2021 Vol. 42, No. 9

Display Method:
Fluid Mechanics
Machine Learning With Physical Empirical Model Constraints for Prediction of Shale Oil Production
ZHOU Jimin, ZHANG Haichen, WANG Moran
2021, 42(9): 881-890. doi: 10.21656/1000-0887.420015
Abstract(518) PDF(121)
Prediction of oil and gas production is an important way to determine its development economy. However, at present the production prediction is still hard to achieve consistency between the physics-based method and the data-based method. For shale oil and gas production analysis, in-depth combination of mathematical advantages brought by BP neural networks and LSTM neural networks, and comprehensive consideration of physics-based models, lead to good improvement in the prediction accuracy of the model. After training with practical testing data, the prediction of oilfield production can be significantly improved. Afterwards, the effects of the reservoir depth, the TOC and the brittleness, etc. on production prediction were studied. In conclusion, the work provides reliable production prediction and economic evaluation for large-scale development of shale oil and gas.
A Low-Order Model Method for 2-Phase Oil Reservoir Simulation
JIA Xinxin, WANG Lei, ZHANG Hao, SUN Xiaoling, DUAN Liya, WANG Xin
2021, 42(9): 891-899. doi: 10.21656/1000-0887.410235
Abstract(315) PDF(47)
At present, the main methods used in reservoir numerical simulation, such as the finite element method and the finite volume method, require long calculation times, which limit their implementation in the real-time prediction and the reservoir production. An efficient data-processing method that based on the POD (proper orthogonal decomposition) was proposed to obtain the empirical coefficients and eigenfunctions of the oil-water 2-phase flow in the reservoir, and build a new low-order Galerkin calculation model. The numerical calculation indicates that, with the POD, the calculated eigenvector energy has proper features. Only a small number of eigenvalues can capture most of the energy, completely describe the reservoir characteristics (pressure, saturation), and help reduce the order of the partial differential equations. The calculation results of the low-order model are in good agreement with those from the IMPES, with much time saved. The proposed method applies well to history matching in numerical simulation of reservoir injection and production.
A “Standard Cross-Section” Method for the Calculation of Riverbed and Bank Shear Stresses
LUO You, ZHU Senlin, CAO Bing, JIANG Chenjuan
2021, 42(9): 915-923. doi: 10.21656/1000-0887.420048
Abstract(328) PDF(30)
Seeking for the “zero shear stress dividing line” and quantifying the apparent shear stress at the interface between adjacent sub-regions are 2 main methods to calculate the riverbed and bank shear stresses. To simplify the empirical expression for apparent shear stresses along the dividing line, a “momentum transfer-equilibrium deviation” (MTED) assumption that the apparent shear stress can be calculated based on the deviation of momentum transportation from its equilibrium value, was proposed. A “standard cross-section” concept was applied to determine the equilibrium value. All the rectangular and trapezoidal cross-sections can be correlated with certain standard cross-sections. Based on the MTED assumption and the concept of standard cross-sections, the empirical expressions for the apparent shear stresses along the dividing line and the bed and bank boundary shear stresses, were established. More than 200 data from different lab experiments were used to verify different methods. The results show that, the proposed method improves the calculation accuracy and can be applied to both rectangular and trapezoidal cross-sections, as well as to both smooth and rough channels.
Existence and Blowup of Positive Solutions to a Class of Multilateral Flow Equations
LI Jianjun, TANG Yina
2021, 42(9): 924-931. doi: 10.21656/1000-0887.420022
Abstract(306) PDF(42)
The global existence and blowup of the solutions to a class of multilateral filtration equations with non-local Neumann boundary conditions and nonlinear absorption terms were studied. First, the super- and sub-solutions were defined for the studied equations and the comparison principle was established. Then, the equation was investigated with constructed functions, differential inequalities, eigenfunctions, ordinary differential equation and elliptic second boundary value solutions. The global existence of non-negative solutions to the equations and the conditions for blowup in a finite time for the parameters, weight functions and initial values in different value ranges were obtained.
Applied Mathematics
Study on Numerical Solutions to Hyperbolic Partial Differential Equations Based on the Convolutional Neural Network Model
GAO Puyang, ZHAO Zitong, YANG Yang
2021, 42(9): 932-947. doi: 10.21656/1000-0887.420050
Abstract(487) PDF(127)
In recent years, artificial neural networks developed rapidly. Application of this method to partial differential equations became a new idea for exploring numerical solutions to differential equations. Compared with the traditional methods, it has some advantages, such as a wide range of applications (i.e. the same model can be used to solve multiple types of equations) and low meshing requirements. In addition, the trained model can be directly used to calculate the numerical solution at any point in the computation domain. The weight coefficients in the traditional finite volume method were optimized based on the convolutional neural network model to get a new numerical scheme with highresolution results on the coarse grid. The proposed model helps solve the Burgers and level set equations efficiently and stably with high accuracy.
Singularly Perturbed and Soliton Solutions to a Class of KdV-Burgers Equations
BAO Liping, LI Ruixiang, WU Liqun
2021, 42(9): 948-957. doi: 10.21656/1000-0887.420011
Abstract(335) PDF(45)
A class of KdV-Burgers equations with large Reynolds numbers and weak dispersions were discussed, which were mathematically expressed as a class of singularly perturbed KdV-Burgers equations. The interaction between the nonlinear term and the dispersion term in the KdV-Burgers equation forms a stable forward-propagation soliton. Through mathematical analysis, the propagation path and speed of the soliton were described. By means of the singularly perturbed expansion method, the asymptotic solution to the problem was constructed. First, the degenerate solution was obtained with the Riemann-Earnshaw method, and the simple wave was obtained. There is a velocity difference between any point of the simple wave shape and the initial point, which makes the wave form continuously distorted in the process of propagation, and finally forms the shock wave surface, namely discontinuity. There is a time-varying jump in the velocity of particles between both sides of the discontinuity. Second, a modified traveling wave transformation was built through substitution of variables at the discontinuity of the degenerate solution, to obtain soliton solutions of the expansion of internal solutions and prove the existence and uniqueness of the internal and external solutions. Finally, the residual term was estimated with the existence of the uniformly bounded inverse operator, and the uniform effectiveness of the asymptotic solution was obtained. The results show that, the perturbations of KdV-Burgers equations with large Reynolds numbers and weak dispersions concentrate on the neighbourhoods of the discontinuities of the degenerate solutions. The soliton links the particles across the 2 sides, and its propagation path is not a linear form of time and space, but leads along the discontinuity of the degenerate solution, forming a stable waveform.
Stability of Vector Optimization Problems Under Approximate Equilibrium Constraints via Free-Disposal Sets
ZENG Yue, PENG Zaiyun, LIANG Renli, SHAO Chongyang
2021, 42(9): 958-967. doi: 10.21656/1000-0887.410244
Abstract(356) PDF(41)
The stability of vector optimization problems under approximate equilibrium constraints (AOPVF) via free-disposal sets was discussed. Firstly, the Berge-semicontinuity of the constraint set mapping and the closedness, the convexity and the compactness of the constraint set were obtained with the weaker convexity assumption. Moreover, under the assumption of Gamma-convergence for the objective functional sequences, the lower Painlevé-Kuratowski convergence of the weak efficient solution set and the Berge-semicontinuity of weak efficient solution mappings for AOPVF were obtained respectively. Some examples illustrate that the results are new and meaningful.
The Phragmén-Lindelöf Type Alternative Results for Binary Heat Conduction Equations
LI Yuanfei, ZENG Peng, CHEN Xuejiao
2021, 42(9): 968-978. doi: 10.21656/1000-0887.420031
Abstract(332) PDF(28)
The asymptotic behavior of the solution to the binary heat conduction equation in the semi-infinite domain was considered, in which the local non-homogeneous Neumann condition was applied to the side of the cylinder. This condition simulates the local damage of the insulation material on the side of the cylinder. By means of the differential inequality technique and the energy analysis method, the Phragmén-Lindelöf-type alternative results of the heat conduction model were obtained.
The Random ADMM and Its Application to Convex Economic Dispatch Problems of Power Systems
CHEN Weijun, LUO Honglin, PENG Jianwen
2021, 42(9): 979-988. doi: 10.21656/1000-0887.420040
Abstract(318) PDF(40)
A new random alternating direction method of multipliers (ADMM) was designed to solve convex economic dispatch problems in power systems. The convergence of the random ADMM was analyzed. Under some mild assumptions, the random ADMM, according to the cycle update rule and the random selection update rule, was proved to converge to an optimal solution of the convex economic dispatch problem. The numerical experimental results show that, the proposed method is effective to solve convex economic dispatch problems.
Block-Sparse Signal Recovery via l2/lq(q=2/3) Minimization
ZHU Dechun, ZHOU Jun, CAO Manxia, HUANG Wei
2021, 42(9): 989-998. doi: 10.21656/1000-0887.420009
Abstract(352) PDF(23)

The recovery of block-sparse signals was mainly studied. By means of the block restricted q-isometry property (block q-RIP) with 0<q≤1, a sufficient condition for block-sparse signal recovery was established through mixed l2/lq(q=2/3) norm minimization with q=2/3,and an error bound for signal recovery in the presence of noise was obtained. Through numerical experiments, it is verified that the model has a high success rate for block-sparse signal recovery.