A Rigorous Pore-to-Field-Scale Simulation Method for Single-Phase Flow Based on Continuous

We propose a pore-to-reservoir simulation approach for singlephase flow. Transport is modeled as a continuous-time random walk (CTRW). Particles make a series of transitions between nodes with a probability c(t)dt that a particle will first arrive at a node from a nearest neighbor in a time t to t+dt. A top-down multiscale approach is used to find the flow field. At the micron scale, c(t) for particle transitions from pore to pore are found from modeling advection and molecular diffusion in a geologically representative network model. This c(t) is used to compute transport on the millimeter-to-centimeter scale. At larger scales, we represent the reservoir as a network of nodes connected by links. For each nodeto-node transition, we compute an upscaled c(t) from a simulation of transport at the smaller scale. We account for small-scale uncertainty by interpreting c(t) probabilistically and running simulations for different possible realizations of the reservoir model. To make the number of computations manageable, c(t) is parameterized in terms of subscale heterogeneity and Péclet number, meaning that only a few representative simulations are required. We apply this method by finding c(t) for pore-scale flow and using it in a million-cell reservoir model. We show that the macroscopic behavior can be very different from that predicted by assuming that the advection/dispersion equation (ADE) operates at the small scale. Small-scale structure does affect macroscopic transport; increasing the pore-level heterogeneity delays breakthrough and leads to longer late-time tails of the production because the solute spends more time in slow-flowing regions of the domain. We discuss extensions to multiphase flow and the development of a novel network-based probabilistic reservoir-simulation approach.