Numerical Well Test Analysis of Condensate Dropout Effects in Dual-Permeability Model of Naturally Fractured Gas Condensate Reservoirs: Case Studies in the South of Iran

<table class="table-group" id="tab3"><tr><td><table class="table"><tr><td class="thead-hr" colspan="4"><hr/></td></tr><tr class="thead"><td class="align_center" colspan="4">Rock properties</td></tr><tr class="thead"><td class="align_center" colspan="2">Matrix</td><td class="align_center" colspan="2">Fracture</td></tr><tr><td class="thead-hr" colspan="4"><hr/></td></tr><tr><td class="align_left"><span style="width: 29.2512ptpx;"><svg height="12.4646pt" id="M28" style="vertical-align:-0.2063999pt" version="1.1" viewbox="-0.0498162 -12.2582 29.2512 12.4646" width="29.2512pt" 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="M480 416C480 431 465 448 438 448C388 448 312 383 252 330C217 299 188 273 155 237H153L257 680C262 700 263 712 253 712C240 712 183 684 97 674L92 648L126 647C166 646 172 645 163 606L23 -6L29 -12C51 -5 77 2 107 8C115 62 130 128 142 180C153 193 179 220 204 241C231 170 259 106 288 54C317 0 336 -12 358 -12C381 -12 423 2 477 80L460 100C434 74 408 54 398 54C385 54 374 65 351 107C326 154 282 241 263 299C296 332 351 377 403 377C424 377 436 372 445 368C449 366 456 368 462 375C472 386 480 402 480 416Z"></path></g><g transform="matrix(.0091,0,0,-0.0091,6.539,-5.741)"><path d="M297 -163V-131C189 -122 187 -119 187 -41V582C187 660 190 663 297 672V704H122V-163H297Z"></path></g><g transform="matrix(.0091,0,0,-0.0091,9.797,-5.741)"><path d="M781 91L765 118C733 86 702 70 693 70C686 70 685 77 692 106L738 297C772 439 736 451 712 451S675 445 647 431C605 410 526 356 452 257H450L459 294C491 426 459 451 429 451C403 451 386 445 361 431C312 404 239 343 170 253H168L188 333C208 411 205 451 175 451C148 451 85 417 24 346L39 318C57 338 100 374 112 374C120 374 122 372 115 339C91 226 62 112 28 -6L37 -12C59 -4 87 3 114 6C125 68 142 127 154 168C184 227 316 383 372 383C397 383 396 366 381 289C362 192 338 92 312 -6L317 -12C339 -5 367 3 396 6L434 170C468 234 598 383 650 383C668 383 676 369 664 319L609 90C593 23 600 -12 629 -12C654 -12 722 23 781 91Z"></path></g><g transform="matrix(.0091,0,0,-0.0091,20.168,-5.741)"><path d="M538 684C542 703 539 710 529 710C512 710 455 682 363 674L361 644H396C444 644 448 642 438 594L405 438C373 450 347 451 336 451C288 451 200 416 147 374C69 312 24 207 24 113C24 29 60 -12 94 -12C126 -12 156 4 196 30C231 53 296 100 346 166H348L328 81C311 10 325 -12 348 -12C380 -12 450 24 512 98L495 125C466 97 431 70 417 70C408 70 408 80 411 98L538 684ZM390 373L361 240C336 196 210 56 145 56C132 56 113 73 113 131C113 216 156 338 220 379C243 394 266 402 303 402C331 402 375 388 390 373Z"></path></g><g transform="matrix(.0091,0,0,-0.0091,25.301,-5.741)"><path d="M237 -163V704H62V672C170 663 172 660 172 582V-40C172 -118 170 -122 62 -131V-163H237Z"></path></g></svg></span></td><td class="align_center">1.2</td><td class="align_center"><span style="width: 29.2512ptpx;"><svg height="12.4646pt" id="M29" style="vertical-align:-0.2063999pt" version="1.1" viewbox="-0.0498162 -12.2582 29.2512 12.4646" width="29.2512pt" 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="M480 416C480 431 465 448 438 448C388 448 312 383 252 330C217 299 188 273 155 237H153L257 680C262 700 263 712 253 712C240 712 183 684 97 674L92 648L126 647C166 646 172 645 163 606L23 -6L29 -12C51 -5 77 2 107 8C115 62 130 128 142 180C153 193 179 220 204 241C231 170 259 106 288 54C317 0 336 -12 358 -12C381 -12 423 2 477 80L460 100C434 74 408 54 398 54C385 54 374 65 351 107C326 154 282 241 263 299C296 332 351 377 403 377C424 377 436 372 445 368C449 366 456 368 462 375C472 386 480 402 480 416Z"></path></g><g transform="matrix(.0091,0,0,-0.0091,6.539,-5.741)"><path d="M297 -163V-131C189 -122 187 -119 187 -41V582C187 660 190 663 297 672V704H122V-163H297Z"></path></g><g transform="matrix(.0091,0,0,-0.0091,9.797,-5.741)"><path d="M781 91L765 118C733 86 702 70 693 70C686 70 685 77 692 106L738 297C772 439 736 451 712 451S675 445 647 431C605 410 526 356 452 257H450L459 294C491 426 459 451 429 451C403 451 386 445 361 431C312 404 239 343 170 253H168L188 333C208 411 205 451 175 451C148 451 85 417 24 346L39 318C57 338 100 374 112 374C120 374 122 372 115 339C91 226 62 112 28 -6L37 -12C59 -4 87 3 114 6C125 68 142 127 154 168C184 227 316 383 372 383C397 383 396 366 381 289C362 192 338 92 312 -6L317 -12C339 -5 367 3 396 6L434 170C468 234 598 383 650 383C668 383 676 369 664 319L609 90C593 23 600 -12 629 -12C654 -12 722 23 781 91Z"></path></g><g transform="matrix(.0091,0,0,-0.0091,20.168,-5.741)"><path d="M538 684C542 703 539 710 529 710C512 710 455 682 363 674L361 644H396C444 644 448 642 438 594L405 438C373 450 347 451 336 451C288 451 200 416 147 374C69 312 24 207 24 113C24 29 60 -12 94 -12C126 -12 156 4 196 30C231 53 296 100 346 166H348L328 81C311 10 325 -12 348 -12C380 -12 450 24 512 98L495 125C466 97 431 70 417 70C408 70 408 80 411 98L538 684ZM390 373L361 240C336 196 210 56 145 56C132 56 113 73 113 131C113 216 156 338 220 379C243 394 266 402 303 402C331 402 375 388 390 373Z"></path></g><g transform="matrix(.0091,0,0,-0.0091,25.301,-5.741)"><path d="M237 -163V704H62V672C170 663 172 660 172 582V-40C172 -118 170 -122 62 -131V-163H237Z"></path></g></svg></span></td><td class="align_center">9000</td></tr><tr><td class="align_left"><span style="width: 7.69399ptpx;"><svg height="9.39034pt" id="M30" style="vertical-align:-3.42943pt" version="1.1" viewbox="-0.0498162 -5.96091 7.69399 9.39034" width="7.69399pt" 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="M559 271C559 395 493 448 433 448C370 448 304 394 275 297C259 245 235 121 219 37C157 54 113 110 113 201C113 310 180 386 276 429L265 457C131 410 23 326 23 186C23 83 86 5 211 -10C180 -159 167 -220 158 -252L165 -261C198 -255 236 -246 251 -218L287 -5C421 9 559 119 559 271ZM484 273C484 144 400 40 293 33L352 331C364 389 382 406 405 406C431 406 484 370 484 273Z"></path></g></svg></span></td><td class="align_center">0.11</td><td class="align_center"><span style="width: 7.69399ptpx;"><svg height="9.39034pt" id="M31" style="vertical-align:-3.42943pt" version="1.1" viewbox="-0.0498162 -5.96091 7.69399 9.39034" width="7.69399pt" 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="M559 271C559 395 493 448 433 448C370 448 304 394 275 297C259 245 235 121 219 37C157 54 113 110 113 201C113 310 180 386 276 429L265 457C131 410 23 326 23 186C23 83 86 5 211 -10C180 -159 167 -220 158 -252L165 -261C198 -255 236 -246 251 -218L287 -5C421 9 559 119 559 271ZM484 273C484 144 400 40 293 33L352 331C364 389 382 406 405 406C431 406 484 370 484 273Z"></path></g></svg></span></td><td class="align_center">1</td></tr><tr><td class="align_left"><span style="width: 37.4564ptpx;"><svg height="20.2833pt" id="M32" style="vertical-align:-6.922501pt" version="1.1" viewbox="-0.0498162 -13.3608 37.4564 20.2833" width="37.4564pt" 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="M645 631C614 643 545 666 457 666C215 666 23 519 23 283C23 90 158 -16 337 -16C412 -16 489 2 522 10C543 39 590 127 606 167L580 181C519 89 459 18 348 18C201 18 122 136 122 287C122 464 244 632 435 632C544 632 602 595 608 472L639 475C643 526 645 581 645 631Z"></path></g><g transform="matrix(.0091,0,0,-0.0091,8.684,-6.844)"><path d="M297 -163V-131C189 -122 187 -119 187 -41V582C187 660 190 663 297 672V704H122V-163H297Z"></path></g><g transform="matrix(.0091,0,0,-0.0091,11.942,-6.844)"><path d="M573 302C573 402 527 451 414 451C386 451 343 446 313 437L330 513L320 522C295 508 261 484 243 463L230 415C194 400 159 383 126 359L131 330C159 344 187 357 222 368L109 -147C96 -204 80 -214 18 -223L13 -255L256 -244L259 -212L236 -210C184 -205 180 -195 191 -141L219 -1C240 -10 268 -12 284 -12C352 4 431 48 484 104C543 166 573 240 573 302ZM481 290C481 165 381 37 305 37C280 37 249 56 235 71L302 395C328 399 353 402 372 402C427 402 481 378 481 290Z"></path></g><g transform="matrix(.0091,0,0,-0.0091,17.376,-6.844)"><path d="M357 391C357 416 325 451 270 451C241 451 179 431 146 400C109 365 97 334 97 307C97 248 143 213 196 180C250 146 261 123 261 101C261 75 237 40 190 40C153 40 110 72 86 109C81 116 68 119 55 112C37 102 24 87 24 66C24 30 85 -12 137 -12C229 -12 331 62 331 140C331 189 304 218 236 260C197 284 164 309 164 346C164 381 194 400 220 400C259 400 282 380 304 350C310 342 321 339 330 344C347 353 357 372 357 391Z"></path></g><g transform="matrix(.0091,0,0,-0.0091,20.925,-6.844)"><path d="M250 606C250 634 233 656 203 656C168 656 146 618 146 593C146 564 169 545 192 545C227 545 250 573 250 606ZM227 95L212 119C187 98 152 71 135 71C129 71 128 78 134 102L207 373C219 418 217 451 194 451C165 451 92 411 30 351L44 326C77 353 106 371 114 371C124 371 121 357 117 341L55 97C32 5 46 -12 70 -12C108 -12 191 51 227 95Z"></path></g><g transform="matrix(.0091,0,0,-0.0091,23.473,-6.844)"><path d="M556 236V289H56V236H556Z"></path></g><g transform="matrix(.0091,0,0,-0.0091,29.033,-6.844)"><path d="M389 0V32C297 38 291 46 291 118V635C234 613 175 595 109 583V556L161 554C203 552 207 547 207 497V118C207 46 201 38 110 32V0H389Z"></path></g><g transform="matrix(.0091,0,0,-0.0091,33.465,-6.844)"><path d="M237 -163V704H62V672C170 663 172 660 172 582V-40C172 -118 170 -122 62 -131V-163H237Z"></path></g><g transform="matrix(.0091,0,0,-0.0091,8.619,4.525)"><path d="M620 667C620 684 593 710 552 710C515 710 459 687 409 634C360 582 334 506 320 433H247L215 400L220 388H310L259 80C224 -129 199 -161 185 -174C175 -183 160 -192 141 -192C123 -192 90 -181 75 -165C69 -158 64 -156 54 -164C39 -178 24 -195 24 -208C24 -231 61 -257 94 -257C124 -257 162 -243 209 -194C267 -134 303 -66 343 107C369 220 378 279 393 385L503 397L523 433H404C432 619 464 660 500 660C522 660 542 646 566 621C573 614 583 615 593 621C603 628 620 648 620 667Z"></path></g></svg></span></td><td class="align_center">4.25E-06</td><td class="align_center"><span style="width: 37.4564ptpx;"><svg height="20.2833pt" id="M33" style="vertical-align:-6.922501pt" version="1.1" viewbox="-0.0498162 -13.3608 37.4564 20.2833" width="37.4564pt" 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="M645 631C614 643 545 666 457 666C215 666 23 519 23 283C23 90 158 -16 337 -16C412 -16 489 2 522 10C543 39 590 127 606 167L580 181C519 89 459 18 348 18C201 18 122 136 122 287C122 464 244 632 435 632C544 632 602 595 608 472L639 475C643 526 645 581 645 631Z"></path></g><g transform="matrix(.0091,0,0,-0.0091,8.684,-6.844)"><path d="M297 -163V-131C189 -122 187 -119 187 -41V582C187 660 190 663 297 672V704H122V-163H297Z"></path></g><g transform="matrix(.0091,0,0,-0.0091,11.942,-6.844)"><path d="M573 302C573 402 527 451 414 451C386 451 343 446 313 437L330 513L320 522C295 508 261 484 243 463L230 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-257 94 -257C124 -257 162 -243 209 -194C267 -134 303 -66 343 107C369 220 378 279 393 385L503 397L523 433H404C432 619 464 660 500 660C522 660 542 646 566 621C573 614 583 615 593 621C603 628 620 648 620 667Z"></path></g></svg></span></td><td class="align_center">1E-4</td></tr><tr class="table-tr"><td colspan="4"><hr class="tbody-hr"/></td></tr></table></td></tr></table>

<div>Rock properties for the reservoir model.</div>

Mathematical Problems in Engineering

tab3

Table 3

Table 3: Numerical Well Test Analysis of Condensate Dropout Effects in Dual-Permeability Model of Naturally Fractured Gas Condensate Reservoirs: Case Studies in the South of Iran 

Table 3 | Numerical Well Test Analysis of Condensate Dropout Effects in Dual-Permeability Model of Naturally Fractured Gas Condensate Reservoirs: Case Studies in the South of Iran 