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A Activity, 354

Activity coefficient ratio, 363

Activity coefficients, see also Distribution co­

efficients; Hyperfiltration in aqueous solutions, 362, 366, 368 in membranes, 362, 366

in water-organic solvent mixtures, 396 Amide-water mixtures, 401

Amortization procedure, 27 Anhydrite, see Calcium sulfate Anion exchange, see Ion exchange

Anion permeable membranes, see Mem­

branes, ion exchange Arid zones, water problem, 3 Availability, 44, 52, 64 Available energy, 44, 63

´ Blasius equation, 412

Blending, desalted and raw water, 520 Boiler condensate

filtration of, 460

ion-exchange treatment of, 461, 467 Boilers

condensate, 454

feed water, table of specifications, 453 Boiling point elevation, 88

Boundary layer, see Concentration polariza­

tion

"Break-even" cost at zone boundaries, 26 Brine, 78

Butane, 311

C

Calcium carbonate, solubility of, as function of p H , 500

Calcium sulfate

different crystal forms, 502

solubility of, in sea water concentrates, 502, 503, 504

transitions between different forms, 504 Carnot principle, 56

Cation exchange, see Ion exchange Cation-permeable membranes, see Mem­

branes, ion exchange Cell exergy, 68

Cellulose acetate membranes acetylation, 386

casting solutions, 384, 388 preparation of, 384 salt rejection, 389, 390 stability of, 389 structure of, 386

transport properties of, 389 Chemical potential, 47, 51, 216

Chemical potential difference, as driving force in hyperfiltration, see Hyperfiltration, driving force

Chemicals, for water treatment, see Water treatment, chemicals for

Chilton-Colburn analogy, in hyperfiltration, 411

Chlorination, 445, 476 Coagulation, 445, 476 Co-ion exclusion

membranes, 363, 397

porous ion exchange bodies, 364, 366 Colt process, see Freezing processes, direct Combination plants, 17

solar power and stills, 193, 195

thermodynamic comparison with plants for distillation only, 83

Compression distillation, see Vapor compres­

sion distillation

Concentration polarization, hyperfiltration, 40J

entrance region, 406 laminar flow, 403 nomogram for, 414 turbulent flow, 410, 414 unstirred systems, 355

5

558

(2)

S U B J E C T I N D E X

559

Concentration potential, 220, 221, 238 Concrete construction, for vapor reheat stills,

146

Condensate, filtration of, 447 Conductance

electrolytic, 12 equivalent, 268 heat exchangers, 148 thermal, 35, 41, 43 Conductivity, 218 Conveyance of water

cost of, 537, 540

effect of electric power costs, 539 of hydraulic gradient, 542 in horizontal pipe lines, 540 in inclined pipe lines, 543 static lift, cost of, 541 Corrosion

boilers, 452

influence on scale formation, 511 power plants, 466

Cost accounting equations, 31 Cost balances, 25

Cost components of conventional water sup­

ply, see names of components, e.g., conveyance of water, cost of

"Cost vector," 31

Coulomb efficiency, see Faraday efficiency Coupled transport processes, 215, 373 Coupling of fluxes, hyperfiltration, 376 Critical velocity, in electrodialysis, 234 Crops, agricultural, water requirement, 3 Current efficiency, in electrodialysis, 225

D Datum constants, 49 Datum level, 49 Deaeration, 448, 449 Deaerator, 329

control of, 476 Debye-Hiickel theory, 10 Dechlorination, 447

Degassing, 448, see also Deaeration Demineralizers, see Ion exchange resins, beds Demonstration Plants

Freeport, Texas, 16 Roswell, New Mexico, 17 San Diego, California, 16 table of, 18

Webster, South Dakota, 17

Wrightsville Beach, North Carolina, 17

Desalination plants, table of, 6

Desalination processes, classification of, 15 Desalting processes, see Desalination processes Diffusion, 57

Diffusion coefficients

in hyperfiltration membrane, 390 in phenomenological analysis of hyperfiltra­

tion, 375, 391

in water-organic mixtures, 397 Dihydrate, see Calcium sulfate

Dispersion plates, for liquid-liquid heat ex­

changers, 137, 146 Dissipation, 64, 67 Distillate, 78 Distillation, 77

boiling, 93 critical, 89 flash, 102

comparison with vapor reheat distilla­

tion, 119, 124, 126, 147 large plants, cost, 147 multistage, 118 high-pressure, 89 multiple effect, 92

near-critical, see Distillation, critical single effect, 87

solar, 152, see Solar distillation systems engineering

general, 77 internal, 87 use of reject heat, 87 vapor compression, 110

vapor reheat, see Vapor reheat distillation Distribution coefficients, membrane-solution,

363, 377

Donnan effect, 214, 215, see also Salt inva­

sion, membranes Draft

firm, 531 reduced, 532, 533 storage curve, 532 years of, 534

Driving forces, relative magnitudes, 217 Dual-purpose plants, see Combination plants

Ε

Economics, comparison of different desalting methods, 424, see also specific meth­

ods, e.g., Hyperfiltration, economics of; Thermoeconomics

(3)

560

SUBJECT INDEX Effective pressure, 351

Electrochemical potential, 221

Electro-decantation, see Electrogravitation Electrodialysis, 200, see also Membranes, ion

exchange as pretreatment, 442 cost of, see economics of current efficiency, 225, 227 current reversal, 245 current utilization, 226, 267 economics of, 277, 280 energy requirements, 201, 271

comparison with distillation, 202 neutral membrane, 204

pH changes, see Electrodialysis, polariza- tion, water splitting

polarization, 230, 268 critical velocity, 234 water splitting, 231 posttreatment of water, 262 pretreatment of water, 260 principle of, 201, 204 pulsing, 245 salinity range, 258

selective, 243, see also Membranes, ion ex- change; Electrodialyzers

water quality, 260 Electrodialyzers

batch, 256, 272 cells, 242, 248

co-current and countercurrent, 248 continuous, 255, 272

crossflow, 252

current-voltage characteristics, 233 dimensions, influence on performance, 269 electrode reactions, 246

energy consumption, 241 feed-and-bleed, 256, 275 instrumentation, 259 internal staging, 276 manifold losses, 227 performance equations, 264 polarity reversal, 245 power requirements, 272 resistance, 267

spacers, 248, 250 stack resistance, 235 stack voltage efficiency, 235 stacks, 242, 252

staging, 253, 276 voltage control, 258

voltage requirements, 234 Electrogravitation, 205, 263, 284 Energy

for desalting, 16

minimum, for desalting, see Exergy, mini- mum for desalting; Enthalpy of desalt-

ing

requirements, distillation, 78, see also sep- arate methods, e.g., Hyperfiltration, energy requirements

Enthalpy, generalized, 60

Enthalpy balance, in distillation, 78 Enthalpy of desalting, 78

Entropy, partial, 59 Entropy creation, 25, 54

Evaporation, for preparation of ultrapure wa- ter, 449

Exergy, 23, 45

availability and, 24, 52 categories of, 25, 69 chemical, 24

definition of, 45, 50, 51, 65

minimum for desalting, 13, 37, 64, 201, 357 thermomechanical, 69

Exergy balance, 56, 66 Exergy dissipation

categories of, 25

related to entropy creation, 25, 70 Exergy function, generalization, 61

Exergy requirements, minimum, for desalting NaCl solutions, 357

Exergy.transport, 70

F

Faraday efficiency, 225 Faraday's constant, 214 Filter media, see Filters Filters, 446, 450, 460

anthracite, 446, 477

carbon, activated, 446, 447, 468, 478 cartridge, 450, 479

cellulosic, 446, 460, 479 diatomite, 447, 478 sand, 446, 478 screen, 480 submicron, 450, 479

Filtration, 446, 460, see also Filters condensates, 447

control of, 476 cost of, 543 Firm draft, 531

(4)

S U B J E C T I N D E X

561

Fixed-charge membranes, see Membranes, ion exchange

Fixed gases, effect on mass transfer, 133 Flash pots, 94

Food chain, and water requirements, 3 Free energy, total, of NaCl solutions, 358 Freezing point depression, 299

Freezing processes, 291 butane, 313

counterwasher, see Wash-separation col­

umn direct, 310, 315

air removal, 329, 333

capital equipment, table of, 335 compressor, 324, 327

cost vs. capacity, 338

counterwasher, see Wash-separation col­

umn economics, 334 flow diagram, 318, 320 heat exchangers, 321 hydroconverter, 319, 324 mass and energy balances, 320 melter, 317, 327

plant layout, 331, 332

power requirements, table, 336 prefreezer, 323

scale model, 333, 334 schematic, 316 energy requirement, 299 history of, 292

hydrates, see Hydrate processes indirect, 309

melter, 317

thermodynamics of, 298

vacuum freezing-vapor compression, see Freezing processes, direct

vapor absorption, 312

G

Gained output ratio, 80

Gas constant, and related expressions, table of, 356

Gibbs chemical potential, 47, 51, 216 Gibbs-Duhem equation, 49

Gibbs function, see Chemical potential Gibbs potential, see Chemical potential Global systems, 49

Glycerol triacetate-water mixtures, 398, 399 Glycol-water mixtures, 399

Graetz-Nusselt heat transfer problem, 404

Η Harned's rule, 397 Heat exchangers

freezing processes, 321

liquid-liquid, 134, 139, 146, see also Vapor reheat distillation

construction of, 137, 146 for large plants, 143 heat transfer coefficients, 140 hydrocarbons for, 134 hydrostatic balance, 138 pumping energy, 144 sectionalized, 136, 145 thermoeconomics of, 35 Heat of transport, membranes, 224

Heat-transfer coefficient, 91, see also Heat exchangers

in distillation, 91 liquid-liquid, 140, 141

table of, 142

Helical boiler, for vapor reheat distillation, PH. 131

Helical condenser, for vapor reheat distilla­

tion, 132

Hemihydrate, see Calcium sulfate Hydrate processes, 339

flow sheet, 340 propane, 341

flowsheet, 342 Hydration, 11

Hydrocarbons, as heat transfer liquids, 134 Hydroconverter, definition of, 319

Hydrogen bonding, in hyperfiltration, 371 Hydrogen bonds, in water, 7, 8

Hyperfiltration, 345 breakthrough curve, 353

concentration polarization, 352, 355, 402, 410, 414

concentration profile in membrane, 377, 378, 380

diffusion coefficients, 375 driving force, 368 economics of, 421

comparison with other methods, 423, 424 effect of membrane cost, 425, 428 optimized conditions, 428 energy requirements, 353

equilibrium thermodynamics, 362, 397 equipment, 416

flux coupling, 376, 377

(5)

Hyperfiltration (continued) history of, 348

irreversible thermodynamic analysis, 371 mechanism of, 370

membranes, 348, 383, 392 cellulose acetate, 348, 384, 389 clay, 393

distribution coefficient, 363, 367 fibers, hollow, 421

ion exchange, 348 miscellaneous, 391, 394 model solutions, 395 salt uptake, 362, 397

solvent mixtures as models for, 395 optimization, 426

phenomenological analysis, 371 principle of, 351, 353

pumping work laminar flow, 415 turbulent flow, 413, 414 porous ion exchange bodies, 364 recovery of compression energy, 361, 422 salt rejection, see Salt rejection

sewage treatment, 430

solvent mixtures, as models for membranes, 395

transport equations, 373 turbines for discharge, 361, 422 urine, 421

I

Ice, see also Sea ice, Ice crystals crystallization, 300

wash column, 307

Icebergs, as fresh water source, 293 Ice crystals

growth, 301 habit, 301 nucleation, 303 purity of, 301, 304

separation from brine, 306, 314 size, 297

supersaturation, 303

Impoundment, cost of, 531, 536, see also Res­

ervoirs

Information theory, 23, 44 Intake

surface, cost of, 544, 545 wells, see Wells

Ion exchange, 447, see also Ion exchange res­

ins

in water treatment, 447, 455

Ion exchange capacity, porous bodies, 365 Ion exchange membranes, see Membranes,

ion exchange Ion exchange resins, 481

beds

backwashing of, 482 control of, 477

counterflow operation of, 487 fouling of, 487

head loss in, 482

mixed, 447, 459, 461, 466, 468 operating characteristics; table of, 459 operating characteristics, table of, 458 precipitation in, 486

pressure loss in, 482 clumping, 483

condensate treatment, 461, 467 high temperature stability of, 485

"nuclear" grade, 466 radiation effects on, 485 regeneration of, 463 solubility of, 483 stability of, 484, 485, 486 sterilization of, 450, 472

table of those manufactured in U.S., 481 testing of, 484

Ion transport, 203, see also Membranes, ion exchange

Ionic membranes, see Membranes, ion exchange

Irreversible thermodynamics in thermoeconomics, 25, 63, 67 membranes, 215, 373

Κ

Keenan availability, see Availability Koppers process, see Hydrate processes

L

Latent heat condensation, 79 evaporation, 79

Limiting currents, electrodialysis, see Electro­

dialysis, polarization

Liquid-liquid heat exchangers, see Heat ex­

changers, liquid-liquid

Logarithmic mean temperature difference, 91

(6)

S U B J E C T I N D E X

563

Μ

Magnesium hydroxide, solubility of, as func­

tion of p H , 500

Make-up water, for nuclear power plants, 465 Mass transfer coefficients

effect of fixed gases on, 133 vapor reheat distillation, 130

Mean temperature difference, logarithmic, 91 Membrane potential, 220, 222

Membranes

for hyperfiltration, see Hyperfiltration, membranes

ion exchange, 201, 206 calcium transport, 244 heat of transport, 224 inorganic, 393

irreversible thermodynamics, 215 manufacturers, list of, 207 permselectivity, 226 polarization, 230 preparation of, 213 properties, 208

table of, 209 salt uptake, 363 selective transport in, 201 transport properties, 201, 213, 218 water transfer, 228

permselective, 203, see also Membranes, ion exchange

Minimum energy for desalting, see Exergy, minimum for desalting, Enthalpy of desalting

Mixed-bed ion exchange, 447, 459, 461, 466, 468

Mobility, electrical, 214 Ν Nernst-Einstein relation, 231 Nernst-Planck equations, 231

Neutral membrane electrodialysis, 204, 262, 282

Nuclear power plants, see Power plants, nu­

clear

Nuclear process water, preparation of, 468 Nucleation, see Scale, nucleation

Ο

O M R , definition of, 538 Optimization

combined distillation and power plants, 83

electrodialysis, 278 exergy-cost balances, 33 hyperfiltration, 426 nonlinear cost equation, 70 procedure, summary of, 42 vapor reheat distillation, 148 Osmosis, reverse, see Hyperfiltration Osmotic coefficient, 354

Oxygen removal, 449, see also Deaeration

Ρ Peclet number, 404

Perchlorates, effect on glycerol triacetate-wa­

ter systems, 402 Performance ratio, 80 Permselectivity, 226

Phase diagram, sea water-ice, 297

Pierre, S. D. water supply, as illustration of components of conventional supply, 547

Pipe lines cost of, 538

horizontal, optimized conveyance condi­

tions, 540 hydraulic gradient, 542 inclined, 543

right of way costs, 537 static lift, 541

Plants, see Desalination plants

Plastic covers, for solar stills, see Solar distil­

lation, plastic covered stills

Polarization, see Concentration polarization, Electrodialysis, polarization

"Potential" scale, see Scale, "potential"

Power plants nuclear

coolant water, 466 make-up water, 465 pool water treatment, 467 water requirements, 452, 465

Power-water plants, see Combination plants Precipitation, annual, 1, 2

Present-value method, water cost estimation, 526, 527

Pressure, effective, 351 Principal product, 27 Product ratio, 121

"Profit taking," at zone boundaries, 26 Pump stations

investment costs, 539

(7)

operation, maintenance, and repair costs, 539

Pumping power, in distillation, 81 Pyrogens, 442, 444, 451, 471

R

Radiation, solar, see Solar radiation Raoult's law, application to brackish water,

356

Rectangular boiler, for vapor reheat distilla- tion, 128, 129

"Reduced 274 day low flow," 532 Reduced draft, 532, 533

Refrigeration, see Freezing processes Regenerative use of heat of evaporation,

79 Reservoirs

cost of, 528 necessary size, 531

operation and maintenance, cost of, 530 Re-use of water, 5

Reverse osmosis, see Hyperfiltration Reynolds number, in hyperfiltration, 410, 412 Runoff, 2

S

Saline water conversion, see Desalination processes

Saline water program, U.S., history of, 15, 516

Salinity, 295

Salt exclusion, see Co-ion exclusion Salt filtering, see Hyperfiltration

efficiency, see Salt rejection

Salt invasion, membranes, 363, 377, 397 Salt rejection, 352, see also Co-ion exclusion,

Salt invasion, Activity coefficients clay membranes, 393

coupled flow, 379 definition, 377

effect of concentration polarization, 409, 412

of distribution coefficients, 382, 390 of pressure on, 382, 390

mechanism of, 370 noncoupled flow, 381 Scale, 497

boundary layer effects, 510

in electrodialysis, 246, 506, 513

influence of evaporator operating tempera- ture on nature of, 501

of nucleation site, 511 of residence time, 510 nucleation, 507, 511 nucleation time, 508, 509

"potential," 505 prevention of, 246, 512 seed control, 512

Sea ice, salinity distribution in, 292 Sea salt solutions

minimum exergy for desalting, 357 osmotic pressure of, 359

Sea water, see Sea salt solutions concentrates, see Sea salt solutions phase diagram, 297

Sediment, 498

Separation processes, general discussion, 14 Shaft work, 55

Shell deodorized spray base, 135 Sludge, 498

Sodium chloride solutions

minimum exergy for desalting, 357 osmotic pressure of, 360

Softening

by electrodialysis, 245 cost of, 543

Solar distillation, 151 basin stills, 175, 176, 183 convection in, 162 cost of, 187

Daytona Beach station, 168, 183 design of stills, 174

direct, 157 economics of, 187

efficiency of, definition, 160 energy balance

qualitative discussion, 157 quantitative relations, 160 experimental studies, 168, 182 glass-covered still design, 174, 182 heat and mass transfer correlations, 173 indirect, 193

indoor still studies, 168

influence of brine depth, 166, 167, 172 laboratory studies of isolated factors, 168,

171

list of sizable installations, 174 miscellaneous designs, 181, 184 plastic-covered still, 177, 184

(8)

SUBJECT INDEX 565

p r i n c i p l e of, 1 5 7 p r o d u c t i v i t y

l a b o r a t o r y still, 1 6 9 , 1 7 1 t h e o r e t i c a l , 1 6 3 , 1 6 4 s c h e m a t i c of b a s i n still, 1 5 8 s m a l l s t i l l s , 1 8 4

t i l t e d w i c k still, 1 7 9 , 1 8 5 m u l t i p l e - l e d g e , 1 8 0 t r a n s i e n t c o n d i t i o n , 1 6 5 S o l a r h e a t s u p p l y , 1 9 3

S o l a r r a d i a t i o n , i n t e n s i t y of, 1 5 2 , 1 5 3 S o l a r stills, see S o l a r d i s t i l l a t i o n S o l i d s

d i s s o l v e d , 4 4 4

s u s p e n d e d , 4 4 4 , 4 4 5 , 4 7 4 t o t a l , 2 9 5 , 4 4 2 , 4 7 0 S o l u b i l i t y p r o d u c t , 5 0 4 S o l u t i o n s

e l e c t r o l y t e

p h y s i c a l c h e m i s t r y of, 1 0 t r a n s p o r t p r o p e r t i e s , 12 n o n e l e c t r o l y t e , 1 0

S p e c i f i c e n e r g y c o n s u m p t i o n , 8 2

S p r a y b a s e , for l i q u i d - l i q u i d e x c h a n g e , 1 3 5 S t e r i l i z a t i o n , 4 5 1 , 4 7 0

Stills, see D i s t i l l a t i o n S t r e a m i n g p o t e n t i a l , 2 2 4 S u s p e n d e d solids, 4 9 8 S u p e r s a t u r a t i o n , 4 9 9

in e l e c t r o d i a l y s i s , 2 4 6 , 5 0 6 , 5 1 3 S w e l l i n g p r e s s u r e , 2 1 4

S y m i s o l a r still, 1 7 8 S y n t h e s i z e d c o s t s , 5 2 4

d e f i n i t i o n of, 5 2 5 S y s t e m

d e f i n i t i o n of, 5 0 g l o b a l , 4 9

Τ

T h e r m a l l o a d , 91

T h e r m o e c o n o m i c s , d e f i n i t i o n of, 2 2 T r a n s f e r e n c e n u m b e r , 2 1 9

d e t e r m i n a t i o n of, 2 2 2

T r a n s p o r t d e p l e t i o n , 2 0 4 , see also N e u t r a l m e m b r a n e e l e c t r o d i a l y s i s

T r a n s p o r t in m e m b r a n e s , see I o n e x c h a n g e m e m b r a n e s , H y p e r f i l t r a t i o n

T r a n s p o r t n u m b e r , 2 0 3 , 2 1 9 T r a n s p o r t p r o p e r t i e s , s o l u t i o n s , 1 2 T r e a t m e n t of w a t e r , see W a t e r t r e a t m e n t

U l t r a f i l t r a t i o n , see H y p e r f i l t r a t i o n U l t r a p u r e w a t e r , 4 4 1

U n i t e d S t a t e s

m a p s h o w i n g p h y s i c a l p r o v i n c e s , 5 2 9 m a p s h o w i n g s o l a r r a d i a t i o n , 1 5 3 s a l i n e w a t e r p r o g r a m , h i s t o r y of, 1 5 , 5 1 6

V

V a p o r c o m p r e s s i o n d i s t i l l a t i o n , 2 7 , 1 1 0 V a p o r c o m p r e s s o r , 3 2 4 , 3 2 7

V a p o r r e h e a t d i s t i l l a t i o n , 1 1 7

c o m p a r i s o n w i t h flash d i s t i l l a t i o n , 1 1 9 , 1 2 4 c o n d e n s e r s , falling film, 1 2 7

o p e n c h a n n e l , 1 2 9 s p r a y , 1 2 7 cost d a t a , 1 4 9 e c o n o m i c s of, 1 4 5 , 1 4 9 e q u i p m e n t

c o n f i g u r a t i o n , 1 2 8 , 1 2 9 m a t e r i a l s of c o n s t r u c t i o n , 1 4 6 flowsheet, 1 1 9 , 1 2 0

h e a t r e q u i r e m e n t s , 1 2 0 , 1 2 1 p H c o n t r o l , for, 1 4 5 p r i n c i p l e of, 1 1 9 p u m p i n g costs, 1 2 4 p u m p i n g e n e r g y for, 1 2 5

W

W a s h - s e p a r a t i o n c o l u m n , 3 0 7 , 3 1 4 , 3 1 5 , 3 2 6 , 3 2 9

W a s t e d i s p o s a l , f r o m w a t e r t r e a t m e n t p l a n t s , 4 9 0

W a t e r

c o s t of, 5 2 1 , 5 4 7

d e m i n e r a l i z e d , see specific p r o c e s s e s , e.g., E l e c t r o d i a l y s i s

d i s s o l v e d g a s e s , 4 4 4 d i s t i l l e d , see D i s t i l l a t i o n i m p u r i t i e s in, t a b l e of, 4 4 4 u l t r a p u r e vs. d e m i n e r a l i z e d , 4 7 2 p h y s i c a l c h e m i s t r y of, 7 p u r e , 4 4 2

s t r u c t u r e of, 7 u l t r a p u r e

a n a l y s i s of, 4 7 4

c o n d u c t i v i t y of, 4 4 3 , 4 4 7 , 4 7 5 c o s t of, 4 9 0

d e f i n i t i o n of, 4 4 2 for l a b o r a t o r y use, 4 7 2

(9)

for pharmaceutical industries, 471 for polymer manufacture, 472 for power plants, 452, 465

for semiconductor manufacture, 469, 470 for television tube manufacture, 470 impurity limit, 442

industries in need of, 451 p H of, 475

preparation of

chemicals for, table, 488 control systems, 476 table, 456

{see also Water treatment; also specific processes, e.g., Coagulation, etc.) recirculation of, 451

resistivity of, 443, 447, 475 re-use of, 490

storage of, 473

Water analysis, ultrapure water, 474 Water consumption, in U.S.A., 3 Water cost estimating procedures, 526 Water costs

fixed, 527

synthesized, 524, 525 variable, 527

Water splitting, in electrodialysis, 231 Water supply

conventional

compared to desalinated water, 519 cost components, table, 521 illustrative total costs, 547, 548 distribution system, investment cost, 522 user cost, 523

Water transfer, 228

effect on membrane potential, 222 Water treatment

chemicals for, table of, 488 cost of, 543

for ultrapure water, table of processes, 445 Water withdrawal, in U.S., 2

Wells, water production from, cost, 546 Work minimum, for desalting, see Exergy,

minimum for desalting

Ζ

Zarchin process, see Freezing processes, di­

rect; Freezing processes, vacuum freez­

ing-vapor compression Zones, in energy-cost balances, 27

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