Control valve flowrates reporting on PCS (plant Control System)

Introduction and Objective

Control valves are one of the critical pieces of instruments available in any plant for controlling the process parameters. When we browse through control valve datasheet, we get following information, which determine overall control valve sizing. The information is:

1. Flowrates- min, normal and max.
2. Pressure drops (inverse of flowrate)
3. Service physical properties
4. Control valve Cv values (at different flowrate), rated Cv.
5. Control valve % opening
6. Control valve type, its trim and characteristic curve.

All the above information defines a particular control valve in gas or liquid service. The objective of this article is to provide the details of how to provide formula in PCS to calculate the flowrate via any control valve based on its opening, which might be required in an operating plant.

The easy answer to provide any flowrate might be to install a flowmeter. However, due to project schedule, piping modification, cost and lead time involved in procurement of any flowmeter, the option for installing any flowmeter might not be feasible.

This means, we will need a digital input/formula to calculate the flowrate via a control valve, with above information at given control valve opening and differential pressure. This formula needs to be fed into PCS logic and the calculated flowrate is required to be displayed along with control valve %age opening.

Case History

This requirement of calculating the flowrate for a gas service control valve started in one my recent project, where installation of flowmeter was not feasible.

The challenge was to input the calculation formula in the PCS logic without much operator intervention and to minimize the error.

Once I start describing the formula and the step-by-step approach, we need to understand what are the inputs required?

The control valve is installed as PCV to flare, while controlling any high pressure from the inlet feed. The pressure sensor is installed on the feed line. Refer to below figure. 

The inputs required for the formula and PCS logic to take the value is shown below:

1.     Control valve upstream pressure (P1). The input to this pressure was taken from the PIT upstream of control valve.

2.     Control Valve downstream pressure. The input is to be taken from PIT installed at flare KO pump suction line. Please remember, the PCV downstream is connected to flare and the mostly the gas release will be in equilibrium with flare KO drum pressure.

3.     Valve rated Cv. This was input from Control valve datasheet

4.     Gas physical properties like Molecular weight, temperature, Z, Cp/Cv. The values are considered constant considering there is no change in gas composition.

5.     Valve Fp (piping geometry factor) value. This value is provided by vendor on the datasheet.

6.     FL (liquid pressure recovery factor of a valve without attached fittings, dimensionless or Xc (pressure drop ratio for the subject valve at critical flow, with Fk = 1.0, dimensionless). The value used is 0.999.

7.     N8= 19.3 (which is part of valve sizing calculation as per GPSA version 14, Fig 4-31).

8.     The Cv of control valve with respect to control valve opening. This value was tabulated based on Characteristic curve provided by vendor. The opening with Cv values is tabulated as below:

Note- Though the opening shown in the above table is not in round numbers, but for ease of calculation in PCS, the rounded values as 10%, 20% till 100% to be considered.

The Control valve sizing equation used is from GPSA, version 14, as shown below:

The Value of N8 is inferred from above Figure. The above formula for control valve sizing will work, only if the value of X and Y are calculated. X is the ratio of pressure drop to absolute inlet pressure, as shown in the figure below. Y is also calculated as per below equation. In the ISA sizing procedure critical flow limitations are addressed by calculating Y, the expansion factor, for utilization within the actual sizing equation.

Once all inputs are provided, the flowrates can be calculated as per control valve sizing calculation by PCS calculation block. The calculated value gas flowrate will be in lb/hr, which was subsequently converted in MMSCD flowrate.

The example of typical calculation for the referred valve is shown below:

Control Valve flowrate calculation for given differential pressure is shown in below table.

The calculated values were also compared with control valve datasheet for correctness of formula. The differential pressure is were adjusted to match the datasheet exactly. The error in the calculation is +/-3-4%. Any error of 5% is acceptable for such calculation. 

Control Valve datasheet (typical)

Conclusion

The gas flowrate calculation from control valve opening can be done in case of flowmeter installation is not feasible. The calculation will be acceptable, if the error is within the range of +/-5%. The basic required document is the control valve sizing datasheet with valve characteristic curves. Referring to the curve, % age opening of control valve and % Cv value (of the rated Cv) can be easily predicted.  Both % opening and corresponding Cv need to be tabulated which will be filled with the calculated gas flowrate at given valve opening. The gas composition needs to be assumed constant, which means the gas physical properties will remain constant. The above formula can be incorporated into PCS calculation logic to perform 2 levels of calculation. The 1st level of calculation will calculate the “X” (pressure ratio) value and Fk, (which are relatively easy and straight forward).  These calculated X and Fk values will be used to calculate the “Y” (expansion factor) value with the given Xc value. The Xc/Fp values will be vendor inputs from control valve datasheet. 

Abbreviations

Cv = valve flow coefficient

Fk = ratio of specific heats factor, dimensionless

Fp = piping geometry factor, dimensionless

k = ratio of specific heats, dimensionless

M = molecular weight, atomic mass units

P1 = upstream absolute static pressure, measured two nominal pipe diameters upstream of valve fitting assembly, psia

P2 = downstream absolute static pressure, measured six nominal pipe diameters downstream of valve fitting assembly, psia

ΔP = pressure differential, P1 – P2

T = absolute temperature of gas at inlet, °R

X = ratio of pressure drop to absolute inlet pressure (ΔP/P1), dimensionless

Xc = pressure drop ratio for the subject valve at critical flow, with Fk = 1.0, dimensionless

Y = expansion factor, ratio of flow coefficient for a gas to that for an incompressible fluid at the same Reynolds number, dimensionless

Z = compressibility factor, dimensionless