Thermodynamic Properties of Aqueous Species Calculated Using the HKF Model: How Do Different Thermodynamic and Electrostatic Models for Solvent Water Affect Calculated Aqueous Properties?

<div>Plots showing the deviation in % of the volumetric properties of water calculated using the HGK84 and ZD05 formulations from those obtained using the IAPWS95 model (25–1000°C, 1–5 kbar): (a) <svg height="11.2432pt" id="M110" style="vertical-align:-5.28229pt" version="1.1" viewbox="-0.0498162 -5.96091 24.3239 11.2432" width="24.3239pt" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink"><g transform="matrix(.013,0,0,-0.013,0,0)"><path d="M516 277C516 378 460 448 376 448C335 448 288 434 240 401C158 345 127 277 107 159C53 -161 38 -221 23 -247L28 -261C43 -260 95 -250 114 -226C122 -216 129 -199 146 -75C152 -29 157 0 164 31C182 9 206 -12 237 -12C267 -12 325 8 376 46C451 102 516 179 516 277ZM432 259C432 134 366 40 259 40C236 40 204 48 171 76L195 203C219 327 253 400 326 400C398 400 432 336 432 259Z"></path></g><g transform="matrix(.0091,0,0,-0.0091,6.162,3.132)"><path d="M729 650H468V622C546 615 554 610 554 527V365H213V527C213 610 221 616 297 622V650H38V622C120 616 128 611 128 527V123C128 39 120 34 40 28V0H303V28C221 34 213 40 213 123V322H554V123C554 39 546 34 460 28V0H728V28C647 34 639 39 639 123V527C639 610 647 615 729 622V650Z"></path></g><g transform="matrix(.0065,0,0,-0.0065,13.159,5.233)"><path d="M452 139L416 148C386 81 373 77 319 77H141L282 220C372 312 414 373 414 464C414 569 332 635 240 635C181 635 132 609 101 574L42 493L70 467C98 506 143 562 209 562C280 562 324 515 324 435C324 347 261 272 197 197C148 139 89 84 34 29V0H417L452 139Z"></path></g><g transform="matrix(.0091,0,0,-0.0091,16.88,3.132)"><path d="M381 665C170 665 44 498 44 318C44 125 188 -15 369 -15C552 -15 703 117 703 333C703 534 550 665 381 665ZM359 629C491 629 601 517 601 306C601 114 502 21 390 21C249 21 146 158 146 346S248 629 359 629Z"></path></g></svg> (water density), (b) <svg height="11.2432pt" id="M111" style="vertical-align:-5.28229pt" version="1.1" viewbox="-0.0498162 -5.96091 25.2243 11.2432" width="25.2243pt" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink"><g transform="matrix(.013,0,0,-0.013,0,0)"><path d="M545 106L524 126C493 85 467 65 455 65C438 65 427 113 405 238C448 295 498 362 543 439L533 448L478 435C453 386 423 331 398 295H395C370 404 347 448 282 448C169 448 23 309 23 153C23 54 65 -12 128 -12C203 -12 283 70 339 155H341C360 29 380 -12 411 -12C444 -12 491 11 545 106ZM333 204C265 95 210 54 169 54C137 54 113 96 113 171C113 302 191 405 252 405C301 405 318 306 333 204Z"></path></g><g transform="matrix(.0091,0,0,-0.0091,7.059,3.132)"><path d="M729 650H468V622C546 615 554 610 554 527V365H213V527C213 610 221 616 297 622V650H38V622C120 616 128 611 128 527V123C128 39 120 34 40 28V0H303V28C221 34 213 40 213 123V322H554V123C554 39 546 34 460 28V0H728V28C647 34 639 39 639 123V527C639 610 647 615 729 622V650Z"></path></g><g transform="matrix(.0065,0,0,-0.0065,14.056,5.233)"><path d="M452 139L416 148C386 81 373 77 319 77H141L282 220C372 312 414 373 414 464C414 569 332 635 240 635C181 635 132 609 101 574L42 493L70 467C98 506 143 562 209 562C280 562 324 515 324 435C324 347 261 272 197 197C148 139 89 84 34 29V0H417L452 139Z"></path></g><g transform="matrix(.0091,0,0,-0.0091,17.777,3.132)"><path d="M381 665C170 665 44 498 44 318C44 125 188 -15 369 -15C552 -15 703 117 703 333C703 534 550 665 381 665ZM359 629C491 629 601 517 601 306C601 114 502 21 390 21C249 21 146 158 146 346S248 629 359 629Z"></path></g></svg> (isobaric expansivity), (c) <svg height="14.5707pt" id="M112" style="vertical-align:-5.28237pt" version="1.1" viewbox="-0.0498162 -9.28833 25.3939 14.5707" width="25.3939pt" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink"><g transform="matrix(.013,0,0,-0.013,0,0)"><path d="M558 587C558 666 497 712 432 712C379 712 330 691 284 650C212 586 178 508 148 348L71 -65C49 -185 35 -229 23 -235L27 -261C49 -259 101 -251 124 -224C131 -216 138 -178 159 -24C171 66 197 200 227 356C264 550 295 668 393 668C443 668 479 632 479 575C479 516 446 458 383 418C361 404 344 398 318 397L296 350C395 338 460 281 460 192C460 110 411 40 300 40C258 40 215 55 192 69L181 51C191 18 222 -16 266 -16C308 -16 351 1 397 26C471 67 545 142 545 221C545 315 486 365 401 395C469 437 558 498 558 587Z"></path></g><g transform="matrix(.0091,0,0,-0.0091,7.228,3.132)"><path d="M729 650H468V622C546 615 554 610 554 527V365H213V527C213 610 221 616 297 622V650H38V622C120 616 128 611 128 527V123C128 39 120 34 40 28V0H303V28C221 34 213 40 213 123V322H554V123C554 39 546 34 460 28V0H728V28C647 34 639 39 639 123V527C639 610 647 615 729 622V650Z"></path></g><g transform="matrix(.0065,0,0,-0.0065,14.225,5.233)"><path d="M452 139L416 148C386 81 373 77 319 77H141L282 220C372 312 414 373 414 464C414 569 332 635 240 635C181 635 132 609 101 574L42 493L70 467C98 506 143 562 209 562C280 562 324 515 324 435C324 347 261 272 197 197C148 139 89 84 34 29V0H417L452 139Z"></path></g><g transform="matrix(.0091,0,0,-0.0091,17.946,3.132)"><path d="M381 665C170 665 44 498 44 318C44 125 188 -15 369 -15C552 -15 703 117 703 333C703 534 550 665 381 665ZM359 629C491 629 601 517 601 306C601 114 502 21 390 21C249 21 146 158 146 346S248 629 359 629Z"></path></g></svg> (isothermal compressibility), and (d) <svg height="12.4698pt" id="M113" style="vertical-align:-3.18147pt" version="1.1" viewbox="-0.0498162 -9.28833 49.3008 12.4698" width="49.3008pt" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink"><g transform="matrix(.013,0,0,-0.013,0,0)"><path d="M300 -147C201 -63 143 98 143 270S200 602 300 686L282 710C136 610 70 450 70 271V270C70 89 136 -72 282 -170L300 -147Z"></path></g><g transform="matrix(.013,0,0,-0.013,4.498,0)"><path d="M471 379C471 433 467 511 427 578C379 658 305 712 208 712C154 712 98 699 70 684C70 668 95 634 111 634C141 651 180 665 234 665C306 665 350 627 372 575C391 530 393 480 393 442V415C371 436 344 448 313 448C280 448 227 437 176 411C100 372 23 279 23 148C23 67 64 -12 180 -12C293 -12 360 46 407 129C450 205 471 310 471 379ZM382 335C382 142 289 50 238 35C226 31 213 28 200 28C139 28 110 91 110 164C110 310 191 382 223 395C245 404 259 409 280 409C305 409 332 404 359 388C379 376 382 362 382 335Z"></path></g><g transform="matrix(.013,0,0,-0.013,10.922,0)"><path d="M545 106L524 126C493 85 467 65 455 65C438 65 427 113 405 238C448 295 498 362 543 439L533 448L478 435C453 386 423 331 398 295H395C370 404 347 448 282 448C169 448 23 309 23 153C23 54 65 -12 128 -12C203 -12 283 70 339 155H341C360 29 380 -12 411 -12C444 -12 491 11 545 106ZM333 204C265 95 210 54 169 54C137 54 113 96 113 171C113 302 191 405 252 405C301 405 318 306 333 204Z"></path></g><g transform="matrix(.013,0,0,-0.013,18.307,0)"><path d="M368 703H309L44 -163H104L368 703Z"></path></g><g transform="matrix(.013,0,0,-0.013,23.668,0)"><path d="M471 379C471 433 467 511 427 578C379 658 305 712 208 712C154 712 98 699 70 684C70 668 95 634 111 634C141 651 180 665 234 665C306 665 350 627 372 575C391 530 393 480 393 442V415C371 436 344 448 313 448C280 448 227 437 176 411C100 372 23 279 23 148C23 67 64 -12 180 -12C293 -12 360 46 407 129C450 205 471 310 471 379ZM382 335C382 142 289 50 238 35C226 31 213 28 200 28C139 28 110 91 110 164C110 310 191 382 223 395C245 404 259 409 280 409C305 409 332 404 359 388C379 376 382 362 382 335Z"></path></g><g transform="matrix(.013,0,0,-0.013,30.093,0)"><path d="M620 675H597C578 656 570 650 541 650H144C112 650 104 653 94 675H72C59 618 42 552 23 493L53 491C71 534 88 564 105 585C124 608 144 615 238 615H290L197 121C182 40 174 34 88 28L82 0H361L367 28C275 34 266 38 281 121L374 615H441C522 615 543 608 553 583C562 560 566 531 565 493L597 494C603 551 612 629 620 675Z"></path></g><g transform="matrix(.013,0,0,-0.013,38.378,0)"><path d="M275 270C275 450 212 609 64 710L45 686C145 604 203 442 203 270S147 -63 45 -147L64 -170C213 -68 275 89 275 270Z"></path></g><g transform="matrix(.0091,0,0,-0.0091,42.876,3.132)"><path d="M622 479C622 589 545 650 400 650H146L140 618C229 609 230 602 215 527L135 132C117 43 112 41 27 32L18 0H305L313 32C213 40 205 44 222 132L251 284L324 262H365C484 269 622 333 622 479ZM528 477C528 356 420 305 344 305C300 305 276 314 259 321L303 554C311 597 313 600 331 606C345 611 361 614 379 614C463 614 528 580 528 477Z"></path></g></svg> (isobaric temperature derivative of the isobaric expansivity).</div>

Geofluids

fig1

Figure 1

Figure 1: Thermodynamic Properties of Aqueous Species Calculated Using the HKF Model: How Do Different Thermodynamic and Electrostatic Models for Solvent Water Affect Calculated Aqueous Properties? 

Figure 1 | Thermodynamic Properties of Aqueous Species Calculated Using the HKF Model: How Do Different Thermodynamic and Electrostatic Models for Solvent Water Affect Calculated Aqueous Properties? 