MiMiC LIQ_FLOW, VAP_FLOW Modeling Blocks Design Basis

The purpose of this technical note is to explain the design basis for the MiMiC LIQ_FLOW and VAP_FLOW modeling blocks.

MiMiC LIQ_FLOW and VAP_FLOW are powerful process modeling function blocks that calculate the flow rate of a stream. The basis of these blocks is calculations found in the "Control Valve Sourcebook - Power & Severe Service." Fisher Controls International, Inc. Marshalltown, 1990.

Basis for liquid stream flow: Chapter 3 - Valve-Sizing Liquid, Eq. 22, Pg 3-7:

• Q = (Fp * Cv) * sqrt[(P1 - P2)/SpGr] where
• Cv = Valve Sizing Factor = Polynomial(Valve Opening or Percentage of Total Travel, and Valve Size)
• Fp = Piping Correction Factor
• P1, P2 = upstream, downstream pressures
• Fisher Control has a formula to calculate the Fp dependent on installed piping factors.

Basis for vapor stream flow: Chapter 4 - Valve-Sizing Gases and Steam, Eq. 8 or 19, Pg 4-4 or 4-6:

• Q = sqrt[ 520/(SpGr * T) ] * C1 * Cv * Fp P1 * sin{ (3417/C1) sqrt[(P1 - P2)/P1]
• C1 = Cg/Cv = Ratio of the gas sizing coeff and the liquid sizing coeff.
• T = temperature
• (Fp * Cv) determine the valve-pipe combination performance and are translated into a correlation with valve opening and valve size (Fp * Cv) = equivalent to (K * Polynomial(Valve Opening))

These calculations are integrated into two function blocks in MiMiC.

MiMiC Liquid Flow Rate Block (LIQ_FLOW):

• Q = K * Polynomial(Valve_Opening) * sqrt[ (P1 - P2)/SpGr ]
• User specified parameters: K, P1, P2, SpGr, ValveOpening, Polynomial_Coeffs (usually 3rd order)

MiMiC Vapor Flow Rate Block (VAP_FLOW):

• Q = K * (Valve_Opening) * P1 * sin{ sqrt[(P1 - P2)/P1] }
• User Specified Parameters: K, P1, P2, ValveOpening

Tips for using these function blocks:

• The users can translate and correlate relevant factors (kind of valves, engineering units, or whatever) into the K-parameter that could be a constant or variable
• The function is robust and universal and does not depend material, unit measurements, or one valve manufacturer's set of calculations and correction.
• Can be used to calculate the mass flow rate or volumetric flow rate
• User can implement a simple form or sophisticated form of the equation at their discretion
• Vapor flow rate was developed after the development of the liquid flow rate function and is even more universal by shifting the task of specifying the polynomial coefficients to K. Another reason that the vapor flow function has no defined polynomial is that the vapor/gas stream could be applied to the gas flow in a duct, pipe, or open space where no valve is on the path (rather, dampers, blowers, etc could be in place)
• The sophistication level of the model is defined by the users via parameter "K": constant or variables