How To Size A Gas Control Valve

November 16, 2009 No comments yet

Sizing a control valve means selecting a valve with the correct size orifice to allow good control of flow rate within a required range.

There are other important factors to consider when selecting a control valve, such as valve type and valve characteristic but this article will concentrate on valve sizing.

The procedure explained in this article applies to gas and vapour control valves including steam control valves.  The method for sizing gas control valves is based on the method for sizing liquid control valves.  More information on sizing a liquid control valve can be found here: “How To Size A Liquid Control Valve”.

Sizing a control valve for a particular duty is governed by the required flow rate the valve must pass and the pressure drop that can be allowed across the valve.

Control Valve

Steps To Accurately Size A Gas Control Valve

  1. Specify the required design flow rate
  2. Specify the allowable pressure drop across the valve
  3. Choose a valve type and body size from the manufacturers’ tables
  4. Calculate the first estimate of the piping geometry factor and pressure drop ratio factor
  5. Determine if the flow through the valve will be sub-critical or critical
  6. Calculate the effective pressure drop ratio across the valve
  7. Calculate the expansion factor
  8. Calculate the first estimate of the required valve Cv
  9. Check that the calculated Cv is less than the actual Cv of the selected valve (re-select suitable valve from manufacturers’ tables if required)
  10. Check that valve control range is OK
  11. If the Cv and control range are suitable the valve is correctly sized.  If not re-select another valve and repeat the sizing procedure from Step 3

Sizing a control valve accurately is an iterative process requiring manufacturer’s information and knowledge of the piping system in which the valve is to be installed.

The procedure is a little bit more complicated than sizing a liquid control valve but is certainly not difficult.  For preliminary estimates of control valve size it is usually OK to assume that the piping geometry factor is 1.

Calculate Control Valve Cv

Gas control valves are sized using a modified version of the liquid control valve equation.  As for liquid control valves, the valve orifice size as given as a “valve flow coefficient” or Cv.

The Cv is defined as the flow rate of water in US gallons per minute that can pass through a valve with a pressure drop of 1 psi at a temperature of 60F.

The equation for calculating the Cv for a gas control valve using metric units is:

Gas Control Valve Equation

Effective Pressure Drop

The effective pressure drop across a gas control valve depends on the properties of the gas flowing through the valve and the valve design.

If the pressure downstream of the valve is lower than a critical value, the flow through the valve will be choked.  Choked flow is also known as critical flow.

The flow is sub-critical if:

GasCritFlowTestEqn

For sub-critical flow:

GasSubCritFlowEqn

For critical flow:

GasCritFlowEqn

Where:

Ratio of Specific Heats Equation

Pressure Drop Ratio Factor, XT

The pressure drop ratio factor is the pressure drop ratio required to produce critical flow through the valve when Fk is equal to 1.

The valve pressure drop ratio is measured experimentally and is tabulated in valve manufacturers catalogues.

If the valve has fittings connected directly upstream and/or downstream, the pressure drop ratio factor must be modified to account for expansion and contraction of the fluid through the fittings.

The modified pressure drop ratio factor, XTP is calculated using:

Modified Pressure Drop Ratio Factor Equation

Where:

Inlet Fittings Head Loss Coefficient Equation

For valves installed with a reducer installed upstream, the inlet fittings head loss coefficient becomes:

Inlet Reducer Head Loss Coefficient

Expansion Factor, Y

The expansion factor accounts for the expansion of gas flowing through the valve as the pressure reduces from inlet to outlet.  The expansion factor is the ratio of flow coefficients for a gas to that for a liquid at the same Reynolds number.

The expansion factor must be less than or equal to a value of 0.667.  The following equation defines the expansion factor:

Expansion Factor Equation

Piping Geometry Factor, Fp

The piping geometry factor is an allowance for the pressure drop associated with fittings that may be connected directly upstream and/or downstream of the valve.

 If no fittings are connected to the valve, the piping geometry factor is 1.

The piping geometry factor is often listed in valve manufacturers catalogues.  Alternatively, it can be calculated using:

Piping Geometry Factor Equation

Most commonly, the fittings connected to a control valve are upstream and downstream reducers.  In this case the sum of the fittings factors for the reducers is:

Fitting Factor Equation

Note:

Determining the control valve Cv becomes an iterative process when the piping geometry factor doesn’t equal 1.

  1. Estimate the required Cv
  2. Select an appropriate valve from the manufacturers’ tables
  3. Calculate Fp and XTP using the actual Cv of the selected valve
  4. Re-calculate the required Cv using the values of Fp and XTP determined in Step 3
  5. Check that the re-calculated Cv is less than the actual Cv of the selected valve
  6. If the re-calculated Cv is less than the actual Cv, the selected valve is adequately sized
  7. If the re-calculated Cv is greater than the actual Cv of the selected valve, select another valve with a larger Cv and return to Step 3

Control Valve Sizing Rules Of Thumb

There are many rules of thumb designed to help with control valve sizing.  The following guidance is taken from “Rules of Thumb For Chemical Engineers” by Carl Brannan and the author’s personal notes.

  1. Set the design flow as the greater of:
    • 1.3 x normal flow rate
    • 1.1 x maximum required flow rate
  2. Set the control pressure drop to equal 50% – 60% of the frictional pressure loss of the piping system
  3. Limit the maximum flow rate : minimum flow rate turndown to 5:1 for linear trim valves and 10:1 for equal percentage trim valves
  4. The valve should be able to control the required range of flow rates between 10% and 80% of valve opening
  5. Ideally select a valve that has a body size 1 pipe size smaller than the pipe in which it is to be installed (e.g. select a 3” valve for a 4” pipe)
  6. Never select a valve larger than the pipe in which it is to be installed

How To Size A Gas Control Valve Example

The following example has been adapted from the Emerson Control Valve Handbook.

We need to size a valve in steam duty.  The required information is given below:

  • Design flow rate = 125000 lb/hr = 56689 kg/hr
  • Upstream pressure = 500 psig = 35.50 bara
  • Downstream pressure = 250 psig = 18.26 bara
  • Pressure drop across valve = 250 psi = 17.24 bar
  • Upstream steam temperature = 500F
  • Density of steam at upstream conditions = 1.0434 lb/ft3 = 16.71 kg/m3
  • Steam ratio of specific heat capacities = 1.28
  • Pipe size = 6 inch

Calculation

Following the steps given at the start of this article:

  1. Design flow rate = 56689 kg/hr
  2. Allowable pressure drop across the valve = 17.24 bar
  3. We will choose an Emerson 4” ED globe valve with linear cage as the preliminary selection.  From the valve table we can see that the actual Cv is 236 and XTP is 0.688
  4. ED Valve Table

  5. We will assume that 6” x 4” reducers will be used to install the selected 4” valve in the 6” pipe.  In this case the piping geometry factor is:
    ΣK = 1.5 (1 – (42 / 62))2 = 0.463FP = [1 + (0.463 / 890)(236 / 42)2]-0.5 = 0.95
    The pressure drop ratio factor, XT = 0.688
    The inlet fittings head loss coefficient is:
    Ki = 0.5 (1 – (42 / 62))2 + 1 – (4 / 6)4 = 0.957
    So the modified pressure drop ratio factor is:
    XTP = 0.688 / 0.952[1 + 0.688 x 0.957 / 1000 (236 / 42)2]-1 = 0.667
  6. Check if flow through the valve is sub-critical or critical:
    Fk = 1.28 / 1.4 = 0.91Fk XTP = 0.91 x 0.667 = 0.607(P1 – P2 ) / P1 = (35.50 – 18.26) / 35.50 = 0.486
    Therefore: (P1 – P2 ) / P1 < Fk XTP so the flow is sub-critical
  7. The effective pressure drop ratio across the valve is (P1 – P2 ) / P1 because the flow is sub-critical:
    Xeff = 0.486
  8. Calculate the expansion factor:
    Y = 1 – 0.486 / (3 x 0.91 x 0.667) = 0.733
  9. Calculate the first estimate of Cv:
    Cv = 56689 / (27.3 x 0.95 x 0.733 (0.486 x 35.50 x 16.71)0.5) = 175.6
  10. The calculated required Cv of 175.6 is less than the actual Cv of the selected valve of 236 so the valve is large enough
  11. Check if the control valve range is OK:
    From the valve table, the selected valve will be a just less 70% open to give the required Cv of 175.6.  This is within the acceptable control range of 10% to 80% of valve opening.
  12. The selected 4” linear cage valve is correctly sized for the specified duty

Result

The selected valve is an Emerson 4” ED globe valve with linear trim and a maximum Cv of 236.

Blackmonk Engineering Calculator Result

The output from the Blackmonk Engineering Liquid Control Valve Calculator is attached below for comparison.  As you can see the calculated Cv is virtually identical to the hand calculation (175.4 compared to 175.6).

Gas Control Valve Calculation

How To Size A Liquid Control Valve

November 13, 2009 No comments yet

Sizing a control valve means selecting a valve with the correct size orifice to allow good control of flow rate within a required range.

There are other important factors to consider when selecting a control valve, such as valve type and valve characteristic but this article will concentrate on valve sizing.

Sizing a control valve for a particular duty is governed by the required flow rate the valve must pass and the pressure drop that can be allowed across the valve.

ControlValve

Steps To Accurately Size A Liquid Control Valve

  1. Specify the required design flow rate
  2. Specify the allowable pressure drop across the valve
  3. Choose a valve type and body size from the manufacturers’ tables
  4. Calculate the first estimate of the piping geometry factor
  5. Determine if the flow through the valve will be sub-critical or critical. That is, will some of the liquid vaporise causing flashing or cavitation?
  6. Calculate the effective pressure drop across the valve
  7. Calculate the first estimate of the required valve Cv
  8. Check that the calculated Cv is less than the actual Cv of the selected valve (re-select suitable valve from manufacturers’ tables if required)
  9. Check that valve control range is OK
  10. If the Cv and control range are suitable the valve is correctly sized.  If not re-select another valve and repeat the sizing procedure from Step 3

Sizing a control valve accurately is an iterative process requiring manufacturer’s information and knowledge of the piping system in which the valve is to be installed.

However, the procedure is fairly simple and straightforward.  It becomes even easier if it is known that the liquid will not flash or cavitate as it flows through the valve.  For preliminary estimates of control valve size it is usually OK to assume that the piping geometry factor is 1.

Calculate Control Valve Cv

Traditionally, control valves are sized using a special form of the orifice equation which gives the valve orifice size as a “valve flow coefficient” or Cv.

The Cv is defined as the flow rate of water in US gallons per minute that can pass through a valve with a pressure drop of 1 psi at a temperature of 60F.

The equation for calculating the Cv in US units is:

Control Valve Cv Equation

Effective Pressure Drop

The effective pressure drop across a liquid control valve depends on the nature of the liquid flowing through the valve and the valve design.

If the pressures upstream, inside and downstream of the control valve are greater than the vapour pressure of the liquid at the flowing temperature, the effective pressure drop is equal to the actual pressure difference between the upstream and downstream sides of the valve.  In this case, the flow is said to be “sub-critical” and the fluid remains in the liquid phase throughout the system.

In the vast majority of cases it is preferable to maintain sub-critical flow as it reduces valve damage, improves controllability and requires simpler, less expensive valve designs.

However, if the liquid vapour pressure exceeds the system pressure inside or downstream of the valve, vaporisation will occur and the flow will become “critical”.  In this case, the effective pressure drop across the valve will be limited by the valve design and the physical properties of the liquid.  When the flow is “critical”, the pressure downstream of the valve does not affect the flow rate.

The flow is sub-critical if:

Sub-Critical Flow Equation

For sub-critical flow:

Sub-Critical Flow Effective Pressure Drop Equation

Where:

Sub-Critical Flow Test Equations

 For critical flow:

Critical Flow Equation

Valve Liquid Pressure Recovery Factor, FL

The valve liquid pressure recovery factor is the ratio of effective pressure drop to the pressure difference between the upstream pressure and the vena contracta pressure.

The valve liquid pressure recovery factor is usually measured experimentally and is tabulated in valve manufacturers’ catalogues.

Liquid Critical Pressure Ratio Factor, FF

The liquid critical pressure ratio factor is a means of estimating the pressure at the vena contracta of the valve under critical flow conditions.

Piping Geometry Factor, Fp

The piping geometry factor is an allowance for the pressure drop associated with fittings that may be connected directly upstream and/or downstream of the valve.

If no fittings are connected to the valve, the piping geometry factor is 1.

The piping geometry factor is often listed in valve manufacturers catalogues.  Alternatively, it can be calculated using:

Piping Geometry Factor Equation

Most commonly, the fittings connected to a control valve are upstream and downstream reducers.  In this case the sum of the fittings factors for the reducers is:

Fitting Factor Equation

Note:

Determining the control valve Cv becomes an iterative process when the piping geometry factor doesn’t equal 1.

  1. Estimate the required Cv
  2. Select an appropriate valve from the manufacturers’ tables
  3. Calculate Fp using the actual Cv of the selected valve
  4. Re-calculate the required Cv using the value of Fp determined in Step 3
  5. Check that the re-calculated Cv is less than the actual Cv of the selected valve
  6. If the re-calculated Cv is less than the actual Cv, the selected valve is adequately sized
  7. If the re-calculated Cv is greater than the actual Cv of the selected valve, select another valve with a larger Cv and return to Step 3 

Control Valve Sizing Rules Of Thumb

There are many rules of thumb designed to help with control valve sizing.  The following guidance is taken from “Rules of Thumb For Chemical Engineers” by Carl Brannan and the author’s personal notes.

  1. Set the design flow as the greater of:
    • 1.3 x normal flow rate
    • 1.1 x maximum required flow rate
  2. Set the control pressure drop to equal 50% – 60% of the frictional pressure loss of the piping system
  3. Limit the maximum flow rate : minimum flow rate turndown to 5:1 for linear trim valves and 10:1 for equal percentage trim valves
  4. The valve should be able to control the required range of flow rates between 10% and 80% of valve opening
  5. Ideally select a valve that has a body size 1 pipe size smaller than the pipe in which it is to be installed (e.g. select a 3” valve for a 4” pipe)
  6. Never select a valve larger than the pipe in which it is to be installed

How To Size A Liquid Control Valve Example

The following example has been adapted from the Emerson Control Valve Handbook.

We need to size a valve in liquid propane duty.  The required information is given below:

  • Design flow rate = 800 US gpm
  • Upstream pressure = 314.7 psia
  • Downstream pressure = 289.7 psia
  • Pressure drop across valve = 25 psi
  • Liquid temperature = 70F
  • Propane specific gravity = 0.5
  • Propane vapour pressure = 124.3 psia
  • Propane critical pressure = 616.3 psia
  • Pipe size = 4 inch

Calculation

Following the steps given at the start of this article:

  1. Design flow rate = 800 US gpm
  2. Allowable pressure drop across the valve = 25 psi
  3. We will choose an Emerson 3” ES globe valve with linear trim as the preliminary selection.  From the valve table we can see that the actual Cv is 135 and FL is 0.89
  4.  Valve Table

  5. We will assume that 4” x 3” reducers will be used to install the selected 3” valve in the 4” pipe.  In this case the piping geometry factor is:
    ΣK = 1.5 (1 – (32 / 42))2 = 0.287
    FP = [1 + (0.287 / 890)(135 / 32)2]-0.5 = 0.96
  6. Check if flow through the valve is sub-critical or critical:
    FF = 0.96 – 0.28 (124.3 / 616.3) = 0.83
    DPmax = (0.89)2 (314.7 – 0.83 x 124.3) = 167.6 psi
    P1 – P2 = 314.7 – 289.7 = 25 psi
    Therefore: P1 – P2 < DPmax so the flow is sub-critical
  7. The effective pressure drop across the valve is P1 – P2 because the flow is sub-critical
    DPeff =25 psi
  8. Calculate the first estimate of Cv:
    Cv = (800 / 0.96)(0.5 / 25)0.5 = 117.9
  9. The calculated required Cv of 117.9 is less than the actual Cv of the selected valve of 135 so the valve is large enough
  10. Check if the control valve range is OK:
    From the valve table, the selected valve will be about 75% open to give the required Cv of 117.9.  This is within the acceptable control range of 10% to 80% of valve opening.
  11. The selected 3” linear trim valve is correctly sized for the specified duty

Result

The selected valve is an Emerson 3” ES globe valve with linear trim and a maximum Cv of 135.

Blackmonk Engineering Calculator Result

The output from the Blackmonk Engineering Liquid Control Valve Calculator is attached below for comparison.  The values used in the example have been converted to metric units.  As you can see the calculated Cv is virtually identical to the hand calculation (118.2 compared to 117.9).

Liquid Control Valve Calculation 

How To Size A Pump

November 11, 2009 8 comments

To size a pump, you must define:

  • The flow rate of liquid the pump is required to deliver
  • The total differential head the pump must generate to deliver the required flow rate

This is the case for all types of pumps: centrifugal or positive displacement.

Other key considerations for pump sizing are the net positive suction head available (NPSHa) and the power required to drive the pump.

Pump System Diagram

 Pump System Diagram

Flow Rate

Usually, the flow rate of liquid a pump needs to deliver is determined by the process in which the pump is installed.  This ultimately is defined by the mass and energy balance of the process.

For instance the required flow rate of a pump feeding oil into a refinery distillation column will be determined by how much product the column is required to produce.  Another example is the flow rate of a cooling water pump circulating water through a heat exchanger is defined by the amount of heat transfer required.

Total Differential Head

The total differential head a pump must generate is determined by the flow rate of liquid being pumped and the system through which the liquid flows.

Essentially, the total differential head is made up of 2 components.  The first is the static head across the pump and the second is the frictional head loss through the suction and discharge piping systems.

Total differential head = static head difference + frictional head losses

Static Head Difference

The static head difference across the pump is the difference in head between the discharge static head and the suction static head.

Static head difference = discharge static head – suction static head

Discharge Static Head

The discharge static head is sum of the gas pressure at the surface of the liquid in the discharge vessel (expressed as head rather than pressure) and the difference in elevation between the outlet of the discharge pipe, and the centre line of the pump.

Discharge static head = Discharge vessel gas pressure head + elevation of discharge pipe outlet – elevation of pump centre line

The discharge pipe outlet may be above the surface of the liquid in the discharge vessel or it may be submerged as shown in these 3 diagrams.

Pump Discharge Above Liquid Surface

Pump Discharge Above Liquid Surface

Submerged Pump Discharge Pipe

Submerged Pump Discharge Pipe

Discharge Pipe Enters The Bottom Of The Vessel

Discharge Pipe Enters The Bottom Of The Vessel

Suction Static Head

The suction static head is sum of the gas pressure at the surface of the liquid in the suction vessel (expressed as head rather than pressure) and the difference in elevation between the surface of the liquid in the suction vessel and the centre line of the pump.

Suction static head = Suction vessel gas pressure head + elevation of suction vessel liquid surface – elevation of pump centre line

Note: gas pressure can be converted to head using:
Gas head = gas pressure ÷ (liquid density x acceleration due to gravity)

Pump Suction

Pump Suction

Frictional Head Losses

The total frictional head losses in a system are comprised of the frictional losses in the suction piping system and the frictional losses in the discharge piping system.

Frictional head losses = frictional losses in suction piping system + frictional losses in discharge piping system

The frictional losses in the suction and discharge piping systems are the sum of the frictional losses due to the liquid flowing through the pipes, fittings and equipment.  The frictional head losses are usually calculated from the Darcy-Weisbach equation using friction factors and fittings factors to calculate the pressure loss in pipes and fittings.

Darcy-Weisbach equation:

Darcy-Weisbach Equation

In order to calculate the frictional head losses you therefore need to know the lengths and diameters of the piping in the system and the number and type of fittings such as bends, valves and other equipment.

Net Positive Suction Head Available

The net positive suction head available (NPSHa) is the difference between the absolute pressure at the pump suction and the vapour pressure of the pumped liquid at the pumping temperature.

It is important because for the pump to operate properly, the pressure at the pump suction must exceed the vapour pressure for the pumped fluid to remain liquid in the pump.  If the vapour pressure exceeds the pressure at the pump suction, vapour bubbles will form in the liquid.  This is known as cavitation and leads to a loss of pump efficiency and can result in significant pump damage.

To ensure that the pump operates correctly the net positive suction head available (NPSHa) must exceed the net positive suction head required (NPSHr) for that particular pump.  The NPSHr is given by the pump manufacturer and is often shown on the pump curve.

Net positive suction head available = absolute pressure head at the pump suction – liquid vapour pressure head

Pump Power

Pumps are usually driven by electric motors, diesel engines or steam turbines.  Determining the power required is essential to sizing the pump driver.

Pump power = flow rate x total differential head x liquid density x acceleration due to gravity ÷ pump efficiency

 How To Size A Pump Example

Let’s look at an example to demonstrate how to size a pump.

30000 kg/hr of water needs to be pumped from one vessel to another through the system shown in the diagram below.  The water is at 20C, has a density of 998 kg/m3 , a vapour pressure of 0.023 bara and a viscosity of 1cP.  We’ll assume that the pump efficiency is 70%.

How To Size A Pump Example

Calculation

The calculation is presented below:

Pump Calculation

Results

Pump flow rate = 30 m3/hr

Pump total differential head = 134.8 m

Net positive suction head available = 22.13 m

Pump power = 15.7 kW


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