Modeling of Single-Phase Fluid Flow Hydraulic Parameters in Layered Media

Researchers have, over the years, noted the refraction-like property of flowline when it crosses the contact interface of different layers in a stratified medium. This is due to the different porosity viz-a-viz permeability characterizing each layer. It has been established that the path \(\left( {\theta_{\max } } \right)\) of maximum volume flux \(\left( {q_{\max } } \right)\) deflects from the normal for a flow from a lower to higher porous medium (Ascending Flow-AF). In contrast, \(\theta_{\max }\) deflects toward the normal for the reverse flow system (Descending Flow-DF). This phenomenon is vital in understanding contaminant fluid flow and dispersion processes in stratified media and Enhance Oil Recovery (EOR) in stratified reservoirs. Currently, no study exists that analyzes and models the relationship between the porosity ratio \(\left( {\phi_{r} } \right)\) of the layers in contact with the resulting \(\theta_{\max }\) and volume flux (q) in both AF and DF systems, based on experimental data. Therefore, this study intends to highlight the flow dynamics based on \(\phi_{r}\) for both flow systems and also propose models which are valid in both systems for predicting \(\theta_{\max }\) and q. The data was obtained from a laboratory intermediate scale experiment of single-phase fluid flowing through 2-layer sand samples of known porosities and permeability. This study found that, due to the presence of the Capillary Barrier Effect (CBE) in AF systems, the mean q of such systems is lower than that of DF systems by a 95% confidence interval of 0.0096–0.0939 ms−1. Similarly, the standard deviation of the q of such systems is significantly lower than that of DF systems. In addition, \(\theta_{\max }\) is dependent on the flow system and would undergo a more significant change for a unit change in \(\phi_{r}\) in AF systems than in DF systems. The q associated with any \(\theta\) is more heavily dependent on the flow system. Furthermore, two models valid in both flow systems have been proposed. The models could be used to predict the \(\theta_{\max }\) , and the q associated with any deflection angle (θ) based on the porosity ratio \(\left( {\phi_{r} } \right)\) of any 2-layer stratified medium. The results obtained from this work could apply to optimizing CBE covers used to protect groundwater from contamination and improve water retention capacity in plants’ root zone. In addition, including the obtained models and interpretation in the smart-injection wells’ algorithm could help improve the EOR capability by guaranteeing an early breakthrough.