Accurate Numerical Simulation of Reaction Front Propagation

Abstract Accurate numerical modeling is essential in order to interpret experimental measurements, developing better understanding and designing of industrial scale processes. Exothermic nature solid-solid and gas-solid reactions results in large concentration and temperature gradients that lead to steep reaction front. Such sharp reaction fronts are difficult to capture using traditional numerical schemes unless by means of very fine grid numerical simulations. Fine grid simulations of such reactions at large scale are computationally expensive. On the other hand, using coarse grid block simulations leads to excessive front dissipation and inaccurate results. In most practical cases, such as heavy oil combustion in oil reservoirs it is not however feasible to choose small grid blocks (large number of grids). Therefore, one needs to account for the small scale gradients that cannot be captured by coarse grid blocks when using traditional methods. We have investigated numerical solution behaviour of different problems related to upscaling of reaction kinetics. These problems include steady-state and transient reaction diffusion, solid-solid, and gas-solid reactions. As a first step toward accurate upscaling of reaction kinetics we have developed equivalent reaction constant for simple steady-state convection-reaction-diffusion. We have shown that numerical solution of linear and isothermal diffusion-reaction systems is not grid sensitive and accurate solutions can be obtained using low-resolution numerical simulations. It has also shown that for steady-state convection-diffusion- reaction the effective reaction constant is a function of Peclet number, Thiele modulus, and size of the reaction zone. These results aid in development of numerical upscaling schemes that improve our ability to perform faster and accurate large scale numerical simulation of reactive flow such as bitumen and heavy oil recovery. Introduction Modeling of reactive flow in porous media has diverse applications in engineering and science. Applications include heavy oil processes, combustion in porous media, ground water flow and hydrate decomposition in porous media. Major studies on the reacting flow have been conducted over the years that significantly advance understanding of such systems but emphasis has basically been on the development of approximate analytical solutions for special cases, fine grid direct numerical simulation, and upscaling of reaction-transport form pore scale to continuum scale (1–15). Currently, accurate numerical simulation of heavy oil and bitumen recovery processes is a challenging issue due to the multi-scale nature of the involving physical phenomena. Physical processes involved in heavy oil recovery include diffusive and reactive processes that have different scales. Reactions in porous media are intrinsically take place at the smaller level causing development of sub-scale concentration and temperature gradients while the diffusive processes such as heat and mass transfer have scales orders of magnitude larger than the reactions. Large-scale simulation of such coupled processes is computationally expensive due to limitations in computational resources. Finding an upscaling methodology that captures the sub-grid (local scale) processes into the coarse numerical grid block are of prime importance. Such methodology will advance our understanding of the processes and improves our capabilities for conducting largescale simulation of the involved processes.

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