Compaction Within the South Belridge Diatomite

Abstract

Summary Compaction is incorporated into a field-scale finite-difference thermal simulator to allow practical engineering analysis of reservoir compaction caused by fluid withdrawal. Capabilities new to petroleum applications include hysteresis in the form of limited rebound during fluid injection and the concept of relaxation time (i.e.. creep). Introduction The physics of compaction has been included in a field-scale finite-difference reservoir simulator in a manner that allows practical engineering analysis of reservoir compaction caused by fluid withdrawal. The physics allows analysis of compaction in several new areas, as demonstrated by example problems for Belridge oil field diatomite. Hysteresis of compaction in the form of limited rebound during fluid injection and the concept of relaxation time (i.e.. creep), borrowed from the field of viscoelasticity, are new in petroleum applications. Compaction may occur initially and be more pronounced in the downdip portions of developed acreage. Furthermore. the effect of water injection on pressure and oil response within the compacting diatomite is shown to be highly sensitive to reservoir rebound. Compaction in Reservoir Simulation The derivation of conservation equations in differential form that include the effects of compaction are described in papers by Finol and Farouq Ali, Rattia and Farouq Ali, and Raghavan. An alternative derivation that lends itself easily to finite-difference discretization is outlined below. We write the mass and energy balances of the fluids contained within the pores of a fixed mass of rock. This frame of reference is appropriate because Darcy's law. which is used to relate fluid velocities to potential gradient. is formulated in terms of velocities with respect to the rock. The conservation of Chemical Species is .....................(1) where integration with respect to volume dV and surface dS denote the volume V(t) containing and the surface S(t) surrounding the fixed mass of rock under consideration. Summation is over index. denoting phases: liquid hydrocarbon. aqueous. and gas. The volume and surface of integration may change with time because of compaction of the rock mass. The first term in Eq. 1 is the rate of change of the mass of Species in the pore space of the volume occupied by the arbitrary mass of rock. The second term is the net flux of Species i across the boundary of the volume under consideration, and the term on the right represents the source and sink terms. The conservation-of-energy equation can be written in a similar fashion. To obtain a finite-difference discretization of Eq. 1. let the fixed mass of rock be that contained within a gridblock and assume that this mass of rock remains constant even though the gridblock may deform owing to compaction. Assume further that compaction acts only to deform the direction of the gridblock. Eq. 1 can then be written .......................(2) where z(t) is written as a function of time because gridblock thickness may change as the reservoir compacts. Porosity is related to z and the rock density through the constancy of mass of rock in the gridblock as follows: ......................(3) Letting subscript zero denote the known initial condition and assuming that and remain constant (compaction occurs only in the direction), we obtain .....................(4) Rock density is known to be a function of pressure and temperature through the equation of state for the rock. z is related to pressure and temperature through a strain function.