Improved Recovery Techniques
Waterflooding Part 2
Deepak Devegowda
Buckley Leverett Frontal
Advance Theory
Objectives
Learn Buckley Leverett frontal advance
theory
Estimate oil recovery using the BuckleyLeverett theory
Waterflood production forecasting using
frontal advance
Motivation
Consider a one dimensional waterflood
Is the waterflood performance going to be
like
Yes, if gravity forces are stronger than
viscous or capillary forces
Motivation
Or is the waterflood performance going to be
like this?
Motivation
Typically waterflood performance is not
piston-like, instead it looks like:
The shape of the profile is predicted by
Buckley Leverett theory
Waterflooding
Once you learn B-L theory, you will be able to
extend your knowledge to 2D and 3D
reservoirs
Understand the role of the various inputs on
the efficacy of the waterflood
Model Description
Model Description
At any point x, 2 phases (oil and water) may
flow
Assume incompressible fluids and that the
injection and production rates are constant
Flow Equations
Flow Equations
From the previous page, we can rewrite the
equations as
Flow Equations
Subtracting eqn 1 and 2 from the previous
slide..
Flow Equations
Now because we are only considering 2
phase flow
Substitute the expression above in to the
equation on the previous slide
Flow Equations
We finally have.
and
Fractional Flow
The fractional flow, fw is defined as:
So, the fractional flow becomes
Fractional Flow
The final expression is:
When capillary pressure is negligible
Assignment
Construct the fractional flow curve for the
data provided in the attached spreadsheet.
Buckley Leverett Applications
Determine Sw vs distance for a 1D coreflood
Determine oil rate and recovery
Model
Mass balance: Mass in Mass out =
Accumulation
Mass Balance for Water
Mass Balance for Water
The mass balance gives us:
Assuming incompressible fluids:
Mass Balance for Water
Sw is a function of time, t and distance, x.
Therefore:
Saturation Tracking
Let us move with any arbitrarily chosen
saturation value
Along this plane, dSw = 0. Therefore the
equation on the previous page becomes:
Recall from 2 slides ago that
Mass Balance
Combining the equations on the previous
slide, we get:
Mass Balance
Since Qt is a constant and the fluids are
incompressible,
Differentiating this equation, we get:
Velocity of the Front
Comparing the equations of the past 2 slides,
we get:
Where V(Sw) is the velocity of a front of
saturation, Sw.
All quantities on the RHS of the equation are
a constant, except dfw/dSw.
Velocity of the Front
Therefore the velocity of the front is
proportional to dfw/dSw.
Assignment
On the provided spreadsheet, construct the
curve, dfw/dSw.
Saturation Profile
Integrating the frontal advance equation, we
get:
Because the flow is assumed incompressible,
the integral above is also just the total water
injected, Wi.
Saturation Profile
Now, we can plot the distance x travelled by a
saturation value, Sw
Saturation Profile
This is clearly a physical impossibility you
cannot have 2 saturation values at the same x
In Reality
Flood Front Estimation
Flood Front Estimation
Now
Or
Therefore
saturation at the front
where Swf is the
Flood Front
Graphically:
Re-draw the Saturation Profile
Oil Recovery at Breakthrough
Oil Recovery at Breakthrough
Note,
At breakthrough
Therefore
and
Improved Recovery Techniques
Waterflooding Part 2
Deepak Devegowda
