batch#
General functional algorithms for batch design.
- size_batch(F_vol, tau_reaction, tau_cleaning, N_reactors, V_wf)[source]#
Solve for batch reactor volume, cycle time, and loading time.
- Parameters:
- Returns:
‘Reactor volume’: float
’Batch time’: float
’Loading time’: float
- Return type:
Notes
By assuming no downtime, the total volume of all reactors is:
\[V_T = F_{vol}(\tau_{reaction} + \tau_{cleaning} + \tau_{loading})\]where \(V_T\) is the total volume of all reactors, \(F_{vol}\) is the volumetric flow rate of the feed, \(\tau_{reaction}\) is the reaction time, \(\tau_{cleaning}\) is the cleaning and unloading time, and \(\tau_{loading}\) is the time required to load a vessel. This equation makes the conservative assumption that no reaction takes place when the tank is being filled.
The working volume of an individual reactor is:
\[V_{i,working} = \frac{V_T}{N_{reactors}}\]where \(N_{reactors}\) is the number of reactor vessels.
The time required to load a reactor (assuming no downtime) is:
\[\tau_{loading} = \frac{V_{i,working}}{F_{vol}}\]Note that the the actual volume of a reactor is:
\[V_i = \frac{V_{i,working}}{f}\]where f is the fraction of working volume in a reactor.
Plugging in and solving for the total volume, \(V_{T}\), we have:
\[V_T = F_{vol}\frac{\tau_{reaction} + \tau_{cleaning}}{1 - \frac{1}{N_{reactors}}}\]Using this equation, \(V_T\) is first calculated, then \(V_{i, working}\), \(\tau_{loading}\), and \(V_i\).
Units of measure may vary so long as they are consistent. The loading time can be considered the cycle time in this scenario.