Paulo Goldfeld

Comparing Genetic Algorithms and Newton-Like Methods for the Solution of the History Matching Problem

In this work we presents a comparison of different optimization methods for the automatic history matching problem of reservoir simulation. The history matching process is an inverse problem that searches a set of parameters that minimizes the difference between the model performance and the historical performance of the field. This model validation process is essential and gives credibility to the predictions of the reservoir model. Derivative-based methods are compared to a free-derivative algorithm. In particular, we compare the Quasi-Newton method, non-linear Conjugate-Gradient, Steepest-Descent and a Genetic Algorithm implementation. Several tests are performed and the preliminary results are presented and discussed.

Performance evaluation of a reservoir simulator on a multi-core cluster

Reservoir simulators are one of the most important tools on reservoir engineering since they allow the prediction of real reservoir’s behavior. However, in order to deal with medium and large scale problems it is necessary to use parallel computing. This work presents the development of a reservoir simulator, based on a two-phase flow model of porous media, and its parallelization. The implementation of the simulator was based on an IMPES scheme and the PETSc library, which uses MPI for data communication between processes, was employed to solve the system of equations. The performance analysis was made in a parallel environment composed by a cluster of multiprocessor computers and the results suggest that the performance of parallel applications strongly depends on the memory contention in multiprocessor computers, such as the quad-cores. Thus, parallel computing should follow certain restrictions regarding the use and mapping of tasks to compute cores.

Automatic history matching in petroleum reservoirs using the TSVD method

History matching is an important inverse problem extensively used to estimate petrophysical properties of an oil reservoir by matching a numerical simulation to the reservoirs history of oil production. In this work, we present a method for the resolution of a history matching problem that aims to estimate the permeability field of a reservoir using the pressure and the flow rate observed in the wells. The reservoir simulation is based on a two-phase incompressible flow model. The method combines the truncated singular value decomposition (TSVD) and the Gauss-Newton algorithms. The number of parameters to estimate depends on how many gridblocks are used to discretize the reservoir. In general, this number is large and the inverse problem is ill-posed. The TSVD method regularizes the problem and decreases considerably the computational effort necessary to solve it. To compute the TSVD we used the Lanczos method combined with numerical implementations of the derivative and of the adjoint formulation of the problem.

Robust two-level lower-order preconditioners for a higher-order stokes discretization with highly discontinuous viscosities

The main goal of this paper is to present new robust and scalable preconditioned conjugate gradient algorithms for solving Stokes equations with large viscosity jumps across subregion interfaces and discretized on non-structured meshes. The proposed algorithms do not require the construction of a coarse mesh and avoid expensive communications between coarse and fine levels. The algorithms belong to the family of preconditioners based on non-overlapping decomposition of subregions known as balancing domain decomposition methods. The local problems employ two-level element-wise/subdomain-wise direct factorizations to reduce the size and the cost of the local Dirichlet and Neumann Stokes solvers. The Stokes coarse problem is based on subdomain constant pressures and on connected subdomain interface flux functions and rigid body motions. This guarantees scalability and solvability of the local Neumann problems. Estimates on the condition numbers and numerical experiments based on a parallel implementation for unstructured meshes are also discussed.

Truncated conjugate gradient and improved LBFGS and TSVD for history matching

We propose a new algorithm for solving the history matching problem in reservoir simulation, truncated conjugate gradient (TCG), which involves a model reparameterization based on the factorization of the prior covariance matrix, CM = LLT. We also revisit the LBFGS algorithm, framing it into the same reparametrization, introducing M-LBFGS. We present numerical evidence that this reparameterization has an important regularizing impact on the solution process. We show how TCG and M-LBFGS, as well as TSVD, can be implemented without the need of actually computing the factor L. Our numerical experiments, including the PUNQ-S3 and the Brugge cases, indicate that TCG and M-LBFGS are effective schemes for history matching.

Truncated Conjugate Gradient Method for History Matching in Reservoir Simulation

History Matching (HM) is an important problem in Oil Reservoir Simulation. We present here the Truncated Conjugate Gradient (TCG) Method to solve this problem. We compare TCG with two other well known schemes, TSVD and L-BFGS, in a numerical experiment using the benchmark problem PUNQ-S3. Our results indicate that TCG is a valuable tool for HM.

Método de Precondicionamento CPR em Simulações de Reservatório de Petróleo

Este trabalho apresenta a implementacao, em MATLAB, de um esquema de dois estagios do tipo CPR (do ingles Constrained Pressure Residual) [5], para a resolucao de sistemas lineares de grande porte oriundos de simulacoes de extracao de reservatorios de petroleo. Vamos descrever o metodo CPR, seus dois estagios e apresentar resultados para matrizes de problemas reais, comparando-os com resultados utilizando precondicionadores classicos.

Implementação paralela de um precondicionador algébrico de dois níveis de decomposição de domínios baseado em ILU(k)

Discutimos a implementacao paralela em Message-Passing Interface (MPI) de um precondicionador algebrico de dois niveis de decomposicao de dominios baseado em fatoracao incompleta LU (ILU(k)) utilizando a biblioteca PETSc e estrategias para melhorar a performance e reduzir a comunicacao entre os processadores durante a construcao e aplicacao.

Nova implementação do precondicionador AINV em acelerador NVIDIA utilizando a biblioteca CUSP

Comparamos o desempenho em placa grafica (GPU) do precondicionador AINV baseado na aproximacao da inversa. Os resultados de nossos experimentos numericos e computacionais indicam que nossa implementacao e competitiva e possui resultados melhores do que a versao disponivel na biblioteca CUSP largamente utilizada em aplicacoes com aceleradores NVIDIA. Alem disso, apresentamos as ideias principais na definicao do precondicionador e detalhes sobre a implementacao.

Comparing Two-Level Preconditioners for Solving Petroleum Reservoir Simulation Problems

Domain decomposition ideas (proven suitable for parallelization) are combined with incomplete factorizations (which are standard in reservoir simulation) at subdomain level, with the ultimate goal of designing a scalable parallel preconditioner for addressing reservoir simulation problems. An ILU(k)-based two-level domain decomposition preconditioner is introduced, and its performance is compared with a two-level ILU(k)-block Jacobi preconditioner.