Scale Up Reactive Flow in Heterogeneous Porous Media Using Continuous Time Random Walk Approach

Abstract

Reservoir heterogeneities strongly affect the fluid flow in porous media. The behavior of transport and reaction of fluid varies at different scales, leading to the discrepancies between laboratory experiments and field observations. The reactive processes in porous media may alter reservoir properties with different spatial and temporal scale, varying future transport and reaction behaviors. This thesis provides an efficient probabilistic approach to scale up coupled transport and reaction processes in heterogeneous porous media to field scale based on laboratory-scale information. The continuous time random walk (CTRW) is a probabilistic framework which is always incorporating with particle tracking (PT) approach to model solute transport in heterogeneous porous medium. In CTRW-PT approach, the motion of solute particles is described as combination of random independent spatial and temporal increments in each walk step. The spatial and temporal increments, or normally called as transition distance and time, are chosen from a joint space-time probability density function by a stochastic process. The CTRW-PT approach simulates reactive fluid transport as non-reactive fluid. The modelling of reaction and dissolution is followed by in each time step, updating the change of porous medium and its effect on following transport and reaction. The characteristic probability density function (pdf) is used to simulate the transport of fluid. Adjusting the ensemble parameter β and t_2 accounts for the effects of heterogeneity which leads to anomalous flow behavior: the fluid propagates along the “preferential” pathways with short transition times and “trapped” in some zones with long transition times. It mimics the macroscopic behavior that fluid has the tendency to propagate in high-permeability zones and bypass the low-permeability zones. Simulations of non-reactive tracer flow and nanofluid flow under various conditions are performed at core-scale to obtain the key parameters in characteristic pdf by matching the experimental results. The effect of reactive process, heterogeneity and flow rate on flow behavior is analyzed. The CTRW-PT simulation captures the characters of anomalous behavior of delayed breakthrough. The model is run at larger scale as reservoir properties are scaled up properly. The core-scale simulation based on the characteristic pdf agrees with the experimental results. The large-scale simulation is implemented by using the characteristic pdf to describe flow behaviors in a large-scale domain. It is shown that CTRW-PT approach is more effective in large-scale modeling than solving advection-diffusion-reaction equation (ADRE) by finite difference method (FDM). The simulation results at large scale show that the flow response is spatial-dependent. Compared to solving traditional ADRE, the utilization of CTRW-PT approach to model reactive fluid flow captures the characters of anomalous flow behavior, especially in highly heterogeneous porous media. By the probabilistic framework and stochastic process, this approach is more computational-efficient for scaling up lab-scale results to larger scale. It can consolidate the lab-scale understanding with field prediction to optimize the field treatment design.