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:
[EQUATION]
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.