Page 48 - Primer on Enhanced Oil Recovery

Reservoir mineralogy and rock-fluid interactions 39

processes. Adapted to the conventional form the Darcy’s Law (Equation) can be
expressed in the form:

kA dP
Q 52
μ dL

where Q is a flow rate, which is an oil volume in a time unit. Traditionally Q was
measured in mL/s. A is area of the opening (this is the whole surface area through
which the flow is measured), µ is viscosity, k is permeability. Depending on the
measuring system units the permeability can be measured either in square microns
(in SI) or milliDarcy (mD) (in CGS). One Darsy is approximately equal to 1 square
2
micron (μm ). The last term, dP/dL, defines differential of the pressure which
invokes the flow.
Usually the conventional oil reservoir rocks are semi-pervious and permeability
2
is roughly in the range between 100 and 10000 milliDarcy (from 0.1 to 10 μm ).
The high values are favorable for oil production as for the same pressure differen-
tial the quantity of flowing oil is higher. Highly fractured rock can have permeabil-
5
ity up to 10 Darcy. On the low of permeability are dense clays and granite with
permeability in the region 10 27 Darcy.
The Darcy’s law deals with a single liquid flow through a porous medium.
Reservoir fluids are mixtures of hydrocarbons (oil and gas) and connate water.
Ability of rock to allow a single phase flow is referred as an absolute permeability.
In the case of two or more phases there are effective, so named partial, permeabil-
ities for each phase. In this case each effective permeability is lower than the abso-
lute permeability and the sum of all effective permeabilities cannot be bigger than
the absolute permeability. All permeabilities are affected by the rock saturations
with all presented phases, rock wettability and speed of liquid flows. This makes
liquid flow in the reservoir rock very complex and the only reliable and accurate
way to assess the oil flow is to do measurements on the rock cores in a laboratory
under reservoir conditions.
It is clear at this point that reservoir fluids flow through openings of different
sizes and the flow is affected by viscosity and interfacial tension. In order to reflect
on this a dimensionless value, named a capillary number N c , is defined in oil indus-
try as

N c 5 μ=σ
26
In small pores the capillary number is very small, usually below 10 . While in
the cracks and pipe-like flow it is approaching 1. In the first case the flow is
defined by the interfacial forces, while in the second case flow is mostly defined by
the viscosity. It has been shown that an increment in capillary number in the in the
formation has benefits in reduction of the residual oil saturation. The approach is
then quite obvious reduction of an interfacial tension leads to the better oil
recovery.