7/26/2019 Waterflooding - II
1/39
Waterflooding Part 2
Deepak
Devegowda
Improved Recovery Techniques
7/26/2019 Waterflooding - II
2/39
Buckley
Leverett
Frontal
Advance Theory
7/26/2019 Waterflooding - II
3/39
Objectives
Learn Buckley
Leverett
frontal advance
theory
Estimate oil recovery using the Buckley
-
Leverett
theory
Waterflood production forecasting using
frontal advance
7/26/2019 Waterflooding - II
4/39
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
7/26/2019 Waterflooding - II
5/39
Motivation
Or is the waterflood performance going to be
like this?
7/26/2019 Waterflooding - II
6/39
Motivation
Typically waterflood performance is not
piston
-
like, instead it looks like:
The shape of the profile is predicted by
Buckley
Leverett
theory
7/26/2019 Waterflooding - II
7/39
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
7/26/2019 Waterflooding - II
8/39
Model Description
7/26/2019 Waterflooding - II
9/39
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
7/26/2019 Waterflooding - II
10/39
Flow Equations
7/26/2019 Waterflooding - II
11/39
Flow Equations
From the previous page, we can rewrite the
equations as
7/26/2019 Waterflooding - II
12/39
Flow Equations
Subtracting eqn 1 and 2 from the previous
slide..
7/26/2019 Waterflooding - II
13/39
Flow Equations
Now because we are only considering 2
phase flow
Substitute the expression above in to the
equation on the previous slide
7/26/2019 Waterflooding - II
14/39
Flow Equations
We finally have.
and
7/26/2019 Waterflooding - II
15/39
Fractional Flow
The fractional flow, fw is defined as:
So, the fractional flow becomes
7/26/2019 Waterflooding - II
16/39
Fractional Flow
The final expression is:
When capillary pressure is negligible
7/26/2019 Waterflooding - II
17/39
Assignment
Construct the fractional flow curve for the
data provided in the attached spreadsheet.
7/26/2019 Waterflooding - II
18/39
Buckley Leverett Applications
Determine Sw vs distance for a 1D coreflood
Determine oil rate and recovery
7/26/2019 Waterflooding - II
19/39
Model
Mass balance: Mass in Mass out =Accumulation
7/26/2019 Waterflooding - II
20/39
Mass Balance for Water
7/26/2019 Waterflooding - II
21/39
Mass Balance for Water
The mass balance gives us:
Assuming incompressible fluids:
7/26/2019 Waterflooding - II
22/39
Mass Balance for Water
Sw is a function of time, t and distance, x.
Therefore:
7/26/2019 Waterflooding - II
23/39
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
7/26/2019 Waterflooding - II
24/39
Mass Balance
Combining the equations on the previous
slide, we get:
7/26/2019 Waterflooding - II
25/39
Mass Balance
Since Qt is a constant and the fluids are
incompressible,
Differentiating this equation, we get:
7/26/2019 Waterflooding - II
26/39
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 area constant, except dfw/dSw.
7/26/2019 Waterflooding - II
27/39
Velocity of the Front
Therefore the velocity of the front is
proportional to dfw/dSw.
7/26/2019 Waterflooding - II
28/39
Assignment
On the provided spreadsheet, construct the
curve, dfw/dSw.
7/26/2019 Waterflooding - II
29/39
Saturation Profile
Integrating the frontal advance equation, we
get:
Because the flow is assumed incompressible,
the integral above is also just the total waterinjected, Wi.
7/26/2019 Waterflooding - II
30/39
Saturation Profile
Now, we can plot the distance x travelled by a
saturation value, Sw
7/26/2019 Waterflooding - II
31/39
Saturation Profile
This is clearly a physical impossibility you
cannot have 2 saturation values at the same x
7/26/2019 Waterflooding - II
32/39
In Reality
7/26/2019 Waterflooding - II
33/39
Flood Front Estimation
7/26/2019 Waterflooding - II
34/39
Flood Front Estimation
Now
Or
Therefore where Swfis the
saturation at the front
7/26/2019 Waterflooding - II
35/39
Flood Front
Graphically:
7/26/2019 Waterflooding - II
36/39
Re-draw the Saturation Profile
7/26/2019 Waterflooding - II
37/39
Oil Recovery at Breakthrough
7/26/2019 Waterflooding - II
38/39
Oil Recovery at Breakthrough
Note, and
At breakthrough
Therefore
7/26/2019 Waterflooding - II
39/39
Waterflooding Part 2
Deepak Devegowda
Improved Recovery Techniques