Seminar on Well Performance Analysis Politecnico di Torino, 3/2/2011
Giuseppe Tripaldi/RESM
[email protected] www.eni.it
Well Performance: the basic plot n IPR
BHP
• Inflow Perfomance Relationship • Related to the reservoir response
n
o
o VLP • Vertical Lift Performance • Related to the tubing response • Also known as OPR (Outflow Performance Relationship)
(0;0)
Q
Bottom Hole Pressure (BHP) plotted vs. surface rate (Q) at standard/stock tank conditions
2
Well Performance: the basic plot P* = Static Reservoir Pressure (no flow)
BHP P*
IPR
AOF = Absolute Open Flow (Maximum Theor. Rate)
VLP
P0 (Q0;P0) = Current Working Point
(0;0)
Q0
AOF
Q
3
When 1. 1. Well Well Testing Testing 2. 2. Completion/workover Completion/workover design design 3. 3. Artificial Artificial lifting lifting 4. 4. Production Production optimization optimization 5. 5. Surface Surface network network optimization optimization 6. 6. Integrated Integrated asset asset modeling modeling 7. 7. Reservoir Reservoir management/monitoring management/monitoring 8. 8. Reservoir Reservoir studies/modeling studies/modeling 4
Agenda
1. Nodal Analysis for Well Performance 2. Inflow Performance Relationship (oil, gas) 3. Vertical Lift Performance (single phase oil/gas, two-phases) 4. IPR/VLP Matching and Workflow 5. Some Applications 6. Further Issues
5
Nodal Analysis
Pi-1 Q Pi
For each segment can be established a relationship:
Segment
Nodes
Pi − Pi −1 = ΔPi (Q)
6
Nodal Analysis NODE Separator end-point
SEGMENT
i Separator
Flow-line outlet
h Flow-line
Flow-line inlet
g Choke
Well-Head
f Tubing
Bottom-hole
e BH completion
Sand-face
d Reservoir
Reservoir end-point
c
7
Nodal Analysis NODE Separator end-point
SEGMENT
i Separator
Flow-line outlet
h Flow-line
Flow-line inlet
g
Well-Head
f
Bottom-hole
Usual
Sometime
Well Performance Analysis whitin Well Testing Framework
e
BH BH completion completion can can be be detailed detailed describing perforations, Chokedescribing perforations, gravel gravel pack packetc. etc. Usually Usuallyititisisaccounted accountedby bythe thetotal total skin Tubing skinof ofthe thereservoir reservoirsegment segment
BH completion Sand-face
d Reservoir
Reservoir end-point
c
8
Nodal Analysis NODE Separator end-point
SEGMENT
1. Well Profile
i Separator
Flow-line outlet
h
Tubing segment isis refined Tubing segment Flow-line refined (internally by the software) to (internally by the software) to Flow-line inlet g take into account different flow take into account different flow regimes regimesdue dueto: to: Choke Well-Head
f Tubing
Bottom-hole
e BH completion
Sand-face
d Reservoir
Reservoir end-point
c
2. PVT
9
Agenda
1. Nodal Analysis for Well Performance 2. Inflow Performance Relationship (oil, gas) 3. Vertical Lift Performance (single phase oil/gas, two-phases) 4. IPR/VLP Matching and Workflow 5. Some Applications 6. Further Issues
10
IPR-Oil
BHP P* Linear trend (undersaturated conditions)
Pb Non-linear P(Q) (saturated conditions)
(0;0)
Qb
AOF
Q
11
IPR-Oil (Undersaturated Conditions) P* and J (Productivity Index) measured with a test
PI ENTRY
TRANSIENT
k: Effective Permeability (mD) h: Net Pay Thickness (ft) μ: Oil viscosity (cP) B: Oil formation factor (rb/stb) S: Skin
t: rw: φ: ct:
Production time (hrs) Wellbore radius (ft) Porosity Total compressibility (1/psi)
12
IPR-Oil (Undersaturated Conditions) PSEUDO-STEADY STATE
k: Effective Permeability (mD) h: Net Pay Thickness (ft) μ: Oil viscosity (cP) B: Oil formation factor (rb/stb) S: Skin x: Drainage Area Factor
For radial flow: x= re /rw rw: Wellbore radius (ft) re: External boundary radius (ft)
Generally,
A: Drainage Area (ft2) CA: Dietz Shape Factor γ: Euler’s constant (1.781)
13
IPR-Oil (Dietz Shape Factors)
31.6
25
14
Vogel Approximation (SPE 1476)
P/P*
IPR-Oil (Saturated Conditions)
Q/AOF
15
IPR-Gas
BHP Generally speaking, non linear shape due both non-Darcy effects and, below dew point, saturated reservoir conditions
(0;0)
AOF
Q
16
IPR-Gas (Rawlins-Schellardt Formula)
17
IPR-Gas (Forcheimer) Rigorously:
Approximately: A: Non-Darcy Coefficient B: Darcy Coefficient o o o
A
B
(0;0)
Q 18
IPR-Gas (Jones)
Ψ:
Pseudopressure (psi2/cp)
Q:
Gas rate (Mscf/D)
β:
Turbulence factor (1/ft)
γg:
Gas specific gravity
T:
Reservoir temperature (°R)
hp: Perforated interval (ft) rw: Wellbore radius (ft) μg:
Gas viscosity (cP)
K:
Gas effective permeability (mD)
S:
Skin
x:
Drainage area factor
19
IPR Matching 4800
120 110
4700 100 4600
90
60 50
4300
Models output: k, S etc.
40 30
4200
20 4100 10 0 4000 130 140 150 160 170 180 190 200 210 220 230 240 250 260 270 280 290 300 310 320 330 340 350 360 370 380 390 Elapsed time (hrs)
BHP
Well testing provides match points
BHP
Use unknown as match parameter
Pressure (psia)
70 4400
Gas Rate (MMscf/D)
80 4500
Target: to find a suitable IPR
(0;0)
Q
(0;0)
Q
20
Agenda
1. Nodal Analysis for Well Performance 2. Inflow Performance Relationship (oil, gas) 3. Vertical Lift Performance (single phase oil/gas, two-phases) 4. IPR/VLP Matching and Workflow 5. Some Applications 6. Further Issues
21
VLP - (Introduction) Mechanical Energy Balance Equation
Kinetic Potential Energy Energy Friction
Shaft Work
g: gravitational acceleration gc: conversion factor ρ: fluid density f: friction factor u: fluid velocity D: tubing diameter
NO Negligible in singlephase flow except at atmospheric pressure or blow-out
22
VLP: Single Phase Oil Incompressible flow: constant ρ
2
ΔL
z
Potential energy, gravity or hydrostatic term.
Q θ
1 Friction term
23
VLP : Friction factor, Moody Diagram
0.001
Typical value
24
VLP: Single-Phase Gas Compressible fluid
+
+ Mech. energy balance (negligible kinetic energy)
From real gas law
Velocity from volumetric rate at sc
+ Numerical integration because Z, T are function of z
Non-Horizontal well, Oilfield units, P1 = BHP
25
Annular
Churn
Slug
Bubble
VLP: Liquid-Gas Flow (Main Regimes in Vertical Pipes)
26
VLP:Liquid-Gas in Vertical Pipes Region 1. Bubble and low velocity slug Region 2. High velocity slug and churn Region 3. Annular Transition. From a liquid continuous to a gas continuous system
Velocity Numbers
qg,ql: gas and liquid rates A: cross-section area g: acceleration of gravity σ: liquid-gas interfacial tension ρl: liquid density
27
VLP: Popular Multiphase Correlations
28
VLP: Pressure-Traverse Calculation
29
VLP Matching
π1, π2, matched with statistical regression They should range in [0.9, 1.1] More tolerance in π2 if there are uncertainties on downhole equipment
30
Agenda
1. Nodal Analysis for Well Performance 2. Inflow Performance Relationship (oil, gas) 3. Vertical Lift Performance (single phase oil/gas, two-phases) 4. IPR/VLP Matching and Workflow 5. Some Applications 6. Further Issues
31
VLP/IPR Matching
Good < 5 % Fair < 10% Otherwise improve match playing with input data.
Usually < 0.1 %
32
Well Performance Workflow Begin Begin System Systemdescription description Survey, Survey,Downhole Downholeeq., eq.,etc. etc. Fluids FluidsPVT PVT IPR IPR VLP VLPcorrelation correlationselection selection VLP/IPR VLP/IPRMatch Match
NO
? YES
End End 33
System description
34
Deviation Survey
Top of perfs
35
Downhole equipment
Top of perfs
36
Fluids PVT
37
IPR (Input data)
38
IPR Plot
39
Tubing correlation comparison (input data)
40
Tubing correlation comparison (output data)
41
Tubing correlation comparison (ouput data)
42
VLP/IPR Match (Input data)
43
VLP/IPR Match Plot
44
Agenda
1. Nodal Analysis for Well Performance 2. Inflow Performance Relationship (oil, gas) 3. Vertical Lift Performance (single phase oil/gas, two-phases) 4. IPR/VLP Matching and Workflow 5. Some Applications 6. Further Issues
45
Case Study 1 Design phase (appraisal oil well) Given reservoir scenario Constraint: WHP (related to Separator Pressure) Aim: verify if we can produce 3000 STB/D or 5000 STB/D Tubing: 4 ½” DST string
Sensitivities k (mD): 500, 1000, 2000 Skin: 0, 3, 10
46
Case Study 1
k = 1000 mD Skin = 0
k = 1000 mD Skin = 10
47
Case Study 2 Well Test Interpretation. Same well of case study 1 Results of PTA
48
Case Study 2 PETROLEUM EXPERT 2
49
Case Study 2 DARCY MODEL
50
Case Study 2
51
Case Study 3 Exploration Gas Well Well Testing Results:
52
Case Study 3
53
Case Study 3
54
Case Study 4 Injection Testing (Water in Oil Reservoir) Well Testing Results:
55
Case Study 4
56
Case Study 4
57
Agenda
1. Nodal Analysis for Well Performance 2. Inflow Performance Relationship (oil, gas) 3. Vertical Lift Performance (single phase oil/gas, two-phases) 4. IPR/VLP Matching and Workflow 5. Some Applications 6. Further Issues
58
Liquid Unloading in Gas Wells BHP
Turner criteria
Vunl: Unloading velocity (ft/sec) σ: Surface tension (dynes/cm) ρ: Density (dynes/cm)
(0;0)
Q qunl
59
Liquid Unloading in Gas Wells
5 ½” TUBING
60
Erosional Velocity in Gas Wells BHP
(0;0)
Q Qma
61
Erosional Velocity
62
VLP: Generic Restrictions
63
VLP: Choke Performance Critical Flow •If the fluid velocity reaches the speed of sound, a compressional wave is generated. The compressional wave prevents fluids particles to flow from downstream to upstream.
Critical Flow upstream
downstream
•Under critical flow condition any adjustment to the pressure at downstream does not affect the upstream pressure. •Critical flow conditions are as follow:
X
Sub-critical flow upstream
downstream
64
VLP: Choke Performance Single-Phase Gas
65
VLP: Choke Performance Two-Phase Gas
66
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