An approach is described for an improved representation of shales in a clastic reservoir. Oil and gas reservoirs are extremely complex, and simulation of their performance is carried out using simplified models. At best, such models are crude representations of true geological complexity and they often fail to predict performance with any degree of reliability. Impermeable zones, or shales, are generally modelled as horizontal and rectangular simulation grid blocks, although natural shales dip, are irregular, and usually better modelled by a dipping ellipse, semi-ellipse or rectangle. For the estimation of an effective vertical permeability, no more than five to ten shales usually need to be included in a model. Correction factors can be applied to model the "real" shales as equivalent horizontal rectangles.
The size of shale is a critical parameter in modelling a sand-shale sequence and can be represented by a "characteristic distance" that is unique to that sequence, and that is composed of:
a dimensionless shale density
a geometric, or shape, factor
an orientation factor.
The simulation of the flow of fluids, (oil, gas or water) through a reservoir requires that a model be constructed from log, core, and outcrop analog data In such a mode, the complex, heterogenous, rock material is replaced by grid blocks with "equivalent" flow properties. One of the most important aspects of building a reservoir model is the calculation of an equivalent vertical permeability for a sequence containing impermeable layers. Models of sequences containing discontinuous impermeable layers (called shales in this paper, although they can be any impermeable unit) commonly assume that the shales:
have a regular shape;
are of the same shape as the simulation grid (usually rectangular);
are of the same size, or an integral multiple, of the simulation grid;
are horizontal and planar on the downstream flow side.
Real shales satisfy none of the above requirements, being irregular in shape, of different sizes, rarely, if ever, horizontal and unlikely to have a planar upper or lower surface. The approach described in this paper is a step towards more realistic models of reservoirs containing discontinuous shales.
The model in this paper is a development of the streamline model described by Haldorsen and Lake1 and developed further by Begg and King2, Begg, Chang and Haldorsen3, and Haldorsen and Chang4.
In a sequence of gross thickness h, containing one horizontal impermeable shale, considering the vertical flow vector, Ls the length of the streamline (i.e., the distance travelled by a fluid "particle" travelling vertically through the sequence), Fig. 1, is the thickness h, plus a "characteristic distance", ρ, travelled below the shale, before it can resume its vertical movement, plus the horizontal distance required to return it to a vertical position above the starting point, which is also ρ. That is;
Ls = h + 2 ρ
For a sequence containing N shales of the same size within the flow path streamline;
Ls = h + 2N ρ
If kve the effective vertical permeability and kv is the matrix permeability;