Determination of the most significant variables affecting the steady state pressure drop in selected foam flow experiments

Foam generated with a surfactant solution and nitrogen is used for oil recovery, acid diversion and aquifer remediation. In laboratory experiments, the foam mobility is expressed in terms of the pressure drop across the porous medium and is related to many physical processes. There is lack of data that relate the pressure drop to a combination of three or more variables simultaneously. This paper investigates the steady state pressure drop for a combination of six variables, viz., permeability, surfactant concentration, pH, salinity, surfactant solution velocity and gas velocity. Fourteen pressure drop histories were measured for an Alpha Olefin Sulphonate solution before and after the injection of nitrogen gas across the unconsolidated sandpacks of two median grain sizes and across a Bentheimer consolidated core. Our data set was combined with data sets from the literature leading to 157 data points. Symbolic regression was applied to the entire data set to produce a number of analytical expressions describing the interactive effect of the variables without prior knowledge of an underlying physical process. A simple model with only one fitting parameter was selected to compare with the experimental data. The slope between the observed pressure drop and the predicted pressure drop turns out to be 0.85±0.03. A sensitivity analysis of the chosen model shows that the variables affecting the predicted pressure drop, in order of importance, are permeability, salinity and surfactant solution velocity. The precision of the model parameter was determined by a bootstrap method. The pressure drop from our data set and one specific data set from the literature show significant deviation with respect to the pressure drop obtained from the regression equation. Possible reasons are that the specific data set from the literature uses mixtures of surfactants and that our data set is confined to conditions that lead to low pressure drops. The purpose of the data driven model applied to experimental data is only to improve the models based on physical processes, i.e., mechanistic models. In addition the data driven model can indicate the variable spaces for which more experiments are needed.