Horizontal well perforation inter-cluster proppant distribution prediction method

Abstract

The invention relates to the technical field of propping agent migration in a horizontal shaft, in particular to a method for predicting distribution of a propping agent between perforation clusters of a horizontal well, which is used for constructing a mathematical model for migration of the propping agent in the horizontal well under the condition of considering two-phase flow of complex particles in multi-cluster perforation of the horizontal well. Performing liquid-particle control equation numerical iteration solution on the model to obtain a proppant distribution result between perforation clusters of the horizontal well; and testing the horizontal wellbore model through a physical experiment, and proofreading a proppant distribution result in the horizontal wellbore. And construction parameters can be input into the model to obtain a distribution result of the proppant among the clusters, so that the problem of quantitatively evaluating the distribution condition of the proppant according to actual shaft configuration is solved.

Description

Technical Field

[0001] The invention relates to the technical field of wellbore proppant prediction, and in particular to a method for predicting proppant distribution between perforation clusters of a horizontal well. Background Art

[0002] In oil and gas production, multi-cluster fracturing in horizontal wells is a key technology for the efficient development of low-permeability or unconventional oil and gas resources. After the target reservoir is opened with conductive fractures, in order to prevent the fractures from closing, a liquid containing proppant is usually pumped into the wellbore and flows into the hydraulic fractures through perforations to maintain the reservoir conductivity and achieve oil and gas production increase.

[0003] In the actual fracturing process, proppant pumping is affected by the properties of particles and fluids, construction parameters, wellbore configuration, etc., and is often unevenly distributed among perforation clusters in horizontal wells. Some fractures lose their conductivity, resulting in large differences in production between fracturing sections. Most perforation clusters contribute little to production. Therefore, uniform distribution of proppant in each cluster is the main goal of optimizing fracturing parameters and increasing the production of each cluster. Since the mixed sand fluid is pumped at high pressure and speed during field construction, the existing fiber optic monitoring technology can monitor the amount of fluid entering, but the distribution of sand between clusters is not clear. At the same time, ground experiments are costly, and there is a lack of effective connection between indoor experiments and actual field production. Therefore, it is a huge challenge to study the transport behavior and distribution characteristics of proppants through laboratory experiments. At present, there is still a lack of an effective model to quantitatively evaluate the distribution of proppants based on actual wellbore configuration.

[0004] In view of the above problems, a proppant distribution prediction model between perforation clusters in horizontal wells is proposed. Considering the complex particle two-phase flow in multi-cluster perforation in horizontal wells, a mathematical model of proppant migration in horizontal wellbore is established. The equations of the proppant migration model involving liquid and particles are numerically solved to obtain the cluster distribution results. Then, the proppant distribution between each perforation cluster is quantified, which can provide a basis for the optimization of field fracturing parameters according to different field conditions. Summary of the invention

[0005] The purpose of the present invention is to provide a method for predicting proppant distribution between perforation clusters in a horizontal well, aiming to solve the problem of quantitatively evaluating the distribution of proppant according to the actual wellbore configuration.

[0006] To achieve the above object, the present invention provides a method for predicting proppant distribution between perforation clusters in a horizontal well, comprising the following steps:

[0007] A mathematical model of proppant migration in horizontal wellbore is established considering the complex particle two-phase flow in multi-cluster perforation of horizontal well.

[0008] The equations of the proppant transport model involving liquid and particles are solved by discretizing the continuity equations and performing numerical iterations;

[0009] Analyze and process the solution data to calculate the distribution of proppants between different clusters in the horizontal wellbore;

[0010] The horizontal wellbore proppant migration model is tested by physical experiments to calibrate the proppant distribution results between horizontal well clusters.

[0011] Among them, a mathematical model of proppant migration in horizontal wellbore was established by considering the complex particle two-phase flow in multi-cluster perforation of horizontal wells, including:

[0012] The fluid control equation and the particle control equation are constructed by bringing the Euler-Lagrangian model into the field wellbore parameters and the perforation parameters.

[0013] The equations of the proppant migration model involving liquid and particles are solved by discretizing the continuity equation and performing numerical iteration.

[0014] The analysis and processing of the solution result data to calculate the distribution of proppants between different clusters in the horizontal wellbore includes:

[0015] Use the key parameters that need to be considered in the actual application of the proppant distribution prediction model, and narrow down the parameters through actual conditions;

[0016] Using laboratory equipment and simulation devices, conduct indoor physical experiments to obtain the distribution of proppant under different conditions;

[0017] The physical experimental data were compared with the proppant distribution results in the horizontal wellbore to verify the accuracy and reliability of the horizontal wellbore model.

[0018] The solution data are analyzed and processed to calculate the distribution of proppants between different clusters in the horizontal wellbore.

[0019] The present invention relates to the technical field of proppant migration in horizontal wellbores, and specifically to a method for predicting proppant distribution between perforation clusters in horizontal wells. A mathematical model of proppant migration in horizontal wells is constructed under the condition of complex particle two-phase flow in multi-cluster perforation in horizontal wells. The model is numerically iteratively solved for liquid-particle control equations to obtain proppant distribution results between perforation clusters in horizontal wells; the horizontal wellbore model is tested by physical experiments to calibrate the proppant distribution results in the horizontal wellbore. Construction parameters can be input into the model to obtain the distribution results of proppant between clusters, which solves the problem of quantitatively evaluating the distribution of proppant based on actual wellbore configuration. BRIEF DESCRIPTION OF THE DRAWINGS

[0020] 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 or the description of the prior art 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 work.

[0021] Figure 1 The present invention provides a flowchart of a method for predicting proppant distribution among horizontal well perforation clusters.

[0022] Figure 2 Schematic diagram of proppant migration in a horizontal well.

[0023] Figure 3 This is the process intention of a method for predicting proppant distribution between horizontal well perforation clusters provided by the present invention. DETAILED DESCRIPTION

[0024] Embodiments of the present invention are described in detail below, examples of which are shown in the accompanying drawings, wherein the same or similar reference numerals throughout represent the same or similar elements or elements having the same or similar functions. The embodiments described below with reference to the accompanying drawings are exemplary and are intended to be used to explain the present invention, and should not be construed as limiting the present invention.

[0025] See also Figures 1 to 3 The present invention provides a method for predicting proppant distribution between perforation clusters in a horizontal well, comprising the following steps:

[0026] S1 established a mathematical model of proppant migration in horizontal wellbore by considering the complex particle two-phase flow in multi-cluster perforation of horizontal wells;

[0027] Specifically,

[0028] The proppant migration model described in S11 is intended to accurately describe the movement of proppant in fluid, taking into account the contact between particles, the various forces of fluid on particles, and the corresponding reaction forces.

[0029] The continuity equation and momentum conservation equation for the fluid phase are as follows:

[0030]

[0031] The force exerted by the particle on the fluid is Fp,

[0032]

[0033] Where U is the velocity of the fluid (m / s); αf is the volume fraction of liquid; p is the fluid pressure shared by the solid phase (Pa); τ is the viscous stress tensor; g is the gravity (m / s2); ρf is the fluid density (kg / m3); vf is the velocity of the fluid (m / s); vp is the velocity of the particle (m / s); and Fp is the force exerted by the particle on the fluid (N).

[0034] Particle phase governing equation:

[0035]

[0036] Where mb is the particle mass (kg); vp is the particle velocity (m / s); ωp is the particle angular velocity (rad / s); Fc is the particle-particle and particle-wall contact force (N); Fd is the drag force (N); FSaff is the shear lift (N); FMag is the rotational lift (N); Fvm is the virtual mass force (N); Fpf is the pressure gradient force (N); FBas is the viscous force (N); I is the moment of inertia of the particle (kg·m2); Tc is the contact torque (N·m); Tf is the torque caused by the fluid (N·m).

[0037] Adopt the drag force model proposed by Di Felice:

[0038]

[0039] The Saffman lift is caused by the shear motion of the fluid, which does not rotate but is subject to lateral lift, expressed as:

[0040]

[0041] ω f =▽×U

[0042]

[0043]

[0044] The particle migration process in the horizontal wellbore is complex. In the fluid with vortex, the Magus force caused by the sphere rotation and vorticity cannot be ignored, which is expressed as:

[0045]

[0046] ω=0.5▽×U-ω b

[0047] When a particle enters a perforation, a large velocity change occurs and the instantaneous acceleration can be of large magnitude. In this case, the Basset force and the virtual mass force are essential in the modeling framework. The virtual mass force is caused by the fluid phase acceleration surrounding the sphere and is expressed as:

[0048]

[0049] Due to the viscosity effect of the fluid, its instantaneous flow field is not only related to the conditions at that time, but also to the motion state of the particles before that. The Basset force is given by the following formula:

[0050]

[0051] Torque of the fluid on the particle:

[0052]

[0053] ρf is the fluid density (kg / m3); Cd is the drag coefficient of the fluid; db is the particle diameter (mm); Rep,a is the particle Reynolds number used to calculate the drag force; μf is the fluid viscosity (mPa·s); ωf is the fluid rotation speed (rad / s); Rep is the Saffman lift Reynolds number; Csaff is the Saffman lift coefficient; CMag is the Magnus lift coefficient; Rec is the particle rotation Reynolds number; ωb is the particle angular velocity (rad / s); Vb is the volume of the sphere (m3); CR is the particle rotation torque coefficient.

[0054] S2 solves the equations of the proppant migration model involving liquid and particles by discretizing the continuity equations and performing numerical iterations;

[0055] Specifically,

[0056] Numerical iterative solution process:

[0057] First, initialize, given the initial fluid velocity field, particle velocity field, and particle position, and perform the following steps for each time step:

[0058] 1. Fluid velocity field prediction:

[0059] The prediction of the fluid velocity field can be based on the time discretization of the incompressible Navier-Stokes equations. The discretization is performed using the Euler method, and the discretization form is as follows:

[0060]

[0061] U * is the predicted fluid velocity field (without considering the influence of particles); U n is the fluid velocity field of the previous time step; Δt is the time step; p n is the pressure field of the previous time step; ν f is the kinematic viscosity; ▽ is the gradient operator; is the external force on the fluid in the previous time step

[0062] 2. Calculate the force on particles:

[0063] Calculate the forces acting on particles, including fluid resistance, interactions between particles, etc.

[0064]

[0065] is the total force on the particle in the previous time step; is the drag force of the fluid on the particles in the previous time step; is the viscous force in the previous time step; is the imaginary mass force of the previous time step (N); is the rotation lift for the previous time step (N); is the shear lift in the previous time step; is the particle-particle and particle-wall interaction force at the previous time (N)

[0066] 3. Particle speed update:

[0067] Based on the force on the particle, use Newton's second law to update the particle velocity:

[0068]

[0069] v n+1 is the velocity of the particle in the next time step; v n is the velocity of the particle in the previous time step; is the position of the particle at the next time step; is the particle position at the previous time step

[0070] 4. Correction of fluid velocity field

[0071] The corrected particle velocity is introduced into the corrected fluid velocity field to obtain the corrected fluid velocity field

[0072]

[0073] U n+1 is the corrected fluid velocity field;

[0074] 5. Pressure correction and coupling

[0075] The corrected pressure field is calculated using the corrected fluid velocity field to satisfy the mass conservation equation for the incompressible fluid;

[0076] ▽ · U n+1 =0

[0077]

[0078] Use the corrected pressure field to correct the fluid velocity field to ensure the coupling relationship between velocity and pressure;

[0079]

[0080] p n+1 is the pressure field for the next time step

[0081] 6. Time step update

[0082] Update the time step. If the simulation end time has not been reached, return to step 1 and continue iterating.

[0083] t n+1 =t n +Δt

[0084] t n+1 is the time of the next time step; t n The time of the current time step; Δt time step;

[0085] S3 analyzes and processes the solution result data and calculates the distribution of proppants between different clusters in the horizontal wellbore;

[0086] Specifically,

[0087] Calculation of proppant distribution results among clusters:

[0088] 1. Solution Data Preprocessing

[0089] The solution obtains the results of particle motion, including information such as particle position and fluid velocity. Check whether there are outliers, missing values, or unreasonable data in the solution. Clear or repair these problems to ensure the accuracy of subsequent calculations. Depending on the actual situation of the problem, some data points may need to be excluded, such as data points where the particle position is outside the hole boundary or data points where the fluid velocity is too small.

[0090] 2. Perforation location extraction

[0091] The perforation positions of each cluster are extracted from the solution results to facilitate the subsequent calculation of proppant outflow conditions.

[0092] 3. Outflow condition function definition

[0093] There are N clusters in the horizontal wellbore, each cluster i has k perforations, and the boundary position of each perforation is represented by ki,j. The proppant outflow condition can be expressed by the function C(x p ,k i,j ), where xp is the particle position, and the condition function returns a value indicating whether the particle meets the condition of flowing out from hole ki,j. If the condition of flowing out is met, 1 is returned, otherwise 0 is returned.

[0094]

[0095] 4. Calculation of the amount of proppant flowing out of each cluster

[0096] For each cluster, the proppant quantity is calculated according to the formula using the preprocessed data and the defined outflow condition function.

[0097]

[0098] S4 tests the horizontal wellbore proppant migration model through physical experiments to calibrate the proppant distribution results between horizontal well clusters;

[0099] Specifically,

[0100] The key parameters that need to be considered in the actual application of the proppant distribution prediction model are used to narrow down the parameters through actual conditions to ensure the feasibility of the experiment and highly restore the actual downhole environment;

[0101] Conduct indoor physical experiments using laboratory equipment and simulation devices to obtain the distribution of proppant under different conditions, providing an experimental basis for model verification;

[0102] The physical experimental data were compared with the proppant distribution results in the horizontal wellbore to verify the accuracy and reliability of the horizontal wellbore model.

[0103] Beneficial effects:

[0104] Through the established numerical model of particle two-phase flow in multi-cluster perforation of horizontal wells, the model is numerically solved to obtain the distribution of proppant along the horizontal well clusters. The constructed proppant migration model restores the actual downhole flow state, which is applicable to any type of horizontal well multi-cluster perforation in actual wells. The construction parameter input model can obtain the distribution of proppant between clusters, and reasonable optimization of construction parameters can improve the distribution of proppant clusters. This method helps to improve the production increase effect and post-fracturing production of horizontal well dense cutting fracturing.

[0105] What is disclosed above is only a preferred embodiment of a method for predicting proppant distribution between perforation clusters in a horizontal well of the present invention. Of course, this cannot be used to limit the scope of rights of the present invention. Ordinary technicians in this field can understand that all or part of the processes of the above embodiments and equivalent changes made according to the claims of the present invention still fall within the scope of the invention.

Claims

1. A method for predicting proppant distribution between perforation clusters in horizontal wells, characterized in that: The following steps are involved: A mathematical model of proppant migration in horizontal wellbore is established considering the complex particle two-phase flow in multi-cluster perforation of horizontal well. The equations of the proppant transport model involving liquid and particles are solved by discretizing the continuity equations and performing numerical iterations; Analyze and process the solution data to calculate the distribution of proppants between different clusters in the horizontal wellbore; The horizontal wellbore proppant migration model is tested by physical experiments to calibrate the proppant distribution results between horizontal well clusters.

2. A method for predicting proppant distribution between perforation clusters in a horizontal well according to claim 1, characterized in that: Considering the complex particle two-phase flow in multi-cluster perforation of horizontal wells, a mathematical model of proppant migration in horizontal wellbore was established, including: The fluid control equation and the particle control equation are constructed by bringing the Euler-Lagrangian model into the field wellbore parameters and the perforation parameters.

3. A method for predicting proppant distribution between perforation clusters in a horizontal well according to claim 2, characterized in that: The equations of the proppant transport model involving liquid and particles are solved by discretizing the continuity equation and performing numerical iteration.

4. A method for predicting proppant distribution between perforation clusters in a horizontal well according to claim 3, characterized in that: The analysis and processing of the solution result data to calculate the distribution of proppants between different clusters in the horizontal wellbore includes: Use the key parameters that need to be considered in the actual application of the proppant distribution prediction model, and narrow down the parameters through actual conditions; Using laboratory equipment and simulation devices, conduct indoor physical experiments to obtain the distribution of proppant under different conditions; The physical experimental data were compared with the proppant distribution results in the horizontal wellbore to verify the accuracy and reliability of the horizontal wellbore model.

5. A method for predicting proppant distribution between perforation clusters in a horizontal well according to claim 4, characterized in that: The solution data are analyzed and processed to calculate the distribution of proppants between different clusters in the horizontal wellbore.

Images