Thermodynamic Algorithms

Four important computational tools are reviewed, each of them is based on thermodynamic principlesSimulated annealing. Simulated Annealing (Sect. 11.1) is presented through two applications: Reconstructing 3D pore space from 2D sectionsReconstructing 3D pore space from 2D sections, and multiphase fluid distribution in porous rocksMultiphase fluid distribution in porous rocks. Lattice Boltzman MethodsLattice Boltzman Methods (LBMs), recently widely used in Digital Rock Physics, are treated in Sect. 11.2, including their theoretical derivation, computational aspects, and generalizations. Their applications include simulation of multiphase flowMultiphase flow, and Knudsen flow in tight shalesKnudsen flow in tight shales. The powerful method of RNG (Renormalization GroupRenormalization Group, Sect. 11.3) has been borrowed from the Theory of Phase TransitionsTheory of Phase Transitions. After a theoretical introduction it is applied to determine the critical point of failureCritical point of failure, and time of failureTime of failure, of stressed rocks; to describe the erosion of tilted landscapesErosion of tilted landscapes, and for permeability upscaling. Section 11.4 is devoted to discrete scale invarianceDiscrete scale invariance, and its use for earthquake predictionEarthquake prediction and rock fragmentationRock fragmentation.