11 research outputs found
How to share underground reservoirs
Many resources, such as oil, gas, or water, are extracted from porous soils
and their exploration is often shared among different companies or nations. We
show that the effective shares can be obtained by invading the porous medium
simultaneously with various fluids. Partitioning a volume in two parts requires
one division surface while the simultaneous boundary between three parts
consists of lines. We identify and characterize these lines, showing that they
form a fractal set consisting of a single thread spanning the medium and a
surrounding cloud of loops. While the spanning thread has fractal dimension
, the set of all lines has dimension . The size
distribution of the loops follows a power law and the evolution of the set of
lines exhibits a tricritical point described by a crossover with a negative
dimension at criticality