4 ipr undersaturated 15
Post on 06-Jul-2018
222 Views
Preview:
TRANSCRIPT
-
8/16/2019 4 IPR Undersaturated 15
1/34
Chair of Petroleum & Geothermal Energy Recovery
Petroleum Engineering
Summer Course 2015
Inflow Performance
Relationship (IPR)
Clemens Langbauer petrowiki.org
-
8/16/2019 4 IPR Undersaturated 15
2/34
Chair of Petroleum & Geothermal Energy Recovery
Page 2
Chair of Petroleum & Geothermal Energy Recovery
Beggs: Production Optimization using Nodal Analysis
Petroleum Production System
-
8/16/2019 4 IPR Undersaturated 15
3/34
Chair of Petroleum & Geothermal Energy Recovery
Page 3
Chair of Petroleum & Geothermal Energy Recovery
Beggs: Production Optimization using Nodal Analysis
Petroleum Production System
-
8/16/2019 4 IPR Undersaturated 15
4/34
Chair of Petroleum & Geothermal Energy Recovery
Page 4
Chair of Petroleum & Geothermal Energy Recovery
Beggs: Production Optimization using Nodal Analysis
Reservoir Types
-
8/16/2019 4 IPR Undersaturated 15
5/34
Chair of Petroleum & Geothermal Energy Recovery
Page 5
Chair of Petroleum & Geothermal Energy Recovery
Reservoir Types
Undersaturated Oil Reservoirs
Reservoir pressure (pe, p) and well flowing pressure (pw ) are above thebubble point pb.
Oil and water are present and flowing
Saturated Oil Reservoirs / Multi-phase Reservoirs
pw and / or the reservoir pressure is / are below the bubble point.
Oil, water and gas are present and flowing
Gas Reservoirs
Gas is present and flowing (little amount of water)
-
8/16/2019 4 IPR Undersaturated 15
6/34
Chair of Petroleum & Geothermal Energy Recovery
Page 6
Chair of Petroleum & Geothermal Energy Recovery
Undersaturated Oil Reservoirs
-
8/16/2019 4 IPR Undersaturated 15
7/34
Chair of Petroleum & Geothermal Energy Recovery
Page 7
Chair of Petroleum & Geothermal Energy Recovery
Darcy‘s Law
L.P.Drake: Fundmentals of Reservoir Engineering
-
8/16/2019 4 IPR Undersaturated 15
8/34
Chair of Petroleum & Geothermal Energy Recovery
Page 8
Chair of Petroleum & Geothermal Energy Recovery
Darcy‘s Law
L.P.Drake: Fundmentals of Reservoir Engineering
Generalized form: (frictionless & laminar flow)
u
.
d
d Φ
d
+g.(zA z)
u … Velocity (m/s, ft/s) k … Permeability (m², D)
ρ … Density (kg/m³, lb/ft³) μ … Viscosity (Pas, cp)
Φ … Potential energy per unit mass l … Length (m, ft)q … Flow rate (m³/s, bbl/day) A … Cross-section (m², ft²)
Incompressible & horizontal flow: Φ
u
.
d
d q
A
.
d
d
Radial form: q
r.
d
d
-
8/16/2019 4 IPR Undersaturated 15
9/34
Chair of Petroleum & Geothermal Energy Recovery
Page 9
Chair of Petroleum & Geothermal Energy Recovery
Diffusivity Equation
L.P.Drake: Fundmentals of Reservoir Engineering
Basic differential equation for radial flow in a porous media
- Homogeneous rock properties and isotropic permeability
- Fully radial flow (entire reservoir thickness covered)
- Formation is completely saturated with one fluid
- Reservoir of cylindrical shape
-
8/16/2019 4 IPR Undersaturated 15
10/34
Chair of Petroleum & Geothermal Energy Recovery
Page 10
Chair of Petroleum & Geothermal Energy Recovery
Diffusivity Equation
L.P.Drake: Fundmentals of Reservoir Engineering
Radial flow of any single fluid in a porous media:
r
ϕcρ
Linearization for incompressible fluids:
-
8/16/2019 4 IPR Undersaturated 15
11/34
Chair of Petroleum & Geothermal Energy Recovery
Page 11
Chair of Petroleum & Geothermal Energy Recovery
Flow Regimes
L.P.Drake: Fundmentals of Reservoir Engineering
Flow regimes describe the outer boundary pressure decline over time:
Steady-State Flow:
=. 0
Constant pressure boundary
Pseudo-(Semi-) Steady-State Flow:
=. const.
No flow boundary
Transient Flow: =.
f (log t)
Infinite acting
so far no boundary response - until pressure wave hits boundary
-
8/16/2019 4 IPR Undersaturated 15
12/34
Chair of Petroleum & Geothermal Energy Recovery
Page 12
Chair of Petroleum & Geothermal Energy Recovery
L.P.Drake: Fundmentals of Reservoir Engineering
Steady State Solution
Steady State applies after the transient period and assumes a constant
pressure over time at the outer boundary.
p
t =.
0
-
8/16/2019 4 IPR Undersaturated 15
13/34
Chair of Petroleum & Geothermal Energy Recovery
Page 13
Chair of Petroleum & Geothermal Energy Recovery
Steady State
SI – Units (m³/s) Field – Units (bbl/day)
Relationship p(r),r p pw ln
+ S p pw ,. ln
+ S
Outer boundary
pressure pe pe pw
ln
+ S pe pw ,.
ln
+ S
Average reservoir
pressure p
p pw
ln
,.
+ S p pw ,.
ln
,.
+ S
C f & G
C f & G
-
8/16/2019 4 IPR Undersaturated 15
14/34
Chair of Petroleum & Geothermal Energy Recovery
Page 14
Chair of Petroleum & Geothermal Energy Recovery
L.P.Drake: Fundmentals of Reservoir Engineering
Pseudo- (Semi-) Steady State Solution
Pseudo Steady State applies after the transient period and assumes no
fluid flow at the outer boundary and a constant pressure drop over time.
p
t =.
const.
Ch i f P t l & G th l E R
Ch i f P t l & G th l E R
-
8/16/2019 4 IPR Undersaturated 15
15/34
Chair of Petroleum & Geothermal Energy Recovery
Page 15
Chair of Petroleum & Geothermal Energy Recovery
Pseudo Steady State
SI – Units (m³/s) Field – Units (bbl/day)
Relationshipp(r),r
p pw ln
²
+ S p pw ,. ln
²
+ S
Outer boundary
pressure pe pe pw
ln
,.
+ S pe pw ,.
ln
,.
+ S
Av. reservoir
pressure p p pw
ln,.
+ S p pw ,.
ln,.
+ S
Ch i f P t l & G th l E R
Ch i f P t l & G th l E R
-
8/16/2019 4 IPR Undersaturated 15
16/34
Chair of Petroleum & Geothermal Energy Recovery
Page 16
Chair of Petroleum & Geothermal Energy Recovery
L.P.Drake: Fundmentals of Reservoir Engineering
Transient Solution
The reservoir is acting infinite – at the beginning of production and time
dependent!
p
t =.
f (log t)
Ch i f P t l & G th l E R
Ch i f P t l & G th l E R
-
8/16/2019 4 IPR Undersaturated 15
17/34
Chair of Petroleum & Geothermal Energy Recovery
Page 17
Chair of Petroleum & Geothermal Energy Recovery
Transient Solution
SI – Units (m³/s) Field – Units (bbl/day)
pi pw
ln
² + 2. S pi pw
,
log
² 3,23 + 0,87. S
re … Outer boundary radius (m, ft)rw … Wellbore radius (m, ft)
pe … Outer boundary pressure (Pa, psi)pi … Initial reservoir pressure (Pa, psi)pw … Well flowing pressure (Pa, psi)q … Production rate under reservoir conditions (m³/s, STB/d)
μ … Viscosity of the fluid (Pas, cp)h … Height of the reservoir (m, ft)
k … Total permeability (m², mD)
Φ … Porosity (-)
c … Compressibility (Pa-1, psi-1) γ … Euler constant = 1,78t … Time (s, h)
S … Skin factor (-)
Ch i f P t l & G th l E R
Ch i f P t l & G th l E R
-
8/16/2019 4 IPR Undersaturated 15
18/34
Chair of Petroleum & Geothermal Energy Recovery
Page 18
Chair of Petroleum & Geothermal Energy Recovery
Economides: Petroleum Production System
Surface Rates from IPR
Conversion of the volumes under reservoir conditions to surface
conditions.
B V
V q
q
B … Formation volume factor (-)V … Volume of fluid under reservoir conditions (m³, bbl, …) Vs … Volume of fluid under stock tank conditions (m³, bbl, …) q … Flow rate under reservoir conditions (m³/s, bbl/day, …) qs … Flow rate under stock tank conditions (m³/s, bbl/day, …)
Ch i f P t l & G th l E R
Ch i f P t l & G th l E R
-
8/16/2019 4 IPR Undersaturated 15
19/34
Chair of Petroleum & Geothermal Energy Recovery
Page 19
Chair of Petroleum & Geothermal Energy Recovery
Surface Rates
Example
IPR rate calculation
Calculate the surface production rate (here p = 0 MPa) and the
quantities at a pressure of 5 MPa for the following reservoir under steady
state conditions.
p = 20 MPapw = 10 MPaμ = 0,003 Pas
k = 100 mDh = 10 m
re = 100 mrw = 0,15 mS = 1
Chair of Petrole m & Geothermal Energ Reco er
Chair of Petrole m & Geothermal Energ Reco er
-
8/16/2019 4 IPR Undersaturated 15
20/34
Chair of Petroleum & Geothermal Energy Recovery
Page 20
Chair of Petroleum & Geothermal Energy Recovery
Surface Rates
L.P.Drake: Fundmentals of Reservoir Engineering
Homework
Calculate the production rate for steady state , pseudo steady state and
transient fluid flow for the well with the following parameters:
pe = pi = 17 MPa μ = 1,62. 10-3 Paspw = 10 MPa B = 1,1
re = 100 m h = 10 m
rw = 6,538” = 83 mm k = 100 mD S = 0
Φ = 0,2 c = 1,3. 10-5 Pa-1 γ = 1,78 t = 30 days = 2592000 s
Chair of Petroleum & Geothermal Energy Recovery
Chair of Petroleum & Geothermal Energy Recovery
-
8/16/2019 4 IPR Undersaturated 15
21/34
Chair of Petroleum & Geothermal Energy Recovery
Page 21
Chair of Petroleum & Geothermal Energy Recovery
Productivity Index J or PI: J
−
Expression describes the deliverability of the wellbore
Constant for undersaturated reservoirs
Maximizing the PI is a major objective
Inflow Performance Relationship
Chair of Petroleum & Geothermal Energy Recovery
Chair of Petroleum & Geothermal Energy Recovery
-
8/16/2019 4 IPR Undersaturated 15
22/34
Chair of Petroleum & Geothermal Energy Recovery
Page 22
Chair of Petroleum & Geothermal Energy Recovery
Productivity Index
Example
Productivity index
The average reservoir pressure of well XY in a depth of 2000 m is 21
MPa. The test point of this undersaturated reservoir was at 18 MPa and
generated 250 m³/day.
Draw the IPR curve!
Calculate the PI-Index and the AOF!
Calculate the skin factor!
μ = 1,62. 10-3 PasB = 1,1
re = 100 m h = 10 m rw = 6,538” = 83 mm k = 100 mD
Chair of Petroleum & Geothermal Energy Recovery
Chair of Petroleum & Geothermal Energy Recovery
-
8/16/2019 4 IPR Undersaturated 15
23/34
Chair of Petroleum & Geothermal Energy Recovery
Page 23
Chair of Petroleum & Geothermal Energy Recovery
Dietz Shape Factor
Up to now only cylindrical reservoirs were considered – the shape of the
reservoir has a significant influence on the IPR.
Dietz Shape Factor: It considers the irregularity of the drainage area.
CA … Dietz shape factor A … Drainage area (m², ft²)
Irregular Drainage Pattern
SI – Units (m³/s) Field – Units (bbl/day)
Steady state
p pw
ln
A
,.²+ S p pw
,.
ln
A
,.²+ S
Pseudo steady state
p pw
ln
A
²+ S p pw
,.
ln
A
²+ S
Chair of Petroleum & Geothermal Energy Recovery
Chair of Petroleum & Geothermal Energy Recovery
-
8/16/2019 4 IPR Undersaturated 15
24/34
Chair of Petroleum & Geothermal Energy Recovery
Page 24
Chair of Petroleum & Geothermal Energy Recovery
Dietz Shape Factor
Chair of Petroleum & Geothermal Energy Recovery
Chair of Petroleum & Geothermal Energy Recovery
-
8/16/2019 4 IPR Undersaturated 15
25/34
Chair of Petroleum & Geothermal Energy Recovery
Page 25
Chair of Petroleum & Geothermal Energy Recovery
Dietz Shape Factor
Example
Dietz shape factor
Compare the surface production rates under steady state conditions for
the two different drainage patterns and the given reservoir data. Draw
the IPR curves and calculate the productivity index.
B = 1,1 A = 570 acre = 24829200 ft²
μ = 1,5 cP S = 0k = 9 mD h = 35 ft
rw = 0,3281 ft γ = 1,78p = 3000 psi pw = 1200 psi
21
Chair of Petroleum & Geothermal Energy Recovery
Chair of Petroleum & Geothermal Energy Recovery
-
8/16/2019 4 IPR Undersaturated 15
26/34
Chair of Petroleum & Geothermal Energy Recovery
Page 26
Chair of Petroleum & Geothermal Energy Recovery
Separation between oil and water production
e.g. steady state solution:
k … Relative permeability oil (-)kw … Relative permeability water (-)
Relative Permeabilities
q 2πkkh p pw μB ln
0,61.rerw
+ S
qw 2πkkwh p pw
μwBw ln0,61.re
rw + S
Chair of Petroleum & Geothermal Energy Recovery
Chair of Petroleum & Geothermal Energy Recovery
-
8/16/2019 4 IPR Undersaturated 15
27/34
Chair of Petroleum & Geothermal Energy Recovery
Page 27
Chair of Petroleum & Geothermal Energy Recovery
Relative Permeabilities
Example
Water and Oil Production
Calculate the oil and water production rate under steady state
conditions. The water saturation is 55 %.
p = 15 MPa pw = 10 MPare = 100 m rw = 83 mmh = 10 m k = 100 mD
S = 3
μi = 1,62. 10-3 Pas Bi = 1,12μwe = 0,8. 10-3 Pas Bwe = 1,04
Chair of Petroleum & Geothermal Energy Recovery
Chair of Petroleum & Geothermal Energy Recovery
-
8/16/2019 4 IPR Undersaturated 15
28/34
Chair of Petroleum & Geothermal Energy Recovery
Page 28
Chair of Petroleum & Geothermal Energy Recovery
The drainage shape for horizontal wells is ellipsoidal. One must
distinguish between horizontal and vertical permeability.
Horizontal Wells
Chair of Petroleum & Geothermal Energy Recovery
Chair of Petroleum & Geothermal Energy Recovery
-
8/16/2019 4 IPR Undersaturated 15
29/34
Chair of Petroleum & Geothermal Energy Recovery
Page 29
Chair of Petroleum & Geothermal Energy Recovery
Horizontal Wells
Steady state flow in the horizontal plane and pseudo steady state flow in
the vertical plane are assumed:
a
0,5 + 0,25 +
, ,
for
≤ 0,9 . reH
Ii kH
k
q k
H
.h.∆p
141,2. Bμ lna + a²
L2 ²
L2
+Iih
L ln Iih
rw(Ii + 1)
Chair of Petroleum & Geothermal Energy Recovery
Chair of Petroleum & Geothermal Energy Recovery
-
8/16/2019 4 IPR Undersaturated 15
30/34
Chair of Petroleum & Geothermal Energy Recovery
Page 30
Chair of Petroleum & Geothermal Energy Recovery
Example
IPR Horizontal Wells
Calculate the production rate for the given horizontal well.
kH = 10 mD k = 3 mD reH = 500 ft
pi = 5000 psi pw = 2750 psih = 55 ft
B = 1,15μ = 1,55 cP
rw = 0,351 ft
Chair of Petroleum & Geothermal Energy Recovery
Chair of Petroleum & Geothermal Energy Recovery
-
8/16/2019 4 IPR Undersaturated 15
31/34
Chair of Petroleum & Geothermal Energy Recovery
Page 31
Chair of Petroleum & Geothermal Energy Recovery
Homework
Deadline: 25.08.2015 09:00
The following examples should be calculated using the following
undersaturated reservoir properties:
Chair of Petroleum & Geothermal Energy Recovery
Chair of Petroleum & Geothermal Energy Recovery
-
8/16/2019 4 IPR Undersaturated 15
32/34
Chair of Petroleum & Geothermal Energy Recovery
Page 32
Chair of Petroleum & Geothermal Energy Recovery
Homework
1) Infinite – acting oil well:
Develop a production rate profile (q – t diagram) for 1 year assuming
that no boundary effects emerge. Do this in increments of 2 months and
use a pw of 3500 psi.
2) Steady state production:
Assume that the well has a drainage area equal to 640 acre (re = 2980ft)and is producing at steady state with an outer boundary (constant)
pressure equal to 5651 psi. Calculate the steady-state production rate ifthe pw is equal to 4500 psi. Use a skin factor of 10. Describe twomechanisms to increase the flow rate by 50%. (Show calculations)
Chair of Petroleum & Geothermal Energy Recovery
Chair of Petroleum & Geothermal Energy Recovery
-
8/16/2019 4 IPR Undersaturated 15
33/34
Chair of Petroleum & Geothermal Energy Recovery
Page 33
Chair of Petroleum & Geothermal Energy Recovery
Homework
3) No-flow boundary reservoir:
What would be the average reservoir pressure if the outer boundary
pressure is 6000 psi, the pw is 3000 psi, the drainage area 640 acresand the well radius is 0,328 ft ? What would be the ratio of the flow rates
before and after the average reservoir pressure drops by 1000 psi?
Assume skin = 0.
4) Irregular well positioning:
Assume that two wells each drain 640 acre. Furthermore, assume that
p =5651 psi (same as pi) and that S = 0. The pw in both wells is 3500psi. Well A is placed at the center of a square, whereas well B is at thecenter of the upper right quadrant of a square drainage shape. Calculate
the production rates from the two wells for pseudo steady state!
Chair of Petroleum & Geothermal Energy Recovery
Chair of Petroleum & Geothermal Energy Recovery
-
8/16/2019 4 IPR Undersaturated 15
34/34
Chair of Petroleum & Geothermal Energy Recovery
P 34
Chair of Petroleum & Geothermal Energy Recovery
Homework
5) Transient IPR:
Construct transient IPR curves for 1, 6 and 24 months. Assume zero
skin!
6) Steady state IPR:
Assume that the initial reservoir pressure of the well is also the constant
pressure of the outer boundary. Draw IPR curves for skin effects equal to
0, 5, 10 and 50. Use a drainage radius of 2980 ft (A = 640 acre).
7) Pseudo steady state IPR:
Calculate the IPR curves for zero skin effect but for average reservoir
pressures in increments of 500 psi from initial 5651 psi to 3500 psi.
drainage radius of 2980 ft
top related