Showing papers by "Mary F. Wheeler published in 2011"

Domain decomposition for poroelasticity and elasticity with dg jumps and mortars

Abstract: We couple a time-dependent poroelastic model in a region with an elastic model in adjacent regions. We discretize each model independently on non-matching grids and we realize a domain decomposition on the interface between the regions by introducing DG jumps and mortars. The unknowns are condensed on the interface, so that at each time step, the computation in each subdomain can be performed in parallel. In addition, by extrapolating the displacement, we present an algorithm where the computations of the pressure and displacement are decoupled. We show that the matrix of the interface problem is positive definite and establish error estimates for this scheme.

Enhanced velocity mixed finite element methods for modeling coupled flow and transport on non-matching multiblock grids

Abstract: The enhanced velocity mixed finite element method, due to Wheeler et al. (Comput Geosci 6(3–4):315–332, 2002), is analyzed and extended to the problem of modeling slightly compressible flow coupled to the transport of chemical species through porous media, on non-matching multiblock grids. Applications include modeling bio-remediation of heavy oil spills and many other subsurface hazardous wastes, angiogenesis in transition of tumors from dormant to malignant states, transport of contaminants in ground water flow, and acid injection from well bores to increase permeability of surrounding rock. The analysis and numerical examples presented here demonstrate convergence and computational efficiency of this method.

Seismic Wave Propagation In Fractured Media: a Discontinuous Galerkin Approach

Abstract: A realistic model of the subsurface should include fractures; these can be observed in many scales, from faults to micro-cracks. In particular, azimuthal velocity anisotropy has been observed in many regions, and this has been attributed to aligned vertical micro-cracks (Schoenberg and Douma, 1988). For this reason there has been recently an increased interest in the characterization of fractured media in the oil industry (e. g. Schoenberg, 1980; Schoenberg and Douma, 1988; Liu et al., 2000; Sen et al., 2007; Zhang and Gao, 2009).

On Interplay of Capillary, Gravity, and Viscous Forces on Brine/CO2 Relative Permeability in a Compositional and Parallel Simulation Framework

Abstract: The effectiveness of CO2 storage in saline aquifers is governed by interplay of capillary, viscous, and buoyancy forces. Recent experimental data reveals the impact of pressure, temperature, and salinity on interfacial tension (IFT) between CO2 and brine. The dependence of CO2-brine relative permeability and capillary pressure on IFT is also clearly evident in published experimental results. Improved understanding of the mechanisms that control the migration and trapping of CO2 in subsurface is crucial to design future storage projects that warrant long term and safe containment. Simulation studies ignoring the variation in interfacial tension and its effect on petrophysical properties of trapped CO2 saturations, relative permeability and capillary pressure have a poor chance of making accurate predictions of CO2 injectivity and its migration. We have developed and implemented a general relative permeability model that combines effects of pressure gradient, buoyancy, and IFT in an Equation of State (EOS) compositional and parallel simulator. The significance of IFT variations on CO2 migration and trapping is assessed. Introduction Saline aquifers can provide vast and safe storage for carbon dioxide pending a proper understanding of the displacement mechanisms of CO2-brine binary system at insitu conditions (Bachu, 2003). These aquifers are widely distributed, have reasonable permeability and porosity values, and have good thickness with large storage capacity (Franklin and Orr, 2004). Geological carbon sequestration involves injecting the produced CO2 into subsurface formations and trapping it through many geological and chemical mechanisms. CO2 injection in subsurface invokes multiphase flow, fluid phase behavior, relative permeability, wettability, gravity and buoyancy, capillary pressure, and geochemical reactions. Several research groups have studied the interplay of the capillary, gravity, viscous forces, and other factors that may affect the trapping (Pruess et al., 2003; Bachu et al., 1994; House et al., 2003). Much experimental research is focused on interfacial tension of oil, water, and gas phases (Taha, 2010). Many achievements have been made to understand the subsurface interaction between CO2 and formation brine (Bachu, 2008; Gunter, et al., 2004; Kumar, et al., 2005). Based on these findings, the injected CO2 in saline aquifers could be characterized in following forms: dissolved in formation brine, trapped by capillary forces in the pore space as residual saturation, adsorbed on minerals by chemical trapping, and free phase that is mobile. However, because the chemical trapping is significant for CO2 sequestration only in geological time scale, it is sometimes neglected for short time behavior studies. The injectivity of CO2 into an aquifer is greatly affected by the relative permeability and interplay of capillary, gravity, and viscous forces. During injection into the aquifers, CO2 displaces formation water at the leading edge of the plume as a drainage process. On the other hand during post injection, the formation brine displaces CO2 at the trailing end as in an imbibition direction. Several hysteresis models have been developed to capture the saturation history dependent relative permeability and capillary pressure relationships (Doughty, 2007). Experimental results show the change in both drainage and imbibition capillary pressure and relative permeability as the results of variations in pressure and salinity and (Bennion and Bachu, 2006). In many simulation studies, relative permeabilities are, however, defined at the beginning of the simulation study and only the variations due to saturation is modeled and the changes of pressure, salinity, and temperature are typically ignored. With the exception of the simulators with hysteretic models, the residual CO2 saturation is also fixed for a given rock type. However, the residual saturation is affected by the interfacial tension between CO2 and water and many experimental results reveal that the IFT between CO2 and brine varies at different pressure, salinity, and temperature conditions (Hauser and Michaels, 1948; Liu et al., 2010; Bennion and Bachu 2008; Al-Abri and Amin, 2009). These results show that the IFT decreases with increasing pressure, and increases with increasing temperature and salinity. The results also

A Family of Multipoint Flux Mixed Finite Element Methods for Elliptic Problems on General Grids

Abstract: In this paper, we discuss a family of multipoint flux mixed finite element (MFMFE) methods on simplicial, quadrilateral, hexahedral, and triangular-prismatic grids. The MFMFE methods are locally conservative with continuous normal fluxes, since they are developed within a variational framework as mixed finite element methods with special approximating spaces and quadrature rules. The latter allows for local flux elimination giving a cell-centered system for the scalar variable. We study two versions of the method: with a symmetric quadrature rule on smooth grids and a non-symmetric quadrature rule on rough grids. Theoretical and numerical results demonstrate first order convergence for problems with full-tensor coeffcients. Second order superconvergence is observed on smooth grids.

Accurate Cell-Centered Discretizations for Modeling Multiphase Flow in Porous Media on General Hexahedral and Simplicial Grids

Abstract: Mary F. Wheeler is supported by the NSF-CDI under contract number DMS 0835745, DOE grant DE-FG02-04ER25617, and the Center for Frontiers of Subsurface Energy Security under Contract No. DE-SC0001114. Guangri Xue is supported by Award No. KUS-F1-032-04, made by the King Abdullah University of Science and Technology. Ivan Yotov is partially supported by the DOE grant DE-FG02-04ER25618, the NSF grant DMS 0813901, and the J. Tinsley Oden Faculty Fellowship, Institute for Computational Engineering and Sciences, University of Texas at Austin.

Benchmark 3D: A multipoint flux mixed finite element method on general hexahedra

Abstract: In this paper we discuss a family of numerical schemes for modeling Darcy flow, the multipoint flux mixed finite element (MFMFE) methods. The MFMFE methods allow for an accurate and efficient treatment of irregular geometries and heterogeneities such as faults, layers, and pinchouts that require highly distorted grids and discontinuous coefficients. The methods can be reduced to cell-centered discretizations and have convergent pressures and velocities on general hexahedral and simplicial grids.

A hybrid algorithm for global optimization problems

Abstract: We propose a hybrid algorithm for solving global optimization problems that is based on the coupling of the Simultaneous Perturbation Stochastic Approximation (SPSA) and Newton-Krylov Interior-Point (NKIP) methods via a surrogate model. There exist verified algorithms for finding approximate global solutions, but our technique will further guarantee that such solutions satisfy physical bounds of the problem. First, the SPSA algorithm conjectures regions where a global solution may exist. Next, some data points from the regions are selected to generate a continuously differentiable surrogate model that approximates the original function. Finally, the NKIP algorithm is applied to the surrogate model subject to bound constraints for obtaining a feasible approximate global solution. We present some numerical results on a set of five small problems and two medium to large-scale applications from reservoir simulations.

Dynamic Decision and Data-Driven Strategies for the Optimal Management of Subsurface Geo-Systems*

Abstract: Effective geo-system management involves understanding of the interplay between surface entities (e.g., locations of injection and production wells in an oil reservoir) and appropriately effecting subsurface characteristics. This in turn requires efficient integration of complex numerical models of the environment, optimization procedures, and decision making processes. The dynamic, data-driven application systems (DDDAS) paradigm offers a promising framework to address this requirement. To achieve this goal, we have developed advanced multi-physics, multi-scale, and multi-block numerical models and autonomic systems software for dynamic, data-driven applications systems. This work has enabled a new generation of data-driven, interactive and dynamically adaptive strategies for subsurface characterization and management. These strategies have been applied to different aspects of subsurface management in strategically important application areas, including simulation-based optimization for the optimal oil w...

A Parallel Stochastic Framework for Reservoir Characterization and History Matching

Abstract: 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.