Simultaneous Determination of Relative Permeability and Capillary Pressure from an Unsteady-State Core Flooding Experiment?

Abstract

For modelling studies of underground storage of carbon dioxide and hydrogen, it is important to have a consistent set of relative permeability and capillary pressure-saturation functions. For consistency reasons, it is an advantage to determine both in one single experiment using the same rock and fluid sample, however, experimental measurements typically have challenges. While unsteady-state type of flow experiments is in principle suited for deriving relative permeability and capillary pressure functions, we provide a methodology to optimize the experimental settings such that the simultaneous determination of these functions can succeed within an acceptable uncertainty range, which involve multi-rate flow experiments and in-situ saturation monitoring. We provide details of the inverse modelling methodology which is a self-contained Python code that includes both the 1D flow model and the optimization method for the assisted history match. This methodology can be used for interpreting experiments, but also to optimize the design of the experiment and to reach a desired/acceptable uncertainty range.The purpose of this work is to provide the concrete assessment of unsteady-state type of experiments with the purpose of simultaneously obtaining relative permeability and capillary pressure-saturation functions by means of a ground-truth example, to detail the methodology used and make the Python code with a self-contained 1D flow solver accelerated by the numba just-in-time compiler publicly available. The results underline that the simultaneous determination of relative permeability and capillary pressure-saturation functions are possible only in specially designed multi-rate experiments where several saturation profiles before breakthrough are captured and the capillary end-effect is fully resolved. These conditions are not necessarily met for the more general type of unsteady-state experiments typically used in the more general Special Core Analysis (SCAL).

On the Identifiability of Relative Permeability and Foam Displacement Parameters in Porous Media Flow

“…When dealing with experimental data, the lack of this ground truth results in difficulties in evaluating accuracy for parameter estimation. This practice has been used in several works (Berg et al., 2021, 2024) that discuss parameter estimation and uncertainty quantification. To create the synthetic data for parameter fitting, we performed computer simulations of the experiments using the Buckley‐Leverett equation; for more details, see (A. R. Valdez et al., 2020).…”