Sunil G. Thomas

A multiscale mortar mixed finite element method for slightly compressible flows in porous media

We consider multiscale mortar mixed finite element discretizations for slightly compressible Darcy flows in porous media. This paper is an extension of the formulation introduced by Arbogast et al. for the incompressible problem [2]. In this method, flux continuity is imposed via a mortar finite element space on a coarse grid scale, while the equations in the coarse elements (or subdomains) are discretized on a fine grid scale. Optimal fine scale convergence is obtained by an appropriate choice of mortar grid and polynomial degree of approximation. Parallel numerical simulations on some multiscale benchmark problems are given to show the efficiency and effectiveness of the method.

Towards dynamic data-driven management of the ruby gulch waste repository

Previous work in the Instrumented Oil-Field DDDAS project has enabled a new generation of data-driven, interactive and dynamically adaptive strategies for subsurface characterization and oil reservoir management. This work has led to the implementation of advanced multi-physics, multi-scale, and multi-block numerical models and an autonomic software stack for DDDAS applications. The stack implements a Grid-based adaptive execution engine, distributed data management services for real-time data access, exploration, and coupling, and self-managing middleware services for seamless discovery and composition of components, services, and data on the Grid. This paper investigates how these solutions can be leveraged and applied to address another DDDAS application of strategic importance – the data-driven management of Ruby Gulch Waste Repository.

Assessing the Value of Sensor Information In 4-D Seismic History Matching

Summary The main objective of the present work is to numerically determine how sensor information may aid in reducing the ill-posedness associated with permeability estimation via 4D seismic history matching. These sensors are assumed to provide timely information of pressures, concentrations and fluid velocities at given locations in a reliable fashion. This information is incorporated into an objective function that additionally includes production and seismic components that are mismatched between observed and predicted data. In order to efficiently perform large-scale permeability estimation, a coupled multilevel, stochastic and learning search methodology is proposed. At a given resolution level, the parameter space is globally explored and sampled by the simultaneous perturbation stochastic approximation (SPSA) algorithm. The estimation and sampling performed by SPSA is further enhanced by a neural learning engine that estimates sensitivities in the vicinity of the most promising optimal solutions. Preliminary results shed light on future research avenues for optimizing the frequency and localization of 4-D seismic surveys when sensor data is

A Multiscale and Metamodel Simulation-Based Method for History Matching

This paper presents a novel framework for history matching using the concept of simulation-based optimization with guided search sampling, multiscale resolution and incremental metamodel (surrogate model) generation, aimed to mitigate the computational burden of large-scale history matching. The initial stage of the framework consists of a multiscale treatment of the permeability field through successive wavelet transformations. The coarsest grid which represents a highly constrained parameter space, is sampled with the aid of a derivative-free stochastic optimization algorithm that detects the most promising search regions. Due to the size of the coarse grid, thousands of simulation runs are possible at a low computational cost. Next, a sequence of intermediate metamodels is built iteratively by gradually increasing the number of sampling points in the decision space and using these temporary models to guide an incremental sampling. This incremental sampling is dictated by the use of an optimization method that finds a local optimum solution in a few iteration steps. The iterative refinement process is terminated when the metamodel solution is capable of reproducing (within a predefined tolerance) the reservoir simulator response. These metamodels are constructed using a support vector machine approach that captures the causal relations embedded in reservoir simulation by discriminating the true signal from the noise without over-fitting the simulation results. Finally, the coarse grid optimal solution is used as an initial point for the next finer grid level with the use of the inverse wavelet transform. The procedure is repeated with a decreasing number of function evaluations as the grid resolution level is increased. The objective function includes well production data and sensor measurements. Numerical experiments on realistic data reveal that the proposed framework improves the history matching process, not only in terms of computing savings and the accuracy of the estimated permeability field.

A Parallel Stochastic Framework for Reservoir Characterization and History Matching

The spatial distribution of parameters that characterize the subsurface is never known to any reasonable level of accuracy required to solve the governing PDEs of multiphase flow or species transport through porous media. This paper presents a numerically cheap, yet efficient, accurate and parallel framework to estimate reservoir parameters, for example, medium permeability, using sensor information from measurements of the solution variables such as phase pressures, phase concentrations, fluxes, and seismic and well log data. Numerical results are presented to demonstrate the method.

Mortar Coupling of Discontinuous Galerkin and Mixed Finite Element Methods

Geological media exhibit permeability fields and porosities that differ by several orders of magnitude across highly varying length scales. Computational methods used to model flow through such media should be capable of treating rough coefficients and grids. Further, the adherence of these methods to basic physical properties such as local mass balance and continuity of fluxes is of great importance. Both discontinuous Galerkin (DG) and mixed finite element (MFE) methods satisfy local mass balance and can accurately treat rough coefficients and grids. The appropriate choice of physical models and numerical methods can substantially reduce computational cost with no loss of accuracy. MFE is popular due to its accurate approximation of both pressure and flux but is limited to relatively structured grids. On the other hand, DG supports higher order local approximations, is robust and handles unstructured grids, but is very expensive because of the number of unknowns. To this end, we present DG-DG and DG-MFE domain decomposition couplings for slightly compressible single phase flow in porous media. Mortar finite elements are used to impose weak continuity of fluxes and pressures on the interfaces. The sub-domain grids can be non-matching and the mortar grid can be much coarser making this a multiscale method. The resulting nonlinear algebraic system is solved via a non-overlapping domain decomposition algorithm, which reduces the global problem to an interface problem for the pressures. Solutions of numerical experiments performed on simple test cases are first presented to validate the method. Then, additional results of some challenging problems in reservoir simulation are shown to motivate the future application of the theory.

Integrated Time-lapse Seismic Inversion for Reservoir Petrophysics and Fluid Flow Imaging

SUMMARY Seismic history matching has been used to reduce uncertainty and increase the accuracy in reservoir characterization. In this paper we propose a joint inversion scheme for quantitative reservoir petrophysics characterization and inside fluid flow imaging, which integrates as many data sources as available, such as timelapse seismic data, production data and sensor information. We demonstrate that this integrated framework leads to accurate seismic history matching and reservoir parameter estimation and that the incorporation of time-lapse seismic data does help speed up the convergence process. In addition, the imaging of the inside fluid flow is also obtained. Considering the unique feature of Bayesian inference in data integration and uncertainty analysis, we also propose a formulation to simultaneously integrate all data sources in a Bayesian framework and solve the problem by stochastically constructing the posterior probability distribution (PPD) using Markov Chain Monte Carlo (MCMC) methods. The coefficients of rock fluid physics models are also incorporated. This means that the coefficients are determined stochastically based on data rather from lab measurements or empirical relationships. Based on MCMC samples, uncertainty can be correctly quantified.

A Learning Computational Engine for History Matching

The main objective of the present work is to propose and evaluate a learning computational engine for history matching, which is based on a hybrid multilevel search methodology. According to this methodology, the parameter space is globally explored and sampled by the simultaneous perturbation stochastic approximation (SPSA) algorithm at a given resolution level. This estimation is followed by further analysis by using a neural learning engine for evaluating the sensitiveness of the objective function with respect to variations of each individual model parameter in the vicinity of the promising optimal solution explored by the SPSA algorithm. The proposed methodology is used to numerically determine how additional sources of information may aid in reducing the ill-posedness associated with permeability estimation via conventional history matching procedures. The additional sources of information considered in this work are related to pressures, concentrations and fluid velocities at given locations in a reliable fashion, which in practical scenarios might be estimated from high resolution seismic surveys, or directly obtained as in situ measurements provided by sensors. This additional information is incorporated, along with production data, into a multi-objective function that is mismatched between the observed and the predicted data. The preliminary results presented in this work shed light on future research avenues for optimizing the use of additional sources of information such as seismic or sensor data in history matching procedures.

Role of Computational Science in Protecting the Environment: Geological Storage of CO2

Simulation of field-scale CO2 sequestration (which is defined as the capture, separation and long-term storage of CO2 for environmental purposes) has gained significant importance in recent times. Here we discuss mathematical and computational formulations for describing reservoir characterization and evaluation of long term CO2 storage in saline aquifers as well as current computational capabilities and challenges.

Parallel Simulations of CO2 Sequestration Using a Non-Isothermal Compositional Model

This paper describes an efficient and parallel numerical scheme for multiphase compositional flow. The underlying theory is first presented followed by a brief description of the equation of state (EOS) and the two-phase flash implementation. An iterative “implicit-pressure and explicit-concentrations” (IMPEC) algorithm is then applied to enforce a non-linear volume balance (saturation) constraint. The pressure system is solved using a mixed finite element method, while the concentrations are updated explicitly in a manner that preserves local mass balance of every component. A major application of this scheme is in the modeling of field scale CO2 sequestration, as an enhanced oil recovery (EOR) process or for storage in deep saline aquifers. Thermal energy transfer also plays an important role in such problems since it can effect the phase properties dramatically. Hence, accurate and locally conservative methods are desirable to model the thermal effects. To this end, the paper also presents a time-split scheme for modeling thermal energy transfer which is sequentially coupled to flow. Finally, some numerical results are presented for challenging benchmark problems.Copyright