Page 136 - Fundamentals of Reservoir Engineering

MATERIAL BALANCE APPLIED TO OIL RESERVOIRS 75

in which the final term (W e − W p)B w is the net water influx into the reservoir. This
has been intuitively added to the right hand side of the balance since any such
influx must expel an equivalent amount of production from the reservoir thus
increasing the left hand side of the equation by the same amount. In this influx
term

W e = Cumulative water influx from the aquifer into the reservoir, stb.

W p = Cumulative amount of aquifer water produced, stb.

and B w = Water formation volume factor rb/stb.

B w is generally close to unity since the solubility of gas in water is rather small
and this condition will be assumed throughout this text. For more detailed
calculations, correlation charts for B w are presented in references 2 and 3.

The following features should be noted in connection with the expanded material
balance equation

− it is zero dimensional, meaning that it is evaluated at a point in the reservoir

− it generally exhibits a lack of time dependence although, as will be
discussed in sec. 3.7 and also in Chapter 9, the water influx has a time
dependence
− although the pressure only appears explicitly in the water and pore
compressibility term as, ∆p = p i − p, it is implicit in all the other terms since
the PVT parameters B o, R s and B g are themselves functions of pressure.
The water influx is also pressure dependent.

− the equation is always evaluated, in the way it was derived, by comparing
the current volumes at pressure p to the original volumes at p i. It is not
evaluated in a step-wise or differential fashion.

Although the equation appears a little intimidating, at first sight, it should be
thought of as nothing more than a sophisticated version of the compressibility
definition

dV = c × V × ∆p
Production = Expansion of reservoir fluids.

and, under certain circumstances, can in fact be reduced to this simple form.

In using the material balance equation, one of the main difficulties lies in the
determination of the representative average reservoir pressure at which the
pressure dependent parameters in the equation should be evaluated. This
follows from the zero dimensional nature of the equation which implies that there
should be some point in the reservoir at which a volume averaged pressure can
be uniquely determined. In applying the more simple gas material balance, equ.
(1.35), such a point could be defined with reasonable accuracy as the centroid
point, at which pressures could be evaluated throughout the producing life of the