Efficient fluid extraction through hydraulic fracture in capillary fiber bundle model

TL;DR

This study models hydraulic fracturing in a capillary fiber bundle, revealing optimal pressure conditions for maximum fluid extraction and demonstrating the transition from non-linear to Darcy flow.

Contribution

It introduces a simulation of fracking effects in a fiber bundle model, identifying optimal pressure and flow conditions for efficient fluid extraction.

Findings

Hydraulic power increases with pressure gradient and fracking amplitude.

An optimal pressure gradient maximizes fluid extraction efficiency.

Transition from non-linear to Darcy flow can be detected via flow profile fluctuations.

Abstract

We have simulated a one dimensional capillary fiber bundle model with fracking events while acted between a pressure gradient across the system. The hydraulic fractures are incorporated through a decreasing nature of capillary thresholds for each tube that replicates an increment in pore spaces due to fracking. An increment in flow rate is evident through the evolved rheology we observe in our study. Analytical approaches for certain limits are adopted to understand the rheology which matches well with the numerical results. The overall hydraulic power increases with pressure gradient as well as with the percentage decrease in capillary threshold due to a single event, defines as the fracking amplitude. This combined with the early onset of linear Darcy flow increases the quality of the fluid extraction. We successfully point towards an optimum pressure gradient at which the fracking events are most effective - maximum change in fluid extracting with a maximum rate. We observed that it is possible to extract the information regarding the change from non-linear to Darcy flow due to fracking as well as the optimum pressure for fluid extraction through local flow profile, something which in much superior from the point of view of computational cost. The former is done by correlating the maximum fluctuation in local flow profile to the onset of Darcy flow. The later is done through the relative change in Shannon entropy with respect to the fracking amplitude that points towards the pressure associated with the maximum fluid extraction criterion.