To show the main features of the GS process, a simplified analysis is first given, in which the complications introduced by the solubility of hydrogen sulfide in liquid water and the vaporization of water into hydrogen sulfide gas are neglected. The effects of the solubility of hydrogen sulfide and the volatility of water on the process are considered in Sec. 11.7. Figure 13.27 shows the flow of gas and liquid assumed and the nomenclature to be used. Figure 13.28 is a McCabe-Thiele diagram for the process. The analysis is formally similar to that given for solvent extraction with constant distribution coefficients in Chap. 4.

To simplify the treatment further, only low deuterium abundances are considered, so that the atom fractions of deuterium in liquid x and in vapor у in the streams leaving stage і are related by

ya = f — (1359)

UC

in the cold tower and

Уы = ~ (13.100)

ah

in the hot tower. These are the equations for the equilibrium lines of the McCabe-Thiele diagram, which pass through the origin with slope jac and 1/ал.

For the cold tower, the overall deuterium material balance is

F{xp-xF) = G(yP-yF)

Figure 13.27 Nomenclature for simplified treatment of dual­temperature process.

The materia] balance above stage і is F(xc,(-1 — xF) = G(yd-yF) (13.102) or yCi=yF + ffxC’i_1 — xF) (13.103) or because of (13.101), Ур ~Ур Усі = УР + у. r (*c,.—i Xp) Xp—Xp ’ (13.104)

This is the equation for the operating line in the cold tower, which passes through the points (yp, xF) and (yp, xp) and has the slope

F _yp~yF G Xp — Xp

Similarly, in the hot tower, the equation for the operating line is

or Уы=Ур + 2—— —(хН’Ц1-XW) (13.107)

Xp-X w •

because

W _ Ур ~yF G Xp —Xyj

This line passes through the points (yF, Xy>) and (yP, xP) and has the slope W/G given by (13.108).

Because the deuterium content of water leaving the cold tower (xp) equals that entering the hot, and the deuterium content of hydrogen sulfide leaving the hot tower (yP) equals that entering the cold, the two operating lines end in a common point at top right. Because the deuterium content of hydrogen sulfide leaving the cold tower (yF) equals that entering the hot, the left end of each operating line is at the same value of y.

It is thus possible to draw the McCabe-Thiele diagram with equilibrium lines established from the separation factors ac and ah, and the operating lines established from specified values of feed, product, and waste compositions xF, xP, and Ху/ and assumed values of the gas-phase compositions yF and yP. The number of theoretical stages needed in the cold tower for a given set of conditions is then determined by the number of horizontal steps required to go from xF to Xp the number of stages in the hot tower, from the number of steps to go from Ху/ to xP. For the separation example of Fig. 13.28, the number of stages in each tower is 16.

The McCabe-Thiele diagram can be used to demonstrate two important characteristics of a dual-temperature plant.

1. If xF, Xyr, and yF are held constant and the number of plates in both towers is increased, the deuterium content of product Xp can be increased to any desired degree.

2. If xp, xF, and yp are held constant and the number of plates is increased, yp decreases and the lower end of each operating line approaches the corresponding equilibrium line. The maximum spread between xw and Xp occurs with an infinite number of plates, at which

(13.109)

The fractional recovery of deuterium is

PxP _ 1 — xw/xF Fxp 1 —x-w/xp

The maximum deuterium recovery possible is

1-— (13.111)

because usually xw/xP < 1.

This shows the importance of using a reaction in which the separation factor in the hot tower differs substantially from that in the cold; in fact, separation is possible only because the slopes of the two equilibrium lines in Fig. 13.28 are different. For the GS process example of Fig. 13.25, the maximum recovery of deuterium possible is

It is found in practice [B7] that the minimum number of stages for a given separation, or the maximum production rate for a given number of stages, is realized where two conditions are satisfied:

1. The approach to equilibrium at the top of the cold tower equals that at the bottom of the hot:

xf _ F ~ xw

and

2. The ratio of the slope of the equilibrium line to the slope of the operating line in the hot tower equals the ratio of the slope of the operating line to the slope of the equilibrium line in the cold tower:

l/a<i _F/G W/G /ac

The approximate validity of these two conditions can be seen qualitatively by considering the effect on the number of stages of changing the location of the operating lines in Fig. 13.28, while keeping xp and Хц> constant.

The diameter of the towers of a GS plant, the principal heat exchanger duties, and the heat consumption are determined mainly by the ratio of gas flow rate to product rate, G/Pxp. The optimum value of G is, from (13.114),

G = y/FWacah (13.115)

When F ** W, and

(13.116)

The gas flow rate per unit product is

G У«сал ,Pxp) min ~xF(l — ochl<*c)

For the GS process with natural water feed, / g V2.32 X 1.80 , „ Штіп * (0.000149X0.224) = 61>10° md ^/mo1 D*° <13’ll9> Although the minimum gas flow rate is large, it is much smaller than in the distillation of water [141,000, from Eq. (13.11)]. Moreover, the GS process can be operated at much higher pressure than water distillation, which also helps to reduce the number and diameter of towers. Equations for the dependence of composition in the cold and hot towers on stage number are obtained by application of Eq. (13.92) to the nomenclature of Fig. 13.27. For the cold tower, (a cFnc <*cyp-xP = ^Q-) (ЯсУр-хр) (13.120)

“c [(<*cF/G)nc — 1] [(G/Wah)nh +1 — 1]

| (xp/xF){[ac(F/G) -1](G/W)[(G/Wah)”*-!] + gJfrcW* — l][(G/№h) — 1]} ac МСГ’ — 1 ] l(G/WahT» +I -1]

(13.126)

(Cont.)

Because G/W depends on xw/xF through

G FG (xp/xF) — (xw/xF) g.

W WF (xP/xF)~ 1 F (.13.127)

Eq. (13.126) is implicit in Xy/xF and must be solved by trial. Figure 13.29 shows values of Xw/xF calculated for the specific case of nc = nh = 16; xP/xF = 4, for a range of values of G/F.

This figure brings out an important characteristic of dual-temperature exchange processes: The recovery (or production rate) of a given plant is very sensitive to the gas-to-liquid flow ratio. There is only a narrow range of flow ratios within which optimum performance is obtained. In the example of Fig. 13.29, the minimum value of xwjxFt 0.8563, is obtained at G/F= 2.03. If G/F is less than 1.85 or greater than 2.25, xw/xF becomes greater than 0.90, and the recovery of deuterium is decreased by 30 percent or more.

At the optimum value of G/F = 2.03, G/W = 2.127 and yF = 0.4558xF. The approach to equilibrium is

At top of cold tower: ^ = (132)^4558) = O’946 (13’128>

At bottom of hot tower: °^- = —= °-958 (13.129)

Хці U. oDo.5

Figure 13.29 Effect of vapor-to-feed ratio on recovery in GS process example, = 1.80; ac = 2.32xp/xF = 4; nc = nh = 16.

The McCabe-Thiele diagram, Fig. 13.28, is drawn for this separation at the optimum flow ratio G/F — 2.03. At this optimum condition, the size of each step in the cold tower is approximately equal to the size of the step in the hot tower at the corresponding plate. In operating the Savannah River plant [B7], the flow ratio of gas to liquid is controlled to give optimum performance by setting it so that the deuterium content of corresponding streams at the middle of the hot and cold towers are equal. In Fig. 13.28 this is illustrated by the fact that the deuterium content of vapor flowing between the eighth and ninth plates of the hot tower (step A) is approximately equal to the deuterium content of vapor flowing between the eighth and ninth plates of the cold tower (step B). Use of this principle greatly simplified what would otherwise be a difficult problem in flow control.