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Review of deep learning algorithms in molecular simulations and perspective applications on petroleum engineering

Geoscience Frontiers 2024年第2期15卷 55-67页

作者： Jie Liu Tao Zhang shuyu sun Physical Science and Engineering Division(PSE) Computational Transport Phenomena LaboratoryKing Abdullah University of Science and Technology(KAUST)Thuwal 23955-6900Saudi Arabia

In the last few decades,deep learning(DL)has afforded solutions to macroscopic problems in petroleum engineering,but mechanistic problems at the microscale have not benefited from *** studies have been the strong demands for the emerging projects,such as the gas storage and hydrate production,and for some problems encountered in the storage process,which are common found as the chemical interaction between injected gas and mineral,and the formation of *** advances in DL technology enable solving molecular dynamics(MD)with quantum *** conventional quantum chemical method is computational expensive,whereas the classical MD method cannot guarantee high accuracy because of its empirical force field *** the help of the DL force field,precision at the quantum chemistry level can be achieved in ***,the DL force field promotes the computational speed compared with first-principles *** this review,the basic knowledge of the molecular force field and deep neural network(DNN)is first ***,three representative opensource packages relevant to the DL force field are *** the most common components in the development of oil and gas reservoirs,water and methane are studied from the aspects of computational efficiency and chemical reaction respectively,providing the foundation of oil and gas ***,in the oil and gas problems,the complex molecular topo structures and various element types set a high challenge for the DL techniques in *** the computational efficiency,it needs improvement via GPU and parallel accelerations to compete with classical *** with such difficulties,the booming of this technique in the area of petroleum engineering can be predictable.

关键词： Deep neural network Molecular dynamics Force field Petroleum engineering

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Contaminant Flow and Transport Simulation in Cracked Porous Media Using Locally Conservative Schemes

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Advances in Applied Mathematics and Mechanics 2012年第4期4卷 389-421页

作者： Pu Song shuyu sun Department of Mathematical Sciences Clemson University ClemsonSC 29634USA Computational Transport Phenomena Laboratory(CTPL) Division of Physical Sciences and Enginerring(PSE)King Abdullah University of Science and Technology(KAUST)4700 King Abdullah University of Science and TechnologyThuwal 23955-6900Kingdom of Saudi Abrabia

The purpose of this paper is to analyze some features of contaminant flow passing through cracked porous medium,such as the influence of fracture network on the advection and diffusion of contaminant species,the impact of adsorption on the overall transport of contaminant *** order to precisely describe the whole process,we firstly build the mathematical model to simulate this problem *** into consideration of the characteristics of contaminant flow,we employ two partial differential equations to formulate the whole *** is flow equation;the other is reactive transport *** first equation is used to describe the total flow of contaminant wastes,which is based on Darcy *** second one will characterize the adsorption,diffusion and convection behavior of contaminant species,which describes most features of contaminant flow we are interested *** the construction of numerical model,we apply locally conservative and compatible algorithms to solve this mathematical ***,we apply Mixed Finite Element(MFE)method to the flow equation and Discontinuous Galerkin(DG)method for the transport *** has a good convergence rate and numerical accuracy for Darcy *** is more flexible and can be used to deal with irregular meshes,as well as little numerical *** these two numerical means,we investigate the sensitivity analysis of different features of contaminant flow in our model,such as diffusion,permeability and fracture *** particular,we study Kd values which represent the distribution of contaminant wastes between the solid and liquid *** also make omparisons of two different schemes and discuss the advantages of both methods.

关键词： Mixed finite element methods discontinuous Galerkin methods reactive transport equation flow equation

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STABILITY AND CONVERGENCE ANALYSIS OF SECOND-ORDER SCHEMES FOR A DIFFUSE INTERFACE MODEL WITH PENG-ROBINSON EQUATION OF STATE

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Journal of Computational Mathematics 2017年第6期35卷 737-765页

作者： Qiujin Peng Zhonghua Qiao shuyu sun Institute for Mathematical Sciences Renmin University of China Beijing 100872 China Department of Applied Mathematics The Hong Kong Polytechnic University Hung Horn Hong Kong Division of Physical Sciences and Engineering King Abdullah University of Science and Technology Thuwal 23955-6900 Kingdom of Saudi Arabia

In this paper, we present two second-order numerical schemes to solve the fourth order parabolic equation derived from a diffuse interface model with Peng-Robinson Equation of state （EOS） for pure substance. The mass conservation, energy decay property, unique solvability and L~ convergence of these two schemes are proved. Numerical results demon- strate the good approximation of the fourth order equation and confirm reliability of these two schemes.

关键词： Diffuse interface model Fourth order parabolic equation Energy stability,Convergence.

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Combined Effect of Magnetic Field and Thermal Dispersion on a Non-Darcy Mixed Convection

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Journal of Thermal Science 2011年第3期20卷 276-282页

作者： M. F. EI-Amin shuyu sun Computational Transport Phenomena Laboratory （CTPL） Division of Physical Sciences and Engineering （PSE）King Abdullah University of Science and Technology （KAUST） Thuwal 23955-6900 Jeddah Kingdom of Saudi Ara-bia Mathematics Department Faculty of Science South Valley University Aswan 81528 EGYPT

This paper is devoted to investigate the influences of thermal dispersion and magnetic field on a hot semi-infinite vertical porous plate embedded in a saturated Darcy-Forchheimer-Brinkman porous medium. The coefficient of thermal diffusivity has been assumed to be the sum of the molecular diffusivity and the dynamic diffusivity due to mechanical dispersion. The effects of transverse magnetic field parameter (Hartmann number Ha), Reynolds number Re (different velocities), Prandtl number Pr (different types of fluids) and dispersion parameter on the wall shear stress and the heat transfer rate are discussed.

关键词： Thermal dispersion non-Darcy convection magneto-hydro-dynamics porous media geothermal systems

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Simulation of buoyancy-induced turbulent flow from a hot horizontal jet

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Journal of Hydrodynamics 2014年第1期26卷 104-113页

作者： El-AMIN M.F. sun shuyu SALAM Amgad Computational Transport Phenomena Laboratory (CTPL) Division of Physical Sciences and EngineeringKing Abdullah University of Science and Technology

Experimental visualizations and numerical simulations of a horizontal hot water jet entering cold water into a rectangular storage tank are described. Three different temperature differences and their corresponding Reynolds numbers are considered. Both experimental visualization and numerical computations are carried out for the same flow and thermal conditions. The realizable k-e model is used for modeling the turbulent flow while the buoyancy is modeled using the Boussinesq approximation. Polynomial approximations of the water properties are used to compare with the Boussinesq approximation. Numerical solutions are obtained for unsteady flow while pressure, velocity, temperature and turbulence distributions inside the water tank as well as the Froude number are analyzed. The experimental visualizations are performed at intervals of five seconds for all different cases. The simulated results are compared with the visualized results, and both of them show the stratification phenomena and buoyancy force effects due to temperature difference and density variation. After certain times, depending on the case condition, the flow tends to reach a steady state.

关键词： turbulent flow realizablc k - e turbulence model heat transfer jet heat storage

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An Energy Stable SPH Method for Incompressible Fluid Flow

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Advances in Applied Mathematics and Mechanics 2022年第5期14卷 1201-1224页

作者： Xingyu Zhu shuyu sun Jisheng Kou Computational Transport Phenomena Laboratory Division of Physical Science and EngineeringKing Abdullah University of Science and TechnologyThuwal 23955-6900Saudi Arabia School of Civil Engineering Shaoxing UniversityShaoxing 312000ZhejiangChina School of Mathematics and Statistics Hubei Engineering UniversityXiaogan 432000HubeiChina

In this paper,a novel unconditionally energy stable Smoothed Particle Hydrodynamics(SPH)method is proposed and implemented for incompressible fluid *** this method,we apply operator splitting to break the momentum equation into equations involving the non-pressure term and pressure term *** idea behind the splitting is to simplify the calculation while still maintaining energy stability,and the resulted algorithm,a type of improved pressure correction scheme,is both efficient and energy *** show in detail that energy stability is preserved at each full-time step,ensuring unconditionally numerical *** examples are presented and compared to the analytical solutions,suggesting that the proposed method has better accuracy and ***,we observe that if we are interested in steady-state solutions only,our method has good performance as it can achieve the steady-state solutions rapidly and accurately.

关键词： Particle method Smoothed Particle Hydrodynamics(SPH)method incompressible fluid flow energy stability numerical stability

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EFFICIENT LINEAR SCHEMES WITH UNCONDITIONAL ENERGY STABILITY FOR THE PHASE FIELD MODEL OF SOLID-STATE DEWETTING PROBLEMS

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Journal of Computational Mathematics 2020年第3期38卷 452-468页

作者： Jie Chen Zhengkang He shuyu sun Shimin Guo Zhangxin Chen School of Mathematics and Statistics Xi'an Jiaotong UniversityXi'an 710049China Computational Transport Phenomena Laboratory Division of Physical Science and EngineeringKing Abdullah University of Science and TechnologyThuwal 23955-6900Kingdom of Saudi Arabia School of Mathematics and Statistics Xi'an Jiaotong Universityy Xi'an 710049China Department of Chemical&Petroleum Engineering Schulich School of EngineeringUniversity of Calgary2500 University Drive N.W.CalgaryAlberta T2N 1N4Canada

In this paper,we study linearly first and second order in time,uniquely solvable and unconditionally energy stable numerical schemes to approximate the phase field model of solid-state dewetting problems based on the novel"scalar auxiliary variable"(SAV)approach,a new developed efficient and accurate method for a large class of gradient *** schemes are based on the first order Euler method and the second order backward differential formulas(BDF2)for time discretization,and finite element methods for space *** proposed schemes are proved to be unconditionally stable and the discrete equations are uniquely solvable for all time *** numerical experiments are presented to validate the stability and accuracy of the proposed schemes.

关键词： Phase field models Solid-state dewetting SAV Energy stability Surface diffusion Finite element method

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Numerical simulation and analysis of confined turbulent buoyant jet with variable source

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Journal of Hydrodynamics 2015年第6期27卷 955-968页

作者： EL-AMIN Mohamed F. AL-GHAMDI Abdulmajeed SALAMA Amgad sun shuyu Mathematics Department Faculty of ScienceAswan University Computational Transport Phenomena Laboratory(CTPL) Division of Physical Sciences and Engineering(PSE)King Abdullah University of Science and Technology(KAUST) College of Engineering and Islamic Architecture Umm Al-Qura University

In this work, experimental and numerical investigations are undertaken for confined buoyant turbulent jet with varying inlet temperatures. Results of the experimental work and numerical simulations for the problem under consideration are presented. Four cases of different variable inlet temperatures and different flow rates are considered. The realizable k-ε turbulence model is used to model the turbulent flow. Comparisons show good agreements between simulated and measured results. The average devia- tion of the simulated temperature by realizable k-ε turbulent model and the measured temperature is within 2%. The results indicate that temperatures along the vertical axis vary, generally, in nonlinear fashion as opposed to the approximately linear varia- tion that was observed for the constant inlet temperature that was done in a previous work. Furthermore, thermal stratification exits, particularly closer to the entrance region. Further away from the entrance region the variation in temperatures becomes relatively smaller. The stratification is observed since the start of the experiment and continues during the whole course. Numerical experime- nts for constant, monotone increasing and monotone decreasing of inlet temperature are done to show its effect on the buoyancy force in terms of Richardson number.

关键词： realizable k-ε model turbulent jet stratification heat stores CFD

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Multilevel Constrained Pressure-Temperature Residual Preconditioners for Large-Scale Non-Isothermal Reservoir Simulation via Restricted Additive Schwarz Algorithms

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Communications in Computational Physics 2023年第8期34卷 837-868页

作者： Mei Zhang Haijian Yang Chao Yang shuyu sun School of Mathematics Hunan UniversityChangshaHunan410082P.R.China Shenzhen Research Institute Hunan UniversityShenzhen518000PR China School of Mathematical Sciences Peking UniversityBeijing100871P.R.China Computational Transport Phenomena Laboratory Physical Science and Engineering DivisionKing Abdullah University of Science and TechnologyThuwal23955-6900Saudi Arabia

The industry-standard constrained pressure residual(CPR)algorithm is often able to effectively improve the robustness behavior and the convergence speed of linear iterations for isothermal reservoir *** this paper,we present and study an improved extension of CPR to the constrained pressure-temperature residual(CPTR)version for non-isothermal reservoir problems in heterogeneous porous *** the proposed preconditioner,the corresponding approximations for the inverse of matrices are computed under a domain decomposition framework by using the restricted additive Schwarz(RAS)algorithm,to equally deal with the coupled thermalpressure-saturation reservoir system and highly exploit the parallelism of supercomputer ***,we introduce and develop a family of multilevel CPTR preconditioners with suitable coarse grid corrections,to further improve the applicability of this two-stage preconditioner for large-scale *** results for strong heterogeneous flow problems show that the new approach can dramatically improve the convergence of linear iterations,and demonstrate the superiority of CPTR over the commonly used RAS *** parallel scalability of the non-isothermal reservoir simulator is also studied versus a supercomputer with tens of thousands of processors.

关键词： Thermal reservoir simulation porous media preconditioning restricted additive Schwarz algorithm strong and weak scalability

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On Stochastic Error and Computational Efficiency of the Markov Chain Monte Carlo Method

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Communications in Computational Physics 2014年第7期16卷 467-490页

作者： Jun Li Philippe Vignal shuyu sun Victor M.Calo Center for Numerical Porous Media King Abdullah University of Science and TechnologyThuwalSaudi Arabia Material Science and Engineering King Abdullah University of Science and TechnologyThuwalSaudi Arabia AppliedMathematics and Computational Science Earth Sciences and EngineeringKing Abdullah University of Science and TechnologyThuwalSaudi Arabia.

InMarkov ChainMonte Carlo(MCMC)simulations,thermal equilibria quantities are estimated by ensemble average over a sample set containing a large number of correlated *** samples are selected in accordance with the probability distribution function,known from the partition function of equilibrium *** the stochastic error of the simulation results is significant,it is desirable to understand the variance of the estimation by ensemble average,which depends on the sample size(i.e.,the total number of samples in the set)and the sampling interval(i.e.,cycle number between two consecutive samples).Although large sample sizes reduce the variance,they increase the computational cost of the *** a given CPU time,the sample size can be reduced greatly by increasing the sampling interval,while having the corresponding increase in variance be negligible if the original sampling interval is very *** this work,we report a few general rules that relate the variance with the sample size and the sampling *** results are observed and confirmed *** variance rules are derived for theMCMCmethod but are also valid for the correlated samples obtained using other Monte Carlo *** main contribution of this work includes the theoretical proof of these numerical observations and the set of assumptions that lead to them.

关键词： Phase coexistence Gibbs ensemble molecular simulation Markov Chain Monte Carlo method variance estimation blocking method

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