Reservoir Fluid Flow and Natural Drive Mechanisms

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Water Drive Reservoir

When speaking of a water drive reservoir, we mean natural water drive as opposed to artificial water injection. Water moves into the reservoir from the aquifer in response to a pressure drop that causes the water and the rock in the aquifer to expand. If the aquifer is small, one may assume that the pressure drop is instantaneously trans mitted throughout the reservoir. Cumulative water influx will then be given by

$W_{e}=V_{w}\, c_{t}\, \Delta p$ …………(47)

where:

W_e= total water influx in reservoir volumes

V_w= volume of water in the aquifer in reservoir volumes

c_t= total compressibility =c_w+c_r, $\tfrac{1}{psi}$

c_w= water compressibility, 1psi

c_r= rock compressibility, $\tfrac{1}{psi}$

Δp=p_i−p, psi

p_i= initial pressure

p= pressure at time t that We is calculated.

The rock and water compressibilities are in the order of 5⋅10⁻⁶ per psia. For an aquifer of 10⁹ RB, and assuming a pressure drop, Δp, of 1000 psi,

$W_{e}=10^9\cdot 10 \cdot 10^{-6}\cdot 1000$

$10^{7}\ RB\ (1.59\cdot 10^{6}\ m^{3})$

Thus, the total water influx amounts to about one-hundredth of the original oil volume if the reservoir is equal in size to the aquifer. Unless the aquifer is very large compared to the oil volume, the effect of water influx on recovery is not significant.

When the aquifer is large, the assumption that the pressure drop is instantaneously transmitted throughout the reservoir is not valid. There is a time lag between the pressure change at the oil-water boundary and when it is felt throughout the aquifer.

This means that W_e is a function of time and Δp, and Equation (47)

$W_{e}=V_{w}\, c_{t}\, \Delta p$

is not adequate for calculating W_e. Chatas (1953) gives a good illustration of the calculation procedure.

Gravity Segregation Effects

Since the density of water is higher than that of oil or gas, the force of gravity tends to segregate water at the bottom part of the reservoir. This segregation, especially in the case of layered dipping reservoirs, can be advantageous. It tends to keep the water front uniform as it moves updip and minimizes water channeling in high permeability layers. The locations of producing wells and the depths of their completed intervals strongly affect the performance of water drive reservoirs. Reservoir simulators are the best tools for studying the combined effects of the above variables.