51st U.S. Rock Mechanics/Geomechanics Symposium,
San Francisco, California, USA
2017. American Rock Mechanics Association
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ABSTRACT: 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are designed to minimize the implementation cost (energy, materials) and maximize the volume of fluid injected (or withdrawn).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.
What fracture network topology optimizes fluid flow in a rock mass? Power laws and fractal dimensions govern most physical processes observed in nature. However, optimization algorithms that shape natural self-organization remain in many cases unknown. Furthermore, engineering approaches rarely consider nature as a guide to improve human systems and very few attempts have been made to explain the fractal nature of the topology observed in many connectivity networks.
The constructal theory (Bejan & Errera, 1997) is an optimization method for finite flow systems with configuration (e.g., slenderness), in which a purpose (e.g., heat collection) and constraints to the flow (e.g. mass balance) are established. This theory can be used to predict the topology of both natural networks, such as the design of the lungs (a H Reis, Miguel, & Aydin, 2004), and man-made networks, such as the layout of cities (Bejan & Lorente, 2008; a. Heitor Reis, 2006). Unlike other biological models of cell networks, the constructal theory is completely deterministic, predicting the layout of a network without prior assumptions. Major limitations are: (a) the need to assume controlling thermodynamic potentials, steady boundary conditions and uniform distribution of connecting points; (b) the absence of interaction dynamics from the formulation which disregards the fluctuations of the environment and the corresponding adaptation of the network. In the same way, Steiner tree algorithms allow finding: The minimum spanning tree from a set of points distributed in space; The global optimum from the creation of Steiner points that minimize the length needed to connect 3 points on the plane; The minimum network length concatenating those full Steiner trees using a combinatorial algorithm (Winter & Zachariasen, 1997).
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