Page 149 - Principles of Applied Reservoir Simulation 2E

134 Principles of Applied Reservoir Simulation

Permeability is a physical constant describing flow in a given sample for
a given fluid and set of experimental conditions. If those conditions are changed,
the permeability being measured may not apply. For example, if a waterflood
is planned for a reservoir that is undergoing gravity drainage, laboratory
measured permeabilities need to represent the injection of water into a core with
hydrocarbon and connate water. The permeability distribution and the relative
permeability curves put in the model need to reflect the type of processes that
occur in the reservoir.
Permeability has meaning as a statistical representation of a large number
of pores. A Micro Scale measurement of grain-size distribution shows that
different grain sizes and shapes affect permeability. Permeability usually
decreases as grain size decreases. It may be viewed as a mathematical conve-
nience for describing the statistical behavior of a given flow experiment. In this
context, transient testing gives the best measure of permeability over a large
volume. Despite its importance to the calculation of flow, permeability and its
distribution will not be known accurately. Seismic data can help define the
distribution of permeability between wells if a good correlation exists between
seismic amplitude and a rock quality measurement that includes permeability.
It is not unusual to find that permeability has a directional component:
that is, permeability is larger in one direction than another [for example, see
Fanchi, et al., 1996]. When a model is being designed, the modeling team should
account for the direction associated with permeability. In principle, simulators
can take all of these effects into account. In practice, however, the tensor
permeability discussed in the literature by, for example, Bear [1972] and Lake
[1988] is seldom reflected in a simulator. The usual assumption is that perme-
ability is aligned along one of three orthogonal directions known as the principal
axes of the tensor. This assumption has implications for model studies that
should be considered when assessing model results (see Chapter 15 and Fanchi
[1983]).
In many cases vertical permeability is not measured and must be assumed.
A rule of thumb is to assume vertical permeability is approximately one tenth
of horizontal permeability. These are reasonable assumptions when there is no
data to the contrary.