Biological and engineering flow systems maximize their efficiency by following the path of minimum energy over the domain they are embedded in. This fact motivates the present research, since industrial fluid extraction and injection processes are designed to minimize the implementation cost (energy, materials) and maximize the volume of fluid injected (or withdrawn). This work presents a bio-inspired fluid flow model to optimize the path that connects resource-rich pores in a rock. We explain the commonalities between the equations governing flow in a porous medium and growth of slime mold, an organism that dynamically deploys tube-like structures and adapts them as a function of their contribution to the overall network. We perform several simulations to analyze the influence of the pore size distribution and of pore spatial distribution on the topology of the extraction network predicted by the slime mold growth algorithm. We discuss the suitability of the biomimicry model to design fracture patterns for optimal fluid extraction from a porous rock.