Separation factor. In the simplified analysis of the water-hydrogen sulfide exchange process in Sec. 113, the effects of the solubility of hydrogen sulfide in water and the vaporization of water into hydrogen sulfide were neglected. In the following they will be taken into account. The deuterium separation factor a for the hydrogen sulfide exchange process is defined as

_*(1 ~y)

а~У( 1-х)

where у and x are the atom fractions of deuterium in the vapor and liquid, respectively. In terms of the molecular species H20, HDO, D20, H2S, HDS, and D2S that make up each phase, a is given by

Table 13.20 Heavy-water production cost at Savannah River Quantity per kg D2 0 Cost, $/kg D20 Direct production cost Feed water, kg 24,000 5.07 Hydrogen sulfide 0.66 0.24 Salaries 2.89 Operating labor 4.37 Miscellaneous 1.12 13.69 Direct maintenance cost Labor 4.37 Materials 7.38 11.75 Utilities Electricity, kWh 604 13.76 Steam, kg (900 psig equiv.) 5,660 41.45 Cooling water, kg 125,000 1.48 Miscellaneous 0.84 57.53 Depreciation 24.95 Administrative and general 15.01 Total cost of production 122.93

(2*d, o + *hdo + 2*d. s + *hdsX2.}’h, o +Yhdo + 2^h. s +Thds)

* 22 a ("13 1331

(2^DjO + УНЭО + 2^DjS + ^HDsX^HjO + *HDO + 2*HaS + *hds) ’

where у refers to the mole fraction of the indicated species in the vapor and x in the liquid.

An expression will be derived for the dependence of a on the physical properties of the water-hydrogen sulfide system, temperature and pressure. The slight dependence of a on deuterium content will be neglected by considering only low deuterium abundances, at which *D, o ^ *hdo і etc. In this limiting case, the expression for a reduces to

(*hdo + *hdsX2th, o + 2thjs)

o = ;—————— . ‘ (13.134)

(Phdo + ThdsX2^h, o + 2xHjs)

The following properties of water, hydrogen sulfide, and their mixtures are used to evaluate

1. The humidity H of H2 0-H2 S vapor in equilibrium with liquid mixtures, defined as

Th2o H = ——

УН, й

2. The solubility S of H2S in liquid in equilibrium with vapor, defined as

*HsS Ss—Ї — *HaO

The dependence of H and S on temperature and pressure has been determined experi­mentally [S4] and is shown in Figs. 13.31 and 13.32.

3. The relative volatility a* of H20 to НЕЮ, defined by Eq. (13.5).

The dependence of a* on temperature has been given in Table 13.4; it is assumed to be unchanged by the presence of H2 S.

4. The relative volatility у of H2 S to HDS, defined as

JHjS*HDS

THDS^HjS

In the design of the Savannah River plant [B7] it was assumed that у equaled a*.

Roth et al. [R9] have determined у for anhydrous hydrogen sulfide and have found it to be substantially equal to unity. No data are available for values of 7 in aqueous solutions of hydrogen sulfide, but its value probably lies in the range 1.00 to 1.05.

5. The equilibrium constant k for the gas-phase deuterium exchange reaction,

H2 0(g) + HDS(g) ^ HDOfc) + H2 S(g)

defined by

T’HDOT’HjS

^HjOJ’HDS

The mole fractions Ущо, *h5s> *hds> /hdo. and xHdo occurring in Eq. (13.134) will be expressed in terms of yHjs> xh, o. and Thds by the following equations derived from those given above defining H, S, 7, к, and a*:

Th, o = HyHiS *Has = s*H2o

•THjS

*a**H30.yHDS J’H. S

The result of substituting Eqs. (13.139) through (13.143) into (13.134) is

(fca*XHao3,HDs/VHas) + (t^h^o^hdsA’h. s) tfyHjS + ^H2s _ ka* + yS # + 1

kHyHDS + ^hds *h, o + SxHio kH+ 1 1+5

(13.144)

The remaining mole fractions have cancelled out, and a has been expressed in terms of H, S, y, k, and a*.

Equation (13.144) is the exact expression for the deuterium exchange separation factor in liquid-vapor mixtures of water and hydrogen sulfide at low deuterium abundances. Values evaluated from it are customarily used without correction up to 15 percent deuterium. When the vaporization of water into H2 S is small (H< 1) and the solubility of H2 S in water is small (S < 1), Eq. (13.144) reduces to Eq. (13.77).

A number of experimental measurements and theoretical calculations have been made of the equilibrium constant к for the gas-phase reaction that have been correlated by the equation

к =АевЯ~ (13.145)

Values of A and В given by four investigators and к zX 32 and 138°C from Eq. (13.145) are listed in Table 1321.

The equilibrium constant ka* for the gas-liquid reaction has also been determined by a number of investigators. Results at several temperatures are given in Table 13.22. Data of Geib and Seuss have been computed from their equation for к given in Table 13.21 and their equation (13.146) fora*:

a* = 0.8624e6s-43/r (13.146)

30 40 50 60 70 во 90 Ю0 HO 120 130 140 150 160 —————————————————- TEMPERATURE *C———————————————————— Figure 13.32 Solubility of H2S in liquid water.

Table 13.21 Comparison of equilibrium constants for gas-phase reaction H20 + HDS ^ HDO + H2Sf Source Geib and Suess Bigeleisen Varshavskii and Vaisberg Roth et aL Reference [C31 [Bill [VI) [R91 A 1.010 1.051 1.0084 1.001 В 233 218 219.0 221.3 к at 32°C 2.167 2.147 2.067 2.067 138°C 1.780 1.786 1.718 1.715 t k = AeB/TM

There are substantial differences among the results for к and for ka* given by the various investigators. The equations of Geib and Seuss have been used by Bebbington and Thayer [B7] in the most complete published account of the Savannah River plant. Table 13.23 compares values of the separation factor a for the hot and cold towers of the Savannah River plant computed by Eq. (13.144) from the data recommended by Bebbington and Thayer with values computed from the data recommended by Roth et al. The data recommended by Bebbington and Thayer have been used in this chapter because they have been successful in interpreting the performance of the Savannah River plant.

The dependence of a on temperature and pressure, as computed from Eq. (13.144), is shown in Fig. 13.33. In the cold tower an increase in pressure decreases a because it increases the concentration of H2 S in the liquid more than it decreases the concentration of H2 О in the vapor. In the hot tower, an increase in pressure increases a because it decreases the concentration of H20 in the vapor more than it increases the concentration of H2S in the liquid.

Optimum operating conditions. Because the deuterium recovery increases with increasing ratio of a in the cold tower to a in the hot, it might be supposed that the optimum operating conditions would be the lowest possible cold tower temperature, the highest possible hot tower temperature, and low pressure. Other factors beside a must be considered, however.

An increase in pressure above atmospheric leads to lower costs, despite the reduced spread in a’s between the hot and cold tower, because of the greater mass flow rate of gas per unit area that can be taken through the towers at higher pressure. At a pressure of 300 psig, however, there is a discontinuous increase in the cost of equipment, because of the need to

Table 13.22 Equilibrium constant ka* for gas-liquid reaction H20(/) + HDS(g) ^ HDO(/) + H2S<g) Temperature, °С ka* Calculated from Geib and Seuss [C31 McClure and Herrick [М3] Haul et al. [H4] Interpolated from Roth et aL [R9] 24 2.38 2.38 2.267 25 2.37 2.35 2.259 78 2.03 2.02 1.948 141 1.79 1.82 1.729

Table 13.23 Comparison of separation factors at conditions of Savannah River plant

Tower

Cold

Temperature, °С 32 138

Pressure, psia 292 313

Humidity Я 0.0036 0.215

Solubility 5 0.027 0.0096

Source of data	DP-400 [B7]	Roth [R9]	DP-400 [B7]	Roth [R9]
к	2.167	2.067	1.780	1.715
a*	1.0686		1.0111
kot*	2.316	2.218	1.800	1.737
У	1.0686	1.000	1.0111	1.000
a	2.275	2.178	1.576	1.518

change to the heavier pipe and fittings required for use in this higher pressure range. This sets the optimum pressure around 300 psi. The same pressure is used in each tower, except for pressure drop due to flow, to keep gas-recompression costs at a minimum.

The optimum temperature of the cold tower is as low as possible without risking formation of a third phase in addition to vapor and aqueous solution. Table 13.24 gives the temperatures at which solid hydrogen sulfide hydrate or liquid hydrogen sulfide form in the system H2S-H20. At 300 psi, the minimum safe cold tower temperature is around 30°C. The rapid increase in condensation temperature above 300 psi is another reason for this being the optimum pressure. Before the first pilot plant for the GS process was operated, the possibility of hydrate formation was not recognized, and freeze-ups occurred until the cold tower temperature was raised above 30°C.

The optimum hot tower temperature is around 130 to 140°C and is determined by a balance between the improvement in separation at higher temperature and the increased costs for heat and for humidifying the gas entering the hot tower at higher temperature.

Effect of hydrogen sulfide solubility and water volatility on analysis of process. The solubility of hydrogen sulfide and the volatility of water introduce changes in flow rates of gas and liquid and deuterium concentrations at the top and bottom of the hot and cold towers. Figure 13.34 illustrates the flow scheme and nomenclature to be used in working out these effects.

The flow rate of liquid into the cold tower is increased from F, in feed water, to Lc leaving the top tray of the tower, owing to formation of a saturated solution of hydrogen sulfide. Lc then remains constant throughout the cold tower. Between the cold and hot tower the liquid flow rate is changed to Lh because of withdrawal of product P, addition of condensate La, and vaporization of some gas, Ga. Lh remains constant through the exchange section of the hot tower down to the point where liquid is drawn off to the H2S stripper and vapor from the humidifying section is returned.

Vapor flows up through the cold tower at a constant rate Gc until in leaving the tower the rate is reduced to G0 owing to solution of some H2S in incoming feed water. The vapor flow rate to the hot tower is increased from G0 to Gh by hydrogen sulfide from the stripper and by the water vapor needed to saturate the hydrogen sulfide at the temperature of the hot tower. Gh remains constant in the hot tower.

It is possible to set independently three of the nine flow rates F, Lc, P, Lh, La, Gc, G0, Gh, and Ga. The other six are determined by the following material-balance equations:

Table 13.24 Equilibrium conditions for three phases in H20-H2S system^ Pressure, psia Temperature, °С Third phase 15 1.1 Hydrate 30 7.5 Hydrate 50 12.2 Hydrate 100 18.6 Hydrate 200 25.0 Hydrate 300 28.9 Hydrate 325 29.5 Hydrate + liquid H2 S 400 38.6 Liquid H2 S 500 48.3 Liquid H2 S 600 56.1 Liquid H2 S tData from Bebbington and Thayer [В7].

1+SC 1 +Hh 1+Sft 1 +HC Around the vapor coolers and condensers (DCHG, Fig. 13.34) Total flow: G* + Ga= La + Gc

In designing a plant, G0 and P might first be set. At several values of F, Eqs. (13.151) through (13.154) would then be used to evaluate Gc, Lc, Gh, and Lh. The ratios a^/G,. and GhlLf, ah would be determined; the optimum value of F that leads to the minimum number of plates is the one at which

Gh <*C^C

Lhah Gc

This is equivalent to Eq. (13.114).

With the values of the flow rates thus determined, the nine atom fractions of deuterium xct, ул, xcb, ycb, xP, xht, yht, xhb, ^ Унъ may be related to the composition of feed xF and the number of plates nc and nh in the cold and hot towers, respectively, by the nine equations (13.161) through (13.169), derived as follows.

At the top of the cold tower, a deuterium balance on the streams above and below the point of H2 S solution gives

_ (Le F)xct LcXa Fxf —

where хл/(/ка*)с is a sufficient approximation for the atom fraction of deuterium in the hydrogen sulfide transferred from gas to liquid. Because Lc « F( 1 + Sc), this may be approxi­mated by

(13.161)

A deuterium balance over the cold tower gives

Ge _ _£c

I УсЪ xcb. yct xct

r-c ljc

The Kremser-type equation (13.120) for the streams at the top and bottom of the cold tower, converted to the notation of Fig. 13.34, leads to

A deuterium balance between the hot and cold towers, on streams flowing across CDEFGH in Fig. 13.34, gives

Lcxcb+Ghyht = PxP + Lhxht + Gcycb (13.165)

Similarly, a deuterium balance over the vapor coolers and condensers, on streams flowing across CDGH in Fig. 13.34, gives

~~ f G^fa ~ ^а^-сУсЬ Gcycb ah

A deuterium balance over the hot tower, on streams flowing across FGHIJ, gives:

Gh _ Gh

xht~J^yht~ xhb ~J^yhb

The Kremser-type equation (13.120) for the streams at the top and bottom of the hot tower, converted to the notation of Fig. 13.34, leads to

(13.168)

The final equation is obtained by making a deuterium balance on the vapor stream entering the bottom of the hot tower. The hydrogen sulfide content of this stream consists of G0/(l + Hc) mol from the top of the cold tower plus LhShj{ + Sh) mol recycled by the stripper and humidifier from the liquid leaving the hot tower. The deuterium content of this latter hydrogen sulfide is approximately xhbj{ka*)h. The water content of this stream consists of G0Hc/(l + Hc) mol from the top of the cold tower plus GbHbl( 1 + Hh) — G0HCI( 1 + Hc) mol supplied by the humidifier and steam from the stripper. The deuterium content of this latter water vapor is approximately xhb. The balance equation expressing the deuterium content of the vapor entering the exchange section of the hot tower is