UNIVERSIT À DEGLI STUDI DI SALERNO

1. Bachelor Degree in Chemical Engineering Course: Process Instrumentation and Control (Strumentazione e ControllodeiProcessiChimici) CONTROL VALVE SIZING: SIMPLIFIED PROCEDURES Rev. 3.85 – April 3, 2019 UNIVERSITÀ DEGLI STUDI DI SALERNO

2. THE CONTROL VALVE SIZING PROBLEM Calculations or choices to do: • Valve type (globe, butterfly, modulating ball, etc.) • Capacity (based on the concept of CV introduced in the 40’s) • DN • Inherent characteristic, if possible • Construction material (depending upon temperature, pressure, corrosive and erosive properties of the fluid) • Body shape, plug and bonnet • Type and size of the actuator, servo-positioning device • Safety items (e.g., action type in case of failure), reliability, maintenance • Noiseevaluation Process Instrumentation and Control - Prof. M. Miccio

3. CONTROL VALVE SIZINGDesign case Taking suitable datafrom the “manufacturer table” • KNOWN DATA: • NOMINAL PIPE SIZE (NPS, DN) OF THE PIPING • FLUID (LIQUID IN OUR CASE) • INLET TEMPERATURE T1 • ΔP = (P1 - P2) • FLOW • mass flow rate, volume flow rate • design at nominal / max / min flow rate • MANUFACTURER TABLE • TO BE CHOSEN: • VALVE TYPE (GLOBE / BALL / BUTTERFLY) • TYPE OF INHERENT CHARACTERISTIC, if possible • CONSTRUCTION MATERIAL • TO BE DETERMINED: • NPS of the VALVE • Cvn of the VALVE • TO BE CHECKED: • CAVITATION (calculation of ΔPcorΔPMAX) Process Instrumentation and Control - Prof. M. Miccio

4. MANUFACTURER TABLEAn example for an angle globe valve Cvn Cvn When FL is not present in MANUFACTURER TABLE: AnnexD_ISA_7501-1985 Process Instrumentation and Control - Prof. M. Miccio

5. VALVE SIZING PROBLEM2 different design cases • the valve is a stand-alone unit • the valve is inserted in an equipment process scheme Process Instrumentation and Control - Prof. M. Miccio

6. DATA: liquid substance, ρ, Pc, Tc, Gf, FF, Pv • Operating Conditions: P1, P2, T1, flow rate • Piping: NPS • Valve: Kc, FL, manufacturer tables, • intrinsic characteristic. SIMPLIFIED SIZING PROCEDURE according to Magnani, Ferretti e Rocco (2007) A valve is to be chosen with a DN lower than tha piping diameter NPS by one size (if possible) Calculate the Flow coefficient: Once NPS and Cv are known, a valve is to be chosen from the manufacturer table such as: 70% rule Check cavitation according to IEC 60534 norm A higher FL valve has to be choosen (low pressure recovery valves) False CHOKED FLOW according to IEC 60534 norm True NORMAL FLOW (possibly) False END OF SIZING True Process Instrumentation and Control - Prof. M. Miccio

7. CONTROL VALVE SIZINGDesign case ROTARY VALVES The simplified procedure presented in the flow chart is valid for globe valves. In fact the rotary valves are not characterized by the relative travel “h”, but by the opening angle θ. For rotary valves, the simplified sizing procedure is referred to an angle θ*, which corresponds the 70% max opening angle (90°): Strictly θ* = (70/100)90° = 63° • θ* = 65° or 70° In practice • Remarks • A rotary valve usually has one and only one inherent characteristic. • Butterfly valves have often an inherent characteristic with an inflection point (such as V-port). • Modulating ball valves have often an equal percentage inherent characteristic. Process Instrumentation and Control - Prof. M. Miccio

8. CONTROL VALVE SIZINGDesign case The manufacturer table: several cases are possible a) For each NPS, the MANUFACTURER TABLE reports Cvn as well as Cv values for different values of h (θ)  Inherent characteristic known “point by point” in a tabular shape b) The MANUFACTURER TABLE only shows the value of Cvn for each NPS, furthermore the manufacturer gives a diagram of ϕ or Cv as a function of h (θ).  For the inherent characteristic use the manufacturer’sdiagram c) The MANUFACTURER TABLE only shows the Cvn value for each NPS  Use formulas for the inherent characteristic Process Instrumentation and Control - Prof. M. Miccio

9. CONTROL VALVE SIZING PROBLEMVerify case • KNOWN DATA: • VALVE TYPE • NOMINAL PIPE SIZE (NPS, DN) OF THE VALVE • NOMINAL FLOW COEFFICIENT Cvn • INHERENT CHARACTERISTIC • FLUID (LIQUID IN OUR CASE) • TEMPERATURE T1 • ΔP = (P1 - P2) • TO BE DETERMINED: • NOMINAL FLOW RATE (h = 1 OR θ = 90°) • FLOW RATE at a given value of h OR θ • TO BE CHECKED: • CAVITATION (calcolo di ΔPc or ΔPMAX) Process Instrumentation and Control - Prof. M. Miccio

10. P3 INSTALLED CHARACTERISTIC • The circuit is formed by a control valve and an user (e.g. serpentine), which, for example, could represent an heat exchanger, in which all the pressure drop is concentrated. • A pump, not indicated, supplies the pressure PM – PS, assumed constant for simplicity. • We can evaluate the role of the pressure drop across the valve comparing it with the total pressure drop of the circuit: • it should be high in order to improve the control of the flowrate; • on the other hand. It should be low in order to reduce costs of pump energy. • The aim is to find a good technical compromise solution between these two opposing evidences. • HYPOTHESES: • ΔP0 = PM - PS = constant • Negligible pressure drop along the pipe: • PM = P1 • PS = P3 • User pressure drop as a square function of the velocity and therefore, for incompressible fluid, is a square function of the mass flowrate : • No accumulation in the circuit ΔPv= P1-P2 ΔP0=ΔPu+ ΔPv ΔPu=P2(w(h)) – P3 = w2(h) Process Instrumentation and Control - Prof. M. Miccio

11. INSTALLED CHARACTERISTIC P3 DEFINITIONS: INSTALLED CHARACTERISTIC: It is the relationship between the flow rate and the (linear or rotary) valve opening when the valve is inserted in the circuit and influenced by process condition. PRESSURE DROP across the valve: NOMINAL (or RATED) PRESSURE DROP across the valve : VALVE AUTHORITY: It is the ratio between the nominal pressure drop (ΔPn) across the valve and the total pressure drop of the circuit (ΔP0). Process Instrumentation and Control - Prof. M. Miccio

12. INSTALLED CHARACTERISTIC Process Instrumentation and Control - Prof. M. Miccio

13. INSTALLED CHARACTERISTIC The installed characteristic will be an implicit function: With these hypotheses, the installed characteristic equation can be evaluated assuming V as parameter. It is important to evidence the trend of the installed characteristic when changing V for a valve having linear or equal percentage inherent characteristic. Process Instrumentation and Control - Prof. M. Miccio

14. INSTALLED CHARACTERISTIC For: where and Replacing in previous equation, we have: see ch.5 in Magnani, Ferretti e Rocco (2007) Process Instrumentation and Control - Prof. M. Miccio

15. INSTALLED CHARACTERISTIC we obtain: Multiplying and dividing numerator and denominator for replacing: → Process Instrumentation and Control - Prof. M. Miccio

16. INSTALLED CHARACTERISTIC After using the AUTORITHYdefinition : Dividing for [Ф(h)]2 and multiplying for V in the square root, we have a non-dimensional final eq.: • The installed characteristic equation simplifies for the particular cases: • V = 1 • (h) = 1 see ch.5 in Magnani, Ferretti e Rocco (2007) Process Instrumentation and Control - Prof. M. Miccio

17. VALVE SIZING PROBLEM2 different design cases P3 • the valve is a stand-alone unit • the valve is inserted in an equipment process scheme Process Instrumentation and Control - Prof. M. Miccio

18. Novel SELECTION criterionof the Control Valve installed characteristic “closer” to linearity The selection of the inherent characteristic (and also of the Cvn) is based on the process requirements of the installed characteristic Cvn is always chosen after the Cv* calculation based on the 70% rule Equal percentageinherent characteristic Linear inherent characteristic • SELECTION CRITERION OF INHERENT CHARACTERISTIC • If V is known a priori, the selection is based on the value of V: • if V > 0.4, the linear inherent characteristic is chosen • if V ≤ 0.25, the equal percentage inherent characteristic is chosen • if 0.25 < V ≤ 0.4, the parabolic or equalpercentage or “modified” linearinherent characteristic is chosen If V is unknown, a parabolic or “modified “ inherent characteristic is chosen Process Instrumentation and Control - Prof. M. Miccio

19. FLOW FACTOR Kv It is not commonly used. It is in SI units. It defines the volume flow rate of water in m3/h at 15°C (5-40°C) which flows across the valve for a known closure member travel producing a pressure drop equal to 1 bar. [=] m3(H2O)/(h(bar)1/2) where: = volume flow rate [m3(H2O)/h] P(Kv) = reference pressure drop (usually 1 bar) P = actual pressure drop [bar] ρ0 = density of water [kg/m3] ρ = actual density of the fluid kg/m3] Cv = 1.16 Kv Kv= 0.865Cv Conversion formulas Process Instrumentation and Control - Prof. M. Miccio

20. CONTROL VALVE SIZING: other cases/problems • Liquid in LAMINAR regime • Compressible fluids (gas and vapors) • Two-phase mixtures (Liquid-gas mixtures) • Pipe size reduction • Noise evaluation Process Instrumentation and Control - Prof. M. Miccio