Page 156 - Chemical process engineering design and economics

Process Circuit Analysis 139

until you can calculate the assumed variables to compared with the original
guesses. Westerberg et al. [16] have reviewed the sequential modular method, as
well as other methods, in detail. This particular method has the advantage that the
calculation procedure can be visualized physically. Also, at any particular time
the number of equations that require simultaneous solution is considerably re-
duced.
For this problem we can solve the reduced set of equations simultaneously,
using POLYMATH (Version 4.0) [19] or by some other suitable mathematical
software. Since POLYMATH cannot solve more than 32 simultaneous, nonlinear
equations and explicit algebraic expressions, we must reduce the number of equa-
tions listed in Table 3.5.3.
First, drop all the repeated equations listed in Table 3.5.3. By substituting
Equations 3.5.30 to 3.5.34 into Equations 3.5.19 to 3.5.22, we eliminate the mole
fraction variables in line seven. We do not need Equations 3.5.35 to 3.5.39 for the
solution, so they can be dropped. Table 3.5.2 lists the specified variables, except
for the nitrogen mole fraction, y, which is now unspecified. Table 3.5.7 lists the
3]6
reduced set of equations.
Before solving the Equations in Table 3.5.7, we must select initial guess
values for all the variables. Selecting guess values for variables to start a calcula-
tion is always a problem. For some initial values of the variables, the solution may
not converge. One strategy for obtaining correct initial guesses is to examine each
variable for limits. For example, values of mole fraction must be limited to the
range from zero to one. Temperatures in heat exchangers are limited by the freez-
ing point of the fluids and the stability of the fluids at high temperatures. Obtain-
ing stable initial guess values is an iterative procedure. Table 3.5.8 lists the com-
position and flow rates from the POLYMATH solution.
To complete the process circuit analysis, we now assign pressures and tem-
peratures in lines 1 to 8. The pressures in the various streams given in Table 3.5.8,
are determined after specifying 100 bar at the reactor inlet, an optimum synthesis
pressure [30]. Then, we assign pressure drops, based on experience, of 0.34 bar
across each heat exchanger [8] and 5.0 bar across the converter. The pressure drop
across the gas-liquid phase separator, PS-1, and piping is small compared to the
other system pressure drops. Starting at 100 bar at the converter inlet we can now
specify pressures in lines 1 to 8, except line 6. The pressure at line 6 should be
high enough to overcome the pressure drop across the upper plates of the first col-
umn, 0.1 bar, plus the pressure across the two condensers. Therefore, the total
pressure drop is 0.1 +2 (0.34) or 0.78 bar which is the pressure at line 6. The
copper-oxide catalyst sinters significantly at high temperatures, i.e., there is
growth of the copper-oxide crystals. Consequently, there will be a corresponding
reduction in surface area and catalytic activity. Thus, limit the gas temperature to
270 °C [8]. Because the compressor work increases with increasing volumetric
flow rate, we must keep the temperature at the compressor inlet low. If we assume
a temperature of 40 °C in lines 1 and 2, then the temperatures in lines 5, 7 and 8
will also be 40 °C. The temperature in line 3 can be determined by an energy bal-

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