# Problems to Solve with Hints

## Questions Related to Syngas and Ammonia Gas Production

You will find more ‘orthodox’ questions in this chapter but questions based on the detailed analysis you should have carried out as part of the mass and energy balances for the ammonia syngas.

There is still a need for basic understanding of the thermodynamics and principles of balancing.

Problem 1:

In the production of the ammonia syngas described in the text, there is an imperative to keep the nitrogen-to-hydrogen ratio as close as possible to the stoichiometric ratio, i.e. 1:3. Some students (and non-students) do seem to have problems handling a non- stoichiometric feed and producing the composition of an output stream. The main thrust of this book has been to produce the mass and energy balances for ammonia syngas production.

As a useful exercise, it helps to consider what happens to the syngas in the ammonia synthesis loop. The stoichiometric ammonia synthesis equation is considered to be: Even using a basic approach to thermodynamics as enshrined in Le Chatelier’s principle, it will be recognised that in equilibrium terms, the pressure should be as high as feasible and, given the exothermic nature of the reaction, the temperature should be as low as possible. This is a dilemma often faced with exothermic reactions. In kinetic terms, we usually find that the higher the temperature, the faster the reaction. In terms of the final equilibrium achieved, we have stated that we want as low a temperature as possible. There is a compromise to be reached in terms of the temperature fixed. This is also a case where an efficient catalyst would be used. Such catalysts exist but are sensitive to the presence of carbon oxides. You will have observed that in mass balancing on the syngas, there is considerable effort made to remove carbon oxides.

In producing ammonia for this question, we are operating at 200 bar (many modern plants can operate at this pressure, but the practical pressure is often set lower). The temperature has been set at 450°C. The challenge is simply that the synthesis gas has a composition that is equimolar in nitrogen and hydrogen. What is the output composition from the reactor assuming equilibrium is reached?

The data available on KP for this reaction indicate that at the operating temperature, the value of KP is 1.44x 10-4.

Problem 2:

Hydrogen can be produced by reacting methane. For the purposes of this calculation, the pressure is set at 1 bar and the reaction is considered to be: For the reactants, their initial ratio H20/CH4 is fixed at 6.0; i.e., as discussed for the primary reformer in the text, it is useful to increase the amount of steam as a diluent and to supress unwanted side reactions. For the purposes of this calculation, the reaction is allowed to go to equilibrium. It is found that a fractional conversion of methane of 0.5 is achieved; calculate the temperature at which the reaction was carried out.

All the necessary KP values are contained in Appendix 1.

Problem 3:

As part of ammonia production, it is necessary to produce a synthesis gas containing stoichiometric proportions of nitrogen and hydrogen. As you will have observed, one of the first stages in the synthesis gas production is carried out in a reformer where methane gas can be considered converted to hydrogen according to the equations: These were the equations used in the text for the primary reformer, and an analysis is given in the text for the reactions in terms of fractional conversions zCH4 and zco-

For the purposes of this calculation, the reformer is operated at a pressure of 1 bar (obviously lower than in practice) and a temperature of 900 K. The methane and steam are the only initial reactants and are fed in the ratio H20/CH4 = 3.5:1.

You are asked to confirm that under these conditions, the fractional conversion of methane in the first reaction should be 89.2% and for the second reaction should be 59.6%. The KP values for these reactions are available in the appropriate appendix, and the values should be found at the quoted temperature. A solution can be obtained using an appropriate convergence procedure (Excel SOLVER was used in this case).

Problem 4:

In teaching the energy balance, one of the classic problems set is trying to find a reactor exit stream temperature when the reactor operates adiabatically. In this type of problem, it is often useful to use mean molar heat capacities. These can be calculated but are often tabulated and can be referenced. If these heat capacity figures are available, then calculations can be carried out and a final temperature reached using the simplest energy balance for the reactor: This requires the output temperature to be known, but that is the parameter being calculated; hence, a number of iterations are required. For each iterated temperature, an appropriate value of the mean molar heat capacity is required.

In Appendix 3, various calculation methods for calculating enthalpy changes are outlined. The most convenient form of enthalpy data available in the appendix for this calculation is to use the polynomial expressions where a base temperature of О К is used. For each component, the appropriate polynomial expression is available. To carry out the balance, the input temperature can be taken as 25°C (298 K). It is the output temperature that has to be calculated, and this can be done using the polynomial expressions.

It should be understood that to do the energy balance, the reactor mass balance should also be known. In the problem, the input fuel composition is known as is the composition of the exit gas after the fuel has been burned. For such a problem, the stoichiometric equations will not be fully known, and using a mass balance fundamental, input atom species=output atom species, it will be possible to carry out the mass balance over the reactor. Once the mass balance is established, it is proposed that the energy balance can be written in terms of enthalpies using the appropriate species polynomials: where subscript i refers to an input species; subscript о refers to an output species; m is a species mass; Г is a temperature in K; a, b, c and d are enthalpy polynomial coefficients; and N is the number of component species.

Having produced the energy balance, the balance needs to be solved for the temperature. This can be done using, for example, M ATLAB or Excel.

Problem

One mole of a fuel gas used to raise steam has the following composition:

 Component Mole Fraction СО 0.21 СО, 0.071 н. 0.286 сн^ 0.074 n2 0.357

This gas was mixed with air and reacted adiabatically. After combustion, the exhaust stream had a composition measured as:

 Component Mole Fraction СО 0.043 СО, 0.0.15 н. 0.0.086 сн^ 0.0.021 N2 0.0.699

Work out a ratio of fuel gas to air.

If the fuel gas and air entered the burner at 20°C, what is the adiabatic flame temperature?

If you are not familiar with this term, then it is important to find out and return to this problem when you are more knowledgeable about the term. Dependent on how you intend to solve the problem, you will find the polynomials for enthalpies of the various species given in Appendix 3 to be useful.

The problems you have so far dealt with in this appendix are specifically linked with aspects of the problems you have dealt with in the text dealing with the balances related to the preparation of ammonia syngas.

It is obvious from the production of the syngas that you have to be able to handle the challenge of: at equilibrium or steady state.

The challenge posed by the need to consider reactions approaching or at equilibrium requires the equilibrium parameter related to the second law' of thermodynamics, the equilibrium constant, to be used and the necessary simple mathematics for solution to be available.

There are certain aspects of the use of the equilibrium constant, and its form for a particular reaction, that allows decisions to be made about possible processing conditions for the reaction.

The following problems illustrate the use of the relatively simple equation for the formation of ammonia from a simple syngas. The problems simply ask for application of basic analysis of the reaction, what the implications of the analysis are and how then to fix conditions as dictated by the balance and thermodynamic calculations.

Problem 5:

a. If a 1:3 mixture of nitrogen and hydrogen is fed to an ammonia synthesis reactor operated so that 20% of the nitrogen is converted to ammonia, what will be the composition of gas leaving the reactor?

b. Suppose that the reactor operates at a total pressure of 150 bar. What will be the partial pressures of each of the components in the exit stream? Indicate the value of KP. Try to find the temperature of operation at which the conversion will be achieved.

The following expression can be used for ammonia synthesis: T is in K.

Problem 6:

Suppose an ammonia synthesis reactor is operated at 200 bar and 454°C. What is the fractional conversion of a stoichiometric mixture of nitrogen and hydrogen? Also, calculate the fractional conversion at 500 bar and 454°C and 200 bar and 399°C.

a. What conclusions could be drawn about the effect of temperature and pressure on the fractional conversion?

b. Are these conclusions what you expected?

c. When the ammonia production reactor is operated, it is usually necessary to operate a recycle stream for the return of unreacted nitrogen and hydrogen. Suppose, operationally, a build-up of inerts in the recycle stream has been allowed instead of being purged; the inerts have reached a point where the level of nitrogen:hydrogen:inerts is 1:3:0.5 kmol. It is unlikely that in normal operations, inert material would rise to this level, but it is a useful exercise to investigate the effect of the inert diluent. If the reactor operates at 200 bar and 454 K, calculate the effect of the presence of the inerts and comment on the result.

## Problems Relating to Syngas Production Not Included in the Main Text

This appendix contains a certain number of problems in mass and energy balancing related to the ancillary equipment associated with the production of ammonia syngas. In carrying out the synthesis of the gas, there are a number of items of equipment that require energy inputs. An examination of the block diagram and the relevant calculations indicates that the primary reformer (Item F101) is a major item requiring a net energy input. The large demand for energy as heat imposed by the endothermic methane-steam reaction is usually met by putting banks of tubes, packed with the necessary catalyst into, what is essentially, a furnace, with the process gas flowing through the tubes.

The energy required for the furnace is supplied by burning a fuel in air that uses the energy from the exothermic combustion reaction to heat the furnace. Obviously, in a text such as this, no attempt is made to look in detail at the furnace and associated equipment design, but the fuel used is the same natural gas used as the syngas feedstock. The burning of the fuel for the primary reformer energy produces a flue gas that has a high temperature and can potentially be used to supply energy to other equipment. This has already been illustrated in the mass and energy balances for the preheater used in the syngas production. There are some other items before the flue gas is sent to a stack that can be considered.

The flue gas stream can be used to transfer energy to other items of equipment, not necessarily part of the syngas production. In this particular set of problems, there is a challenge to use the flue gas energy to produce superheated steam. There is also a mass and energy balance associated with the superheater where there has to be a radiant shield. The radiant shield associated with a boiler protects the following superheater from transient conditions where there could be damage to the superheater metal.

Problem 1:

It is known that energy from the flue gas stream will be used to produce steam from an existing steam/water system that exists under the following conditions:

 Steam/Water Input Output Temperature (°C) 278 278 Pressure 62 62

At the point where the flue gas stream enters the radiant shield heater, it has the following properties:

 Flue Gas Input Output Temperature (°C) 950 892

To calculate the energy available from the flue gas, it is necessary to do an energy balance. Enthalpies can be calculated using the enthalpy polynomials available in Appendix 3.

The available energy should be calculated as: Realistically, you would expect to lose about 2% of this energy, so the energy available for steam raising will be: Using steam tables to find the latent heat at vaporisation at 62 bar and 278°C, we find a value of You should find that the amount of steam raised is A detailed solution to this problem is given as Solution 1 in Chapter 6.

Problem 2:

The flue gas from the radiant stream boiler now enters a superheater, and more energy is exchanged from the flue gas to raise steam. The amount of steam entering the superheater is 9704 kg at the conditions shown below:

 Steam/Water Input Output Temperature (°C) 278 420 Pressure 62 58.5

The pressure drop through the superheater is incorporated. This will depend on the actual design layout of the heat exchanger system supplying the energy.

At the point where the flue gas stream enters the superheater, it has the following entry and exit conditions:

 Flue Gas Input Output Temperature (°C) 892 ?

The mass balance will not alter.

This situation will require an energy balance to be carried out. Often in these situations, the energy balance is used to fix an output temperature. In this case, you are asked to carry out the energy balance and fix the flue gas exit temperature.

You should find a temperature of 726.9°C.