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Schlumberger

1. Importance to Schlumberger

2. The concept of NodalTM Analysis

3. Segments in the reservoir/well system where pressure loss occurs

4. Solution node

5. Inflow performance curve

6. Tubing curve

7. System graph

8. Small Project-Multilayer Nodal Analysis

1. Explain the concept of Nodal Analysis.

2. List the four major segments between the reservoir and the

separator where pressure loss occurs.

3. Give definitions for each of the following terms:

• Inflow performance curve

• Tubing performance curve

• System graph

• Solution node

4. Explain the importance to you and Schlumberger

Stimulation candidate selection

Production prediction

Treatment type and design

More objectives of Nodal analysis

Estimate WHP from IPR, Pr, completions and target rate

Estimate rates from WHP, IPR, Pr, completions

Size completions from IPR, Pr and WHP constraints

Determine choke size for target rate and system description

Design AL system

Predict hydrate formation

…

P1 = Pr - Pwfs = Loss in reservoir

P2 = Pwfs - Pwf = Loss across completion

P3 = Pwf - Pwh = Loss in tubing

P4 = Pwh - Psep = Loss in flowline

Pr Pe Pwfs Pwf

P1 = (Pr - Pwfs)

P2 = (Pwfs - Pwf)

P3 = Pwf - Pwh

P4 = (Pwh - Psep)

Psep

Sales line Gas

Liquid

Stock tank

PT = Pr - Psep = Total pressure loss

Adapted from Mach et al, SPE 8025, 1979.

Pwh

P1 = Pr - Pwfs = Loss in reservoir

P2 = Pwfs - Pwf = Loss across completion

P3 = Pwf - Pwh = Loss in tubing

P4 = Pwh - Psep = Loss in flowline

Pr Pe Pwfs Pwf

P1 = (Pr - Pwfs)

P2 = (Pwfs - Pwf)

P3 = Pwf - Pwh

P4 = (Pwh - Psep)

Psep

Sales line

Gas

Liquid

Stock tank

PT = Pr - Psep = Total pressure loss

Adapted from Mach et al, SPE 8025, 1979.

Pwh

2111 STB/D

1957.1 psi

0

500

1000

1500

2000

2500

3000

3500

0 500 1000 1500 2000 2500 3000 3500 4000 4500

Production rate, STB/D

Flo

win

g b

ott

om

ho

le p

res

su

re, p

si

Inflow (Reservoir) Curve

Tubing Curve

9 Initials

27-Aug-13

10 Initials

27-Aug-13 10

27-Aug-13

qk h

B

P P

nr

rS

o

o

o o

r wf

e

w

0 00708

10 472

.

. '

Inflow Performance

Radial Flow Equation

Flow rate (bpd)

permeability (mD) net pay (ft) average reservoir

pressure (psi)

flowing bottom hole

pressure (psi)

viscosity (cp)

formation volume

factor (rb/stb) wellbore radius (ft) drainage radius (ft)

Total skin

Q: What can we do to really influence the flowrate ?

Single phase liquid:Darcy’s law for radial flow

through a permeable medium as follows:

Productivity Index - Oil Wells - Single phase liquid

4

306.10ln

2

12

wArC

APD

11

27-Aug-13

2

06.10ln

2

1

wArC

APD

DtEiPD

4

1

2

1

2

wrC

ktt

t

D

sPB

kh

pp

qJ

Dwf

2.141

Stabilized rate

Productivity index

Pressure drawdown

Dimensionless pressure

Infinite-Acting Solution Steady State Solution Pseudo steady State Solution

wfPPiP

wfPPP wfPPeP

P

CA = Dietz Shape factor

No-Flow Boundaries:Pseudo steady State Solution

12

27-Aug-13

Constant Well Rate Constant Well Pressure

Changing pwf Constant pwf

Radial Pressure Profiles

No-Flow

Boundary t

r3

r2

t2= 1 day

t3= 3 days

t4= 10 days

r4

No-Flow Outer

Boundary

r1

t1= 0.3 day

t5

t5

Fluid at the farthest

boundary starts moving

toward the well

t1

t1

r1 r1 r2

t2

t2

r2

t4

t4

r4 r4

t3

t3

r3 r3

Constant-Pressure Boundaries : Steady State Solution

13

27-Aug-13

r3

r2

t2= 1 day

t3= 3 days

t4= 10 days

r4

Constant-Pressure

Outer Boundary

r1

t1= 0.3 day

Constant Well Rate Constant Well Pressure

Changing pwf Constant pwf

Radial Pressure Profiles

Constant-Pressure

Boundary

Fluid at the farthest

boundary starts moving

toward the well

t1

t1

r1 r1 r2

t2

t2

r2

t4

t4

r4 r4

t3

t3

r3 r3

Shape Factors - Pseudo Steady State Solution

srC

AB

kh

pp

qJ

wA

oo

wf

4

306.10ln

2

1

1008.7

2

3

14

27-Aug-13

Shape Dietz

CA

Odeh

CA, Odeh

Fetkovich

sCA

Shape Dietz

CA

Odeh

CA, Odeh

Fetkovich

sCA

31.62 0.564 0.573

2

1 10.84 0.964 1.108

31.6 0.565 0.573

2

14.51 1.494 1.546

27.6 0.604 0.6412

12.077 2.202 1.934

60° 27.1 0.610 0.6502

13.157 1.786 1.725

1/3{21.9 0.678 0.756

2

1

0.581 4.162 2.571

0.098 10.14 3.4612

1

0.111 9.529 3.399

30.9 0.571 0.584

1

4 5.38 1.368 1.458

13.0 0.881 1.018

1

42.69 1.935 1.805

4.51 1.494 1.546

1

40.232 6.591 3.030

3.34 1.738 1.697

1

4

0.1155 9.337 3.379

1

2

21.8 0.679 0.7581

5

2.361 2.065 1.870

Dietz Shape Factor

sr

ACB

kh

pp

qJ

w

OdehA

oo

wf

4

3ln

1008.7 3

Odeh Shape Factor

ssr

rB

kh

pp

qJ

CA

w

e

oo

wf

4

3ln

1008.7 3

Fetkovich Shape Factor Skin

Are

Combination Single Phase Liquid and Two Phase Flow

15

27-Aug-13

psiDSTBpp

qJ

wf

//

2

8.02.01p

p

p

p

q

q wfwf

max

+ Mathematical model for Vogel’s curve

Two-phase flow in the reservoir when pressure drops

below bubble point pressure

Assumptions: Initial Pr at Pb, Radial flow, undamaged well & pseudo steady state

Multiphase Flow

Combination Darcy/Vogel

16

27-Aug-13

qmax

J pb

1.8

q O

O

qb

Rate

pwf

pb

Pre

ss

ure

p

Multiphase Flow

How to find qmax:

17

27-Aug-13

2

max8.02.01:thenfor

:applieslawsDarcy',for

b

wf

b

wf

bbb

wfb

p

p

p

pqqqqqq

ppJqqq

8.1

pJqq b

bmax

Reservoir Conditions:

Original Pressure = 2150 psi

Bubble Point = 2150 psi

Crude oil PVT. Characteristics

and relative permeability

Characteristics from Ref. 7

Well spacing = 20 acres

Well radius - 0.33 foot

Cumulative recover,

percent of original

oil in place

Producing rate, bopd

Bo

tto

m h

ole

we

ll p

ressu

re,

psi

Multilayer Reservoirs

19

27-Aug-13

Input individual IPR for each layer

Composite IPR node solution at top Layer

Jones’ Gas IPR

Problem -

• Darcy’s law valid for laminar flow only

• High permeability gas wells produce in turbulent flow

near the wellbore

bqaqpp wf 222

Turbulence Term Laminar flow Term

Jones Equation

Assumptions

Darcy’s and Jones’ laws assume that the average

pressure( ) is constant

Drainage radius, re, is constant

These assumptions are true in pseudo-steady

state only, i.e. when all of the outer

boundaries of the reservoir are reached.

p

The time to reach pseudo-steady state (pss), tstab, can be

calculated with the following equation

k

rc948t

2et

stab

t-hrs Ct-1/psi

K-md re-feet

U-cp Porosity-fraction

t1

t2

t3

tstab

q

pwf

p tstab > t3 > t2 > t1

tstab = Pseudosteady

State (PSS) IPR

(Darcy) @ Time

to PSS

Oil Reservoir IPR’s Well PI (Pwf > PB)

• For undersaturated oil

• Can also be applied to flow below bubble

point with minor changes

Vogel’s* (Pwf < PB) • Empirical relationship

• C = 0.8 by default

Fetkovich/Backpressure • where n which ranges from 0.5 to 1

represents degree of turbulence

Jones* • modified PI and Darcy equation accounting

for turbulent flow

Pseudo-steady-state (Pwf > PB) : • based on Darcy IARF

)( wfR PPJq

2

max

)1(1

R

wf

R

wf

P

PC

P

PC

q

q

n

wfR PPCq )(22

2BqAqPP wfR

Sr

rB

PPkhq

w

e

wfR

75.0ln

00708.0

Gas Reservoirs IPR Well PI

Backpressure* • n = 0.5 to 1

Jones* • modified PI equation accounting for

turbulent flow

Pseudo-steady-state (based on

Darcy IARF)

• pseudo-pressure (for all P)

• OR pressure squared (for low P)

222BqAqPP wfR

)(22

wfR PPJq

n

wfR PPCq )(22

Sr

rTZ

PPkhq

w

e

wfR

75.0ln

10703226

wfR PmPmCq

dPZ

PPm

2 where

27 Initials

27-Aug-13

dZ

dv

g

v

dg

vf

g

g

dZ

dP m

c

mm

c

mmmm

ctot

2sin

2

Elevation

Friction

Acceleration

Vg

VL

gL

LL

VV

VH

gLLLm HH 1

Based on dimensional analysis by Duns and Ros

Duns and Ros (1963)

Hagedorn and Brown (1963)

Orkiszewski (1967)

Beggs and Brill (1973)

Mukherjee and Brill (1983)

Suggested application of correlations

Duns and Ros (1963) (vertical upflow)

Orkiszewski (1967) (vertical upflow)

Hagerdorn and Brown (1965) (vertical upflow)

Beggs and Brill (1973) (vertical or inclined,

upflow or downflow)

Mukherjee and Brill (1985) (vertical or inclined,

upflow or downflow)

Dukler (1964) (only horizontal flow)

Pressure Gradient

Factors affecting Pressure

Gradient Profile include:

Producing Rate

GOR

WCT

Tubing Size

Tubing geometry

Skin factor The Skin Factor (St) is a constant which relates the

pressure drop due to skin to the flow rate and

transmissibility of the formation. Thus:

Kh

q

PS

oo

skin

t2.141

wfwfskin PPP '

The Concept of Skin Damage Skin is an additional pressure drop through a zone of reduced

permeability (kd) in the near wellbore region

rw rd

re

k

kd

What causes this damage skin?

Pwf (no skin)

Pwf (with skin)

pskin

r (distance from wellbore)

rd

kd

rw

kPwf (no skin)

Pwf (with skin)

pskin

r (distance from wellbore)

rd

kd

rw

k

Skin Factor – graphical representation

Pr

P’wf

Pwf

rw

rd

Positive skin ~ Damaged wellbore or

Reduced wellbore radius

The Skin Equation

75.0ln

00708.075.0ln

00708.0 w

doo

w

d

d

ooskin

r

r

kh

Bq

r

r

hk

BqP

rw rd

re

k

kd

75.0ln

00708.0

w

eoo

wfRo

o

r

rB

PPhkq

skin

oo

PBq

khS

2.141

1ln

00708.0 dw

dooskin

k

k

r

r

kh

BqP

S

1ln

dw

d

k

k

r

rS

Skh

BqP oo

skin00708.0

Recalling the original Darcy equation

Sources of Skin

Positive skin

Drilling-induced or other formation damage

Migration of formation fines.

Perforation skin

Partial completions (and partial penetration) cases.

Gravel packs.

Reservoir flow turbulence

Negative skin:

Stimulated formations.

High density perforated completions.

Flow Efficiency:

FE < 1 for Damaged well

FE >1 for a Stimulated well

......, soturbpppdt SSSSSSS

Skin factor

St = total skin effect, (+ damaged; - stimulated)

Sd = skin effect due to formation damage (+)

Spp = skin due to partial penetration (+)

Sp = skin effect due to perforation (+)

Sturb = Dq, skin effect due to turbulence (+)

So = skin effect due to slanting of well (-)

Ss = skin effect due to stimulation (generally -)

Pressure Loss in Perforations

The effect of perforations on productivity can be

quite substantial.

It is generally believed that if the reservoir pressure

is below the bubble point, causing 2 phase flow

through the perforations, the pressure loss may be

an order of magnitude higher.

2 Methods for calculating presssure loss in

perforations, McLeod (1983) and Karakas &Tariq

(1988).

Are you ready?

Given the surface _____ pressure and the _____ pressure, along with the

physical properties of each system segment, we can calculate the

______ at which the well will produce.

(i) Flow rate

(ii) Separator

(iii) Water salinity

(iv) Reservoir

(v) API gravity

(vi) Tubing ID

43

27-Aug-13

Pre

ssure

Before After Incremental

Q1=250 BPD Q2=300 BPD

Pwf1=1750 Psia Pwf2=1900 psia

J1(pss)=1.0 BPD/psia J2(pss)=3.0 BPD/psia J=2 times

Q1, Pwf1

Q2, Pwf2

What is the productivity index before and after the stimulation?

For the same bottom hole flowing pressure(1750), what is the expected incremental oil?

Exercise 3 : Before and after Stimulated well Pr=2000 psia. Assume Pwf1>Pb

Tell me…

How do you see this

class benefiting your

daily job?