Water influx Fetkovich Aquifer Model

 Fetkovich (1971) proposed a model to simplify water influx calculations further.

This method uses a pseudo-steady-state aquifer productivity index (PI) and an

aquifer material balance to represent the system compressibility. Like the Carter￾Tracy method, Fetkovich’s model eliminates the use of superposition and there￾fore, it is much simpler than van Everdingen-Hurst method. However, because

Fetkovich neglects the early transient time period in these calculations, the calcu￾lated water influx will always be less than the values predicted by the previous two

models.

The Fetkovich model applies to finite-acting aquifers; the model is applicable to

both radial and linear aquifers. The Fetkovich aquifer model applies to edge-water

and bottom-water drive reservoirs, while the Carter-Tracy aquifer model applies to

edge-water drive reservoirs. In edge-water drive, water influx occurs around the

flanks of the reservoir. In bottom-water drive, the reservoir is underlain by the

aquifer which encroaches vertically into the reservoir. These are represented in the

Fig. 4.4.

Fetkovich used an inflow equation similar to fluid flow from a reservoir to a well,

to model the water influx to the reservoir. Assuming constant pressure at the original

reservoir/aquifer boundary, the rate of water influx is derived as follow:

The inflow equation is given as:

q ¼

Where qw ¼ water influx rate, j ¼ aquifer productivity index, P ¼ Pressure at the

reservoir fluid contact i.e. inner aquifer boundary pressure, Pa ¼ average pressure in

the aquifer & We ¼ cumulative water influx.

The total aquifer influx due to the total pressure drop is:

The results are plotted in the figure below. This shows that there is a closeness in

value between the Van Everdingen and Fetkovich model with little deviation

from the Carter-Tracy model but that does not mean that Carter-Tracy model cannot

estimate water influx well. In some reservoir, Carter-Tracy model fits the aquifer

model used in matching historical data. Thus, these aquifer models are tested on the

reservoir to see which matches the past field performance with a minimum tolerance

of error.