1

Introduction

• Pressure Transient Analysis (PTA) Theory

• Mini-Frac Theory

• Interpretation Examples

2

Pressure Transient Analysis (1)

• General production/injection tests

– Static reservoir properties only (do not change with time)

• Much larger field of testing than mini-frac analysis

• Goals of PTA

– Initial pressure

– Permeability

– Static Fracture properties

3

Pressure Transient Analysis (2)

• Why not use it in mini-frac analysis ?

– Past: New flow regimes to consider

– Special cases not handled • PDL, HRTS, tip extension

– Today: No significant issues

4

PTA Approach - Assume Radial Flow • Drawdown

• Build-up

Ctd

Pdt

tCP

)(

)(

...)ln(

Ctd

Pdt

tt

ttt

tCP

er

er

p

p

er

er

)(

)(

...)ln(

ter is the Agarwal equivalent time

with a radial basis function

1 - Drawdown

2 - Build-up

5

Bourdet Log-Log Derivative Plot for

Radial Flow

6

Early Time Slope = 0

Late Time Slope = -1.0

DT log-log

derivative plot

td

Pdt

)(

-1/1

0

Plot hinders flow regime

identification process td

7

Radial Flow Analytical

Solution Case

Holistic Method

td

PdPPD

)(

-1/1

-2/1

0

Radial Flow Analytical

Solution Case

Bourdet log-log

derivative plot

With PPD

td

8

PTA Method

9

Early Time Slope = 0.5

Late Time Slope = -0.5

Middle Time = Variable

-½ ½

Plot hinders flow regime

identification process

DT log-log

derivative plot

td

Pdt

)(

td

10

Linear Flow Analytical

Solution Case

Holistic Method

Even though radial basis

function used there is no

great distortion for linear

flow

That is why radial basis

function is used almost

exclusively in PTA

½

½ Linear Flow Analytical

Solution Case

Bourdet log-log

derivative plot

td

11

PTA Method

Mini-Frac in Oilsands/Caprocks

• Goals

– Determine closure stress

• Pump-in/Fall-off tests only

• Unique features to oilsands/caprock testing

– Multi-Zone

– Multi-Cycle

• Attempt to get repeatability within a zone

12

FP_02_FO FP_04_FO FP_06_FO FP_08_FO

Mini-Frac Test in McMurray Oilsand

Pump-in/Fall-off

p

tpt

13

Mini-Frac Theory

• Nolte (1979)

– The first rigorous approach to mini-frac analysis

– Came up with ‘G Time’ concept

• Applies during a fall-off and while a fracture is open

• Generalized to ‘Nolte Flow’

p

dt

tt

14

)()0( 1 dtGCpDTpPDP

1)1(3

16)( 5.15.1 ddd tttG

Traditional G Function Method

• Traditional interpretation

• Go right to ‘special plots’

15

First Attempts at Closure Picks

Deviation from straight line is closure

as a new post-closure flow regime begins

16

PTA Based Method

• Recent interpretation technique from 2011 to the

present

17

Early Time Slope = 1

Late Time Slope = 1.5

1/1

3/2

Nolte Flow Analytical

Solution Case

Bourdet log-log

derivative plot

-1/2

0

td

18

PTA Method

Example 1 - Constant Leak-off Case

• Tight Oil Well (not oilsand)

• From SPE 160169

– Reappraisal of the G Time Concept in Mini-Frac

Analysis

19

pfoc = 8400 kPa Combination G

Function plot

20

Holistic Method – Plot 1

Cross over of ‘Middle’

and ‘Late’ ½ Slope

Delta Time = 0.28

Days

pfoc = 8300 kPa

½

½

-½

DT log-log

derivative plot

21

Holistic Method – Plot 2

½

-½

22

Bourdet log-log

derivative plot

With PPD

PTA Method

½

-½

3/2

-½

End of Nolte Flow

Fracture has closed

pfoc = 8300 kPa

23

Bourdet log-log

derivative plot

With PPD

PTA Method

½

-½

3/2

-3/2

Bourdet log-log

derivative plot

With PPD

24

PTA Method

Example 2 - Tip Extension

• From SPE 107877

– Holistic Fracture Diagnostics:

Consistent Interpretation of Prefac Injection Tests

Using Multiple Analysis Methods

25

Ever increasing GdP/dG

And no flattening of dP/dG

indicate fracture may not

have closed

Combination G

Function plot

26

Holistic Method – Plot 1

1/4

DT log-log

derivative plot

27

Holistic Method – Plot 2

Late time unit slope

No ¼ slope so no

bilinear flow

Apparent ¼ slope in ‘DT

derivative’ is artifact of

not using the Bourdet

derivative

What causes late time

unit slope?

It is not Nolte Flow

1/1

-1/1

Bourdet log-log

derivative plot

With PPD

28

PTA Method

Bourdet Derivative

Kinner=0.1 md

Kinner=1.0 md

Kinner=10 md

Kouter=0.001 md

End of unit slope

Starting to see the

true value of the

outer permeability

1/1

Kinner

Kouter

Kinner=0.01 md

29

PTA Method

Approximate end of constant slope

Starting to see the true value of the outer

permeability

Constant slope not seen if perm contrast <100

Kouter=0.001 md

Kinner=0.1 md

Kinner=1.0 md

Kinner=10 md

Kinner=0.01 md

30

DT Normalized Bourdet Derivative

Nolte Flow/Formation Linear Flow

Composite Permeability Concept

for a Vertical Well

Kinner

High Permeability

Due to influence of

fracture

Kouter

Fracture

31

Example 3 - Tip Extension

• Deep Oilsand Formation

– High permeability

– High viscosity fluid

32

Ever increasing GdP/dG

And no flattening of dP/dG

indicate fracture may not

have closed

Combination G

Function plot

33

Holistic Method – Plot 1

1/4

End of ½ slope at DT=0.00038 days

Ever increasing derivative at end indicates

fracture may not have closed (holistic theory)

½

34

DT log-log

derivative plot

Holistic Method – Plot 2

-¾ slope

Slope between

-½ and -3/2

End Fracture Linear

Flow at DT=0.0075 days

½

1/1 Bourdet log-log

derivative plot

With PPD

35

PTA Method

Bourdet derivative and

specialized derivative

function

1/DT * dDP/dTer

Giving zero slope

when Bourdet

Derivative has unit

slope

End of Unit Slope for Bourdet

Derivative

At DT=0.025 days

Latest time fracture may be open is

at DT=0.025 days

0

1/1

36

DT Normalized

Bourdet Derivative

Earliest possible closure time

End fracture linear flow

DT=0.0075 days

Fracture not closed yet

according to Holistic theory Latest possible closure time

composite permeability theory

DT=0.025 days

In oilsands allowable Maximum

Operating Pressure (MOP) for thermal

projects is directly related to closure

pressure of the cap rocks

37

Comparative Closure Picks

Example 4 – G*dp/dG Overreliance

• McMurray Oilsand

– High permeability

– High viscosity

38

39

Combination G

Function plot

Holistic Method – Plot 1

40

Combination G

Function plot

Holistic Method – Plot 1

Ambiguous as no Nolte Flow

Some analysts would pick

closure at the blue circles

G = 0.95

P = 1600 kPa

Gradient = 13.4 kPa/m

41

Combination G

Function plot

Holistic Method – Plot 1

½

End ¼ slope line

DT= 0.007 days

P = 1503 kPaa

Gradient = 12.6 kPaa/m

1/4

42

DT log-log

derivative plot

Holistic Method – Plot 2

End Linear DT=0.0008 days

P = 2040 kPaa

Gradient = 17.1 kPaa/m

½ -½

-½

43

Bourdet log-log

derivative plot

With PPD

PTA Method

Conclusions

• G-Function analysis of mini-fracs can give erroneous results (or no results)

• PTA is a more universal analysis method

• PTA method identifies two new flow regimes

– Pre-closure linear flow

– Composite permeability

• Tip extension as conventionally defined does not occur

44