0024]

[0025] Where: subscripts l,p and d,p refer to the liquid phase and particle phase at the p node respectively; F D,d is the total drag force; F D,d,p is the drag force at the p node; β l-d,p is the momentum exchange coefficient between the liquid phase and the particle at the p node; U is the average phase motion velocity; α d is the total solid fraction; ρ is the density; C D,p is the drag coefficient at the p node, Re p is the particle Reynolds number at the p node, and h is the distance from the particle to the crack wall.

[0026] A further technical solution is that the masses of the proppant of each particle size segment and the total sieve analysis sample in step S3 are tested after being dried at 40° C. for 15 minutes.

[0027] On the other hand, the present invention provides a multi-size proppant transport numerical simulation system based on a population equilibrium model, comprising the following modules:

[0028] A mathematical model building module is used to combine the population equilibrium model and the two-fluid model to build a solid-liquid multiphase flow mathematical model that can describe the proppant particle size-velocity distribution;

[0029] A discrete numerical model building module is used to close the solid-liquid multiphase flow mathematical model constructed in step S1 using a moment integration method, build a discrete numerical model and embed it into the open source code library OpenFOAM;

[0030] The simulation input parameter acquisition module is used to take a certain amount of proppant sample for particle size screening and calculate the proportion of proppant in each particle size segment in the total screening sample as the simulation input parameter;

[0031] For numerical simulation, an engineering-scale fracture grid model is established based on the structured grid generation method. After defining the boundaries and assigning initial values ​​to the grid model and numerical model, the proppant transport numerical simulation is carried out.

[0032] On the other hand, the present invention provides a computer device, comprising a memory, a processor, and a computer program stored in the memory and running on the processor, characterized in that when the processor executes the computer program, the steps of the multi-size proppant transport numerical simulation method described in any one of the above claims are implemented.

[0033] On the other hand, the present invention provides 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 multi-size proppant transport numerical simulation method described in any one of the above claims are implemented.

[0034] The present invention has the following advantages: the present invention provides a numerical simulation method for multi-particle size proppant transport based on a population balance model, which describes the distribution characteristics of proppant particles with different particle sizes and movement speeds by introducing a population balance equation, captures the polydisperse characteristics of proppant particles in dense solid-liquid multiphase flow, and considers the influence of wet particle stacking cohesion in the mathematical model, thereby further improving the calculation accuracy and efficiency compared with the simulation method in the prior art. BRIEF DESCRIPTION OF THE DRAWINGS

[0035] In order to more clearly illustrate the embodiments of the present invention or the technical solutions in the prior art, the drawings required for use in the embodiments will be briefly introduced below. Obviously, the drawings described below are only some embodiments of the present invention. For ordinary technicians in this field, other drawings can be obtained based on these drawings without paying creative labor.

[0036] Figure 1 It is a schematic diagram of the method flow of the present invention;

[0037] Figure 2It is a bar chart showing the particle size screening results of the proppant sample in the embodiment of the present invention;

[0038] Figure 3 This is a numerical simulation diagram of proppant transport in an embodiment of the present invention. DETAILED DESCRIPTION

[0039] The following will be combined with the drawings in the embodiments of the present invention to clearly and completely describe the technical solutions in the embodiments of the present invention. Obviously, the described embodiments are only part of the embodiments of the present invention, not all of the embodiments. Based on the embodiments of the present invention, all other embodiments obtained by ordinary technicians in this field without creative work are within the scope of protection of the present invention.

[0040] The object of the present invention is to provide a numerical simulation method for multi-size proppant transport based on a population equilibrium model. In order to make the above-mentioned objects, features and advantages of the present invention more obvious and easy to understand, the present invention is further described in detail below with reference to the accompanying drawings and specific implementation methods.

[0041] In the prior art, the two-fluid model is used to simulate the flow law of engineering-scale granular flow, but it cannot take into account the particle size distribution characteristics of the particles and cannot capture the polydispersity characteristics of the particle system. In addition, the solid-phase friction viscosity closed model in the TFM model should consider the stacking characteristics of wet particles. Therefore, the performance of proppant transport simulation based on the Euler method needs to be improved in terms of calculation accuracy and efficiency.

[0042] Based on this, Figure 1 As shown, the present invention provides a multi-size proppant transport numerical simulation method based on a population equilibrium model, comprising the following steps:

[0043] S1. Combine the population equilibrium model and the two-fluid model to establish a solid-liquid multiphase flow mathematical model that can describe the proppant particle size-velocity distribution;

[0044] Specifically, without considering the extrusion of the fracture wall on the proppant, there is no particle aggregation, crushing and phase change during the proppant transportation process, and the expression of the population balance equation is as follows:

[0045]

[0046] Specifically, considering only two attribute variables, proppant size and velocity, and assuming that particles of the same size have the same velocity, the particle size-velocity joint distribution function f d The expression is as follows:

[0047]

[0048] Specifically, the solid-phase friction viscosity closed model takes into account the cohesion of wet particle stacking. The internal friction angle and cohesion of wet particle stacking are 28.5° and 2000Pa, respectively, and the expressions are as follows:

[0049]

[0050] S2, using the moment integration method to close the solid-liquid multiphase flow mathematical model constructed in step S1, establish a discrete numerical model and embed it into the open source code library OpenFOAM;

[0051] Specifically, the moment integral method is used to obtain the joint distribution function f d The k- and k+1-order moment balance equations are expressed as follows:

[0052]

[0053] Specifically, the drag force between the solid and liquid phases is obtained by summing the drag forces at each integration node, and its expression is as follows:

[0054]

[0055] S3, taking a certain amount of proppant sample for particle size screening, and calculating the proportion of proppant in each particle size segment in the total screening sample as the simulation input parameter;

[0056] Specifically, before sieving, the 70 / 140 mesh proppant sample was dried at 40°C for 15 minutes, and the total mass of the dried sample was weighed before sieving. The proppant components after sieving were dried at 40°C for 15 minutes, and the mass of the proppant components was weighed. The statistical results are as follows: Figure 2 The proportion of proppant of each particle size is determined by the ratio of the mass of each component proppant to the total mass of the sample.

[0057] S4. An engineering-scale fracture grid model is established based on the structured grid generation method. After defining the boundaries and assigning initial values ​​to the grid model and numerical model, a numerical simulation of proppant transport is performed.

[0058] Specifically, the delivery displacement is set to 16m 3 / min, the viscosity of the fracturing fluid is 20mPa·s, and the proppant concentration is assigned according to the step-type sand concentration design in the actual fracturing design; the population equilibrium model in the calculation provides the p-node solid fraction α for the solution of the two-fluid model d,p , particle size d p and the average solid velocity U p The two-fluid model provides the solid phase average velocity U for solving the population equilibrium model. d and interface mass transfer rate, the simulation results at a certain moment are as follows Figure 3 shown.

[0059] It can be seen that the multi-size proppant transport numerical simulation method in the present invention introduces a population balance equation, wherein the population balance equation can describe the distribution characteristics of proppant particles with different particle sizes and movement speeds, thereby capturing the polydisperse characteristics of proppant particles in dense solid-liquid multiphase flow. In addition, the influence of the stacking cohesion of wet particles is considered in the mathematical model, which further improves the calculation accuracy and efficiency compared with the simulation method in the prior art.

[0060] Although the embodiments of the present invention have been described in conjunction with the accompanying drawings, those skilled in the art may make various modifications and variations without departing from the spirit and scope of the present invention, and such modifications and variations are all within the scope defined by the appended claims.

Claims

1. A numerical simulation method for multi-size proppant transport based on a population equilibrium model, characterized in that: The following steps are involved: S1. Combine the population equilibrium model and the two-fluid model to establish a solid-liquid multiphase flow mathematical model that can describe the proppant particle size-velocity distribution; S2, using the moment integration method to close the solid-liquid multiphase flow mathematical model constructed in step S1, establish a discrete numerical model and embed it into the open source code library OpenFOAM; S3, taking a certain amount of proppant sample for particle size screening, and calculating the proportion of proppant in each particle size segment in the total screening sample as the simulation input parameter; S4. An engineering-scale fracture grid model is established based on the structured grid generation method. After defining the boundaries and assigning initial values ​​to the grid model and numerical model, a numerical simulation of proppant transport is performed.

2. According to the numerical simulation method for multi-size proppant transport according to claim 1, the population equilibrium model in step S1 does not consider particle aggregation, crushing and phase change processes.

3. The method for numerical simulation of proppant transport with multiple particle sizes according to claim 1, wherein the population equilibrium model in step S1 only considers two attribute variables, particle size and velocity, and assumes that particles of the same particle size have the same velocity, then the particle number distribution function n d Expressed as particle size-velocity joint distribution function f d .

4. According to the multi-size proppant transport numerical simulation method of claim 1, the solid-phase friction viscosity closed model in the two-fluid model takes into account the influence of the wet particle stacking cohesion.

5. The method for numerical simulation of multi-size proppant transport according to claim 1, wherein the step S2 uses the moment integral method to obtain the joint distribution function f d The k- and k+1-order moment balance equations are expressed as follows: Where k represents the kth order; U is the particle velocity.

6. The method for numerical simulation of multi-size proppant transport according to claim 1, wherein the step S2 further comprises obtaining the drag force between the solid and liquid phases by summing the drag forces at each integration node.

7. The method for numerical simulation of multi-size proppant transport according to claim 1, wherein the masses of the proppant in each size segment and the total sieve analysis sample in step S3 are tested after being dried at 40°C for 15 minutes.

8. A numerical simulation system for multi-size proppant delivery based on a population equilibrium model, comprising the following modules: A mathematical model building module is used to combine the population equilibrium model and the two-fluid model to build a solid-liquid multiphase flow mathematical model that can describe the proppant particle size-velocity distribution; A discrete numerical model building module is used to close the solid-liquid multiphase flow mathematical model constructed in step S1 using a moment integration method, build a discrete numerical model and embed it into the open source code library OpenFOAM; The simulation input parameter acquisition module is used to take a certain amount of proppant sample for particle size screening and calculate the proportion of proppant in each particle size segment in the total screening sample as the simulation input parameter; For numerical simulation, an engineering-scale fracture grid model is established based on the structured grid generation method. After defining the boundaries and assigning initial values ​​to the grid model and numerical model, the proppant transport numerical simulation is carried out.

9. A computer device comprising a memory, a processor, and a computer program stored in the memory and running on the processor, characterized in that: When the processor executes the computer program, the steps of the multi-size proppant transport numerical simulation method described in any one of claims 1 to 8 are implemented.

10. 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 multi-size proppant transport numerical simulation method described in any one of claims 1 to 8 are implemented.

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