Simulation of the Cranfield CO2 Injection Site with a Drucker-Prager Plasticity Model

Coupled fluid flow and geomechanics simulations have strongly supported CO2 injection planning and operations. Linear elasticity has been the popular material model in CO2 simulation for addressing rock solid material behaviors. On the other hand, nonlinear constitutive models can take into account more realistic rock formation behaviors to model complex, chemically active, and fast injecting operations. For example, failure or damage may occur for rock formation near wellbores due to high fluid injection pressures or flow rates. The damaged formation near wellbores results in the changes in rock porosity or permeability, which impacts fluid flow behaviors. Such failure or damage of rock formations can be well described by the Drucker-Prager plasticity theory.

The Drucker-Prager plasticity solid mechanics module has been implemented into IPARS (Integrated Parallel Accurate Reservoir Simulators developed at the Center for Subsurface Modeling, The University of Texas at Austin). The coupled poro-plasticity system is solved using an iterative coupling scheme: the nonlinear flow and mechanics systems are solved sequentially using the fixed-stress splitting, and iterates until convergence is obtained in the fluid fraction. To the best of our knowledge, the application of this algorithm is new for poro-plasticity. To achieve fast convergence rates for solving the nonlinear solid mechanics problems, a material integrator is consistently formulated and implemented in the IPARS geomechanics module. An enhanced parallel module for general hexahedral finite elements is also developed for IPARS for solving large-scale problems in parallel. A driver for the direct solver SuperLU has been implemented in cases when the linear systems are difficult to converge. A Cranfield CO2 injection model is set up according to the reservoir geological field data and rock plasticity parameters based on Sandia national lab experimental results. This Cranfield model is solved using IPARS and the prediction on CO2 flow and formation deformation is presented.

Figure 1 shows a comparison between poro-elastic and poro-plastic results in an injection well case with homogeneous Cranfield data and rectangular geometry. Figure 2 shows poro-elastic results in an injection well case with heterogeneous Cranfield properties and geometry. Future work includes the incorporation of plastic yielding into the initial condition so that the heterogeneous Cranfield properties and geometry can be used in the poro-plastic case. Together with stress dependent permeability and fluid fraction, this will give us an accurate predictive geomechanics model for matching CO2 injection results at the Cranfield site.

Figure 1. Comparison of elasticity (left) and plasticity (right) models with homogeneous parameters and rectangular geometry. Fluid pressure, vertical displacement, and plastic strain are shown (below).

Comparison of elasticity (left) and plasticity (right) models

Figure 2. Elasticity model with heterogeneous Cranfield properties and geometry. 3D (left) and 2D (right) plots of the vertical displacement component at final simulation time (below).

Elasticity model with heterogeneous Cranfield properties and geometry