Page 59 - Principles of Catalyst Development
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40 Principles of Applied Reservoir Simulation
Frontal advance theory is an application of the law of conservation of
mass. Flow through a small volume element (Figure 5-1) with length Ax and
/ A
v
Porous Material /
/ (e.g. Rock)
Figure 5-1. Flow Geometry
cross-sectional area A can be expressed in terms of total flow rate q t as
9* = QO + <? w (s.i)
where q denotes volumetric flow rate at reservoir conditions and the subscripts
{o, w, t} refer to oil, water, and total rate, respectively. The rate of water entering
the element on the left hand side (LHS) is
q tf w = entering LHS (5.2)
for a fractional flow to water f w. The rate of water leaving the element on the
right hand side (RHS) is
+
q t (f w A/ w) = leaving RHS (53)
The change in water flow rate across the element is found by balancing mass
for an immiscible, incompressible system, thus
rate change = water entering - water leaving
(54)
The change in water saturation per unit time is the rate change in Eq. (5.4)
divided by the pore volume of the element, thus
Ax
