Page 229 - Fundamentals of Enhanced Oil and Gas Recovery

Waterflooding 217

flow. Stiles was able to develop equations for fractional recovery, as well as that for
water cut in terms of the fraction of a fraction of capacity, thickness, and permeability
with the assumption that the flow was linear, which still holds. However, Paul makes
us understand that as water is injected into the reservoir, the direction of flow occurs
in three phases: the initial direction, which is that of a radial flow, transition from
radial to linear, and then the linear flow. Paul and Franklin [27] then developed the
equations of water cut and fractional recovery by assuming that fraction of recovery
and production rates are proportional to the volumes created.
Radial fractional flow is an important factor to be considered in the waterflood
design because it gives a good unit displacement efficiency with a minimal fraction of
water flowing, thereby giving a good prediction to the recovery factor. This can be
seen as described by Singh and Kiel [29], and the unit displacement efficiency is got-
ten by plotting a fractional flow curve against water saturation.
Ekwere [30] showed that fractional flow is important because it helps predict a
stable frontal displacement at all mobility ratios. Millian and Parker [31] also helped
validate that with fractional flow analysis, the waterflooding process is successful and
it helps maintain the reservoir pressure, thereby increasing oil recovery.
The radial displacement method helps improve the prediction of reservoir perfor-
mance unlike the Buckley Leverette theory, which results in the much lower recov-
ery process, and so, this process is, therefore, an important supplement to the
Buckley Leverette method as the process shows a short process of water break-
through [32].

Example 7.1: A pilot-scale injection is performed on field alpha to ascertain the
distinction between linear and radial displacement systems. Field alpha is a sandstone
formation with no existing waterflooding scheme. The following parameters in
Table 7.1 are utilized for model analysis.

Field alpha assumed a radial displacement scenario. The comparison analysis used
the same inputs for the correlations for both displacement systems and the impact on
results was critically observed.
First, the plot of relative permeability of oil and water (K ro and K rw ) with increas-
ing water saturation was generated to ascertain if the reservoir follows the conven-
tional trends. Fig. 7.5 depicts the plot, which shows a normal trend.
The linear system pioneered by Buckley Leverett assumed that capillary pressure
is negligible. For the radial system, capillary-pressure effect is included in fractional
flow calculations. It is important to note that for the total negligence of capillary pres-
sure for both systems, the Buckley Leverett equations are valid for both systems.
Bearing this in mind, and considering incorporating the effect of capillary pressure
into our pilot-scale analysis, the major challenge was how best to calculate the effect
of capillary pressure accurately.