Modified rand algorithms for multiphase geochemical reactions

Underground geological storage (UGS) of CO2 in saline aquifer or oil reservoirs is an effective means to reduce CO2 emission at scale. To evaluate these UGS processes and understand the long-term fate of the injected CO2, we need a simulator that can account for multiphase equilibrium involving CO2, speciation reactions in brine, and the reactions with minerals.

The calculation algorithms for multiphase geochemical reactions are essential to the robustness and efficiency of such a simulator. We applied the modified RAND method (SPE 182706-PA) to electrolyte systems to calculate phase equilibrium together with speciation reactions and mineral dissolution/precipitation.

Modified RAND is a non-stoichiometric approach for simultaneous chemical and phase equilibrium calculation. The method linearizes the species chemical potential and eventually uses the elemental chemical potentials as the main independent variables. This greatly reduces the size of the equations for geochemical systems with many species and reactions.

Modified RAND is more structured than the classical methods, for which we need to reselect the independent variables during the calculation to reduce round-off errors, and thus more suitable for UGS in oil reservoirs, where both hydrocarbon phase equilibrium and brine-mineral reactions are important.

It is 2nd-order and its solution can be guided by minimizing the Gibbs energy. Modified RAND can be applied directly to geochemical systems at a fixed overall composition. Some geochemical applications, however, require analysis at constant chemical potential of a neutral species (e.g., CO2) or a charged species (e.g., H+), the latter case expressed usually as constant pH.

We also extended modified RAND to those open systems. For the former, a new state-function can be constructed through the Legendre transform and the obtained algorithm is an energy minimization. For the latter, the problem is no longer minimization but we can still formulate a 2nd-order convergent algorithm.

We tested the modified RAND algorithms with phase equilibrium cases relevant to UGS in closed systems, open systems with specified CO2 fugacity, and open systems with specified pH. Modified RAND provides a more efficient solution than the classical equation solving approach used in PHREEQC. The algorithms for closed and open systems exhibit 2nd-order convergence in all the tested cases.

We then integrated modified RAND into a 1-D simulator and included the kinetic reactions, and compared the simulator with PHREEQC for 1-D geochemical simulations. The study provides the foundation for a future reactive transport simulator using modified RAND for the core multiphase reaction calculation.