Effects of Water Production, Relative Permeability

Provided volumetric flow rates of undersaturated oil reservoirs as functions of the permeability, k. This permeability was used as a reservoir property. In reality this is only an approximation, since such a use of permeability is correct only if the flowing fluid is also the only saturating fluid. In such case the “absolute” and “effective” permeability values are the same.

In petroleum reservoirs, however, water is always present at least as connate water, denoted as S_wc. Thus, in all previous equations the permeability should be considered as effective, and it would be invariably less (in certain cases significantly less) than the one obtained from core flooding or other laboratory techniques using a single fluid.

If both oil and free water are flowing, then effective permeability must be used. The sum of these permeability values is invariably less than the absolute permeability of the formation (to either fluid).

These effective permeability values are related to the “relative” permeability values (also rock properties) by

and

Relative permeability values are determined in the laboratory and are characteristic of a given reservoir rock and its saturating fluids. It is not a good practice to use relative permeability values obtained for one reservoir to predict the performance of another.

Usually, relative permeability curves are presented as functions of the water saturation, S_w, as shown in Figure 2-8. When the water saturation, S_w, is the connate water saturation, S_wc, no free water would flow and therefore its effective permeability, k_w, would be equal to zero. Similarly, when the oil saturation becomes the residual oil saturation, S_or, then no oil would flow and its effective permeability would be equal to zero.

Figure 2-8. Relative permeability effects, water production.

Thus, in an undersaturated oil reservoir, inflow equations must be written for both oil and water. For example, for steady-state production,

and

with relative permeability values, k_ro and k_rw, being functions of S_w, as shown in Figure 2-11. Note that the pressure gradients have been labeled with subscripts for oil and water to allow for different pressures within the oil and water phases.

The ratio q_w/q_o is referred to as the water–oil ratio. In an almost depleted reservoir it would not be unusual to obtain water–oil ratios of 10 or larger. Such a well is often referred to as a “stripper” with the production rates of less than 10 STB/d of oil. In mature petroleum areas, stripper wells may constitute the overwhelming majority of producers. Their economic viability is frequently one of the most important questions confronting production engineers.