Multiscale high-order methods for reactive transport in porous media

Subsurface reactive processes play an important role in addressing energy and climate challenges of the 21st century. Example applications are CO2 sequestration, enhanced oil recovery, and contaminant transport. Understanding the complex nonlinear interplay of flow, transport, and reactions at the multiple length scales that characterize subsurface systems is one of the main challenges for advancing the analysis of reactive transport. To address these challenges, this dissertation presents three main contributions towards accurate and efficient simulations of subsurface reactive transport. Chapter 2 develops a multiscale scheme for the sequential formulation of reactive transport involving two fluid phases. Instead of solving the transport problem on the global fine-scale model, the domain is decomposed into coarse gridblocks that are aggregates of fine gridblocks. The transport problem is defined and solved on each of the coarse blocks, and a prolongation operator that allows for accurate reconstruction of the fine-scale solution is defined. The prolongation operator is independent of the details of the chemical reactions involving the particular component being transported and does not interfere with the chemical module, providing flexibility of implementation and applicability to a wide range of conditions. The more confined concentration gradients obtained with high-order approximation of the numerical fluxes lead to a better performance of the scheme when compared to low-order fluxes. Test cases include applications to chains of homogeneous decay reactions, heterogeneous reactions with changes in rock properties, coupling with a chemical solver to model the calcium carbonate reactive system, variable time step sizes, and changes in operational conditions. A high-resolution adaptive implicit method for reactive transport is proposed in Chapter 3. The adaptive implicit method (AIM) reduces the computational cost related to simulations of field scale displacements in porous media. Standard AIM uses single-point upwind and a mixed implicit/explicit time discretization that overcomes the time step size limitations of purely explicit approaches. To reduce numerical diffusion and improve the accuracy of AIM, we introduce a scheme that in addition to blending implicit and explicit time discretizations, deliberately blends single-point upwind and a high-order flux-limited total variation diminishing approximation of the numerical fluxes. The proposed scheme does not interfere with the discretization of the implicit terms and the structure of the matrices that need to be solved is the same of standard AIM, making the scheme easy to apply in existing simulators. Numerical results indicate significant gains in accuracy at the additional expense of slightly more involved flux computations in the explicit regions, that represent a small fraction of the total CPU cost. In Chapter 4, a new upscaling procedure that provides 1D representations of 2D mixing-limited reactive transport systems is developed and applied. A key complication with upscaled models in this setting is that the procedure must differentiate between interface spreading, driven by the spatially variable velocity field, and mixing, through which components contact one another and react. Our model captures the enhanced mixing caused by spreading through use of a time-dependent effective dispersion term. The early-time behavior of this dispersion is driven by flow kinematics, while at late times it reaches a Taylor-dispersion-like limit. The early-time behavior is modeled using a very fast (purely advective) particle tracking procedure. The only unknown parameter in the model is the late-time asymptotic effective dispersion. This quantity is estimated using a fit involving a dimensionless grouping of system variables and a few reference results, or by calibrating with the corresponding conservative (non-reacting) case. Numerical results for bimolecular reaction systems are generated using a pseudo-spectral approach capable of resolving fronts at high Peclet numbers. Results are presented for three different types of 2D velocity fields over a wide range of parameters. The upscaled model is shown to provide highly accurate results for the conversion factor, along with reasonable approximations of the spatial distribution of reaction occurrence. The model is also shown to be valid to upscale mixing in non-reacting systems

Keywords: Energy Resources Engineering.
Advisor: Tchelepi Hamdi
Durlofsky Louis
Kovscek Anthony R. (Anthony Robert)