The estuarine zone is an area of strong interaction between fresh and salty water. Dynamics in these areas is complex due to the interaction of the forcing mechanisms such as wind, tides, local coastal currents and river discharges. The difference of density between fresh water and salted water causes the formation of the buoyant plumes which have been investigated by means of numerical models and field studies. Plumes play a significant role in the transport of pollutants and the ecology in the frontal areas where density gradients are strong. Therefore, in order to investigate the horizontal and vertical dispersion of salinity and temperature the YAXUM/3D baroclinic numerical model was developed. The model is validated and applied for two particular cases. The first one consists of modeling the discharge of a jet of hot water where the gradients of temperature prevail and the second to study the discharge of the mouth of the estuary Leschenault toward the Koombana bay, Australia where salinity gradients are analyzed. The results derived from the YAXUM/3D are satisfactory and in agreement with other models which have been already validated.

We study a parallel Newton-Krylov-Schwarz (NKS) based algorithm for solving large sparse systems resulting from a fully implicit discretization of partial differential equations arising from petroleum reservoir simulations. Our NKS algorithm is designed by combining an inexact Newton method with a rank-2 updated quasi-Newton method. In order to improve the computational efficiency, both DDM and SPMD parallelism strategies are adopted. The effectiveness of the overall algorithm depends heavily on the performance of the linear preconditioner, which is made of a combination of several preconditioning components including AMC, relaxed ILU, up scaling, additive Schwarz, CRP-like (constraint residual preconditioning), Watts correction, Shur complement, among others. In the construction of the CRP-like preconditioner, a restarted CMRES is used to solve the projected linear systems. We have tested this algorithm and related parallel software using data from some real applications, and presented numerical results that show that this solver is robust and scalable for large scale calculations in petroleum reservoir simulations.

A nonlinear parabolic system is derived to describe compressible miscible displacement in a porous medium in non-periodic space. The concentration is treated by a characteristics collocation method, while the pressure is treated by a finite element collocation method. Optimal order estimates in $L^2$ is derived.

The purpose of mathematical reservoir simulation models in petroleum applications is to try to optimize the recovery of hydrocarbon from permeable underground reservoirs. To accomplish this, one must be able to predict the performance of the reservoir under various production schemes. There are two essential issues, modeling and software architecture design, while developing a comprehensive oil reservoir modeling platform that should be an integration of subsurface models, facility network models and economic models. Effective subsurface models must be constructed to describe the complex geomechanical, physical, and multiphase fluid flow processes that accompany the various recovery mechanisms. Upscaling needs to be utilized to provide effective rock properties for coarse-grid models used for field-scale simulations. However, localized flow regimes at sub-coarse grid scales must often be resolved using local grid refinement techniques. Finite volume element methods for accurate resolution of localized geometrics can be coupled with cell-centered finite difference methods used in many existing simulators. Aspects of coupling different grids, different discretization schemes, and different physical equations via mortar techniques will be presented. Reservoir simulation is an integration of various technologies through the construction of a reservoir model as well as optimization of production strategies. A comprehensive oil reservoir modeling platform should be an integration of different software applications or components and its software architecture should be scaleable, extendable and should have the capability to create and modify a workflow. Beyond the traditional three-tier software architecture, data, application, and user-interface, separation of control and business logic through those three tiers is proposed to achieve those goals. The aspect of the software architecture design will be discussed.

In this paper we develop a pseudo function approach to obtain relative permeabilities for the numerical simulation of three-dimensional petroleum reservoirs. This approach follows the idea of an experimental approach and combines an analytical solution technique for two-phase flow with a numerical simulation technique for cross-sectional models of these three-dimensional reservoirs. The advantages of this pseudo function approach are that the heterogeneity of these reservoirs in the vertical direction and various forces such as capillary and gravitational forces can be taken into account in the derivation of the relative permeabilities. Moreover, this approach considers more physical and fluid factors and is more robust and accurate than the experimental approach. To reservoir engineers, the study of pseudo functions for the cross-sectional models of different types itself is the study of numerical simulation sensitivity of displacement processes in reservoirs. From this study they can understand the reservoir production mechanism and development indices.

Numerical simulation of migration-accumulation of oil resources in porous media is to describe the history of oil migration and accumulation in basin evolution. It is of great value to the evaluation of oil resources and to the determination of the location and amount of oil deposits. This thesis puts forward a mathematical model, a careful parallel operator splitting-up implicit iterative scheme, parallel arithmetic program, parallel arithmetic information and alternating-direction mesh subdivision. For the actual situation of Tanhai region of Shengli Petroleum Field, our numerical simulation test results and the actual conditions are coincident. For the model problem (nonlinear coupled system) optimal order estimates in $l^2$ norm are derived to determine the errors. We have successfully solved the difficult problem in the fields of permeation fluid mechanics and petroleum geology.

We consider overlapping Additive Schwarz Method (ASM) with Robin conditions as the transmission conditions (interior boundary conditions). The main difficulty left in this field is how to select the parameters for Robin conditions — these parameters have strong effect on the convergence rate of ASM. In this paper, we proposed the parameters for linear elliptic problems which seemed to be near optimal.

The subject of mesh generation and optimization is very important in many scientific applications. In this paper, we investigate the issue of mesh optimization via the construction of Centroidal Voronoi Tessellations. Given some initial Delaunay meshes with only average quality, it is shown that the CVT based mesh optimization generates a robust, high quality mesh which does not rely critically on the choice of the initial mesh. In comparison, other smoothing techniques, such as the classical Laplacian smoothing, tend to be more sensitive to the initial distributions of vertices. Thus, the CVT based optimization may be advocated as a preferred choice for mesh optimization and smoothing.

By simply transforming the quadratic matrix equation into an equivalent fixed-point equation, we construct a successive approximation method and a Newton's method based on this fixed-point equation. Under suitable conditions, we prove the local convergence of these two methods, as well as the linear convergence speed of the successive approximation method and the quadratic convergence speed of the Newton's method. Numerical results show that these new methods are accurate and effective when they are used to solve the quadratic matrix equation.

In this paper, a hybrid conjugate gradient algorithm with weighted preconditioner is proposed. The algorithm can efficiently solve the minimizing problem of general function deriving from finite element discretization of the p-Laplacian. The algorithm is efficient, and its convergence rate is mesh-independent. Numerical experiments show that the hybrid conjugate gradient direction of the algorithm is superior to the steepest descent one when $p$ is large.

History matching is an inverse problem of partial differential equation on mathematics. We adopt the constrained non-linear optimization to handle this problem, defining the objective function as the weighted square sum of differences between the wells simulation values and the corresponding observation values. We develop an optimization computing program that include Zoutendijk feasible direction method, Quasi-Newton method (BFGS) and improved Nelder-Mead simplex method, combined with a black-oil simulator, and discuss the convergence characters of algorithms in case studies about determining average porosity and directional permeability, determining low permeability strip between two wells and determining oil-water relative permeability curves.

In this paper, taking account of the major physical and chemical mechanisms, such as: for polymer, shearing property, permeability reduction, adsorption, inaccessible porous volumes, for gel, gelation speed, water viscosity changing with gel, permeability reduction, adsorption and retention in reservoir rocks, a three-dimensional, three-phase (oleic, vapor, aqueous) and six-component mathematical model has been established for polymer flooding and profile control. By use of full implicit finite difference method and calling PETSc linear solving system, the full implicit polymer flooding and profile control simulation software has been developed on PC-Linux environment based on black oil simulator, water flooding, polymer flooding and profile control simulation methods are integrated and applied into practice.

Tazhong Oil Field located in the center of Tarim Basin is one of the greatest discoveries during the petroleum exploration in Tarim Basin. The course of many years for hydrocarbon exploration and development has proved that there existed a much larger ancient reservoir than present-day reservoir and residual oil section below present WOC is of obvious characteristics of water displacement. Study shows that after it early formed, the paleo-reservoirs had been reformed to a great extent by hydrodynamic pressure caused by compacted water flow, which had played a dominant role in the redistribution of oil and gas in the evolution process of paleo-reservoir to present one. The previous method to study secondary migration caused by hydrodynamic pressure is as follows: to draw oil and water potential energy diagrams by utilizing pressure data of exploratory wells; to judge hydrocarbon migration direction and possible accumulation position by combining them with geological conditions; thereafter, to forecast potential oil reservoirs from the macroscopic view. Application of reservoir numerical simulation technology to hydrocarbon migration by hydrodynamic pressure has its advantage whether in its mechanism or in the accurate description of oil and water distribution. This paper has first presented the existence of the paleo-reservoir, and then constructs its geological model on the basis of recognizing its configuration at different geological stages.

After years of production, most oilfields with nonmarine deposits in China have been at their mature stage with high water cut and high recovery. The remaining oil is, on one hand, highly scattered in the reservoir, but on the other hand, relatively concentrated in some locations. The identification of the exact distribution of these locations with relatively abundant remaining oil is of great importance for improving oil recovery, but is very difficult. The oilfield development, which has been complicated by all the above factors, calls for more powerful numerical reservoir simulation techniques. The large-scale sophisticated numerical simulation technique with high efficiency, high precision, and high computing speed will be the key to the study on the remaining oil distribution for oilfields at their mature stage with high water cut. As for various types of complicated reservoirs, it is essential to develop different fluid flowing models and corresponding numerical simulation techniques.

Going through the development more than forty years, the overall water-cut to Daqing Oilfield has almost reached 90%. But there is still considerable residual oil in the place. Reservoir engineers want to know the residual oil spatial distribution and how to dig it. This requires large-scale reservoir simulation within limited time. Enlarged scale and highly expected efficiency need higher technical capability for reservoir simulation. By using PC-Cluster technique developed in recent years, large-scale reservoir simulation can be carried out at a relatively low cost. The first PC-Cluster used for reservoir simulation in Daqing Oilfield was designed and built. Based on this developing environment, the serial black oil simulator was parallelized by using the SLES components in PETSc. Then this parallel simulating technique was applied in seven oil production districts of Daqing Oilfield, where the PC-Clusters were configured and the parallel black oil simulator PBRS2.1 we had developed was installed and good results were achieved. In this paper, the hardware and system software configuration of PC-Clusters built is briefly introduced, the idea and method for parallelizing the serial black oil simulator is discussed, and the simulation study at seven typical field blocks and their application results are described and presented.

Based on percolation mechanism of fractured reservoirs and simulation technique, the numerical simulation software of fractured reservoirs has been developed on PC-Linux environment, which is on the basis of DQHY simulator of three dimensions and three phases. It can treat dual-porosity/single-permeability and dual-porosity/dual-permeability model. The results of examples indicate that the performance of fractured reservoirs could be simulated with the software.

In this paper, we introduce Explorer, a visualization system for reservoir simulations. It is designed for large-scale data sets and many technologies have been used during its implementation, such as a 3-layer Client-Commware-Server (CCS) structure, Object-Oriented method, VTK based rendering and etc. Compared with current commercial softwares, Explorer has many features including more data formats support, many user-defined properties and full support for Chinese characters.

Aim at large scale fine reservoir numerical simulation application research on Shenwei computer, the multilayer two dimension two phase parallel software transplanted successfully and a large scale integral simulation about ten million nodes were realized in the environment of Shenwei parallel computer. The whole preconditioning alternating Schward and another many improved algorithm, the parallel optimal methods about coefficient matrix and saturation calculation made the parallel efficiency increased effectively about multilayer two dimension two phase parallel software. Especially the deep research about the communication and load-balanced technology fitting for Shenwei computer make the parallel function of the software to large scale increase. The multilayer two dimension two phase parallel software transplanted and the parallel computer resource of homegrown Shenwei high behavior parallel computer with 112 CPUs was to simulate the production history of 12 sandgroups of the second Shahejian in second block of Shengtuo. The simulation scale is 10 million nodes and the time exhausted is about 5 hours which satisfies the application requisition of reservoir simulation. This verifies the reliability and stability of the software and makes the whole parallel efficiency to 79%. It is first time to bring out the independent copyright reservoir simulation parallel software with satisfactory back and forth processing function in homegrown Shenwei computer. Especially the application of the whole preconditioning alternating Schward region decomposition algorithm, the deep research of load-balanced technology and the large scale application etc. are all innovative.

3D prestack depth migration is an important and commonly used way to obtain the images of complex structures in seismic data processing. In this paper, 3D prestack depth migration with hybrid four-way splitting scheme is investigated. Wavefield extrapolation is based on the 3D acoustic one-way. The hybrid four-way splitting algorithm based on factorization is derived. Numerical calculations of 3D post-stack depth migration for an impulse and 3D prestack depth migration for SEC/EAEG benchmark model are implemented. The result of 3D post-stack depth migration show that the numerical anisotropic errors can be reduced effectively and the errors are small when the lateral velocity variations is small. Moreover, the 3D prestack depth migration for SEC/EAEG model both with two-way and four-way hybrid splitting scheme can yield its good images. The Message Passing Interface (MPI) programme is adopted on PC cluster as the large scale computation of 3D prestack depth migration. The parallel efficiency is high because of high parallel feature of 3D prestack depth migration. The methods presented in this paper can be applied in field data processing.

In this paper, a robust iterative method for the 2D heterogeneous Helmholtz equation is discussed. Two important ingredients of the method are evaluated, namely the Krylov subspace iterative methods and multigrid based preconditioners. For the Krylov subspace methods we evaluate GM-RES and Bi-CGSTAB. The preconditioner used is the complex shifted Laplace preconditioner [Erlangga, Vuik, Oosterlee, Appl. Numer. Math. 50(2004) 409-425] which is approximately solved using multigrid. Numerical examples which mimic geophysical applications are presented.