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Water-rock interaction and reactive-transport modeling using elemental mass-balance approach: I. The methodology

Water-rock interaction and reactive transport modeling is an important tool for deciphering chemical and physical reactions occurring in sediments and rocks. The modeling methodology calls for solving conservation equations to account for the interaction between mass-transfer and reaction processes using a sequential iteration numerical method. The formalism presented here improves upon the traditional approach by reformulating conservation equations to express chemical elemental mass evolution. The elemental conservation equations describe mass change through mass-transfer and kinetic reactions of solids, and solute-solute interaction (equilibrium) reaction expressions. The system of equations is solved using a sequential iteration method, whereby globally discretized mass-transfer coefficients of conservation equations are injected explicitly into the conservation equations and solved locally at each node. The result is a mathematically simple approach that eliminates the traditionally required use of primary and secondary species classification. The formalism also allows the use of solute-specific diffusivities. In addition, the tight coupling between mass-transfer and reactions achieved by the methodology also allows nonlinear self-organization or pattern-forming phenomena to be captured. The methodology is demonstrated with simulations of (1) a diffusive-reaction system involving patterned hematite nucleation, and (2) a flow-through system where CO2-charged water interacts with formation water in a sandstone reservoir. Both are isothermal one-dimensional simulations. In the first example, convergent diffusive infiltration of Fe++ and O2 from two opposite ends produces patterned precipitates. A natural analog of such phenomena is the occurrence of iron-oxide concretions in Navajo Sandstones of Utah and Arizona. The second example demonstrates the formation of a diffusive solute migration front ahead of advective effluent displacement and reaction fronts. Such phenomena are observed when large quantities of CO2 are injected into geologic formations. The early arrival of diffusive solute fronts at nearby monitoring wells are noted by decreasing water pH and raised alkalinity some time before the arrival of the effluent.