Steve Bryant

Coupled fluid flow and geomechanical deformation modeling

Accurate prediction of reservoir production in structurally weak geologic areas requires both mechanical deformation and fluid flow modeling. Loose staggered-in-time coupling of two independent flow and mechanics simulators captures much of the complex physics at a substantially reduced cost. Two 3-D finite element simulators—Integrated Parallel Accurate Reservoir Simulator (IPARS) for flow and JAS3D for mechanics—together model multiphase fluid flow in reservoir rocks undergoing deformation ranging from linear elasticity to large, nonlinear inelastic compaction. The loose coupling algorithm uses a highlevel driver to call the flow simulator for a set of time steps with fixed reservoir properties. Pore pressures from flow are used as loads for the geomechanics code in the determination of stresses, strains, and displacements. The mechanics-derived strain is used to calculate changes to the reservoir parameters (porosity and permeability) for the next set of flow time steps. Mass is conserved in the coupled code despite dynamically changing reservoir parameters via a modification to the Newton system for the flow equations, and an approximate rock compressibility becomes a useful preconditioner to help with convergence of the modified flow equations. Two numerical experiments illustrate the accuracy of the coupled code. The first example is a quarterfive-spot waterflood undergoing poroelastic deformation, which is validated against a fully coupled simulator. Vertical displacements at the well locations match to within 10%. Moreover, experimentation shows that 13 mechanics time steps (taken over the course of 5 years of simulation time) were sufficient to achieve this result (a substantial cost savings over full coupling in which both the mechanics and flow equations must be solved at each time step). The second numerical example is based on real data from the Belridge Field in California, which illustrates one of the complex plastic constitutive relationships available in the coupled code. The results mimic behavior which was observed in the field. The coupled code serves as a prototype for loosely coupling together any two preexisting simulators modeling diverse physics. This technique produces a coupled code relatively quickly and inexpensively and has the advantage of accurately modeling complex nonlinear phenomena often

Coupled geomechanics and flow simulation for time‐lapse seismic modeling

To accurately predict production in compactible reservoirs, we must use coupled models of fluid flow and mechanical deformation. Staggered‐in‐time loose coupling of flow and deformation via a high‐level numerical interface that repeatedly calls first flow and then mechanics allows us to leverage the decades of work put into individual flow and mechanics simulators while still capturing realistic coupled physics. These two processes are often naturally modeled using different time stepping schemes and different spatial grids—flow should only model the reservoir, whereas mechanics requires a grid that extends to the earths surface for overburden loading and may extend further than the reservoir in the lateral directions. Although spatial and temporal variability between flow and mechanics can be difficult to accommodate with full coupling, it is easily handled via loose coupling. We calculate the total stress by adding pore pressures to the effective rock stress. In turn, changes in volume strain induce up...

Computational methods for multiphase flow and reactive transport problems arising in subsurface contaminant remediation

A mathematical formulation and some numerical approximation techniques are described for a system of coupled partial differential and algebraic equations describing multiphase flow, transport and interactions of chemical species in the subsurface. A parallel simulator PARSIM has been developed based on these approximation techniques and is being used to study contaminant remediation strategies. Numerical results for a highly complex geochemistry problem involving strontium disposal in a pit at Oak Ridge National Laboratory are presented.

A preliminary computational investigation of a macro-model for vuggy porous media

A vug is a relatively large void region or cavity in a rock. A vuggy porous medium has many vugs scattered throughout its extent; moreover, these vugs may be interconnected. A Darcy-Stokes system of equations is needed to describe the flow on the micro-scale. Recently a macro-model of flow was derived by mathematical homogenization that provides the effective permeability of a vuggy medium. In this paper we present two computational studies to illustrate and verify this macro-model. In the first study, we illuminate the nature of the effective permeability itself by considering vuggy media with (i) layered vugs (ii) meandering vug channels, (iii) constricted vug channels, and (iv) disconnected vugs. We find that vug connectivity is the most critical variable in predicting macroscopic properties. In the second study, we consider the macro-model. We compare fluid flow in a vuggy medium on the micro-scale to that on the macro-scale. We find support for the macro-model, and again find that vug interconnectivity is the critical variable to preserve in the upscaling process.

Staggered In Time Coupling of Reservoir Flow Simulation and Geomechanical Deformation: Step 1 - One-Way Coupling

An isothermal, implicit, mixed finite element black oil reservoir simulator from the University of Texas is coupled to an explicit, quasistatic, nonlinear finite element solid mechanics code from Sandia National Laboratories. Both codes are 3d and parallel. The former models (in a locally conservative manner) the flow of oil, gas, and water fluid phases in the reservoir while the latter has been specialized to solve large-scale geomechanics problems involving significant inelastic deformations. In this paper we illustrate a uni-directional coupling of the two codes in which flow simulation output (pore pressures) from a 10-year test case based on the Belridge Field in California drives the geomechanics simulation for the same time period. The highporosity, low-permeability Belridge diatomite undergoes significant compaction including 6 feet of vertical displacement at the top of the reservoir.

History Matching Using Probabilistic Approach in a Distributed Computing Environment

The focus of the paper is to present a novel methodology for delineating multiple reservoir domains, for the purpose of history matching in a distributed computing environment. A fully probabilistic approach to perturb permeability within the delineated zones is implemented. The combination of robust schemes for identifying reservoir zones and distributed computing significantly increase the accuracy and efficiency of the probabilistic approach. The information pertaining to the permeability variations in the reservoir that is contained in dynamic data is calibrated in terms of a deformation parameter rD. This information is merged with the prior geologic information in order to generate permeability models consistent with the observed dynamic data as well as the prior geology. The relationship between dynamic response data and reservoir attributes may vary in different regions of the reservoir due to spatial variations in reservoir attributes, well configuration, flow constrains etc. The probabilistic approach then has to account for multiple rD values in different regions of the reservoir. In order to delineate reservoir domains that can be characterized with different rD parameters, principal component analysis (PCA) of the Hessian matrix has been done. The Hessian matrix summarizes the sensitivity of the objective function at a given step of the history matching to model parameters. The eigenvectors obtained during the PCA are suitably scaled and appropriate grid block volume cut-offs are defined such that the resultant domains are neither too large (which increases interactions between domains) nor too small (implying ineffective history matching).

Prediction of imbibition in simple porous media

Pore level processes in porous media, such as drainage or imbibition of wetting phase, are of great importance in different branches of soil science, petroleum engineering and water research. In this work we describe a new way of modeling imbibition, based upon a physically consistent dynamic criterion for the imbibition of a pore. We illustrate this approach in a simple but physically representative porous medium, the “ideal soil” (a dense random packing of equal spheres). The results of geological processes, such as cementation (e.g., quartz overgrowth), are simulated in the sphere pack to yield a model of sedimentary rock. Complete knowledge of the pore space geometry in the model rock then allows making a priori predictions of pore level processes. Imbibition is simulated in a network that faithfully represents the pore-level geometry of the model rock. This approach allows studying the effects of contact angle, initial conditions (for example, different drainage endpoints), and sample geology (amount of cement). It also provides a basis for a mechanistic understanding of phenomena such as “snap-off” of nonwetting phase in the pore throats. The simulations show that the capillary pressure curve is very sensitive to the wettability conditions (value of contact angle) and geological features of the sample. Predicted capillary pressure curves are compared to experimental data, presented in the literature, and found consistent with most of them.

Grand challenge problems in environmental modeling and remediation: groundwater contaminant transport

This report describes briefly the work of the Center for Subsurface Modeling (CSM) of the University of Texas at Austin (and Rice University prior to September 1995) on the Partnership in Computational Sciences Consortium (PICS) project entitled Grand Challenge Problems in Environmental Modeling and Remediation: Groundwater Contaminant Transport.