U.S. Department of Energy

Pacific Northwest National Laboratory

Modeling Flow of two Fluids through Pores

(a) Pore structure. Pore spaces are shown in black, and the solid phase is in white; (b) Three-dimensional configuration.

The Science

In a recent studypublished in Advances in Water Resources, researchers performed a set of well-controlled drainage and imbibition experiments using six identically manufactured microfluidic cells to study the reproducibility of multiphase flow experiments. The result: a variability (upwards of 200%) among the cells and within each cell, confirming that multiphase flow experiments should be considered as a stochastic process. Researchers proposed a stochastic model with randomly varying injection rate, which was able to reproduce both the average behavior and variability observed in the experiments. 

The Impact

The collected data set reveals variability in pore-scale multiphase flow, which was explained by the proposed numerical model. Both data and model can provide an improved understanding of the multiphase flow physics, which can ultimately help mitigate important environmental challenges including subsurface contaminant remediation. 


DOE sites, such as the Hanford Site, have a history of contaminants discharged into the ground. They mix, separate, and flow at varying speeds depending on the subsurface composition, temperature, moisture, and pressure. Researchers want to predict the flow of these various contaminants to devise more effective remediation solutions. Recent advances in numerical methods allow simulations of multiphase flow at pore, field, and regional scales, but researchers need to be able to validate the numerical results. The traditional approach to model validation is through comparison with experiments. Microfluidic devices and pore-scale numerical models are commonly used to study multiphase flow in biological, geological, and man-made porous materials. The thin plastic devices, each resembling a miniaturized slice of Swiss cheese, help researchers understand the physics of how water, particulates, contaminants, and other constituents flow in the subsurface. In this study, researchers used microfluidic cells to understand the physics of multiphase flow in porous media. Six identical cells were manufactured, and a precise pump was used to inject the liquids into the device. The flow in 30 experiments (five experiments for each of the six cell replicas) varied by close to 200 percent. The findings were surprising because they revealed significant variability in pore-scale multiphase flow cell experiments due to cell manufacturing defects and fluctuations in the pump injection rate. “It’s extremely difficult to replicate multiphase flow experiments in a lab,” said lead researcher Alexandre Tartakovsky, a scientist at the Pacific Northwest National Laboratory. Miniscule differences in manufacturing of the cell devices and small fluctuation in the pump injection rate can cause large variations in the experimental results. Such variations are virtually uncontrollable and can wreak havoc on results. Researchers proposed a stochastic model with randomly varying injection rate, which was able to reproduce both the average behavior and variability observed in the experiments. The standard deterministic models, on the other hand, cannot explain variability and give a poor estimate of the average behavior. 


This research was partially supported by the U.S. Department of Energy, Office of Biological and Environmental Research, Subsurface Biogeochemical Research (SBR) Program through the SBR Scientific Focus Area at Pacific Northwest National Laboratory (PNNL), and by the National Science Foundation. A. Tartakovsky was partially supported by DOE's Office of Advanced Scientific Computing (ASCR) as part of the Early Career Award “New Dimension Reduction Methods and Scalable Algorithms for Multiscale Nonlinear Phenomena.” 


B Ling, et al., “Modeling variability in porescale multiphase flow experiments.” Advances in Water Resources.105, (2017), doi.org/10.1016/j.advwatres.2017.04.005



July 2017
| Pacific Northwest National Laboratory