pseudo steady state
DESCRIPTION
PerminyakanTRANSCRIPT
Page 1
By:
1. Yoanita Warapsari - 22212011
2. Singgih Suganda - 22212015
3. Subihi Eka Prasetya - 22212049
4. Ghadafi Maksum - 22212079
Page 2
INTRODUCTION:
When well is producing, there is a pressure drop along the wellbore, and then propagate through the reservoir radius with function of time
Page 3
Occured when Pressure propagation hasn’t reached the reservoir boundary.P = Pi at t = 0, for all rP = Pi at r = infinite, for all t(solution will be explained in ch. 7) [Ei solution]
Stabilized Flow ConditionStabilized Flow Condition
Flow condition based on the Pressure Propagation
Stabilized flow
Unstabilized flowUnstabilized flow
Unstabilized Flow ConditionUnstabilized Flow Condition
Will be describe in the next slide
What is Stabilized flow Condition?
Recall:When well is producing, there is a pressure drop along the wellbore, and then propagate through the reservoir radius with function of time
When the ‘pressure propagation’ has reached the reservoir boundary, and continues to flow, it called “Stabilized flow Conditions”.
1 PI equation
Knowing the Skin effect (wellbore damage)
Knowing the steam soaking effect
Effect of Stimulation to PI ratio
Knowing the Volumetric Res. (ch. 7)
Knowing the reservoir variabel (ch. 7)
23456
7 Knowing the Reservoir shape (ch. 7)
Type of Flow:
-Semi-steady state condition
- Steady-state condition
Steady-stateSemi-steady state
Stabilized flow
Applications
Steady stateSemi-steady state
Stabilized flow
Applications
Semi-steady state conditions
Figure of Pressure distribution and geometry appropriate for the solution of the radial diffusivity
equation under semi-state conditions
Semi steady state :
constant ,
Chain Rule :
q
t
pt
Vq tcons
tan
t
p
p
V
t
V
t
pVC
t
Vt
Vt
p
p
V
V
1
Vc
q
t
p
t
hrc
q
t
p
e2
Mathematic Equation
Radial Flow
Integrating this equation
At the outer no-flow boundary
integrating
t
p
k
c
r
pr
rr
.1
hrk
q
e2
12
2
2C
khr
rq
r
pr
e
0r
p
2
1
1
2
,2
er
r
rkh
q
r
p
sokh
qC
r
rwe
pp r
rr
kh
qp r
wf
2
2
2ln
2
Mathematic Equation cont’d
negligible
In the case when r = re
PI relationship :
And then determination
or then
2
2
2
2
22ln
2 eewfr r
rw
r
r
rw
r
kh
qpp
Srw
r
kh
qpp ewfe 2
1ln
2
S
rwrekh
pp
qPI
wfe
21
ln
2
re
rw
re
rw
dV
pdVp
hrr
drrhpp
we
re
rw22
2
re
rwwe
prdrrr
p22
2
2er
re
rwe
prdrr
p2
2
Mathematic Equation cont’d
Combine with previous equation, then
Inflow equation with average pressure :
re
rwee
wf drr
r
rw
rr
kh
q
rpp
2
2
2 2ln
2
2
4ln
2ln
22ee
re
rw
r
rw
rerdr
rw
rr 82
2
2
3e
re
rw e
rdr
r
r
Srw
r
kh
qpp ewf 4
3ln
2
Mathematic Equation cont’d
Steady-state condition
Steady state solution well flow for production when P/ t =0
Steady-state condition Darcy’s Law for radial flow of single phase oil
STEADY STATE SOLUTION
dr
dpkAq
From Darcy’s Law for radial flow of single phase oil :
rhA 2
dr
dprkhq
2
drrkh
qdp
r
r
P
P wwf
1
2
wwf r
rIn
kh
qPP
2
Where
STEADY STATE SOLUTION
Equation for steady state :
wwf r
rIn
kh
qPP
2
Since the outer boundary pressure cannot be measured directly, therefore need P average within drainage volume.
e
w
e
w
r
r
r
r
dV
pdV
P drrhdV 2
e
w
e
w
r
r
r
r
drrh
drrhp
P
2
2
hrr
drrhp
Pwe
r
r
e
w
22
2
e
w
r
rwe
prdrrr
P22
2
STEADY STATE SOLUTION
wwf r
rIn
kh
qPP
2
e
w
r
re
prdrr
P2
2
222222 )/1( eewewe rrrrrr
e
w
r
rwe
prdrrr
P22
2
Substituting
e
w
r
r wewf rdr
r
rIn
kh
q
rPP
2
22
e
w
r
r we
drr
rInr
kh
q
r
2
22
drr
rw
kh
q
r
e
w
e
w
r
r
r
r
e rr
Inr
2
12
2
2 2
2
2
2
1
2 w
ewf r
rIn
kh
qPP
422
2 22
2e
w
ee
e
r
r
rIn
r
kh
q
r
General Solutions for Stabilized flow Condition
wwf r
rIn
kh
qPP
2
w
ewfe r
rIn
kh
qPP
2
2
1
2 w
ewf r
rIn
kh
qPP
4
3
2 w
ewf r
rIn
kh
qPP
2
2
22 ewwf r
r
r
rIn
kh
qPP
2
1
2 w
ewfe r
rIn
kh
qPP
Steady State Semi Steady State
General relationship between P and r
Inflow equation,P = Pe at r = re
Inflow equation, average pressure
Steady State Solutions
kh
q
2 kh
Bq o2.141
4
3
2 w
ewf r
rIn
kh
qPP
s
ww err
Applications of Stabilized flow solution
1 Stimulating Well by steam soaking
Flow simulating in wellbore damage condition
Skin prediction
PI ratio
2
3
4
Stimulated well dy steam soaking
Viscosity Difference
Temperature Difference
Steam Soaking Stimulated Well
A well is stimulated by steam soaking.For rw < r < rh Ts is uniform = Steam temperatureFor r > rh Apply Tr as reservoir temperatureWhere Viscosity of the oil at Ts
and Viscosity of the oil at Tr
oh
oc
Stabilized Flow Equation for Steam Soaking
w
ohwfr r
rIn
kh
qPP
2
h
ochr r
rIn
kh
qPP
2
Inflow equation under steady state flow condition :
hw rrr eh rrr
w
hohwfh r
rIn
kh
qPP
2
h
eoche r
rIn
kh
qPP
2
h
eoc
w
hohwfe r
rIn
r
rIn
kh
qPP
2
h
e
w
h
oc
ohocwfe r
rIn
r
rIn
kh
qPP
2 For stimulated well
hh
w
h
e
w
h
oc
ohocwfe r
rwIn
r
rIn
r
rIn
r
rIn
kh
qPP
2
w
oc
r
reInS
kh
q
2
ww
h
w
h
oc
ohoc
r
reIn
r
rIn
r
rIn
kh
q
2
w
h
w
h
oc
oh
r
rIn
r
rInS
w
eocwfe r
rIn
kh
qPP
2
Inflow equation for Unstimulated well :
welledunstimulat PI
wellstimulated PI increase ratio PI
w
eoc
h
e
w
h
oc
ohoc
rr
Inkh
rr
Inrr
Inkh
q
q
2
2
Then the effect on productivity index due to steam soaking :
h
e
w
h
oc
oh
w
e
r
rIn
r
rIn
r
rIn
Stabilized Flow Equation for Steam Soaking
Wellbore Damage
Wellbore Damage
Skin FactorSkin Factor
There will be a skin factor due to wellbore damage
There will be a skin factor due to wellbore damage
PI stimulatedPI stimulated
In order to increase permebility value besause of skin factor, stimulating well applied. And this method will increase the PI value
In order to increase permebility value besause of skin factor, stimulating well applied. And this method will increase the PI value
APPLICATION OF THE STABILIZED INFLOW EQUATIONS
IN WELLBORE DAMAGE
The inflow equations appropriate for the pressure distribution shown
In particular,
a. Skin Factor
i.e.
Skin Factor
b. PI ratio
Case: During drilling, a well is damaged out to a radius of 4 ft from the wellbore so that the permeability within the damaged zone is reduced to 1/100 th of the undamaged effective permeability. After completion the well is stimulated so that the permeability out to a distance of 10 ft from the wellbore is increased to ten times the undamaged permeability. What will be the PI ratio increase if the wellbore radius is 0.333 ft and the drainage radius 660 ft?
since,
2 General solution for Steady state flow:
Conclusions
1 General solution for Semi-steady state flow:
4
3
2 w
ewf r
rIn
kh
qPP
2
1
2 w
ewf r
rIn
kh
qPP
3 Solution form stabilized flow eq, is used to
-Determining the skin effect-PI equation and its ratio-Well test applications (ch. 7)
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Questions?
THANK YOU…