Selecting the diameter of a valve opening to optimize the mass flow of liquid acrylonitrile

An engineer working for a chemical manufacturer is asked by his manager to find a way to optimize the flow rate of acrylonitrile, a key ingredient used in the manufacture of certain types of synthetic rubbers and fibers, from a tank. According to the process specification, acrylonitrile must flow from a tank at a rate of no more than 0.40 kg/s. 

Current Conditions: Liquid acrylonitrile in the tank has a temperature of 120˚F. The height of liquid in the tank is kept at 3 m, the tank pressure above the liquid is 0.2 barg, and it is safe to assume that there is normal pressure outside the tank.

The engineer has to select the diameter of the valve opening in the tank discharging acrylonitrile to ensure the specified flow rate. For the initial calculations, he assumes the diameter to be 15 mm.

Calculating the mass flow of liquid acrylonitrile

The engineer wants to find an equation to calculate the mass flow rate through an opening (hole) of varied diameter.  He searches on Knovel for ‘liquid discharge through a hole.’ Click on the search image below to see the results.

He clicks on the title Guidelines for Chemical Process Quantitative Risk Analysis (2nd Edition) and found the answer in example 2.1.1 which shows a chart of discharge rate models. He clicks on the highlighted chart to open an interactive Excel spreadsheet containing the required calculations. The only variable the engineer seems to be missing is the density of acrylonitrile at 120˚F.

To find it, the engineer then searches Knovel for ‘density acrylonitrile’ and determines that Yaws' Handbook of Thermodynamic and Physical Properties of Chemical Compounds would be useful. He uses the interactive Equation Plotter to find the density of acrylonitrile as a function of temperature. At 120˚F, it is 773.4 kg/m3.

Inserting this value of density into the Excel spreadsheet, the engineer finds that the mass flow of acrylonitrile under the given conditions is 0.91 kg/s.

Diameter of relief needs to be smaller

Since the mass flow of acrylonitrile is higher than required, the engineer has to reduce the diameter of the valve opening.  By altering the ‘hole diameter’ parameter in the interactive spreadsheet, the engineer determines that to ensure the flow rate of 0.40 kg/s, the tank should have an opening of 10 mm. See the final excel worksheet below.

Knovel helped the engineer save valuable time by providing easy access to all the reliable technical information needed to solve the problem in one place. He was able to solve the problem from start to finish by finding both the means of calculating the mass flow rate of acrylonitrile and the density of liquid acrylonitrile at a given temperature.

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