Propagation of Pore Pressure and Stress in Saturated Porous Media Based on a Darcy-Brinkman Formulation

<table class="table-group" id="tab1"><tr><td><table class="table"><tr><td class="thead-hr" colspan="5"><hr/></td></tr><tr class="thead"><td class="align_left">Mode</td><td class="align_center">Observed [<a href="/journals/geofluids/2021/1301044/#B15" target="_blank">15</a>]</td><td class="align_center">Observed [<a href="/journals/geofluids/2021/1301044/#B17" target="_blank">17</a>]</td><td class="align_center">Darcy’s law</td><td class="align_center">Darcy-Brinkman formulation</td></tr><tr><td class="thead-hr" colspan="5"><hr/></td></tr><tr><td class="align_left">First wave (km/s)</td><td class="align_center"><span style="width: 57.1008ptpx;"><svg height="8.69875pt" id="M64" style="vertical-align:-0.3499298pt" version="1.1" viewbox="-0.0498162 -8.34882 57.1008 8.69875" width="57.1008pt" 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="M412 140C382 77 369 73 315 73H129L270 222C362 320 402 379 402 466C402 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103S58 78 58 46C58 11 82 -12 113 -12Z"></path></g><g transform="matrix(.013,0,0,-0.013,44.331,0)"><path d="M241 635C89 635 35 457 35 312C35 153 89 -12 240 -12C390 -12 443 166 443 312C443 466 390 635 241 635ZM238 602C329 602 354 454 354 312C354 172 330 22 240 22C152 22 124 173 124 313S148 602 238 602Z"></path></g><g transform="matrix(.013,0,0,-0.013,50.571,0)"><path d="M244 635C114 635 38 519 38 422C38 317 111 240 217 240C236 240 255 244 277 256L345 292C311 140 203 39 59 15L64 -15C89 -15 150 -5 204 17C339 72 440 202 440 386C440 521 368 635 244 635ZM228 602C326 602 352 479 352 390C352 370 351 347 348 324C327 308 293 296 258 296C174 296 124 369 124 458C124 517 152 602 228 602Z"></path></g></svg></span></td><td class="align_center">2.78</td><td class="align_center">2.36</td></tr><tr><td class="align_left">Second wave (km/s)</td><td class="align_center"><span style="width: 57.1008ptpx;"><svg height="8.69875pt" id="M66" style="vertical-align:-0.3499298pt" version="1.1" viewbox="-0.0498162 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354 312C354 172 330 22 240 22C152 22 124 173 124 313S148 602 238 602Z"></path></g><g transform="matrix(.013,0,0,-0.013,50.572,0)"><path d="M412 140C382 77 369 73 315 73H129L270 222C362 320 402 379 402 466C402 571 322 635 234 635C177 635 130 609 99 576L42 495L64 475C90 514 133 568 201 568C274 568 318 519 318 435C318 349 255 267 193 193C144 135 87 78 32 23V0H405C417 45 427 89 440 131L412 140Z"></path></g></svg></span></td><td class="align_center"><span style="width: 57.1008ptpx;"><svg height="8.69875pt" id="M67" style="vertical-align:-0.3499298pt" version="1.1" viewbox="-0.0498162 -8.34882 57.1008 8.69875" width="57.1008pt" 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="M241 635C89 635 35 457 35 312C35 153 89 -12 240 -12C390 -12 443 166 443 312C443 466 390 635 241 635ZM238 602C329 602 354 454 354 312C354 172 330 22 240 22C152 22 124 173 124 313S148 602 238 602Z"></path></g><g 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443 166 443 312C443 466 390 635 241 635ZM238 602C329 602 354 454 354 312C354 172 330 22 240 22C152 22 124 173 124 313S148 602 238 602Z"></path></g><g transform="matrix(.013,0,0,-0.013,41.369,0)"><path d="M113 -12C146 -12 170 11 170 46C170 78 146 103 114 103S58 78 58 46C58 11 82 -12 113 -12Z"></path></g><g transform="matrix(.013,0,0,-0.013,44.333,0)"><path d="M241 635C89 635 35 457 35 312C35 153 89 -12 240 -12C390 -12 443 166 443 312C443 466 390 635 241 635ZM238 602C329 602 354 454 354 312C354 172 330 22 240 22C152 22 124 173 124 313S148 602 238 602Z"></path></g><g transform="matrix(.013,0,0,-0.013,50.573,0)"><path d="M412 140C382 77 369 73 315 73H129L270 222C362 320 402 379 402 466C402 571 322 635 234 635C177 635 130 609 99 576L42 495L64 475C90 514 133 568 201 568C274 568 318 519 318 435C318 349 255 267 193 193C144 135 87 78 32 23V0H405C417 45 427 89 440 131L412 140Z"></path></g></svg></span></td><td class="align_center">0.67</td><td class="align_center">0.78</td></tr><tr class="table-tr"><td colspan="5"><hr class="tbody-hr"/></td></tr></table></td></tr></table>

<div>Comparison of calculated and observed wave velocities.</div>

Geofluids

tab1

Table 1

Table 1: Propagation of Pore Pressure and Stress in Saturated Porous Media Based on a Darcy-Brinkman Formulation 