Injection Calculation - Advantek International

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Injection Calculation - Advantek International
Produced Water Reinjection
Performance
Joint Industry Project
TerraTek, Inc.
Triangle Engineering
Taurus Reservoir Solutions (DE&S)
E-first Technologies
Advantek
VIPS
Calculation of injectivity index (II)
Motivation: II is used internally by companies to report
and compare data, our aim is to correlate II with PW
characteristics
It is necessary to use consistent definitions
Principle: II is supposed to be a parameter characterizing
the injectivity which is “constant” for a given completion
and can be used to predict rate or pressure
Standard definition of II (matrix)
Q
kw  hi
II 

Pbhi  Pe 141.2    B   ln re  S 

w
w 
r
w


Q = inj. Rate
Pbhi, Pe = BH inj. And outside radius pressure
kw hi = water perm x inj. Height
rw, re = wellbore and outside radius
S = skin (account for completion, fracturing)
Standard definition of II
Q
kw  hi
II 

Pbhi  Pe 141.2    B   ln re  S 

w
w 
r
w


Assumptions:
Matrix (radial) flow
Single phase, pressure maintained at outside radius
No thermal effects
Etc. etc.
Proper use of parameters (best practices
for matrix II evaluation):





Use effective TOTAL mobility of fluids:
k ( krw/ w + kro/ o)
Use effective injection kh, if well test available,
adjust accordingly
Use some “average” values for viscosities to account
for temperature effects (weighted towards cooled
region)
Do not include induced fracture in the skin (except
propped/acid frac)
What do we use the above II for:



Formula gives EXPECTED II without plugging and S
effects – maximum possible injectivity
If we exclude S, allows us to determine total skin
from comparison of measured and calculated
(theoretical) values
By including various parts of S hopefully we will be
able to separate plugging and mechanical
(geometry) skin components
II in fracture injection regime

No longer linear relationship between Q and
(pwfi – pe)

Pressure controlled by fracture mechanics:

Pbhi = Smin + Pcompl + Pnet = Pf
– Smin = minimum stress = Pfoc
– Pcompl = pressure drop through completion
– Pnet = net pressure in the fracture

May be again linear BUT with (Pf – Pfoc)
II in fracture vs matrix injection regime
P2f
P1f
Pfo
Pwf
P2
P1
Pe
Q1
Q2
Injection rate
Q1f
Q2f
Definition of II in fracture inj mode
– Matrix definition II = Q / (Pbhi – Pe) gives
VARIABLE II depending on rate
– Correct definition is “differential” :
IIf = [(Q2 – Q1) /(P2 – P1)]f
– Another expression (for predictions):
Pwf = Pf0 + IIf (Q – Qf0)
II in fracture mode
II1
II2
IIf
P2f
P1f
Pfo
Pwf
P2
P1
Pe
Qfo
Q1
Q2
Injection rate
Q1f
Q2f
Calculation of II from P,Q vs time data
(observed II)
– Matrix mode: customary calculation is correct
IIn = Qn /(Pwfn – Pe)
– Fracture mode: customary calculation is incorrect
and will UNDERESTIMATE actual II
– Best way to calculate not obvious
– Conventional evaluation may appear to give a
“constant” value because of operation constraints
Example: Heidrun B3H
Heidrun B3H injection history
45000
Injection rate (m3/d)
Sandface pressure (kPa)
Initial horiz. stress
Series4
Initial horiz. stress
Injection rate (M3/d)
12000
40000
10000
35000
8000
30000
initial
pressure
6000
25000
4000
20000
2000
15000
0
0
200
400
600
800
1000
time (days since 10/24/95 )
1200
1400
1600
10000
1800
Sandface inj. pressure (kPa)
14000
Example: Heidrun B3H conventional II
Heidrun B3H injector - conventional II plot
10
Injectivity index (m3/kPa/day)
II = Q/(Pinj-Pres)
1
IIfrac
IImatrix
0.1
0.01
0
200
400
600
800
1000
time (days)
1200
1400
1600
1800
Methods for calc of II in fracture regime



Take subsequent time series data:
IIn = (Qn – Qn-1)/(Pn – Pn-1)
- this produces large scatter
Use Hall plot data:
IIn = (QSUMn – QSUMn-1)/(PSUMn-PSUMn-1)
- is equivalent to the MATRIX (wrong) formula
Use cumulative Hall data:
IIn = QSUMn/PSUMn
- averages the previous (also incorrect)
II methods for fractured inj
Heidrun B3H injector - II plot (various definitions)
1000
II = Q/(Pinj-Pres)
II = (Q2-Q1)/(P2-P1)
II=cumQ/cumP (from Hall plot)
Injectivity index (m3/kPa/day)
100
10
1
0.1
0.01
0
200
400
600
800
1000
time (days)
1200
1400
1600
1800
Recommended method for calc of II in
fracture regime




Evaluate fracture p vs Q trend from p vs Q
plot - INTERPRETATION
Determine intercept Pint at Q=0
Calculate II by
IIn = Qn/(Pn – Pint)
Discard values if (Pn – Pint) < (Pf0 - Pint) –
this will eliminate matrix data.
a) Intercept and slope from p vs Q
Heidrun B3H injection history
50000
Injection sandface pressure (kPa)
45000
Init. Horiz. Stress
40000
Intercept
35000
30000
Pres = 28010 kPa
Measured inj pressure, frac mode
25000
Measured inj pressure, matrix mode
Initial horiz. stress
20000
0
2000
4000
6000
Inj rate (m3/d)
8000
10000
12000
b) Calculate II
Heidrun B3H injector - II plot (various definitions)
1000
II = Q/(Pinj-Pres) - matrix calc
II = (Q2-Q1)/(P2-P1) - Eqn (7) for fracture mode
II by Eqn. (10) for fracture mode
Injectivity index (m3/kPa/day)
100
10
1
0.1
0.01
0
200
400
600
800
1000
time (days)
1200
1400
1600
1800
Conclusions



Conventional calculations should not be used in
fracture mode (underestimates II, rate
dependent)
Proper determination requires independent
analysis of slope and intercept in P vs Q plot
Serious problems can result if conventional II is
used to develop trends and correlations (e.g., II
as a function of water quality and k …)

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