GAT2004-GKP-2010.

009
September, 2010
Page 1

Control of Flow Rates at Startup

Either by nature, or by training, engineers are conservative. That is generally a good thing,
but we sometimes go too far. For example, chokes and control valves are often oversized
even for normal operation, and are sometimes far too large to provide adequate control of
low flow rates at initial startup.

Startup planning should include an assessment of the operability of chokes and control
valves.

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Five different conditions exist for flow through restrictions:

1) Liquid flow
2) Non-critical gas flow
3) Critical gas flow
4) Non-critical two-phase flow
5) Critical two-phase flow

Vapor Phase Critical Flow

For a gas stream, critical flow occurs when the velocity through the orifice reaches sonic
velocity. For pressure drop calculations, the important feature of critical flow is that
Figure 1: Pressure Ratio Y = 0.5 decreasing downstream pressure no longer impacts the flow rate. Critical flow in a vapor
occurs when the downstream pressure is about half of the upstream pressure, see Figure
1, (pressure ratio Y = 0.5), or more precisely as determined via equation 3.

It is a common misconception that, in critical flow, changing the pressure or the pressure
drop doesn’t change the flow rate. Changing the upstream pressure always changes the
flow rate as illustrated in Figure 2.

Why Does Critical Flow Occur

Critical flow occurs because pressure waves in a fluid travel at a finite speed (speed of
sound in the fluid). At critical flow, the velocity of the fluid equals the speed of the
pressure wave; hence, downstream pressure information cannot be communicated
upstream through the orifice and the feedback loop is broken.

Two-Phase Critical Flow

Critical flow occurs in two-phase streams (vapor/liquid) as well. The calculations are more
complex as shown below, but the phenomena is analogous to vapor critical flow.

Calculation Methods
Figure 2: Changing the Upstream
With five possible flow conditions we need five calculation methods. We can collapse this
Pressure into three methods by substituting the effective P2 for the downstream pressure in critical
flow conditions. This results in three calculations methods:
1) Liquid flow
2) Gas Flow
3) Two-phase flow

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 Control of Flow Rates at Startup GAT2004-GKP-2010.009
September, 2010
Page 2

Given three equations, we then need to worry about discontinuities between the
calculations methods at the transition points. We use the Sachdeva (1986, SPE 15657-MS)
correlation for two-phase calculations. Though not currently state-of-the-art, Sachdeva is

q= .525 Cd d

accurate enough for most purposes. And it has the very useful feature of being accurate in
2 ∆P
(Equation 1) all flow regimes (liquid, two-phase non-critical, two-phase critical, gas and gas critical)
ρl
with no discontinuities at either regime or critical flow boundaries.

M= .525 Y d ���� ∆P ρg

2
(Equation 2) Liquid flow through Chokes

k⁄k-1 Liquid flow through chokes is described effectively via equation 1 from Crane (1988).
yc =

2
(Equation 3)
k+1
Non-Critical Vapor Flow through Chokes

 
a
b Vl (1-yc )
 
a+ Non-critical vapor flow is described by equation 2, also from Crane (1988).
yc =  2
Vg1

a+ n +bn Vl + n b Vl  
(Equation 5)
Vg2 2 Vg2 
Vapor Phase Critical Flow
2
For critical flow use equation 2, but substitute the critical pressure drop for ∆P. Critical flow
k 1-x1
Where: a= b= in a vapor occurs when the downstream pressure is about half of the upstream pressure
k-1 x1 (pressure ratio yc = 0.5), or more precisely as determined via equation 3.

Variables List Two-phase Flow through Chokes

A area, ft2
Cd orifice coefficient
Cv valve coefficient, gal/min-psi 0.5 Sachdeva solved the mass, momentum and energy balance equations assuming no-slip
cp gas heat capacity – constant P, btu/lb-oF
cv gas heat capacity – constant volume, btu/lb-oF
flow and no mass transfer between phases at the orifice to develop this equation for two-
d diameter, inches phase flow through a choke:

1-x1 (1-y)
FWHP Flowing Wellhead Pressure, psig

M= A Cd 2 gc 144 P1 ρ2m2   + x1

Vg1 - yVg2 
0.5
gc gravity force factor, 32.2 ft-lbm/lbf-sec 2 k
k cp / cv (Equation 4)
M mass flow rate, lb/sec ρl k-1
n polytropic exponent for gas
∆P pressure drop, psi
P pressure, psia

Vg2= Vg1 y-1/k = x1 Vg1 y-1/k+ (1-x1 )Vl

P1 pressure upstream of choke, psia 1
P2 pressure at choke throat, psia Where: ρm2
q flow rate, gal/min
ρ density, lb/ft3
ρl liquid density, lb/ft3 Note that the equations for Vg2 and ρm2 follow from the assumption of no-slip flow and no
ρg1 gas density upstream of choke, lb/ft3
ρg2 gas density at choke throat, lb/ft3
mass transfer between phases at the orifice. Further note that Vg2 must be calculated
ρm1 mixture density upstream of choke, lb/ft3 exactly as shown above, though the astute reader may detect an apparent error.
ρm2 mixture density at choke throat, lb/ft3
Vg1 gas specific volume gas upstream of choke, ft3/lb
Vg2 gas specific volume gas at choke throat, ft3/lb Two-phase Critical Flow
Vl liquid specific volume, ft3/lb
x1 gas mass fraction
Y gas expansion coefficient The Sachdeva correlation above applies to non-critical flow. Sachdeva provides equation 5
y pressure ratio, P2/P1
yc critical pressure ratio, P2/P1 for determining the critical flow boundary.

Critical flow exists when y > yc. When critical flow exists, yc is used in equation 3 rather
than y.

Upstream engineering for offshore Correlation of CV to d

oil and gas specializing in:
Information on chokes is usually given in the form of CV tables or CV plots. The Sachdeva
• Chemical Systems Engineering correlation uses orifice area. A method of converting CV to d or A is required.
• Materials & Corrosion
CV is defined by the Comparing this to the Crane
• Flow Assurance equation:
For water at standard conditions:
equation for liquid flow:
• Waterflood
q= 0.525 Cd d

2 ∆P
• Commissioning & Startup
q=Cv
q=Cv
ρ q=7.9 Cv

∆P ∆P ∆P ρl
SG l ρl
62.4 Yielding:
2
0.525 Cd d =7.9 Cv

Using a Cd of 0.85 as suggested by Sachdeva for two-phase flow: 2

d =0.04 Cv

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16360 Park Ten Place Ste 206 | Houston | TX | 77084 | T 281-398-5781 | F 281-398-0935 | info@gatellc.com
© 2009 GATE, LLC