Section 4.5.2: Modelling a Vaporiser

The following is a model of a single component vaporiser or boiler, developed using the approach described in section 4.2.

Step 1: Draw a Diagram

The diagram below shows a vaporiser:

Some things to note:

The boiler contains a time varying amount of material M kmol.
Its total internal energy is U kJ.
The inflow rate of liquid is specified as F kmol/s.
The vapour outflow rate is through a valve with an idealised linear pressure-flow relationship and valve constant k_v.

Step 2: Material and Energy Balance Equations

Mass balance equation:

Energy balance equation:

Step 3: Rate Equation

The flowrate leaving the vaporiser is determined by the following rate equation:

Step 4: Equations of State

The pressure in the vessel can be determined from the vapour pressure:

The temperature can be determined approximately from the energy content:

The last equation of state gives us the enthalpy of the outlet vapour stream:

Step 5: Count the Equations and Unknowns

From the above we see that we have 6 equations.

There are obviously more than 6 variables mentioned in the above analysis so now we have to think which ones have constant values which can be fixed:

Tb = 1 atm boiling point of the material
Cp = molar heat capacity
= Molar latent heat
kv = outlet vapour valve constant
F = flowrate in to boiler
Tf = temperature
Q = heat input to boiler

This leaves the following 6 variables as unknowns:

M, U, V, hv, P, T

Hence we have 6 unknowns and 6 equations and so the system can be solved.

Write the Model

The final stage before creating the spreadsheet is to rewrite the above equations in our modelling language. This gives the following:


! Balance equations
 .M = F - V       ; ! mass balance
 .U = F*Tf*Cp - V*hv + Q ; ! heat balance

! rate equation
 V = kv*(P-1.0)  ;  ! outflow vapour rate

! equations of state
 P = @exp(10*(1-Tb/T))  ; ! vapour pressure gives pressure in vessel
 T = U/M/Cp ; ! temperature, approximately, from energy content
 hv = Cp*T+lambda ! enthalpy of outlet vapour stream

You can copy the complete model file from here.

Click here to go to the model generator.

Next - Section 4.5.3: Modelling the Vaporiser with a Control System
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Last Modified 4/9/00