Linear Fracture Flow Analysis
Subtopics:
Summary of Equations for Linear Fracture Flow
Summary of Equations for Linear Fracture Flow Derivative Analysis
Linear fracture flow is one of the flow regimes that can exist when a well has been hydraulically fractured. The purpose of analyzing linear fracture flow data is to determine the fracture halflength (Xf).
Constant Rate Solution (Field Units)
For oil and water:
For gas:
Linear fracture flow data will form a straight line when placed on a semilog plot of pressure versus a square root time function (p vs. sqrt (time function)) for a buildup as shown below.
The slope (m) of this line is used to calculate the product of the fracture halflength and the square root of permeability (Xf sqrt(k)) as follows:
For oil and water:
For gas:
The permeability can be obtained from the radial flow analysis, or estimated from core data, or other tests. After permeability is determined, fracture halflength is found using the following equation:
Summary of Equations for Linear Fracture Flow (Field Units)
Flow Period  Fracture HalfLength * Square Root of Permeability (ft md0.5)  

Oil 
Drawdown


Buildup



Gas 
Drawdown


Buildup


Other Required Equations (Field Units)
Skin 

For infinite conductivity fractures, when kf is large (FCD > 20) 
Derivative (Field Units)
The signature of linear fracture flow data on a derivative plot is a straight line with a slope of 1/2. The position of this line is used to calculate the product of fracture halflength and root permeability (Xf sqrt(k)). Note that the product of fracture halflength and root permeability increases as the position of this line moves to the right.
Starting with the constant rate solution (see above), the derivative with respect to the logarithm of squareroot time is:
For oil and water:
For gas:
Taking the logarithm of both sides:
For oil and water:
For gas:
This result is linear with time and, as a result, the derivative of linear fracture flow data falls on a straight line with a slope equal to 1/2 on a log Dp versus log Dt plot as shown below.
Using any derivative point on this line, the product of fracture halflength and root permeability (Xfsqrt(k)). can be determined as follows:
For oil and water:
For gas:
Summary of Equations for Linear Fracture Flow Derivative Analysis (Field Units)
Flow Period  Fracture HalfLength * Root Permeability (ft md0.5)  

Oil 
Drawdown


Buildup



Gas 
Drawdown


Buildup

