# Ninth Year Annual Report:

Carbon Storage: Advances in Geomechanical Modeling

Important refinements have been made in the Dynaflow model used to simulate CO_{2} storage and
leakage. A vertex-centered calculation scheme has been implemented that permits more accurate
coupling of flow and stress analysis. Systematic evaluation of stabilization schemes has indicated
the methods permitting the most rapid and accurate calculations. Special elements have been
developed that enable accurate calculation of heat and mass transport in fields that are effectively
infinite in extent.

## Coupling Reservoir and Geomechanics Simulators

Reservoir simulators typically use a different numerical scheme for calculating flow processes than for geomechanical stresses and strains, so it is difficult to couple the two problems together. Typically, the two calculations run separately, with information being passed back and forth at each time step.

Jean Prévost and colleagues have quantified the errors associated with this procedure by using it to solve a simple problem for which they can derive the exact analytical solution. The researchers computed upper and lower bounds for the errors, and analyzed their magnitude for a variety of cases. They found that, in general, the errors are substantial. More importantly, they show how to avoid these errors by using the same (vertex-centered finite volume) calculation scheme for all reservoir and geomechanical variables.

## Removing Harmonic Oscillations in Numerical Solutions

Numerical solutions for problems in coupled poromechanics suffer from spurious pressure oscillations when small time increments are used. This has prompted many researchers to develop stabilization methods to overcome these oscillations. This year, Prévost's group published an overview of the most promising methods. They investigated stability of three methods for solving a simple one-dimensional test problem and show that one of them (bubble functions) does not remove oscillations for all time step sizes. Numerical tests in one and two dimensions confirm the effectiveness of two other stabilization schemes, which the team now employs.

## Thermal Effects in Reservoir Modeling

Many engineering problems exist in physical domains that can be said to be infinitely large. A common problem in the simulation of these unbounded domains is that a balance must be met between a practically sized mesh and the accuracy of the solution. Prévost and colleagues have developed a methodology for modeling transient heat conduction in an infinite domain, and validated the approach for a case in which the exact solution is known. The methodology was shown to provide an accurate model of heat loss in thermal reservoirs.