Time-Dependent Two-Dimensional Fluid Flow Model for Basin History Reconstruction
Kazuo Nakayama, Christopher G. St. C. Kendall, Ian Lerche
To simulate a basin history in the geologic past, we have developed a two-dimensional dynamic fluid flow model that includes a model of hydrocarbon generation. In our model, the fluid movement can be expressed by Darcy's law as:
where e = void ratio, P = excess pressure, f = density of fluid, Kx and
Kz = permeability of x- or z-direction. Here, x and z represent lateral and vertical coordinates, respectively, and t represents time. Because modeling the depositing sediment would create moving boundary conditions at the sedimentary surface and so produce numerical instability, we have found a novel set of fractional coordinates in which the boundaries are fixed as are the boundary conditions. This transformation completely stabilizes the numerics. Furthermore, the void ratio and the excess pressure can be related to the effective overburden (Pf: frame pressure) that can be supported by grain-to-grain contact in the sediment. Using a finite difference scheme, we apply the alternate directional implicit method (ADIM) to solve the fluid-flow equation allowing for variable sedimentatio with lateral position and with different lithologies.
The resulting fluid flow model is tied to a heat-transfer model and the pair of these in turn are related to a Tissot-type generation model in order to reconstruct the paleogeologic history of these sediments as well as the timing of generation and migration of hydrocarbons. The study shows that the accessibility of carrier beds for hydrocarbons to clastic source rocks is sensitive to the evolution with time of the porosity distribution. The model applied to a Japanese petroleum field demonstrates the dynamic timing of hydrocarbon generation and resulting migration pathways.
AAPG Search and Discovery Article #91043©1986 AAPG Annual Convention, Atlanta, Georgia, June 15-18, 1986.