IPR VLP

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


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


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


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


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


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


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


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

67

IPR VLP

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