This document provides an overview and analysis of hydraulic fractured wells. It discusses: 1) Reasons for fracturing wells including bypassing near-wellbore damage, extending a conductive path, and minimizing drawdown. 2) Key fracture properties like half-length, permeability, width, and conductivity that impact flow. 3) The hydraulic fracturing process including initiating fractures, propagating fractures with proppant, and the idealized induced fracture shape. 4) Models for fractured well flow including infinite and finite conductivity models and the different flow regimes of linear, bilinear, and radial flow. 5) Methods for analyzing fractured well test data including type curves and evaluating

1. Well Testing Analysis
(Hydraulic Fractured Wells)
2023
Hesham Mokhtar Ali
Senior Reservoir Engineer
in/heshammokhtarali/

2. Fractured Wells
• Reasons:
 Bypass near-wellbore damage.
 Extend a conductive path deep into a formation and thus increase productivity.
 Minimize the drawdown.
• To fracture, pump fluid against higher resistance, so that the bottom hole pressure rises above the
fracture gradient of the formation.
• Vertical fractures are characterized by the following properties:
• Fracture half-length xf , ft
• Fracture permeability kf , mD
• Fracture width wf , ft
• Fracture conductivity FC, kfwf
Reservoir permeability, k
Wellbore
Fracture half length, Xf
Fracture permeability, kf
Fracture
width, wf

3. Hydraulic Propped Fracturing – Overview
• Create high conductive
path between the
reservoir and the
wellbore.
Initiate Fracture Propagate Fracture
Placing Proppant Flowback Idealized View of Induced Fracture
Typical pressure response during DFIT
Pumping
Before-closure
After-closure

4. Net Fracture Pressure (NFP)
• Instantaneous Shut-in Pressure (ISIP) is the pressure at
sand face when friction removed.
• Net fracture pressure, Pnet = ISIP - closure P
• Pnet controls fracture width and height.
Effect of net pressure on the
fracture propagation

5. Typical Minifrac Injection Test

6. Fracture Shape & Dimensions
• Hydraulic fracturing is the process of using hydraulic
pressure to create an artificial fracture in a reservoir.
• The fracture grows in length, height and width by
pumping a mixture of fluid and proppant at high
pressure.
• W= the fracture width
• Xf= the fracture penetration or half-length
• Hf= Fracture Height
7

7. Fracture Models
• There are 2 basic fracture models:
• High or “Infinite Conductivity”: the pressure drop along the inside of the fracture is negligible
• Infinite-Conductivity Fracture:
• Assumes NO pressure drop along the fracture.
• Uniform Flux Fracture:
• Assumes a uniform production per unit length of fracture.
• Low or “Finite conductivity”: the pressure drop along the fracture is significant.

8. Flow Regimes In Fractured Wells
Fracture Linear Flow
Bilinear Flow
Formation Linear Flow
Well
Fracture
Well
Fracture
Well
Fracture
 Fracture linear flow:
 Initially, the flow is only through fractures
 Never observed in practice in case of high WBS.
 Fracture bilinear flow:
 The pressure front extends both linearly along the fracture and linearly
into the reservoir close to the fracture.
 Formation linear flow:
 The pressure front moves linearly out from the fracture into the reservoir.
 Formation radial flow
 The flow is IARF.
Pseudoradial Flow

9. Flow Regimes In Fractured Wells
  2
1
2
1
2
1
t
m
t
b
t
m
t
t
p
t L
L
L








• Pressure & derivative have slope of 1/2 (separated by a
factor of 2.
4
1
2
1
1
1
.
44


















k
c
t
wk
h
qB
p
t
f 

• Derivative:
  4
1
4
1
4
1
t
m
t
b
t
m
t
t
p
t B
B
B








• Pressure & derivative have slope of 1/4 (Separated by a
factor of 4.
Fracture linear flow: Infinite conductivity fracture
Fracture bi-linear flow: Finite conductivity fracture

10. Infinite-Conductivity Fracture Model
• The linear flow is characterized by a pressure
change proportional to the root of time:
• On a loglog plot, the linear flow is characterized
by a ½ -unit slope in both the pressure and
derivative curves.
• The derivative is lower than the pressure, this
shift corresponding to a factor 2 on a linear
scale.

11. Finite-Conductivity Fracture Model
• It represents the time at which the pressure drop
along the fracture is significant.
• Even with no storage, the data does not exhibit a 1/4-
unit slope, and can be matched on a high-
conductivity fracture type-curve with an immediate
1/2-unit slope.
• Generally, the fracture model must surely be finite-
conductivity fracture, as there must always be a
pressure drop along the fracture
• FCD, the dimensionless fracture conductivity, considers
the fracture width (w) and the fracture permeability (kf)
and is compared to ‘kh’.

12. Sensitivity Analysis
• Multiplying the permeability by 100 will:
• Shift the stabilization of the derivative down 2 log cycles.
• The half slope of the linear flow will only be shifted down 1 log cycle.
Sensitivity to Xf Sensitivity to kh

13. Fractured Well: Infinite Conductivity
• It shows the
behavior of the
linear and bilinear
flow,
• Liner derivative
stabilizes across
the fracture-related
floe regimes.

14. Hesham Mokhtar
Hesham Mokhtar
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Mokhtar
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Mokhtar
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Mokhtar
Hesham Mokhtar