Relative
permability
Resented by : Khawlah Ajaj
Supervised by : Dr Omar
Alayadi
Contents

Introduction

Factors Effecting on Kr

Relative permeability Functions

Effect of wettability for Increasing Sw

Application of Relative Permeability

Two-Phase Steady-State and Unsteady-State Relative
Permeability.
Introduction
 What
is relative permeability?
Relative permeability is a parameter describing how the mobility of
a phase is affected in presence of other fluids in a porous medium.
Accurate measurements of relative permeability are required for
making reliable predictions and decisions at field scale. Such
measurements are traditionally performed either by the unsteady
state method where one fluid is injected to displace the other or the
steady state method where both fluids are co-injected. The former
method is similar to the displacement taking place in the reservoir,
while stable and uniform flow can be achieved in the latter.
the relative permeability of each phase at a specific saturation is
the ratio of the effective permeability of the phase to the absolute
permeability, or:
kro= 𝑘𝑜
𝑘
krg=
𝑘𝑔
𝑘
𝑘𝑟w =
𝑘𝑤
𝑘
Where :
 kro = relative permeability to oil
 krg = relative permeability to gas
 krw = relative permeability to water
 kw = effective permeability to water at some given water
saturation
 k = absolute permeability
 ko = effective permeability to oil for a given oil saturation
 kg = effective permeability to gas for a given gas saturation
Factors Effecting on Kr
Relative permeability depends not only on the overall fluid saturations, but
also on the geometry of the pore space and the geometry of the fluids
distributed within the pore space. These factors depend in turn on:
o •Wettability;
o •Pore structure;
o •Ratio of capillary to viscous forces;
o •Interfacial tension;
o •Saturation history.
Applications of relative
permeability

Reservoir Simulation .

Flow calculation that involves multiphase Flow in reservoir .

Estimation of Residual Oil (and/or Gas ) Saturation .
Two-Phase Steady-State
and Unsteady-State Kr
relative permeability can be categorized into two major
groups which consist of steady-state and unsteady-state
methods. For intermediate (mixed) wettability rocks, steadystate methods are preferred to unsteady-state methods by
some reserchers1. Unsteady-state methods however, almost
always yield faster results compared to the steady-state
methods due to the nature of processes involved in each
method.
In the steady-state method, two fluids are injected
simultaneously at a constant rate through a core until the
produced fluid ratio achieves an equilibrium condition with
the injected fluid ratio. At this saturation, the effective
permeability to each phase is obtained by using Darcy's law.
The ratio of the effective permeability to the base permeability
will yield the relative permeability at that saturation value.
Relative permeability values for different saturations are
obtained by changing the fluid ratio of the injection rate2. Some
examples of the steady-state method are the Penn-State
method, Hassler method, Single-Sample Dynamic method and
Hafford method.
In the unsteady-state method however, in-situ fluid is displaced
by a driving fluid at a constant rate. The saturation within the
core changes with time. The changes in pressure and fluid
produced are measured with respect to time. Relative
permeability values of the in-situ and the driving fluid are then
calculated using an equation originally developed by Buckley
and Leverett3. Examples of the unsteady-state methods are
Johnson-Bossler-Naumann, Welge and Jones-Roszelle.
Laboratory measurement of relative permeability using either
steady-state or unsteady-state methods can be expensive and
time consuming. Laboratory measurement is considered a
micro process because a single measurement is insufficient to
represent the entire reservoir.
An accurate numerical procedure for determining relative
permeability values provides an alternative technique, and
at the same time it can overcome the previous
shortcomings. In contrast to laboratory measurement, this is
a macro process which provides a better statistical
representation of relative permeability values for the
reservoir as a whole.
Thank you for your
Attention