3_Introduction to Nodal Analysis

7/28/2019 3_Introduction to Nodal Analysis

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= density,v = velocity,

d = pipe diameter, (ID),

g = acceleration due to gravity,

gc = garvity conversion factor,

f = fanning friction factor,

= pressure gradient,

m = mixture properties,

q = angle of inclination from horizontal

Multiphase Flow in Pipes

1. The pressure gradient equation for multi-phase flow can be written as:

dL g

dvv

d g 2

v f sin

g

g

dL

dp

c

mmm

c

2

mmm

c

q

Where:

dL

dp











Gradient Curves



Vertical Multiphase Flow: How to find the BHFP



Vertical Multiphase Flow: How to find the WHFP



Vertical Multiphase Flow: How to find the WHFP



Exercise:

Given:

Pwh=100 psig WH Temp.= 70o

FGLR = 400 scf/bbl BHST = 140o F

gg = 0.65 TD = 5,000 ft (mid – perf)

Tbg ID = 2.0 in API Gravity = 35o API

Calculate and plot the Tubing Intake Curve

Vertical Multiphase Flow: How to plot the

Tubing Intake Curve



• Using Fig. 4.10, start at the top of the gradient curve at a pressure of

100 psig. Proceed vertically downward to a GLR of 400 scf/bbl.

Proceed horizontally and read an equivalent depth. Add the TVD to the

depth in question. Read a depth of 6,600 psig and proceed horizontally

to the 400 scf/bbl curve. From this point proceed vertically and read

the tbg intake pressure for 200 bpd of 720 psig.

• Repeat this procedure for flow rates of 400, 600, and 800 bpd using the

corresponding graphs.

• Plot the obtained values of Pwf to plot a Pwf vs q , the desired tubing

intake curve.


Tubing Intake Curve




Tubing Intake Curve

Assumed q, (bpd) Pwf , psig

200 720

400 730600 900

800 1000



Tubing Intake Curve

600

650

700

750

800

850

900

950

1000

1050

1100

0 200 400 600 800 1000

Rate q, bpd

P r e s s u r e P

w f , p s i g



Pressure Loss AcrossPerforations



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).



D p p calculated using the modified Jones, Blount &Glaze equations.

Treats the perforation tunnel as a miniature wellwith a compacted zone of reduced permeabilityaround the tunnel.

– 10% of K f , if perforated overbalanced

– 40% of K f , if perforated underbalanced

The thickness of the crushed zone is assumed to be 0.5 in.

Pressure Loss in Perforations- McLeod Method



McLeod Method, cont….




• For an Oil well:

o

2

owf wfs bqaqPP

– where:

in5.0r r , k L10x08.7

r

r ln

b

k

10x2.33 ,

L

r

1

r

1

10x3.2a

pc

p p

3-

p

c

o

1.201

p

10

2

p

c p

2

o

14-

, q is flow rate through perforation




• For a gas well:

g

2

g

22 bqaqPPwf wfs

– where:

in5.0r r , k L

r

r lnTZ10x424.1

b

k

10x2.33 ,

L

r 1

r 1TZ10x16.3

a

pc

p p

p

c3

1.201

p

10

2

p

c p

g

12-

g

, qg is flow rate through perforation



Karakas and Tariq Method, (1988)

• Semi-analytical solution to the problem of 3D

flow into a spiral system of perforations. Two

cases:

– 2D case, valid for small dimensionless perforationspacings (large perf penetration or high shot

density).

– 3D flow problem around the perf tunnel, valid inlow density perforations.



Karakas and Tariq Method, cont…

t

w

e

wr

Sr

r ln

PPkh2q

• For steady-state flow into a perforation:

• Where:

St = total skin = S p +

Sdp

and:

S p = Sh + Swb + Sv



S p = perforation skin factor Sdp= damage skin factor

Sh= pseudo skin due to phasing =

where: r we(q) is the effective wellbore radius as a function of the phasing angle (q)

and perf tunnel length. 0.25 l p , if q = 0o

rw(q) =

aq (r w + l p) , otherwise

Swb= pseudo skin due to wellbore effects (dominant in zero

degree phasing).

Sv= pseudo skin due to vertical converging flow (negligible in

the case of high shot density; 3D effect)


qwe

w

r

r ln




Perforation

Phasingaq

(360o) 0o 0.250

180o

0.500120o 0.648

90o 0.726

60o 0.813

45

o

0.860

Dependance of aq on Phasing Swb(q) = C1(q) exp[C2(q)r wd]

Perforation

PhasingC1 C2

(360o) 0o 1.6E-1 2.675

180o

2.6E-2 4.532120o 6.6E-3 5.320

90o 1.9E-3 6.155

60o 3.0E-4 7.509

45

o

4.6E-5 8.791



• Crushed zone effect

– In conditions of linear flow, the effect of

compacted or crushed can be neglected.

– In the case of 3D flow, an additional skin due tothe crushed zone can be calculated as follows:


p

c

c p

c

r

r ln1

k

k

l

hS

Note: Rc and rp may be calculated using McLeod (1983) method

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3_Introduction to Nodal Analysis