Overview

At the Center for Subsurface Modeling, we strive to meet today’s numerical modeling challenges by bringing together mathematicians, engineers, geoscientists, and computing experts in a cooperative environment. We believe that a multidisciplinary approach is the best way to obtain accurate, reliable, and efficient solutions to real-world problems.

Our researchers work with visitors and industrial partners throughout the world to stay on the cutting edge of scientific advancement. We continually seek to improve existing numerical models by using better physical interpretations, better numerical techniques, and high performance computing. Funds from our Industrial Affiliates program and federal agencies have helped us to develop our own parallel computing environment, which enables us to test and prove new concepts in advanced modeling and simulation.

In a rapidly changing world, the Center for Subsurface Modeling is dedicated to developing solutions to tomorrow’s modeling challenges today.

The accurate and efficient simulation of subsurface phenomena requires a blend of physical and geochemical modeling of subsurface processes and careful numerical implementation. Compounding these issues is a general lack of high quality data for model calibration and verification. CSM researchers collaborate with outside experts to find suitably accurate representations of physical systems, including such processes as fluid phase behavior, particle transport and dispersion, capillary pressure effects, flow in highly heterogeneous media possibly fractured and vuggy, geomechanical response and subsidence, and well production. These and other processes must be simulated accurately so as to avoid nonphysical numerical artifacts that can cloud engineering judgment regarding risk assessment and the intervention and optimization of management objectives.

Discretization and Adaptivity

Many subsurface modeling problems involve localized phenomena, such as concentrated plumes, sharp fronts, shocks, and layers, which may also change with time. The efficient simulation of these problems requires effective, dynamic, and self-adaptive local grid refinement and coarsening guided by accurate a-posteriori error estimators and fast projections preserving important physical properties, including local mass conservation. Major objectives to achieve in this area include:

• Accurate and efficient locally conservative discretization methods on general meshes;
• Characteristic methods for transport processes;
• Robust and efficient multiblock discretization techniques for multiscale, multiphysics and multi-algorithmic implementations;
• Robust a-posteriori error estimators;
• Mesh adaptivity based on a-posteriori error estimates;
• Spatial and temporal adaptivity with goal-oriented error estimators;
• Account for and reduce upscaling error.

Solvers

Our solver effort is based on the development of efficient and scalable algorithms for solving large-scale systems of algebraic equations arising in multiphase flow and its coupling with other physical models. Efforts in this area focus on the following:

• Physics-based multilevel and domain decomposition preconditioners for solving problems in highly heterogeneous media;
• Supercoarsening and algebraic multigrid;
• Newton-Krylov and Krylov-secant methods for solving nonlinear equations;
• Iterative coupling between models;
• Utilizing multiscale information in the design of physics-based preconditioning strategies;
• Efficient solvers for discretization on general meshes;
• Efficient solvers for coupled flow and geomechanics.

Optimization and Control

The development of robust and efficient optimization is critical in parameter estimation and in the optimal management and control of reservoir systems. Our group is dedicating an important effort to the implementation of:

• Stochastic and hybrid optimization algorithms;
• Parameterization strategies to effectively cope with the curse of dimensionality;
• Model reduction for highly nonlinear and multiphysics problems;
• Improved data assimilation models;
• Metamodels to perform sensitivity analysis and improve the estimations.

Uncertainty Analysis

A significant challenge in subsurface modeling arises from the fact that properties are sparcely known. Our modeling and inverse approaches are designed to account for this source of uncertainty. By modeling and sampling known probabilistic properties of uncertain parameters, we are able to address this uncertainty and devise robust strategies that deliver optimal results, even in the presence of insufficient knowledge. Major objectives in this area include:

• Uncertainty propagation through different scales in data and models;
• Accurate and efficient parameterization of uncertainty;
• Efficient uncertainty assessment through non-intrusive approaches such as stochastic and probabilistic collocation methods;
• Stochastic domain decomposition to model non-stationary random media;
• Incorporation of a-priori information through Bayesian approaches;
• Utilization of ensemble-based methods for history matching and parameter estimation.

Parallel and Grid Computing

IPARS has been successfully tested on the IBM Blue Gene/P clusters, the Lonestar and Ranger clusters at the TACC, and the Bevo2 cluster at ICES, UT Austin. We are thus able to evaluate the potential of grid computing for challenging subsurface simulations at much larger scales. Some of the challenges addressed here include:

• History matching and model reduction: IPARS now has the capability to perform history matching simulations using SPSA in parallel for parameter estimation. In addition, MATLAB invoked IPARS instances have been implemented within an EnKF (ensemble Kalman filter) framework for model reduction;
• Large dataset management and integration: Pre-processors enable integration of large datasets from real-field experiments. An efficient framework distributes this data among several computing nodes. These have been tested in the simulation of the Frio CO2 sequestration tests;
• Interactive computing and visualization: IPARS has been coupled to DISCOVER, an interactive and collaborative engine that allows for web-based portal access to our computing applications. Users can steer applications in real-time by directly altering input to the simulator, based on observed parameters (e.g., economic value) of the production process.

Coupled Flow and Geomechanics

Diverse geomechanical effects take place due to changes in pressure and saturation over the production lifetime of a reservoir. This is particularly critical in naturally fractured reservoirs, faulty and highly compressible formations, and in assessing borehole stability. To this end we have developed parallel scalable multiphase poroelasticity models. Theoretical analyses of stress dependent permeability has been obtained for single phase flow as well as the fomulation and implementation of a multiscale domain decomposition algorithm that allows for non-matching subdomain grids for modeling elasticity. Future work will include:

• Incorporation of plasticity models;
• Adaptive modeling using mortar multiscale domain decomposition to reduce computational costs;
• Iterative coupling to a reservoir simulator utilizing multiple time scales;
• Investigating the effects of coupling geomechanics with other subsurface processes, e.g., geochemical and thermal.

Multiscale Modeling

A complete subsurface characterization requires modeling a variety of processes which occur at vastly different scales, from the nanoscale and the pore scale, to the field scale, and from less than a second to millennium time scales. While a numerical simulation cannot span all of these scales, given today’s computational resources, it is nevertheless necessary to incorporate relevant fine scale effects into a coarse scale model. Our group is exploring the following avenues of research:

• Subgrid upscaling and homogenization techniques for incorporating heterogeneities and other fine-scale processes within coarse grid cells;
• Computationally tractible and accurate modeling of vuggy and fractured systems;
• Pore-scale modeling of non-Newtonian fluids in granular materials;
• Physical multiscale and domain decomposition approaches;
• Coupling of stochastic and deterministic multiscale modeling;
• Goal oriented multiscale and upscaling via optimization methods;
• Utilizing a-posteriori error estimates to account for errors at different scales.

Applications

Despite the above described particular algorithmic challenges for the accurate and efficient modeling of multiphase flow, chemical reactions, and geomechanics, the group has been pursuing research on a wide portfolio of applications. These efforts are in-line with the increasing interest shown by environmental agencies and the oil industry toward a much better understanding of coupled flow, geochemical and geomechanical effects in long-term simulations.

• CO2 Sequestration in Saline Aquifers: Our ongoing efforts involve extending existing algorithms and the parallel computing capabilities of IPARS toward physically accurate flow models with special focus on CO2 sequestration coupled to geochemical processes. This involves improving discretization methods and solvers for better treatment of arbitrary geometries and medium heterogeneities. For this application, a hysteresis model and a thermal energy balance have been coupled to the compositional flow model.
• CO2-EOR: Our ongoing efforts involve extending existing capabilities of IPARS with special focus on CO2 injection in oil reservoirs as combined enhanced oil recovery and CO2 storage. The enhanced velocity mixed finite element method (EVMFEM) has been successfully implemented for compositional flow. This allows us to solve these computationally intensive problems on non-matching multiblock grids with the freedom of both choosing grid sizes, and, in a multimodel setting, using single phase flow in a majority of the computational domain. The EVMFEM has already been tested on practical problems in multiphase and compositional flow as well as flow coupled to reactive transport. For better treatment of general geometries, a robust Multipoint Flux Mixed Finite Element (MFMFE) method has been developed for the pressure equation and is being coupled to flow models.
• Non-Newtonian Polymer Flow: We have broadened the application of IPARS to the modeling of commercial scale polymer floods. Aqueous species such as anions, divalent cations, and polymer molecules are handled in the TRCHEM module of IPARS. High molecular weight water soluble polymers increase the viscosity of water significantly. Polymer solutions often exhibit non-Newtonian rheological behavior where the viscosity decreases as the shear rate increases. We also investigate flexible gridding, solvers, multiscale algorithms and dynamic load balancing issues that arise in parallel simulations.
• Aqueous Chemistry: Several published laboratory experiments have reported on the effect of potential determining ions such as Ca++, Mg++, and SO4-- on oil recovery from carbonate chalk. We plan to model the water chemistry including rock dissolution/precipitation and the impact on wettability of carbonates and subsequent oil recovery improvement during seawater injection using TRCHEM.