12. 13,

14.

W. A. Bain and O. A. Hougen, "Flooding velocities in packed columns," Chem. Eng,, riO, No. i, 29-49 (1944). Yu. L. Sorokin, A. G. Kirdyashkin, and B. G. Pokusaev, "Investigation of the film flow of liquid in a vertical pipe with an upward flow of Mashinostr., No. 5, 35-38 (1965). T, Wallis, Unidimensional Two-Phase Flow [Russian translation], Mir,

COMPUTER DESIGN OF EVAPORATORS

FOR MULTICOMPONENT

Trans. Amer. Inst. of the stability gas," Khim, Neft. Moscow (1972).

CRYSTALLIZING SOLUTIONS UDC 66,048.54.001,24 681.3

V. S. Postnikov and V. M. Ronkin

The design of multi-effect evaporators (ME) is greatly complicated by the need to account for the composition of real, m~iticomponent solutions. At the same time, the effect of the amount and composition of precipitated components on the processes taking place during concentration by evaporation becomes significant to the extent that the components of the solution become saturated and crystallize [i]. When the product quality depends on the composition of the components of the concentrated solution, it is also necessary to determine the operating program of the ME and the locations at which the solid phase is drawn off that will e n s u r e the production of a product of the specified composition. A familiar method of designing ME for the evaporation of saturated salt solutions [2] was developed without accounting for their multicomponent character. We have developed a method of ME design that takes the composition of multicomponent solutions into account and is not especially difficult with the use of a computer: a system of linear equations serves as balance equations and an additional component is accounted for formally by increasing the order of the system by unity. It is not only possible to solve the system of linear equations with a standard subroutine on the computer, but it is also possible to choose design quantities and vary the number of crystallizing components with the use of a program module for solving the system of balance equations for the apparatus. The algorithm for this module is outlined below. When there are k components in the solution to be evaporated, the control system consists of 2 + k equations: one for material balance, one for heat balance, and k equations for salt balance. For 3 + 2k given enthalpies

~; =

4 t',

I; = c'2 t',

t

t~ = ~ t', . . . .

l~=c'~t",l;=e;t", . . . . I;=c'~t";

I~ = % t';

l'=c't';

1[ = ~ r',

I"--=c"t";

1==1 (0)] t

I

1

'!

and 2k11 concentrations of the components in a saturated solution (b'~, b2, b3, .... bk; bl, 11 11 b2, b3, ,.., b k) that are dependent on temperature and solution composition, we must assign (k + i) of the 3 + 2k material flow rates (G', G~, G~, . ., G~; . G?. . .G",. G~. , G k,''" S', S", W) in order to calculate the remaining (2 + k) flow rates (in these expressions, I denotes the specific enthalpy KJ/kg; c is the specific heat, kJ/kg.~ t and 0 denote the temperature of the solution and the secondary vapor, ~ b is the concentration of the solution, %; G, S, and W denote the flow rates of the crvstals, solution, and secondary, vapor, respectively, kg/h; and the symbols ', ", a n d O , respectively, denote parameters of the incoming and outgoing streams and of the original solution). Such an assignment may be carried out with (3 - 2 k)~ (2n-k)! (1 :-k)! variants.

Uo w i l l

cousider

an

algorithm

for

the

calculatiou

of

one of

these

variants.

Assign a flow rate for the streams at the inlet and then we must determine the flow rate of the streams at the outlet of a direct-flow apparatus. In this case we have the following system of equations:

Translated from Khimicheskoe i Neftyanoe Mashinostroenie,

224

0009-2355/83/0506-0224507.50

No. 6, pp.

9 1984 Plenum Publishing

18-21, June, 1983.

Corporation

i-l,

1, 1, ,,,,

-o', "~ [ 1; l, ) ..... ~, io; ] t 1 " 4 ' t ; :.,1;,1' a~] , , o , o . . . . . o,~;

1, 1, 1

it, 1 , I s . . . . .

lk, 1", 1 (0) fl

l, O, 0 , . , . , O, b~, 0 O, I, 0 . . . .

, O, b2, 0

'

O, O, I,

, O, b3, 0

,

/

al )

O, I, 0,'... , O, b'2

=

0, 0, 1 . . . . .

0, b~ k

,,

o,o,o .....

,

S'

~,b;

The solution of this problem on the computer reduces to the formation of a matrix of coefficients and of the right sides of the equation system for conversion to d subprogram that solves a system of linear equations of n = k + 2 order, To do this, it is necessary to set up a table of the original information (Table i), which consists of a sequence of files in the computer memory consisting of 3 + 2k elements each and contains: stream directions (assigned "ones" with + and -- signs for incoming and outgoing streams respectively); strewn flow rates arranged in a fixed sequence (for example, G~, G~, G3, ..., Gk; G~, G2) G ~ .,., I! ! ,I Gk; S , S , W); variant code, defined by a set of (k + i) "ones" (for the assigned values) and (k + 2) zeroes (for calculated values); values of the stream enthalpies arranged in a fixed sequence corresponding to the arrangement of the flow rates; files for each of the k components for the registration of (2k + 3) concentration values in an assigned sequence corresponding to that of the flow rates, wherein, for the m-th component in the ~-th file of concentrations (~, m = i, 2, 3, .,., k)

bl, m

I,

if

l=m;

O,

if

l#m,

for streams of solution S' and S" the saturation ary vapor streams W, b = 0.

:

concentrations

are b

and bl, and for second-

Table 1 lists the original information for the variant in question. Note that in solving any other variant, the table has an analogous form, only the variant code changing. A block diagram of the solution of the variant in question is shown in Fig. I. The variant of the solution of the system of balance equations described above is realized step by step over the course of the heating vaporin the design of the direct-flow ME. A program module is used for which the algorithm is shown in the figure. This program module can also be used to design a countercurrent ME by appropriately specifying the directions of the streams in the original information table. ~ with parallel direct-flow input or a direct-flow ME. with a recirculating stream require the addition of one stream with assigned enthalpy and component concentrations. The TABLE

1 notation

Column

Line

'

designation

Line

i notation

.

,

Stream direction

j

dz

I

xl U ,

[ i

Vlowrate

V~antcode

! x'2,1

E.t.oipy

i "3,

+I

centrations

weight

fraction

b2 I "

I

I

X(3-~2),i

I

I

t

--O; G:i.

lj r 11I"

,; 1; I

.

J

.

.

.

,

-El ~, . . .!;I+I

o Compon e n t con-

.

3

I Gk

5'

S"

W"

: I

--I

i--t

. .

.

--I

-:-1

--!

--1

t O~

"iI I

i 4 o

o] o ' , . . f o i , j o! ' o : - , T - ..... . - - - - 7 J:'F J/!-lk / , ~ l...... . . j . 'o....., 1 t]

0

I

,

. .

0

1

bit X(3.+k),f I 0

., 0

.~..I..I,.I.

.

.

.

.

.

.

.

.

.

.

oj ,I ol ojo 225

'Table of original information'i ~'[ j=O, yj =O,y~ = Q [

lj=J+~ J 1" [~o0, zog I I i=z§ ]

Y

e

~

~

Fig. i~ Block diagram of the solution of the system of balance equations for the evaporator.

__

Yes . 9 ~ No Solution of the equation

. system

]

flow rate of the stream is either assigned or calculated, depending on the variant of the solution of the balance equation system for the apparatus. The program contains (2k + 4) flow f ! ~ ~ f! 11 11 rates: GI, G2, G3, ..., Gk; G~, G2, Gs, ... Gk, So', S', S", W, and the system consists of (k + 2) heat balance equations. Of all the possible variants of the solution of the balance equation system, two are of the greatest interest in the ME design and they differ from the 9 . . ! one dlscussed above by the addltlon of a stream So to the set of assigned input streams (for instance, a recirculating stream) or by the fact that the flow rate So is calculated for an assigned value of one of the output streams. In the latter instance, one can for example calculate the distribution of parallel feed streams to the ~ for a given distribution of the solid-phase concentrations of one of the crystallizing components at the ME outlet. The method we have described for taking crystallizing components into account was used for the computer design of a Nairi-2 installation for concentrating electrolytic alkalies with direct-flow and parallel direct-flow feed input. We will present as an example the results of a design of a four-stage direct-flow installation with and without removal of the solid phase. The calculation was performed with the following input data: heat-exchange surface the same for all the stages: productivity of the installation with respect to the original solution So = i000 kg/h;original concentration in the solution of NaOH boo = 9.6 wt, %, NaCI bol = 16.7 wt. %, Na2SO4 bo2 = 0.5 wt. %, NaOH concentration in the evaporated solution b" = 50 wt. %; temperature of the original solution at the inlet to the first Stage 424.82~ with removal of solid phase and 424.49~ without removal with vapor bleed from the first stage 36.86 and 36.5 kg/h, respectively, from the second staF~e 41.64 and 42.75 kg/h, respectively; pressure of the heating vapor in the first stage 0.981 MPa, temperature of the secondary vapor in the fourth stage 313~ loss of available temperature difference; I~ in secondary vapor pipelines, 2.5~ in reheating the solution in the first-stage pipes, and 1.5~ in the second, third, and fourth-staRe pipes. The calculations made use of data from [3] for the determination of enthalpy, heat of condensation, and pressure of the saturated vapor, and data from [4] for the determination of the physical properti4s and composition of the saturated solution. The specific heat of the solution )and the solid phase were. taken to be 3.18 and 0.91 kJ/(kg.~ respectively; the heat transfer coefficient in the first stage was taken as 2650 W/(m2.~ It was assumed that the heat of hydration and heat of crystallization compensate for each other. The temperature program was calculated by familiar procedures [5, 6] and we used a standard subprogram for solving a linear system of equations to solve the system of balance equations. The results of the calculation (Table 2) show that k = 0 in the first stage (no crystallization) and the order of the balance equation system in n = 2; k = 1 in the second and third stages (crystallization of NaCI) and n = 3; k = 2 in the fourth stage (crystallization of NaCI and Na2SO~) and n = 4. If we compare the calculated variants, we also see that re-

226

TABLE 2

K,/KI 0, K

St~go

First

1

I

0,481

t " /< A K bNaOH' hNaClo'

440,0~' 17,75

11,8~6

;~,884

Sr162

0,679[- 1,0507

6,566

413,20

_L.t

2~,~80

15,49

16,6;~

2,654

2 0 1 1608,4, 1 0 0~ j 839,1~ ,

I130,30 162,76

o0,6747 ,,1283 7,218 3~,00

,73~

23,~o~

Io,363

Forth

0,8527 1.402g! 11,342 356,83

43,83

50,015 I ~,SB~

i

I

7,83

601,95

6~,ll

1,81o

1~8,9~ 141,~6 16,09

403,00

57,~9

0,09~3

157,6~ 169,89

],gl,?B

2,685

ThUd

0

0,093

--

16~,~ I,

0

0

0 o

4,,2

Notes: ]) Numerator denotes the value for removal of the solid'phase; denominator, without removal. 2) Notation: Q) heat load; K) heat-transfer coefficient; v) available temperature difference; A) temperature depression; D) flow rate of the heating vapor; R) amount of vapor arising from self-evaporation of the condensate~ moval of solid phase in the second and third stages results in increasing the flow rate of the heating vapor but permits the production of sodium chloride without any sodium sulfate imp uri ty. LITERATURE CITED i. 2. 3. 4. 5. 6.

V . I . Leverash, "Evaporator design and optimum conditions for the evaporation of nitrate-phosphate slurries," Khim. Prom., No, i, 49-52 (1975). V. So Pokin, "Design of multistage evaporators for the evaporation of saturated solutions," Khim. Tekhnol., No. i, 40-42 (1974). M . P . Vuka!ovich, S. L. Rivkin, and A. A. Aleksandrov, Tables of Thermophysical Properties of Water and Water Vapor [in Russian], Izd. Standartov, Moscow (1969). L . M . Yakimenko and H. N. Pasmanik~ Handbook for the Production of Chlorine, Cuastic Soda, and Basic Chlorine Products [in Russian], Khimiya, Moscow (1976). M . A . Tishchenko, Theory and Design of a Multistage Evaporator [in Russian] ~ Mosko Inst. Khim. Mashinostroenie (MIKhM), Hoscow (1938). N . I . Gel'perin, Evaporators [in Russian], Goskhimizdat (1947).

APPLICATION OF THE ENTROPY INDEX TO EVALUATE THE EFFICIENCY OF SEPARATOR OPERATION R. Ya. Agranonik, S. Yu. Shishmakov, and Sh. Sh. Shamanaev

UDC 66.067.55.001.24

The selection of the optimum operation regime for centrifuges, separators, or hydrocyclones in separating and thickening wastewater sludges is attended with appreciable difficulties because of the lack of generalizing criteria for evaluating the efficiency of their operation. Optimizing the process of thickening wastewater sludges calls for ensuring a high apparatus productivity, and a maximum degree of clarification of the overflow (effluent) and a maximum ratio of the volume o f effluent to that of thickened product. As data from studies of the process of thickening the activated sludge from treatment works on an NV-600 separator of (1.5-7.5)-10 -3 m3/sec, with discharge nozzles (1.6-4).10 -3 m in diameter indicate [I], an increase in the solids content of the thickened product leads simultaneously to an increase in solids content of the effluent: at an original solid phase content of 6-12 kg/m ~, this figure varies within the limits 18-80 and 0.1-3 kg/m 3 in the thickened product and the effluent, respectively. It is possible to determine the separator operation regime which ensures an optimum ratio of the solid phase contents of the thickened activated sludge and of the effluent by Translated from Khimicheskoe i Neftyanoe Mashinostroenie, No. 6, pp. 21-22, June, 1983o

0009-2355/83/0506- 0227507.50

9 1984 Plenum Publishing Corporation

227