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.
Five different conditions exist for flow through restrictions:
- Liquid flow
- Non-critical gas flow
- Critical gas flow
- Non-critical two-phase flow
- 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 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.
With five possible flow conditions we need five calculation methods. We can collapse this into three methods by substituting the effective P2 for the downstream pressure in critical flow conditions. This results in three calculations methods:
- Liquid flow
- Gas Flow
- Two-phase flow
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 accurate enough for most purposes. And it has the very useful feature of being accurate in all flow regimes (liquid, two-phase non-critical, two-phase critical, gas and gas critical) with no discontinuities at either regime or critical flow boundaries.
Liquid flow through Chokes
Liquid flow through chokes is described effectively via equation 1 from Crane (1988).
Non-Critical Vapor Flow through Chokes
Non-critical vapor flow is described by equation 2, also from Crane (1988).
Vapor Phase Critical Flow
For critical flow use equation 2, but substitute the critical pressure drop for ΔP. Critical flow in a vapor occurs when the downstream pressure is about half of the upstream pressure (pressure ratio yc = 0.5), or more precisely as determined via equation 3.
Two-phase Flow through Chokes
Sachdeva solved the mass, momentum and energy balance equations assuming no-slip flow and no mass transfer between phases at the orifice to develop this equation for two-phase flow through a choke:
Note that the equations for Vg2 and ρm2 follow from the assumption of no-slip flow and no mass transfer between phases at the orifice. Further note that Vg2 must be calculated exactly as shown above, though the astute reader may detect an apparent error.
Two-phase Critical Flow
The Sachdeva correlation above applies to non-critical flow. Sachdeva provides equation 5 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.
Correlation of CV to d
Information on chokes is usually given in the form of CV tables or CV plots. The Sachdeva correlation uses orifice area. A method of converting CV to d or A is required.