Page 38 - Fundamentals of Enhanced Oil and Gas Recovery

26 Amirhossein Mohammadi Alamooti and Farzan Karimi Malekabadi

microscopic displacement efficiency (E v ), and macroscopic displacement efficiency
(E D )asfollows:
If displacement performance data are available, one can estimate the volumetric
(sweep) efficiency using the above equation. For example, if water injection efficiency
data are at hand, the equation can be changed as follows in order to solve volumetric
efficiency:

N P
E V 5
V P ððS o1 =B o1 Þ 2 ðS o2 =B o2 ÞÞ
where N P is the amount of oil produced in the injection operation.

1.14.4 Areal and Vertical Sweep Efficiency
Volumetric displacement efficiency is defined based on areal sweep efficiency (E A ) and
vertical sweep efficiency (E I ). A reservoir has several layers, and each porosity layer has
the same thickness and percentage of saturated hydrocarbon. Therefore the definition
of volumetric displacement efficiency will be as follows:

E v 5 E A 3 E I
In the above equation, E A represents areal displacement efficiency in an ideal reser-
voir and E I is vertical displacement efficiency. In a region with high areal displacement
efficiency, E I is small and limited. A real reservoir is characterized by conditions such
as porosity, thickness, saturation percentage, and regional hydrocarbon; hence E V is
expressed as pattern sweep efficiency:

E v 5 E P 3 E I
In the above relation, E P signifies pattern sweep efficiency, which is defined as
hydrocarbon of the pore space behind the injected-fluid front divided by the pore
space of the region or project. Thus E P is the areal displacement efficiency that is
expressed based on changes in thickness, porosity, and saturation percentage. Total
efficiency coefficient is expressed as:

E 5 E P 3 E I 3 E D
One has to estimate and calculate E P (or E A ) and E I in order to use the above
equations. It is difficult to estimate and compute these parameters because E A and E I
are not independent from one another during three-dimensional (3D) displacement.
In the absence of vertical displacement factors, areal sweep efficiency can be obtained
through equations developed on the basis of a physical or mathematical model. Also
the methods of using these models are subject to limitations. E V is usually calculated
on the basis of suitable functional relationships or by using mathematical models based
on a three-dimensional system that does not depend on E A and E I [1].