8/10/2019 User's guide 12-02-2009 TLSD

1/45

The use of the software is restricted to participants to

Imperial College JIP on Deconvolution.

If you are a participant, click I agree

Your Company

Your Company

Your Company

YourCompany

Your Company Your Company

8/10/2019 User's guide 12-02-2009 TLSD

2/45

TLSD is a pre-processor that converts a variable rate pressure history into a unit

rate drawdown with a duration equal to the total duration of the pressure history.

TLDS

* von Schroeter, T., Hoellander, F. and Gringarten, A. C.:

Deconvolution of Well test Data as a Non-linear Total Least Square Problem, SPEJ

(Dec. 2004) 375-390

TLSD uses a deconvolution algorithm

based on the Total Least Squaremethod*, which provides stable results.

The algorithm estimates both rates

(called adapted rates herein) and

normalised derivative by minimising an

error measure, E, which is a weightedcombination of pressure match, rate

match, and a penalty term based on

the overall curvature of the graphed

derivative and whose purpose is to

enforce smoothness of the resultingdeconvolved derivative.

Data: p, q

Curvature operator: matrix D, vectork

Parameters:

: relative weight : regularization parameter

4342132144 344 21

curvaturematchratematchpressure

222

kzDqygyppE i ++=

Guess g , discretize into D(z), minimize E over pi , y, z

8/10/2019 User's guide 12-02-2009 TLSD

3/45

The weight of the pressure match is normalized to one and the estimate

depends on two weights, for the rate match, and for the roughness penalty.

is usually set at a default value and only the regularisation parameter is

varied.

Regularisation introduces bias, however, and thus the user must choose a level

of that imposes just enough smoothness to eliminate small-scale oscillations

on the derivative while preserving genuine reservoir features.

The methodology for well test analysis using deconvolution is summarised in the

schematic in the following page:

8/10/2019 User's guide 12-02-2009 TLSD

4/45

Deconvolved mn(p) derivative Adapted rates

Convolved pseudo-pressure with adapted rates

Pressure data p

Unit rate convolved pseudo-pressure drawdown

Interpretation

model

Pressure data

Adapted rates

END

Pseudo-pressure mn(p)

Rates

mn(p) vs. p

NO

YES

Deconvolve

Compare

Convolve

Convolve

Analyse ConvolveRefine

match

Unit rate

p vs. mn(p)Unit rate convolved

pressure drawdown

Well test analysis using deconvolution

8/10/2019 User's guide 12-02-2009 TLSD

5/45

1. Deconvolution with various levels of regularisation is applied to pressure andrate data (for gas, pressures are first converted to normalised pseudo-

pressure in order to approximate a linear system).

2. Once a satisfactory derivative has been obtained, a convolved pressure

history is calculated with that derivative, the adapted rates and the initialpressure obtained from deconvolution, and compared with the measured

pressures.

3. If the match is acceptable, a unit-rate pseudo-pressure drawdown is

generated for a duration equal to that of the test, using the deconvolvedderivative.

4. This unit-rate drawdown is analysed in the conventional way.

5. The resulting model is then used applied to the measured pressure datausing the adapted rates and the model parameters are refined until an

acceptable match is obtained.

Well test analysis using deconvolution

8/10/2019 User's guide 12-02-2009 TLSD

6/45

Maureen A2

Test 1 (Exploration)

FP06

Test 2 (Product ion)

FP35

The procedure is illustrated with Well A2 from the Maureen reservoir

8/10/2019 User's guide 12-02-2009 TLSD

7/45

Maureen A2

Test 2 (Build-up)

Test 1 (Bui ld-up)

Test 2 (Drawdown)

RADIAL FLOW

SPHERICAL FLOW

WELLB

ORE

STOR

AGE

Changing

Wellbore

Storage

No boundaries are apparent on a Log-log plot

8/10/2019 User's guide 12-02-2009 TLSD

8/45

Maureen A2 Test 1 (Exploration)Yet, an interpretation model of infinite extent applied to one of the tests fails to match the other test

Exploration test

Production testExploration

test

Exploration test

8/10/2019 User's guide 12-02-2009 TLSD

9/45

Production

test

10-3 10-1 10 103

Elapsed time, t ( hours)

PressureChan

geand

Derivative(psi)

104

103

102

10

1

10-1

10-2

Maureen A2 Test 2 (Production)

Decreasing wellbore storage(gas goingback into solution)

Exploration test

Production test Production test

8/10/2019 User's guide 12-02-2009 TLSD

10/45

Test 1 (build-up)

Test 2 (build-up)

Maureen A2: Evidence of depletionThe only suggestion of boundaries comes from the superposition plot

8/10/2019 User's guide 12-02-2009 TLSD

11/45

Time from the start of the test (hours)

0 4000 8000 12000 16000

Pressure

(psia)

3600

3400

3200

3000

2800

2600

2400

2200

Maureen A2 : Closed rectangle model

Test 1 Test 2

(pav)i psia

(pav)f at the

end of the test psiakh mD.ft

k(xy) mD

k(z) mD

C1 bbl/psi

C2 bbl/psi hrs

hw/h

hw ftS(w)

S(c)

S(t)

Zw ft

d1 ft

d2 ft

d3 ft

d4 ftA

3471.1

346989170

442

4

0.44

0.35

70-3.3

12.8

3.3

166.5

15900

8120

16000

29093.52E+08 ft

2

3478.6

256584090

416

6

0.37

0.06

7.551E-03

0.35

70-3.7

12.2

1.4

166.5

5233

25923

7947

17343.65E+08

Based on this suggestion, in conventional analysis, a closed reservoir model is used

and the distances to the boundaries are adjusted by regression. The distances to

boundaries are highly non-unique, but the area is reasonably constrained

Boundaries can be made to appear

by deconvolution

8/10/2019 User's guide 12-02-2009 TLSD

12/45

Click TLSD

to start

Then click Deconvolution & Convolution

8/10/2019 User's guide 12-02-2009 TLSD

13/45

Input: Variable rate pressure file

Input: Rate history file

Select rate history range from rate history file (default: all rates are used)

Select of flow periods to deconvolve from pressure file

Select initial pressure

input or calculation

STEPS

1

2

3

4

Get default

parameters

Start deconvolution

Deconvolved derivative

Unit rate drawdown with total duration of test calculated from deconvolved derivative

Adapted rates, corrected for errors as determined by deconvolution

Not implemented yet

Input: pseudo-pressure vs. pressure file for gas data deconvolution

Verification

11

Final analysis

12

Advanced options: do not modi fy

Select Excel file to display deconvolution results or ignore for default7

9

Convolved pressure history, calculated from deconvolved derivative, to be compared with input data

Data derivative plot 10

5 Number of points calculated forthe deconvolved derivative (does

not converge if too many points)

8

6

8/10/2019 User's guide 12-02-2009 TLSD

14/45

STEP 1: Input variable rate pressure history file

Format:

1st line: text

1st column: time from start

2nd column: pressure

8/10/2019 User's guide 12-02-2009 TLSD

15/45

STEP 2: Input rate history file

Format:

1st line: text

1st column: duration

2

nd

column: rate

To avoid resolution

problems, choose unitsso that rate values are

small (e.g., MMscf/Dinstead of Mscf/D)

8/10/2019 User's guide 12-02-2009 TLSD

16/45

Additional STEP if gas: Input pseudo-pressure file

2

1

Format:

1st line: text

1st column: pressure

2nd column: pseudo-pressure

8/10/2019 User's guide 12-02-2009 TLSD

17/45

STEP 3: Select rate to be included in deconvolution (default: ALL)

2

43

1

This STEP 3 can be skipped if all rates are to be included in deconvolution

8/10/2019 User's guide 12-02-2009 TLSD

18/45

STEP 4: Select flow periods to be included in deconvolution

2

2

43

1

8/10/2019 User's guide 12-02-2009 TLSD

19/45

STEP 5: Impose a value for the initial pressure

Enter initial pressure

Default: highest

pressure value2

1

8/10/2019 User's guide 12-02-2009 TLSD

20/45

STEP 5: Alternatively, let deconvolution calculate the initial pressure

Only if an initial DST is included in the pressure history

8/10/2019 User's guide 12-02-2009 TLSD

21/45

STEP 6: Initialise to obtain default weights and

8/10/2019 User's guide 12-02-2009 TLSD

22/45

STEP 7: Select an existing output Excel file (or accept the default name)

This Excel fi le is

automaticallycreated to display

the deconvolved

derivative

8/10/2019 User's guide 12-02-2009 TLSD

23/45

STEP 7: Rename the output Excel file (or accept the default name)

8/10/2019 User's guide 12-02-2009 TLSD

24/45

STEP 8: Start deconvolution

8/10/2019 User's guide 12-02-2009 TLSD

25/45

STEP 8 (contd): Deconvolution proceeds

8/10/2019 User's guide 12-02-2009 TLSD

26/45

8/10/2019 User's guide 12-02-2009 TLSD

27/45

STEP 9 Deconvolved derivative plotted in Project Excel File

8/10/2019 User's guide 12-02-2009 TLSD

28/45

STEP 9 (contd): Increase and redo deconvolution from STEP 8

Repeat with different values of until satisfactory pressure

match, rate match and deconvolved derivative are obtained

8/10/2019 User's guide 12-02-2009 TLSD

29/45

BETTER DECONVOLVED DERIVATIVE

(i.e., converging to the most likely behaviour)

Increasing

Successive deconvolved derivatives are plotted together

8/10/2019 User's guide 12-02-2009 TLSD

30/45

Successive deconvolved derivatives are compared in the Project Excel

File which is automatically generated by the software in Step 8

Deconvolved derivative files, *.pd , for various deconvolutions

Number of deconvolutions

STEP 10: Successive deconvolved derivatives can be compared with

8/10/2019 User's guide 12-02-2009 TLSD

31/45

1

2

STEP 10: Successive deconvolved derivatives can be compared with

actual data by adding Data Derivative (rate-normalised)

Ratio of derivative window length to total

length of data on a superposition plot

3 4

STEP 10: Data derivatives

8/10/2019 User's guide 12-02-2009 TLSD

32/45

STEP 10: Data derivatives

STEP 10: Data derivatives can be imported if the derivative calculated in

8/10/2019 User's guide 12-02-2009 TLSD

33/45

Rate for flow period 34

Column G is

derivative

divided by rate

Column E is

Elapsed time

Number of points plotted

Number of data derivatives plotted

STEP 10: Data derivatives can be imported if the derivative calculated in

The Project excel file is too noisy

8/10/2019 User's guide 12-02-2009 TLSD

34/45

STEP 10: Deconvolved derivative can also be plotted from TLSD

1

2

8/10/2019 User's guide 12-02-2009 TLSD

35/45

PLOTS: Deconvolved derivative

8/10/2019 User's guide 12-02-2009 TLSD

36/45

PLOTS: Input pressure and rate histories

1

2

8/10/2019 User's guide 12-02-2009 TLSD

37/45

PLOTS: Input pressure and rate histories

8/10/2019 User's guide 12-02-2009 TLSD

38/45

STEP 11: rate match (adapted rates vs. input rates)

1

2

8/10/2019 User's guide 12-02-2009 TLSD

39/45

STEP 11 : rate match (adapted rates vs. input rates)

8/10/2019 User's guide 12-02-2009 TLSD

40/45

STEP 11 : Pressure match

(convolved pressure history vs. input pressure history)

1

2

This plot must be made to verify the quality of the deconvolution

8/10/2019 User's guide 12-02-2009 TLSD

41/45

STEP 11 : Pressure match

(convolved pressure history vs. input pressure history)

Match shown only for the flow periods used for deconvolution

8/10/2019 User's guide 12-02-2009 TLSD

42/45

STEP 11 : Pressure match- zoomed

(convolved pressure history vs. input pressure history)

Match shown only for

the flow periods used

for deconvolution

STEP 12: Select the unit rate drawdown corresponding

8/10/2019 User's guide 12-02-2009 TLSD

43/45

3470.58

3470.60

3470.62

3470.64

3470.66

3470.68

3470.70

3470.72

3470.74

-2000 0 2000 4000 6000 8000 10000 12000 14000 16000 18000

Pressur

e(psia)

Elapsed time (hrs)

0.0

0.2

0.4

0.6

0.8

1.0

1.2

1.4

1.6

1.8

2.0

TotalRate(STB/D)

STEP 12: Select the unit rate drawdown corresponding

to the best deconvolved derivative (*.up)

STEP 12 (contd): Analyse the unit rate drawdown corresponding

8/10/2019 User's guide 12-02-2009 TLSD

44/45

0.0001

0.001

0.01

0.1

0.0001 0.01 1 100 10000 1000000

PressureChangeandDerivative(psi)

Elapsed time (hrs)

Log-Log Diagnostic - Flow Period 2

0.00001

0.0001

0.001

0.01

0.1

1

0.0001 0.01 1 100 10000 1000000

Pres

sureChangeandDerivative(psi)

Elapsed time (hrs)

Log-Log Match - Flow Period 2

3470.59

3470.60

3470.61

3470.62

3470.63

3470.64

3470.65

3470.66

3470.67

3470.68

3470.69

-4 -3 -2 -1 0 1 2 3 4 5

Pressure(psia)

Superposition Function (STB/D)

Horner Analysis - Flow Period 2

3470.61

3470.62

3470.63

3470.64

3470.65

3470.66

3470.67

3470.68

3470.69

3470.70

3470.71

-3 -2 -1 0 1 2 3 4

Pressure(psia)

Superposition Function ( STB/D)

Horner Match - Flow Period 2

3470.58

3470.60

3470.62

3470.64

3470.66

3470.68

0 2000 4000 6000 8000 10000 12000 14000 16000 18000

Pressure(psia)

Elapsed time (hrs)

Simulation (Constant Skin) - Flow Period 2

3470.56

3470.58

3470.60

3470.62

3470.64

3470.66

3470.68

3470.70

3470.72

3470.74

-5000 0 5000 10000 15000 20000

Pressure(psia)

Elapsed time (hrs)

0.0

0.2

0.4

0.6

0.8

1.0

1.2

1.4

1.6

1.8

2.0

TotalRate(STB/D)

Pressure History Model

Partially Penetrating Well with C and SHomogeneousRectangle

Results

(pav)i 3470.690 ps ia(pav) f 3470.611 ps iapwf 3470.595 psiakh 94881 mD.ft

k(xy) 469.7 mDk(z) 46.47 mDC 0.2573 bbl/psihw/h 0.3276Hw 66.17 ftS(w) -1.78S(c) 10.88S(t) 5.46Zw 56.24 ftType top No FlowType bot No Flow

d1 5548.55 ftd2 9851.6 ftd3 6218.37 ftd4 20754.1 ftA 3.6013E+008 ft2Type d1 No FlowType d2 No FlowType d3 No FlowType d4 No FlowPI 65.02 B/D/psiPI-SS 45.21 B/D/psiFE 1.340 fraction

Dp(S) -0.007519 ps i

STEP 12 (cont d): Analyse the unit rate drawdown corresponding

to the best deconvolved derivative

STEP 13: Use the unit rate drawdown interpretation model to analyse

8/10/2019 User's guide 12-02-2009 TLSD

45/45

p y

the measured pressures with the adapted rates (*.ar)

1

10

100

1000

0.0001 0.001 0.01 0.1 1 10 100

PressureChangeandDe

rivative(psi)

Elapsed time (hrs)

Log-Log Diagnostic - Flow Period 34

0.1

1

10

100

1000

0.0001 0.001 0.01 0.1 1 10 100 1000 10000

Pres

sureChangeandDerivative(psi)

Elapsed time (hrs)

Log-Log Match - Flow Period 34

2250

2300

2350

2400

2450

2500

30000 40000 50000 60000 70000 80000 90000 100000

Pressure(psia)

Superposition Function (STB/D)

Horner Analysis - Flow Period 34

2200

2300

2400

2500

2600

0 20000 40000 60000 80000 100000

Pressure(ps

ia)

Superposition Function (STB/D)

Horner Match - Flow Period 34

2200

2400

2600

2800

3000

3200

3400

3600

-2000 0 2000 4000 6000 8000 10000 12000 14000 16000 18000

Pressure(psia)

Elapsed time (hrs)

Simulation (Constant Skin) - Flow Period 34

-4000

-3000

-2000

-1000

0

1000

2000

3000

4000

5000

6000

-5000 0 5000 10000 15000 20000

Pressure(psia)

Elapsed time (hrs)

0

10000

20000

30000

40000

50000

60000

70000

80000

OilRate(STB/D)

Pressure History Model

Partially Penetrating Well with C and SHomogeneousRectangle

Results

(pav)i 3470.690 ps ia(pav) f 2545.409 ps iapwf 2277.907 psiakh 60681 mD.ft

k(xy) 300.4 mDk(z) 30.00 mDC 0.08331 bbl/psihw/h 0.3416Hw 69.00 ftS(w) -3.86S(c) 10.39S(t) -0.92Zw 101.00 ftType top No FlowType bot No Flow

d1 5548.55 ftd2 9851.6 ftd3 6218.37 ftd4 20754.1 ftA 3.6013E+008 ft2Type d1 No FlowType d2 No FlowType d3 No FlowType d4 No FlowPI 52.34 B/D/psiPI-SS 48.30 B/D/psiFE 2.185 fraction

Dp(S) -343.5 psi

THE END