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United States
Department of Interior
Bureau of Mines

Synthetic Fuels Demonstration Plant

Louisiana, Missouri

K-23

W. M. Sternberg

Fuel Gasification Processes and Their Expression in the Terbeck Diagram

By Paul Dolch, Linz (Donau)

Brennstoff-Chemie, vol. 32, pp. 193-198

    Graphic expressions of processes are important in the study of any problems.  Methods of water gas production differ in principles; a satisfactory graphic expression of the processes would therefore be highly desirable.  Efforts were made in the past to express equilibrium conditions in concentration-temperature diagrams, in which the equilibrium concentrations for every gas component could be found for any temperature.  Such concentration-temperature diagrams are difficult to read and give the practical man no help in planning his experiments according to some simple scheme as an aid in his investigations.

    W. Terbeck has recently proposed a diagram based on stoichiometry of the water gas production, which is supposed to give valuable help to the practical chemist because of its simplicity and its clarity.

I.

    The two equations:

express the basic processes of interaction of steam with carbon according to the practical experience in water gas production.  Reaction I proceeds practically completely towards the right, while reaction II is a typical equilibrium reaction in which the four gas components are generally present in appreciable amounts after the termination of the reaction.  The mass action law demands that when equilibrium condition is reached, the products of concentration of the reacting substances divided by the product of concentration of the reaction products equals a characteristic number for a given temperature, the so-called equilibrium constant; for the water gas equilibrium (reaction II) we have therefore

where the expressions in parentheses are symbols for molecular concentrations of the components.

    The producer gas equilibrium (Boudouard) as well as the water gas equilibrium is important in reactions of carbon:

The equilibrium constant of the producer gas equilibrium assumes the form

where PCP and PCO₂ are the partial pressures of CO and CO₂.  The question whether the simultaneous equilibrium of the water gas and producer gas equilibria (complete equilibrium) is reached in the interaction of steam and carbon will not be discussed here, and demands special investigation.  The assumption of a simultaneous water gas and producer gas equilibria offers the possibility, however, to refer gasification processes to an ideal process, similar to the thermodynamic methods which test the operations of a motor on the basis of an ideal cycle process.

    Should the gasification be referred to 1 mol C (12 kg.), the carbon balance will require that

CO + CO₂ = 1;

the oxygen of CO and CO₂ is furnished by the decomposed steam, so that

H₂ = CO + 2 CO₂:

moreover, the hydrogen introduced as total steam w forms elementary hydrogen according to the equation, while the undecomposed steam leaves as (H₂O) _exc..  It follows, therefore, from the carbon balance:

CO + CO₂ = 1;    CO₂ = 1 - CO.

From the oxygen balance:

H₂ = CO + 2 CO₂;    H₂ = 2 - CO.

From the hydrogen balance:

W = (H₂0) _exc. + H₂; (H₂O) exc. = w - (2 - CO).

In addition, assumption of gas equilibria requires that

    CO, CO₂, H₂ are expressed in mole per mol of gasified carbon, (H₂O) exc. is the excess steam in the gas and w the amount of steam introduced, with both values also in terms of mols/mol C gasified.

    Five equations are therefore available for the determination of the five values CO, CO₂, H₂, (H₂O) _exc. and w, and permit a definite solution.

    Should CO be equal to x mols/mol gasified C, equation IV assumes the form for water gas equilibrium:

    The following must be considered in the determination of partial pressures (equation V):  1 mol C produces by interaction with w mols of steam

(CO) + (CO₂) + (H₂) + (H₂O) exc. total mols;

since (CO) + (CO₂) = 1 and (H₂) + (H₂O) exc. = w,

w + 1 is the total mols of wet water gas.

    The total pressure is assumed to be equal to 1 and partial pressures are converted to molar concentration by

Introducing the partial pressures in equation V gives

for the producer gas equilibrium.

    Finding K values by solving the two equations IVa and Va for different temperatures gives the relationship between gas composition and temperature as shown, e.g. by Terbeck  in figure 6.  This concentration-temperature diagram is difficult to read and not suited to practical applications.

II.

    The Terbeck diagram expresses graphically the reactions given by chemical equations, and all conversions are referred by definition to 1 mol C.  For pure water gas gasification of carbon we get

CO + CO₂ = 1,

H₂ = 2 - CO = 1 + CO₂.

    CO₂ and H₂ are now expressed as functions of the CO content, x, in the water gas.  The upper part of the diagram represents, therefore, the composition of the dry gas formed by interaction of steam and carbon.

    The composition of the wet gas is found by assuming simultaneous water gas and producer gas equilbria from equations IV and V.  This explains the basis of the Terbeck diagram for the gasification of carbon with steam.  The bottom part of the Terbeck diagram may contain in addition the temperature curve from equibria values, as shown in figure 1.

    The Terbeck diagram was first designed for the gasification of pure carbon.  It can be directly used for the gasification of bituminous fuels with steam.  In this case, the amount of hydrogen from steam is increased by the net hydrogen in the fuel  mols/mol C; the hydrogen line of pure water gas production from carbon is then increased by the value  .  The addition of the net hydrogen shifts the water gas equilibrium, and different values for (H₂O) exc. will therefore be obtained for different fuels, and the equilibrium temperatures in the bottom part of the diagram must always be made to agree with the different fuels used.

    Gasification with oxygen and steam (oxy-water gas) can be derived in a way similar to that for pure steam gasification.

    Were we to assume that the oxygen added will burn the corresponding amount of hydrogen in the gas with formation of water, each mol O₂/mol C in the oxygen-steam mixtures will reduce the hydrogen content of pure steam gasification by 2 mols H₂.  The Terbeck diagram represents these conditions by lines parallel at proper distances to the hydrogen line.  The curve for the (H₂O) _exc. must again be determined for each case.

    The manner in which the oxidation with oxygen proceeds in the oxy-water gas production is unimportant for calculations (application of stoichiometrical and thermochemical laws) as may be shown in one example.

    Final results obtained by both methods are the same.  The understanding of the different physical and chemical partial processes during gasification based on observation and experiment is not merely useful but is of the greatest importance for progress to supplement the formal treatment discussed above.  The role of the net hydrogen in the powdered fuel gasification should, in this connection, be especially considered (Terbeck, loc. cit.).  The explanation of the role of equilibrium during the action of H₂-CO₂ mixture of the fuels of different reactivity permits making important conclusions on gasification processes of these fuels.  A discussion of the use of computations based on experiment might be of interest in this connection.  The words of Partington may be remembered:

    "In the older treatises...a proper balance between theory and experiment was observed, but the later tendency has been to write books more and more devoted to the mathematical theory, without any regard being paid to experimental methods or their results, which are introduced merely for the purpose of proving or disproving the theory set out.

III.

    Computation and diagrams are based on simultaneous water gas and producer gas equilibria, as previously mentioned.  Changes in the diagram without the simultaneous formation of the Boudouard equilibrium might be of interest.  The basic equation of water gas formation is used as before as a basis for the water gas equilibrium.  The measure of conversion of carbon monoxide, according to the computation shown and the notations in the diagram, is assumed to be (1 - x), i.e. (1 - x) mols were converted with steam into CO₂ form each 1 mol of CO, and x mols of CO are left behind:

C + H₂O = CO + H₂

(1 - x) CO + (1 - x) H₂O = (1 - x) CO₂ + (1 - x) H₂.

    Should c represent the amount of undecomposed steam,

C + w H₂O = (1 - x) CO₂ + x CO + (2 - x) H₂ + c (H₂O) _exc..

It must be remembered, that hydrogen balance requires that the excess steam (c), be equal to the amount of the total steam (w) reduced by the equivalent amount of hydrogen produced (2 - x).  Water gas equilibrium can be expressed, therefore, as

Disregarding the formation of the Boudouard equilibrium, only the indefinite equation IVb remains, and

    Kw determines the equilibrium temperature, c is the excess steam, and the non-formation of the Boudouard equilibrium requires that a given dry gas analysis will correspond to a number of wet gas analyses, for which must be maintained a simple relationship between the equilibrium temperature and the amount of undecomposed steam, namely,

For instance, the value of c/K_w is equal to 0.933 for a gas with 0.6 mols CO/mol C.

    Selecting a few values at random, the excess steam c in the wet gas for temperatures

Assuming the formation of both the water gas and the Boudouard equilibria for

which is a definite composition of the equilibrium gas, as was shown elsewhere (Brennstoff-Chemie, vol. 32, 1951, in print).

    The compostion of the dry gas is in both cases:

The assumption of an incomplete equilibrium leaves, therefore, the upper part of the Terbeck diagram unchanged, since both cases are referred to the same dry gas composition; this also applies to the amount of net hydrogen in a fuel and to the application of the Terbeck diagram to oxygen-steam gasification.  The lower part of the diagram will be changed correspondingly by replacing the (H₂O) _exc. curve in figure 1 by the curve for (H₂O) _exc./K_w.  Substitution of constant K_w values at constant temperatures gives the isotherms of the c values (fig. 2) for different x values.

    This fully explains what Terbeck has stated in these words: "A closer examination shows that the Terbeck diagram tells nothing more than the effect of the conversion reaction CO + H₂O = CO₂ + H₂."

    It should be added that the Terbeck diagram can be generally used for chemical conversions in which carbon monoxide and steam, or carbon dioxide and hydrogen, are participating, as e.g. in cracking reactions, or in the formation of hydrogen cyanide from ammonia and carbon monoxide:

CO + NH₃ = HCN + H₂O.

    The wet gas analysis can be derived from the Terbeck diagram when the Boudouard equilibrium is not reached, when proper assumptions are made from the experimental evidence on the equilibrium temperature.  This applies first of all to the interaction of steam and carbon.  The relationships are retained in the gasification of bituminous fuels and for the production of oxy-water gas, but undergo formal changes by increasing the (H₂O)_exc. by the amount of H₂O formed by combustion of hydrogen, i.e. by having (H₂O) _exc. = (w - b - x - 2), and the amount of hydrogen in the gas is increased by the net hydrogen in the fuel, and the oxygen reduced by a corresponding amount, i.e.

(H2) = (2 + d - b - x).  This leads to

Should the difference (d - b) be used as a parameter, all the possible experimental results will be included in the Terbeck diagram in the curves at the bottom for (H₂O) _exc./K_w.

    The corresponding (H₂O)_exc./K_w curves are shown in figure 3 for

The Terbeck diagram in this form is an exact expression of the gas composition and of the processes during gasification of any fuels with steam and with steam-oxygen or with steam-air, and is of general significance.  This "general form of the Terbeck diagram" expresses accurately all gasification processes in a single diagram, but lacks the clarity of the isothermal diagram of Terbeck, of the composition of wet gas and the effect upon it of changes of operating conditions (temperature, amount of  steam, etc.).

IV.

    Examples of practical applications of the deductions will be shown below.  The problem of composition of the water gas produced under given operating conditions will be first treated in a general form.  It will be followed by a practical example, and in conclusion, operating conditions will be found from fuel and gas analyses in a further example.

A.    General Case

    Net hydrogen d in the fuel, expressed in mols /mol C gasified, the steam input w mols H₂O/mol of C and the oxygen input b/2 mols O₂/mol C are given.  The temperature of formation of water gas equilibrium, which varies with operating conditions, concurrent or countercurrent gasification, and the reactivity of the fuel (bituminous coal or lignite) are taken from experimental data.  Computations permit a simultaneous derivation of heat changes, taking into consideration the heat required for the conversion of the solid carbon with steam which is different for lignite and bituminous coal carbon:

C + H₂O = CO + H₂ - 29.3 kcal. for bituminous coal, and

C + H₂O = CO + H₂ - 27.5 kcal. for brown coal.

Bituminous coal is used in the example below.

    The following applies to partial processes:

    Should the dry gas composition of the water gas be assumed known, the gasification processes are derived from the dry gas composition as follows:

    The net hydrogen content (Hⁿ) of the gasified fuel is assumed to be known for exact computations, since otherwise the oxygen consumed in the combustion of the net hydrogen cannot be calculated and the oxygen requirements found will be too low, as already pointed out by Terbeck in discussing Sabel's results (loc. cit., p. 65).

                            Since        CO = x
                                            H₂ = 2 + d - b - x
                                            (CO + H₂) = 2 + d - b

and the relation between oxygen consumption (b/2) and the amount of (CO + H₂) in the water gas can be derived from the effect of net hydrogen in the fuel:

    The oxygen consumption is, therefore

            b = d + 2 - (CO + H₂).

        The fuel is assumed to be the same as above, but calculations are made in the reverse direction by trying to find the gasification processes from the dry gas composition.

The excess steam (H₂O)_exc. in the gas and the composition of the wet gas are found for the equilibrium temperature 700° C. (K_w = 0.64).

Gasification results, in mols/mol C, are expressed by the general formula B:

Starting with the fuel and gas compositions, we get results which were the basis for finding the gas composition and gas yield.

    In conclusion, an example will be shown of arranging the results of computations into the Terbeck diagram (fig. 4).

    The example used is the oxygen-steam gasification of a bituminous fuel, and the trapezoid AHDC in the Terbeck diagram is first plotted for the amounts of , d (line GH).  The application to the Terbeck diagram may now proceed either on the basis of composition and amount of gasifying agent to determine the composition of the gas produced, or the reverse, finding the amount and the composition of the gasification agent from the composition of the gas.

A.    w and b are given, the composition of the gas is to be found:

1.      is drawn parallel to  at a distance b (hydrogen line).

2.    In the bottom part of the diagram, the isotherms for the given operating conditions (b, w, d) are drawn in accordance with:

3.    A parallel is drawn to the hydrogen line through the point Q at a distance w + b - 1 from point A, and it intersects the equilibrium curve at the point P:  Determination of (H₂O)_exc..

4.    A vertical through P gives the composition of the gas in mols/mol C.

B.    The composition of the dry gas is given, and w and b are to be found.

1.    Location of the gas composition on the diagram (hydrogen line).   = GJ

2.    The intersection P with the equilibrium curve determines (H₂O)_exc..

3.    The intersection Q with the abscissa of a line through P parallel to the hydrogen line gives 

    Results of computations and the graphic expression of the process of gasification in a Terbeck diagram show that the diagram gives a comprehensive, simple, and readily understood expression.