Digital Slot: A Tool for Optimization and Development of New Hydraulic Fracturing Technologies

2021 ◽  
Author(s):  
Semen Vasilievich Idimeshev ◽  
Vadim Ismailovich Isaev ◽  
Alexey Alexandrovich Tikhonov ◽  
Leonid Georgievich Semin ◽  
Denis Viktorovich Bannikov ◽  
...  
Keyword(s):  
Mathematical Model ◽  
Hydraulic Fracturing ◽  
Finite Volume ◽  
Numerical Algorithm ◽  
Lubrication Theory ◽  
Lagrangian Approach ◽  
Narrow Channels ◽  
Solids Transport ◽  
Viscosity Contrast ◽  
Fiber Components

Abstract We present the digital slot — a tool for the development of new hydraulic fracturing technologies via digitization of slurry flow in narrow channels. We consider slurry containing fluid, proppant, and fiber components. The flow is described by a continuum mathematical model based on the lubrication theory. The numerical algorithm utilizes Lagrangian approach with finite volume pressure solver. We present the results of laboratory validation and simulation examples showing the key effects affecting solids transport in hydraulic fracturing: settling, bridging, gravity slumping, materials degradation, viscosity contrast, and bank formation.

Study on Superalloy Tube Extrusion Process Using Finite Volume Method

2012 ◽  
Vol 572 ◽  
pp. 267-272
Author(s):  
Yi Lun Mao ◽  
Qing Dong Zhang ◽  
Chao Yang Sun ◽  
Xiao Feng Zhang
Keyword(s):  
Mathematical Model ◽  
High Temperature ◽  
Finite Volume Method ◽  
Finite Volume ◽  
Extrusion Process ◽  
Equivalent Strain ◽  
High Temperature Alloy ◽  
Squeeze Pressure ◽  
Tube Extrusion ◽  
Volume Method

In this paper, complexity of the process of high temperature alloy tubing extrusion is studied using the Finite Volume Method (FVM). We establish mathematical model of high temperature alloy tube extrusion process by using the Finite Volume Method. We develop the simulation program by the control equation of the Finite Volume Method and numerical simulation of the key technologies of the axisymmetric problem in cylindrical coordinates. Inconel690 high temperature alloy tubing extrusion process, for example, we got the squeeze pressure in the steady-state extrusion, Velocity field and the corresponding equivalent strain rate field. By comparing the results obtained by the finite volume method and simulation results from Finite Element Method (FEM) software on DEFORM-2D, we find our mathematical model on high temperature alloy tubing extrusion process is reasonable and correct.

Calculation of Flow in Mixing Vessels With Various Turbulence Models

Volume 4 ◽  
2004 ◽  
Author(s):  
Branislav Basara ◽  
Ales Alajbegovic ◽  
Decan Beader
Keyword(s):  
Experimental Data ◽  
Mathematical Model ◽  
Finite Volume Method ◽  
Finite Volume ◽  
Turbulence Model ◽  
Unstructured Grids ◽  
Turbulence Models ◽  
Cfd Applications ◽  
Volume Method ◽  
Rushton Impeller

The paper presents calculations of flow in a mixing vessel stirred by a six-blade Rushton impeller. Mathematical model used in computations is based on the ensemble averaged conservation equations. An efficient finite-volume method based on unstructured grids with rotating sliding parts composed of arbitrary polyhedral elements is used together with various turbulence models. Besides the standard k-ε model which served as a reference, k-ε-v2 model (Durbin, 1995) and the recently proposed hybrid EVM/RSM turbulence model (Basara & Jakirlic, 2003) were used in the calculations. The main aim of the paper is to investigate if more advanced turbulence models are needed for this type of CFD applications. The results are compared with the available experimental data.

scholarly journals Mathematical model of methane driven by hydraulic fracturing in gassy coal seams

2020 ◽  
Vol 38 (3-4) ◽  
pp. 127-147
Author(s):  
Weiyong Lu ◽  
Bingxiang Huang
Keyword(s):  
Mathematical Model ◽  
Hydraulic Fracturing ◽  
Pore Pressure ◽  
Hydraulic Fracture ◽  
Water Saturation ◽  
Reduction Rate ◽  
Space Time ◽  
Matrix Block ◽  
The Matrix ◽  
Pore Pressure Gradient

During hydraulic fracturing in gassy coal, methane is driven by hydraulic fracturing. However, its mathematical model has not been established yet. Based on the theory of ‘dual-porosity and dual-permeability’ fluid seepage, a mathematical model is established, with the cleat structure, main hydraulic fracture and methane driven by hydraulic fracturing considered simultaneously. With the help of the COMSOL Multiphysics software, the numerical solution of the mathematical model is obtained. In addition, the space–time rules of water and methane saturation, pore pressure and its gradient are obtained. It is concluded that (1) along the direction of the methane driven by hydraulic fracturing, the pore pressure at the cleat demonstrates a trend of first decreasing and later increasing. The pore pressure gradient exhibits certain regional characteristics along the direction of the methane driven by hydraulic fracturing. (2) Along the direction of the methane driven by hydraulic fracturing, the water saturation exhibits a decreasing trend; however, near the cleat or hydraulic fracture, the water saturation first increases and later decreases. The water saturation in the central region of the coal matrix block is smaller than that of its surrounding region, while the saturation of water in the entire matrix block is greater than that in the cleat or hydraulic fracture surrounding the matrix block. The water saturation at the same space point increases gradually with the time progression. The space–time distribution rules of methane saturation are contrary to those of the water saturation. (3) The free methane driven by hydraulic fracturing includes the original free methane and the free methane desorbed from the adsorption methane. The reduction rate of the adsorption methane is larger than that of free methane.

An efficient numerical algorithm for solving viscosity contrast Cahn–Hilliard–Navier–Stokes system in porous media

2020 ◽  
Vol 400 ◽  
pp. 108948 ◽  
Author(s):  
Chen Liu ◽  
Florian Frank ◽  
Christopher Thiele ◽  
Faruk O. Alpak ◽  
Steffen Berg ◽  
...  
Keyword(s):  
Porous Media ◽  
Numerical Algorithm ◽  
Stokes System ◽  
Navier Stokes ◽  
Viscosity Contrast

scholarly journals Numerical Study of Shear Banding in Flows of Fluids Governed by the Rolie-Poly Two-Fluid Model via Stabilized Finite Volume Methods

Processes ◽  
2020 ◽  
Vol 8 (7) ◽  
pp. 810
Author(s):  
Jade Gesare Abuga ◽  
Tiri Chinyoka
Keyword(s):  
Finite Volume ◽  
Numerical Algorithm ◽  
Numerical Study ◽  
Fluid Model ◽  
Shear Banding ◽  
Numerical Algorithms ◽  
Viscoelastic Fluids ◽  
Two Fluid Model ◽  
Two Fluid ◽  
Good Agreement

The flow of viscoelastic fluids may, under certain conditions, exhibit shear-banding characteristics that result from their susceptibility to unusual flow instabilities. In this work, we explore both the existing shear banding mechanisms in the literature, namely; constitutive instabilities and flow-induced inhomogeneities. Shear banding due to constitutive instabilities is modelled via either the Johnson–Segalman or the Giesekus constitutive models. Shear banding due to flow-induced inhomogeneities is modelled via the Rolie–Poly constitutive model. The Rolie–Poly constitutive equation is especially chosen because it expresses, precisely, the shear rheometry of polymer solutions for a large number of strain rates. For the Rolie–Poly approach, we use the two-fluid model wherein the stress dynamics are coupled with concentration equations. We follow a computational analysis approach via an efficient and versatile numerical algorithm. The numerical algorithm is based on the Finite Volume Method (FVM) and it is implemented in the open-source software package, OpenFOAM. The efficiency of our numerical algorithms is enhanced via two possible stabilization techniques, namely; the Log-Conformation Reformulation (LCR) and the Discrete Elastic Viscous Stress Splitting (DEVSS) methodologies. We demonstrate that our stabilized numerical algorithms accurately simulate these complex (shear banded) flows of complex (viscoelastic) fluids. Verification of the shear-banding results via both the Giesekus and Johnson-Segalman models show good agreement with existing literature using the DEVSS technique. A comparison of the Rolie–Poly two-fluid model results with existing literature for the concentration and velocity profiles is also in good agreement.

scholarly journals Numerical Modeling on Hydraulic Fracturing in Coal-Rock Mass for Enhancing Gas Drainage

2018 ◽  
Vol 2018 ◽  
pp. 1-16 ◽  
Author(s):  
Zhigang Yuan ◽  
Yaohua Shao
Keyword(s):  
Mathematical Model ◽  
Rock Mass ◽  
Hydraulic Fracturing ◽  
Gas Flow ◽  
Numerical Solutions ◽  
Fracture Initiation ◽  
Engineering Practice ◽  
Gas Drainage ◽  
Fracturing Process ◽  
Coal Rock

The mechanism of how hydraulic fracturing influences gas drainage in coal-rock mass is still not clear due to its complex mechanism. In this work, statistical distributions are firstly introduced to describe heterogeneity of coal-rock mass; a novel simultaneously coupled mathematical model, which can describe the fully coupled process including seepage-damage coupling during hydraulic fracturing process and subsequent gas flow during gas drainage process, is established; its numerical implementation procedure is coded into a Matlab program to calculate the damage variables, and it partly uses COMSOL solver to obtain numerical solutions of governing equations with damage-flow coupling; the mathematical model and its implementation are validated for initial damage pressure and mode of a single solid model without considering flow-damage coupling, as well as fracture initiation pressure and influence of heterogeneity on damage evolution of hydraulic fracturing considering flow-damage coupling; and finally, based on an engineering practice of hydraulic fracturing with two boreholes, the mechanism of how hydraulic fracturing influences gas drainage is investigated, numerical simulation results indicate that coal-rock mass pore-fissure structure has been improved, and there would exist a gas migration channel with characteristics of higher porosity and lower stresses, which demonstrates significant effects and mechanism of hydraulic fracturing on improving coal-rock permeability and enhancing gas drainage. The research results provide a guide for operation of hydraulic fracturing and optimal layout of gas drainage boreholes.

A general finite volume based numerical algorithm for hydrocarbon reservoir simulation using blackoil model

2014 ◽  
Vol 24 (8) ◽  
pp. 1831-1863 ◽  
Author(s):  
Mehdi Mosharaf Dehkordi ◽  
Mehrdad T. Manzari ◽  
H. Ghafouri ◽  
R. Fatehi
Keyword(s):  
Finite Volume ◽  
Numerical Algorithm ◽  
Numerical Results ◽  
Hydrocarbon Reservoirs ◽  
Pressure Equation ◽  
Content Type ◽  
Structured Grids ◽  
Hydrocarbon Reservoir ◽  
Computational Performance ◽  
Wide Range

Purpose – The purpose of this paper is to present a detailed algorithm for simulating three-dimensional hydrocarbon reservoirs using the blackoil model. Design/methodology/approach – The numerical algorithm uses a cell-centred structured grid finite volume method. The blackoil formulation is written in a way that an Implicit Pressure Explicit Saturation approach can be used. The flow field is obtained by solving a general gas pressure equation derived by manipulating the governing equations. All possible variations of the pressure equation coefficients are given for different reservoir conditions. Key computational details including treatment of non-linear terms, expansion of accumulation terms, transitions from under-saturated to saturated states and vice versa, high gas injection rates, evolution of gas in the oil production wells and adaptive time-stepping procedures are elaborated. Findings – It was shown that using a proper linearization method, less computational difficulties occur especially when free gas is released with high rates. The computational performance of the proposed algorithm is assessed by solving the first SPE comparative study problem with both constant and variable bubble point conditions. Research limitations/implications – While discretization is performed and implemented for unstructured grids, the numerical results are presented only for structured grids, as expected, the accuracy of numerical results are best for structured grids. Also, the reservoir is assumed to be non-fractured. Practical implications – The proposed algorithm can be efficiently used for simulating a wide range of practical problems wherever blackoil model is applicable. Originality/value – A complete and detailed description of ingredients of an efficient finite volume-based algorithm for simulating blackoil flows in hydrocarbon reservoirs is presented.

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