Key equations for Process Engineers Process Control Process Design

Detailed theory for control valve sizing

Control valve sizing is relatively easy. The available information plays important role and that is why control valve sizing is done differently for different design stage i.e. FEED (or conceptual design) or details design or troubleshooting. Most of the engineers size the valve for only maximum case and somehow overlook minimum case requirement.

Control valve, like any other process unit operations gives best performance in certain range and if it has to operate beyond that, it loose control and leads to process upsets.

Control valve sizing can be represented by simple term Cv. Cv of control valve can be written as

Cv ∝ F√(ρ/∆P)

Where

Cv is Valve flow coefficient

F is mass flowrate

ρ is specific gravity of fluid at inlet conditions

ΔP is pressure drop across the control valve

Above equation is valid for single phase and correction needs to be applied for two or multiple phases. The proportional constant is typical vendor correction factors and varies between 0.85 and 1.0. Some vendors apply various factors as viscosity correction, density correction, etc.

Depending of the stage, one need use engineering judgement to estimate Cv requirement

  • Early stage of FEED (Conceptual design): In this case, mostly upstream and downstream equipment specification preparations are in progress. Full details are not available. Hence, pressure drop across control valve can be assumed as 1-3 bar. For level control valve or pressure reducing valve pressure drop should be difference between upstream and downstream unit operations.
  • Later stage of FEED and Detail design, usually all the upstream as well as downstream equipment details are known and upstream and downstream piping details are also available.

When sizing the control valve few things needs to be known such as flow variations, fluid variations, temperature variations, pressure drop variations.

Typical schematic of any control valve system is as follows

screenshot-2016-10-15-13-25-09

We should know following

Psou= Source pressure and elevations of liquid level

Inlet pipe (including lengths, material-roughness), fittings details (elbows, valves, tees, etc), elevations details (from source till inlet of control valves), etc.

Outlet pipe (including lengths, material-roughness), fittings details (elbows, valves, tees, etc), elevations details (from control valves to the end equipment), etc.

Pend = End or destination pressure

With these details, we can estimate the

  • Pressure at the inlet of control valve, Pin i.e. difference between Psou and pressure drop in inlet pipe (including elevation). The pressure drop is termed as ΔPin
  • Pressure at the outlet of control valve, Pout i.e. addition of Pend and pressure drop in outlet pipe (including elevation). The pressure drop is termed as ΔPout.

Above detail can be written as,

Psou-Pend = ΔPin+ΔPcv+ΔPout

Above equation is valid for system without any pressure increase (like with pump or compressor). The same can be written as

ΔPcv = Psou+ Pincr-Pend - ΔPin - ΔPout

Where, Pincr is the pressure increase in pump or compressor. Please use the performance curve to estimate the pressure increase when characteristic or performance curve is available.

Please note that, pressure drop in piping is function of flowrate.  Discharge pressure (discharge head) in pump or compressor is also function of flowrate. If the flowrate increases, then pressure drop is higher in piping. Essentially it means that, for same source and end pressures, control valve typically get lesser pressure drop with increase in flowrate.

For proper of sizing of control valves all possible flowrate scenario and its pressure drop across (and effectively Cv) to be reviewed and proper characteristics can be selected. Ratio of maximum Cv i.e. Cvmax and minimum Cvmin is determines rangeability of control valve.

Depending upon the requirement the valve characteristic can be selected. Usually control works when the operating Cv (Cvmax and Cvmin) is between 15% and 85% of selected Cv. The range of useful operations changes from operator to operator as well as vendor to vendor. Cv of 15% to 85% of rated Cv is approximate healthy range of control valve operations.

When sizing control valve, vendors or design engineers use Cvmax as 85% and select design Cv, it is termed as Cvrated. If the ratio of Cvmin and Cvrated is more than 15% then selected control valve will work for whole range of control valve. This represents the case linear characteristic of control valve. Other type of characteristic are represented in following diagram -

control valve characteristics

The characteristic of control valve are function of trim. Trim type can be selecting depending on the range of CV required. The characteristics of control valve are as follows

  • Linear – This type of control valves are typically globe valve and this is linear behavior and flow capacity increases linearly with valve opening.
  • Equal percentage - This type of control valves are typically globe valve and flow capacity increases exponentially with valve opening. Equal increments of valve opening produce equal percentage changes in the Control valve. Other natures like parabolic (Low flow capacity) and hyperbolic (High flow capacity) are achieved by modifying trim to suit to the requirements.
  • Quick opening – This type of control valves opens quickly provide larger opening and provides large changes in flow for very small increase in opening. These types of valve are used for on-off service, such as sequential operation in either batch or semi-continuous processes.

Special care needs to be taken where service is two phase, above critical conditions, fluid which can use flashing after pressure drop, or even the downstream is quite close to vapor pressure of liquid. These situations can lead to cavitation inside control valve.

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