Estimation of orifice size for dosing of liquids

Good morning everyone....!!!

Hope everyone is safe and healthy, Today i wish to post about estimation of orifice sizing for dosing of liquids. Usually, this dosing of liquids is a pretty common scenario, as multiple operations require dosing of liquids like for semi batch reactions or any kind of anti-solvent isolation and to control the flowrate during these scenario's we'll prefer an orifice.

Though we can prefer certain kind of dosing pumps, but our first preference is always an orifice, because we feel it as "Less Lugguage More Comfort". However, at some junction in our mind we know that flow through orifice is not constant, but we'll still prefer an orifiice since it is being encouraged by management.

And coming to few drawbacks of using the orifice plates is that, the flow will reduce with time i.e., as the liquid level at source is reducing then the flow through orifice will also reduce and the second thing is making a hole of exact diameter is going to be difficult for the orificeplates.

Anyhow, lets get into the topic to check how to estimate the diameter for orifice...?

Before going into calculation part, lets take some time to get the basics and terms right.

What is Cd ?

Cd is referred as coefficient of discharge, it is the ratio of actual discharge to ideal discharge.

What is pressure drop ?

Pressure drop is the differnece between pressures i.e., difference between the pressure accumulated in the overhead space of the receiver from which the liquid is added and the pressure accumulated in the receiving end i.e., usually a reactor.

Lets start the calculation part through an illustration.

Case study:

For better understanding, i'll take the case of a semi batch reaction where there is an energy liberation of 500 KJ per Kg of starting material and there reaction is being executed in a 5 KL SS reactor (13.1 m2 heat transfer area) with an occupancy of 60% and the addition temperature is 20℃  , utility used to control the exothermicity is chilled water at ~5℃.

Soln.

In this case we need to perform controlled addition, hence proposed to use an orifice plate. The diameter to be estimated.

Before estimating the diameter, we need to understand the rate of addition.

To calculate the addition time, i'll prefer the energy balance approach.

Many engineers were asking me to demonstrate the energy balance, but the thing is whenever we are playing with heat loads, the energy balance is involved.

Demand from process = 500 x 500 = 250000 KJ = 59751.43 KCal

(Batch size considered is 500 Kg)

Cooling capacity required = 59751.43 / 3024 = 19.76 TR

Supply from jacket = U x A x LMTD

U (OHTC) = 250 KCal/hr.m2.C

A, effective = 13.1 x 0.6 = 7.86 m2

LMTD = ((20 - 7) - (20 - 11))/ln((20 - 7) / (20 - 11)) = 10.87 C

Supply rate = 250 x 7.86 x 10.87 = 21359.55 KCal/hr

Addition rate = 59751.43 / 21359.55 = 2.79 hours.

Now, lets come to the estimation of orifice size.

Lets say the volume of reagent is 400 L, (Density is 1500 Kg/m3)

To avoid the flow variations through orifice due to variations in liquid level, i'll prefer to maintain contsnt pressure in the addition vessel overhead space by closing the vent line and the pressure is 

~0.15 Kg/cm2.g = 14710 Pas.

Rate of addition (Q) = 400 / 2.79 = 143.37 L / hr = 3.98 E-05 m3/sec

Cross sectional area of orifice (A) = Q / (Cd x (2 x ΔP / ρ)^0.5) 

Cd is considered as 0.8 considering the physical symmetry 

= 3.98 E-05 / (0.8 x (2 x 14710 / 1500)^0.5) = 1.12 E-05 m2

Diameter of cross section (d) = (4 x 1.6419 E-05 / 3.141)^0.5 = 3.78E-03 m = 3.78 mm ~ 4 mm

This is how we need to estimate the orifice sizing for performing a liquid addition.

Hope you liked the illustration, for any queries please feel free to write us at pharmacalc823@gmail.com

Comments are most appreciated.....!!!

SuperSurvey

About The Author

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Hi! I am Ajay Kumar Kalva, Currently serving as the CEO of this site, a tech geek by passion, and a chemical process engineer by profession, i'm interested in writing articles regarding technology, hacking and pharma technology.
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