# 03.6 - Energy Balance for Reacting Systems

### Iterating Mass Balances in Excel(7min)

You can turn Excel into a crude process simulator (e.g. ASPEN, ChemCAD, ProSim, HYSYS, ...) by implementing an xls feature that is often overlooked. (7min, uakron.edu) You need to enable the iteration feature and then you simply need an initial guess about the masses of any recycle streams. This presentation illustrates the mass balance calculation for the dimethyl ether process (2CH3OH = CH3OCH3 + H2O). A subsequent video (below) shows how to add stream enthalpy calculations using the path of Figure 2.6c and Eqn 3.5. Then you can easily perform the energy balances. One important feature of having the energy balance is to facilitate performing an adiabatic reactor calculation, also illustrated below.

Comprehension questions:
1. Choose any process flow diagram from your material and energy balances (MEB) textbook that has a recycle stream. Solve the problem using this technique and compare to the answer you obtained in MEB class.
2. A process for decaffeination requires us to know: (A) the amount of decaffeination solvent (DCS) and (B) composition of the DCS recycle stream. In the process, coffee beans are fed directly to a mixing tank. The DCS is mixed with the DCS recycle stream then fed to the mixing tank. The solution is filtered and the wet coffee beans are sent to a dryer in which 90% of the DCS is recovered and returned to the mixing tank; the other 10% of DCS exits with the coffee beans. (This is NOT "the DCS recycle stream" mentioned above.) The liquid from the filtration is fed to a separation unit where the caffeine exits at 95wt% and "the DCS recycle stream" exits at a concentration that needs to be determined as (B). Additional information(assume a basis of 100kg coffee beans): (a) Coffee beans contain 1.5wt% caffeine. (b) Coffee beans exiting the filtration are 90% caffeine-free. (c) For each 100kg of coffee beans entering the mixing tank, 20kg of DCS go with them, hence the need for the dryer. (d) The concentration of DCS entering the mixing tank (after mixing recycle with fresh DCS) is 95% DCS and 5% caffeine. (e) The DCS-rich stream exiting the mixing tank is 88%DCS and 12% caffeine. Solve for (A) and (B) above. The process flow diagram and complete solution are available, (Learncheme.com, 12min) but try to solve as much as possible on your own by using the pause button frequently.

### Performing Energy Balances in Excel

In case you need a little extra help on energy balances after iterating mass balances, this video walks you through the process. (8min, uakron.edu) for the same process flow diagram related to dimethyl ether synthesis.

Comprehension Questions:

1. Choose any process flow diagram from your material and energy balances (MEB) textbook that has a recycle stream. Solve the problem using this technique and compare to the answer you obtained in MEB class. Estimate stream enthalpies for every stream and compute the overall energy balance of all product streams to all feed streams. Does the process require net heat addition or removal?
2. Suggest limitations of this approach. What are the assumptions? Which assumptions seem most suspect?

### Reactor example following Figure 3.5a

Heat Removal from a Chemical Reactor (LearnChemE.com, 8min) determines heat removal so that a chemical reactor is isothermal following the pathway of Figure 3.5a. The reaction is N2 + 3H2 = 2NH3 at 350C and 1 bar. The pathway to go from products to reactants is to cool the products to 25C (the reference temperature), then "unreact" them back to their initial feed state (reactants), then to heat the reactants back to the inlet condition of the reactor (350C,1bar). Summing up the enthalpy changes over these three steps gives the overall change in enthalpy at the reactor conditions.

Comprehension Questions:
1. Suppose the reaction had been carried out at 2 bars. How would we compute the enthalpy change then?
2. Use this approach to compute the heat of reaction for 2 CH3OH = CH3OCH3 + H2O at 250C and 1 bar.
3. Methanol, dimethyl ether, and water are all liquids at 25C and 1 bar. Did you account for the heat of vaporization when answering Question #2 above? Explain.

Adiabatic Reactor Temperature (LearnChemE.com, 7min) calculate the adiabatic temperature for a reactor with 30% conversion. The reaction is NO + 0.5 O2 = NO2. The strategy is to guess the temperature at which the reactor operates, then compute the heat evolved at that temperature by either method of Fig 3.5a or 3.5b (see above). If the heat evolved is equal to the heat required to warm the products to that reactor temperature, then you have guessed the right temperature. If the heat evolved is negative, then you need to guess a higher temperature.

Comprehension Question:
1. Estimate the adiabatic reactor temperature for the ammonia synthesis reactor discussed above.

### Heat removal from an Isothermal Reactor using Figure 3.5b

Heat Removal from a Chemical Reactor (uakron, 8min) determines heat removal so that a chemical reactor is isothermal following the pathway of Figure 3.5b using the pathway of Figure 2.6c if a heat of vaporization is involved. The reaction is: N2 + 3H2 = 2NH3 at 350C and 1 bar. The pathway to go from products to the reference condition is to correct for any liquid formation at the conditions of the product stream then cool/heat the products to 25C (the reference temperature), then "unreact" them back to their elements of formation. Summing up the enthalpy changes over these steps gives the overall enthalpy of the reactor outlet stream. The same procedure applied to the reactor inlet gives the overall enthalpy of reactor inlet stream. Then the heat duty of the reactor is simply the difference between the two stream enthalpies.

Comprehension Questions:
1. Use this approach to compute the heat of reaction for 2 CH3OH = CH3OCH3 + H2O at 250C and 1 bar. Compare to your answer when using the pathway of Figure 3.5a.
2. Methanol is a liquid at 45C and 2bars. Compute the enthalpy of a stream that is 100 mol/h of pure methanol at 45 C and 2 bars according to the method of Figure 3.5b. Hint: this is different from the pathway of Figure 2.6c because it includes the heat of formation.

### Equilibrium Limited Adiabatic Reactor Temperature

Adiabatic reactor temperature for an equilibrium limited reaction (LearnChemE.com, 7min) In many situations, the extent of reaction is not specified outright. Instead, a problem might be specified as operating at or near equilibrium in an adiabatic reactor. The problem is that the equilibrium constant that relates "products/reactants" changes with temperature according to ln(Ka/Kref) = -(ΔHrxn/R)*(1/T-1/Tref) For example, in an exothermic reaction, the equilibrium constant decreases with temperature. This leads to a coupling between the adiabatic constraint to determine the temperature and the equilibrium constraint to determine the extent of reaction: two equations and two unknowns. The methodology is presented here for a hypothetical reaction of A->B in a liquid phase reactor where CpA=CpB=const.

Comprehension Questions:

1. What name is mentioned in the video for the equation that relates the equilibrium constant to temperature?
2. Why does the version of this equation in the video reverse the order of the reciprocal temperature subtraction, ie. (1/Tref-1/T)? Is this a typographical error?
3. How would your solution change if CpA = 50 and CpB = 40?

Adiabatic reactors in chemical processes (uakron.edu, 6min) are not uncommon. Therefore, it is useful to illustrate how to perform the calculation in the context of the dimethyl ether process. Fortunately, the calculation is greatly simplified by the stream enthalpy calculations presented above. All we really need to do is iterate on the reactor outlet temperature until the stream enthalpy of the outlet stream equals that of the inlet stream. This is easy because our choice of thermodynamic pathway refers back to the formation elements at standard conditions. Hence, any changes in composition and component enthalpies are automatically reflected in the enthalpy of the stream. This provides a powerful illustration of the benefits of thermodynamic pathway analysis.

Comprehension Questions:

1. 100 kmol/h of N2 is reacted with 300 kmol/h of H2 to form NH3 with 55% conversion. Only a single distillation column is required to provide a 99.99% split on N2 (the light key) and 1% split on NH3. On the other hand a purge stream is required with a 20:1 recycle ratio. The inlet to the reactor needs to be at 200C and the reactor operates adiabatically. Compute the molar flow rates and enthalpies of all streams and the outlet temperature of the reactor.