/pdf/development-of-an-efficient-embedded-discrete-fracture-model-24f3tauvjl.pdf

Development of an Efficient Embedded Discrete Fracture Model for 3D Compositional Reservoir Simulation in Fractured Reservoirs

Automatic Differentiation (AD) is a maturing computational technology. It has become a mainstream tool used by practicing scientists and computer engineers. The rapid advance of hardware computing power and AD tools has enabled practitioners to generate derivative enhanced versions of their code for a broad range of applications in applied research and development. Automatic Differentiation of Algorithms provides a comprehensive and authoritative survey of all recent developments, new techniques, and tools for AD use.

Automatic Differentiation Of Algorithms: From Simulation To Optimization

Dynamics. Differential Algebraic Techniques. Fields. Maps: Calculation. Maps: Properties. Spectrometers. Repetitive Systems.

Modern map methods in particle beam physics

In variational data assimilation (VDA) for meteorological and/or oceanic models, the assimilated fields are deduced by combining the model and the gradient of a cost functional measuring discrepancy between model solution and observation, via a first-order optimality system. However, existence and uniqueness of the VDA problem along with convergence of the algorithms for its implementation depend on the convexity of the cost function. Properties of local convexity can be deduced by studying the Hessian of the cost function in the vicinity of the optimum. This shows the necessity of second-order information to ensure a unique solution to the VDA problem. In this paper a comprehensive review of issues related to second-order analysis of the problem of VDA is presented along with many important issues closely connected to it. In particular issues of existence, uniqueness, and regularization through second-order properties are examined. The focus then shifts to second-order information related to statistical properties and to issues related to preconditioning and optimization methods and second-order VDA analysis. Predictability and its relation to the structure of the Hessian of the cost functional is then discussed along with issues of sensitivity analysis in the presence of data being assimilated. Computational complexity issues are also addressed and discussed. Automatic differentiation issues related to second-order information are also discussed along with the computational complexity of deriving the second-order adjoint. Finally an application aimed at illustrating the use of automatic differentiation for deriving the second-order adjoint as well as the Hessian/vector product applied to minimizing a cost functional of a meteorological problem using the truncated-Newton method is presented. Results verifying numerically the computational cost of deriving the second-order adjoint as well as results related to the spectrum of the Hessian of the cost functional are displayed and discussed.

/pdf/second-order-information-in-data-assimilation-2jjrgchdcf.pdf

Second-Order Information in Data Assimilation*

Development of a Coupled Dual Continuum and Discrete Fracture Model for the Simulation of Unconventional Reservoirs

This paper was selected for presentation by an SPE Program Committee following review of information contained in an abstract submitted by the author(s). Contents of the paper, as presented, have not been reviewed by the Society of Petroleum Engineers and are subject to correction by the author(s). The material, as presented, does not necessarily reflect any position of the Society of Petroleum Engineers, its officers, or members. Papers presented at SPE meetings are subject to publication review by Editorial Committees of the Society of Petroleum Engineers. Electronic reproduction, distribution, or storage of any part of this paper for commercial purposes without the written consent of the Society of Petroleum Engineers is prohibited. Permission to reproduce in print is restricted to an abstract of not more than 300 words; illustrations may not be copied. The abstract must contain conspicuous acknowledgment of where and by whom the paper was presented. Abstract A fully implicit parallel equation-of-state (EOS) compositional simulator for large-scale reservoir simulation is presented. This simulator is developed under the framework named IPARS (Integrated Parallel Accurate Reservoir Simulator) and is constructed using a Newton-type formulation. The Peng-Robinson EOS is used for the hydrocarbon phase behavior calculations. The linear solvers from the PETSc package (Portable Extensible Toolkit for Scientific Computation) are used for the solution of the underlying linear equations. The framework provides input/output, table lookups, Fortran array memory allocation, domain decomposition, and message passing between processors for updating physical properties in mass-balance equations in overlapping regions. PETSc handles communications between processors needed for the linear solver. Many test runs were performed with up to four million gridblocks for a dry-gas injection process on an IBM SP machine and half a million gridblocks on a cluster of 16 PCs. Results indicate that the scalability of the simulator is very good. The linear solver takes around half of the total computational time for homogeneous reservoirs. For layered heterogeneous reservoirs, the linear solver took a larger fraction of the total computational time as the permeability contrast increased. The time for the communication between processors for updating the flow equations is insignificant. The PC cluster is roughly a factor of two slower than the SP for parallel runs, which is very encouraging. This factor is strongly related to the hardware configuration of the computers, which is detailed in the paper.

A Fully Implicit Parallel EOS Compositional Simulator for Large Scale Reservoir Simulation.

This article describes approaches to computing second-order derivatives with automatic differentiation (AD) based on the forward mode and the propagation of univariate Taylor series. Performance results are given that show the speedup possible with these techniques relative to existing approaches. The authors also describe a new source transformation AD module for computing second-order derivatives of C and Fortran codes and the underlying infrastructure used to create a language-independent translation tool.

/pdf/algorithms-and-design-for-a-second-order-automatic-3zotht38e1.pdf

Algorithms and design for a second-order automatic differentiation module

The authors have ported a fully implicit equation-of-state (EOS) compositional parallel reservoir simulator to run on clusters of PCs. They report on the performance of the code on two clusters, both in terms of scalability and in absolute performance relative to an IBM SP. The simulator scales well through 16 processors on the clusters and is comparable in execution time with the SP.

Parallel Compositional Reservoir Simulation on Clusters of PCs

A hosting platform includes a main server layer and an auxiliary server layer. The main server layer includes one or more servers and a server of the one or more servers is designated to process requests for one or more hosts. The auxiliary server layer may be removably coupled to and in communication with the main layer. The auxiliary layer may process the request redirected from the main layer when the designated server of the main layer is overloaded.

Multi-layer system for scalable hosting platform

Often the most robust and efficient algorithms for the solution of large-scale problems involving nonlinear PDEs and optimization require the computation of derivatives. We examine the use of automatic differentiation (AD) for computing first and second derivatives in conjunction with two parallel toolkits, the Portable, Extensible Toolkit for Scientific Computing (PETSc) and the Toolkit for Advanced Optimization (TAO). We discuss how the use of mathematical abstractions in PETSc and TAO facilitates the use of AD to automatically generate derivative codes and present performance data demonstrating the suitability of this approach.

Jason Abate

Papers

A Fully Implicit Parallel EOS Compositional Simulator for Large Scale Reservoir Simulation.

Algorithms and design for a second-order automatic differentiation module

Parallel Compositional Reservoir Simulation on Clusters of PCs

Multi-layer system for scalable hosting platform

Integrating AD with object-oriented toolkits for high-performance scientific computing