Energy efficiency in steam reforming is improved by recovering heat from the burner exhaust gas, which leaves the firebox at 960°C. The exhaust gas is cooled in a series of heat-exchange operations that preheat the reformer feed streams to 450°C, produce superheated steam at 4.5 MPa and 100°C superheat from boiler feedwater at 30°C, and preheat the combustion air to 300°C. The superheated  steam is used to drive turbines elsewhere in the process or it can be exported, for example to generate electricity. The burner exhaust gas leaves the heat-recovery units and enters a stack at 150°C for release to the atmosphere.

Problems

The context of this case study is the possible purchase of a plant using the above described methanol production technology. A company is offering to sell a complete plant that produces 420,000 t/y of specification-grade methanol, when operating 350 d/y. The ultimate aim of this case study is to evaluate what price should be offered to that company for building the plant.

1. The process objective can be described most simply as converting methane and water into methanol and hydrogen, and then purifying the methanol so that it meets specifications. The overall process stoichiometry is given by the following relationship:

CH4 + H2O → CH3OH + H2                                                                          (3)

From this statement, estimate the feed rates of the natural gas (both in kmol/h and in m³/h at STP) and steam (kmol/h, kg/h) fed as reactants (as opposed to fuel) to the reformer. (Note: The requested estimate neglects formation of by-products and the carbon monoxide and carbon dioxide lost in the purge stream.) (5 marks)

2. Seven percent excess air is used in burning the reformer fuel; it is drawn into the system at 25°C and 60% relative humidity. Estimate the average molecular weight of the air.

(Compare the value with that obtained for dry air. Why does the result differ from this value?) Determine the flow rate of this stream (kmol, m³) per kmolof natural gas burned. (5 marks)

Hint: The relative humidity (φ) of air is defined as the ratio of the partial pressure of water vapour to the saturation vapour pressure at a given temperature as follows:

φ = p sat(p H)2(T(O))                                                            (4)

The molecular weight of moist air is calculated as:

Mmoist air =( 1 − y H2 O)(0.21 × MO2 +0.79 × MN2)+yH2 O MH2 O                     (5)

where y H2 O is he mole fraction of water vapour and M is the molecular weight.

3. What are the compositions (mole and mass fractions) and volumetric flow rates (m³/kmol

CH4 fed to burners) of (a) the effluent gas from the reformer burners and (b) the gas entering the stack? What is the specific gravity, relative to ambient air (25°C, 1 atm, 60% relative humidity), of the stack gas as it enters the stack? Why is this quantity of importance in designing the stack? Why might there be a lower limit on the temperature to which the gas can be cooled prior to introducing it to the stack? (10 marks)

Use a methane feed rate to the reformer of 1600 kmol/h as a basis for subsequent calculations.

with similar nomenclature to the previous question.

(a) Taking into account the occurrence of reactions given by both Eq. 1 and 2, estimate the composition of the product gas leaving the reformer and the conversion of CH4, assuming the product stream leaving the reformer has achieved chemical equilibrium at 832°C and 1.5 MPa. What is the total flow rate of this stream in both kmol/h and kg/h? What effect does the water–gas shift reaction have on the production of CO at the reformer conditions? (10 marks)

(b) The ratio of CO to H2 can be an important variable in efficient use of raw materials. In this case study a 3:1 steam-to-methane molar ratio of feed streams was specified.

Determine how this feed ratio affects the ratio of CO to H2 in the product from the reformer assuming the reaction products are in chemical equilibrium at 832°C and 1.5 MPa. (7 marks)

6. Quantitatively demonstrate that high temperatures and low pressures favour the formation of CO and H2 in the reformer. Do this by calculating and then plotting the production rates (kmol/kmolof CH4 fed) of CO and H2 in the reformer product stream over the temperature range 750–950°C at 1.2, 1.6, and 2.0 MPa. Furthermore, construct plots showing the effect of temperature and pressure on selectivity (defined as kmol CO formed per kmol CO2 formed) over the same range of conditions. Assuming that your results support the hypothesis that high temperatures and low pressures favour the formation of CO and H2,  speculate as to why the temperature and pressure are at the values specified in the Process Description (832°C and 1.5 MPa) rather than at a higher temperature and lower pressure.

(15 marks)

7. The reformer product gas leaves the reformer at 832°C.

(a) Using the flow rate of the product gas determined in Question 5, calculate the rate (kJ/h) at which heat must be transferred from the combustion gases to the gases flowing through the inside of the reformer tubes. (5 marks)

(b) What is the required flow rate of natural gas (kmol/h and m²/min at STP) to the reformer burners? Assume that the natural gas is burned to completion in the reformer firebox and that the combustion gases leave the firebox at 960°C. (5 marks)

(c) The thermal efficiency of the firebox may be defined as the percentage of the lower heating value of the fuel transferred to the reformer gases. Estimate the lower heating value of methane and, assuming the combustion gases leave the firebox at 960°C, the corresponding thermal efficiency of the firebox. (5 marks)

8. The heated tube length in the reformer is 10 m and the external diameter of the tubes is

10.5 cm. If the rate of heat transfer (Q) from the combustion gases in the firebox to the  reformergases were accomplished entirely by convection, the following equation would apply:

where Uo is an overall heat transfer coefficient based on the external surface area of the

reformer tubes in the firebox, Ao is the total external surface area of the tubes, and Δ T LM is an average difference between temperatures of the heat source (combustion gases) and the  heat sink (reformer reaction gases):

where Δ T 1 and Δ T2 are differences in temperature between the reformer gas and combustion gas at the inlet and at the outlet of the firebox. If the combustion gases are assumed to have a constant temperature in the firebox of 960°C (i.e., they are perfectly mixed), and Uo ≈300 W/m²K, what is the required number of tubes in the firebox? In fact, a large fraction of the heat transferred to the tubes is accomplished by a mechanism other than convection. What is that mechanism? What will consideration of this additional mechanism  mean in terms of the number of tubes required in the firebox? (10 marks)