Waterflooding - II

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 Buckley Buckley-Leverett 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