Fuel Processing Calculations

Example 10-8 Methane Reforming - Determine the Reformate Composition

Given a steam reformer operating at 1400°F, 3 atmospheres, pure methane feed stock, and a steam to carbon ratio of 2 (2 lb mol H2O to 1 lb mol CH4), (a). List the relevant reactions, (b) Determine the equilibrium concentration assuming the effluent exits the reactor in equilibrium at 1400°F (c) Determine the heats of reaction for the reformer's reactions. (d) Determine the reformer's heat requirement assuming the feed stocks are preheated to 1400°F. (e) Considering LeChâtelier's principle, indicate whether the reforming reaction will be enhanced or hindered by an elevated operating temperature (f) Considering LeChâtelier's principle, indicate whether excess steam will tend to promote or prevent the reforming reaction.

Solution:

(a) The relevant reactions for the steam reformer are presented below:

CH4 + H2O o 3H2 + CO (Steam Reforming Reaction)

A third relevant reaction is also presented below. However, this reaction is simply a combination of the other two. Of the three reactions, any two can be utilized as an independent set of reactions for analysis, and should be chosen for the user's convenience. Here we have chosen the steam reforming and the shift reactions.

CH4 + 2H2O 4H2 + CO2 (Composite Steam Reforming Reaction)

(b) The determination of the equilibrium concentrations is a rather involved problem, requiring significant background in chemical thermodynamics, and therefore will not be solved here. One aspect that makes this problem more difficult than Example 10-6, which accounted for the steam reforming reaction within the fuel cell, is that we cannot assume the reforming reactions will proceed to completion as we did in the former example. In Example 10-6, hydrogen is consumed within the fuel cell thus driving the reforming reaction to completion. Without being able to assume the reforming reaction goes to completion, we must simultaneously solve two independent equilibrium reactions. The solution to this problem is most easily accomplished with chemical process simulation programs using a technique known as the minimization of Gibbs free energy. To solve this problem by hand, however, is a arduous, time-consuming task.

For interest, an ASPEN™ computer solution of this problem is given below:

Inlet Composition (lb mols/hr)

Effluent Composition (lb mols/hr)

Effluent Composition (mol fraction)

CH4

100

11.7441

2.47

CO

0

64.7756

13.59

CO2

0

23.4801

4.93

H2

0

288.2478

60.49

H2O

200

88.2639

18.52

Total

300

476.5115

100.00

(c) This problem is rather time-consuming to solve without a computer program and will therefore be left to the ambitious reader to solve64 from thermodynamic fundamentals. As an alternative, the reader may have access to tables that list heat of reaction information for important reactions. The following temperature dependent heats of reaction values were found for the water gas shift and reforming reactions in the Girdler tables (1).

Note: a positive heat of reaction is endothermic (heat must be added to maintain a constant temperature), while a negative heat of reaction is exothermic (heat is given off).

64 The reader can refer to Reference 2, Example 4-8 for the solution of a related problem.

(d) With knowledge of the equilibrium concentration and the heat of reactions, we can easily calculate the heat requirement for the reformer. Knowing that for each lb mol of CH4 feed, 88.3% [(100-11.7)/100_ 88.3%] of the CH4 was reformed, and 26.6% [23.5/88.3_ 26.6%] of the formed carbon monoxide shifts to carbon dioxide, then the overall heat generation for each lb mol of methane feed can be developed from

(1 lbmol CH4)f 88 3% CH4 reactedY97,741 _BiH_1 _ 86,300 _^_

v 4\ 100% CH4 feed A lbmol reformed CH4J lbmol CH4 feed

/,„ /88.3% CH4 rxtd.Y 1 lbmol CO Y 26.6% CO shifts Y -13,982 Btu } Btu

100% CH4 feed A lbmol CH4 rxtdA lbmol CO Feed Albmol CO rxn^ lbmol CH4 feed

Therefore the heat requirement for the reformer is 83,000 Btu/lb mol of CH4 fed to the reformer.

Because this value is positive, the overall reaction is endothermic and heat must be supplied.

(e) LeChatelier's principle simply states that "if a stress is applied to a system at equilibrium, then the system readjusts, if possible, to reduce the stress" (3). The power of this simple principle is illustrated by the insight that it provides in many situations where little is known. In our reforming example, we can learn from LeChatelier's principle whether higher or lower temperatures will promote the reforming reaction just by knowing that the reaction is endothermic. To facilitate the application of principle, we shall write the endothermic reforming reaction with a heat term on the left side of the equation.

Now if we consider that raising the temperature of the system is the applied stress, then the stress will be relieved by the reaction when the reaction proceeds forward. Therefore, we can conclude that the reforming reaction is thermodynamically favored by high temperatures.

(f) To solve this application of LeChatelier's principle, we shall write the reforming reaction in terms of the number of gaseous molecules on the left and right sides.

2Molecules(g) o 4Molecules(g)

Now if we imagine a reforming system at equilibrium, and increase the pressure (the applied stress), then the reaction will try to proceed in a direction that will reduce the pressure (stress). Because a reduction in the number of molecules in a system will reduce the stress, an elevated pressure will tend to inhibit the reforming reaction. (Note: reforming systems often operate at moderate pressures, for operation at pressure will reduce the equipment size and cost. To compensate for this elevated pressure, the designer may be required to raise the temperature.)

Example 10-9 Methane Reforming - Carbon Deposition

Given the problem above, (a) list three potential coking (carbon deposition, or sooting) reactions, (b) considering LeChatelier's principle, indicate whether excess steam will tend to promote or inhibit the coking reactions, (c) determine the minimum steam to methane ratio required in order to prevent coking based on a thermodynamic analysis, and (d) determine the minimum steam to methane ratio to prevent coking considering the chemical kinetics of the relevant reactions.

Solution:

(a) Three of the most common/important carbon deposition equations are presented below. CH4 o C + H2O (Methane Cracking)

2CO o C + CO2 (Boudouard Coking)

(b) Considering LeChatelier's principle, the addition of steam will clearly inhibit the formation of soot for the methane cracking and CO reduction reactions. (The introduction of excess steam will encourage the reaction to proceed towards the reactants, i.e., away from the products of which water is one.) Excess steam does not have a direct effect on the Boudouard coking reaction except that the presence of steam will dilute the reactant and product concentrations. When the Boudouard coking reaction proceeds towards the left, the concentration of CO will increase faster than the concentration of CO2. Thus, dilution steam will cause the Boudouard coking reaction to proceed toward the left. Clearly, the addition of steam is quite useful at preventing sooting from ruining the expensive catalysts that are utilized in reformers and fuel cell systems. Too much steam, however, will simply add an unnecessary operating cost.

(c) The determination of the minimum steam to carbon ratio that will inhibit carbon deposition is of interest to the fuel cell system designer, but it is, however, beyond the scope of this handbook. The interested reader is referred to references (4), (5), and (6).

(d) A steam quantity that will preclude the formation of soot based upon a thermodynamic analysis will indeed prevent soot from forming. However, it may not be necessary to add as much steam as is implied by thermodynamics. Although soot formation may be thermodynamically favored under certain conditions, the kinetics of the reaction can be so slow that sooting will not be a problem. Thus, the determination of sooting on a kinetic basis is of significant interest. The solution to this problem is, however, beyond the scope of this handbook, so the interested reader is referred to reference (6). When temperatures drop to about 750°C, kinetic limitations preclude sooting (7). However, above this point, the composition and temperature together determine whether sooting is kinetically precluded. Typically, steam reformers have operated with steam to carbon ratios of 2 to 3 depending on the operating conditions in order to provide an adequate safety margin. An example calculation presented in Reference 6, however, reveals that conditions requiring a steam to carbon ratio of 1.6 on a thermodynamic basis can actually support a steam to carbon ratio of 1.2 on a kinetic basis.

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