Effect of Lower Surface Roughness on Nonlinear Hydraulic Properties of Fractures

<table class="figure-group"><tr class="fig-image" id="a"><td><object data="https://static-preview.hindawi.com/articles/geofluids/volume-2021/6612378/figures/6612378.fig.008a.svgz" name="6612378.fig.008a" type="image/svg+xml"></object></td></tr><tr class="fig-caption"><td><b>(a) </b>Relationships between <svg height="6.1673pt" id="M123" style="vertical-align:-0.2063904pt" version="1.1" viewbox="-0.0498162 -5.96091 6.7023 6.1673" width="6.7023pt" 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="M483 97L471 123C436 91 401 65 392 65C388 65 384 74 390 106C414 239 444 378 457 429L455 433C444 433 429 436 416 439C392 444 368 448 344 448C281 448 204 415 152 376C71 315 23 205 23 103C23 21 57 -12 85 -12C114 -12 149 6 185 34C231 70 285 119 329 183H331L309 81C292 0 308 -12 326 -12C350 -12 421 24 483 97ZM374 387C370 363 356 291 345 261C315 193 181 50 139 50C124 50 110 71 110 118C110 224 153 331 218 379C238 394 271 402 301 402C329 402 359 394 374 387Z"></path></g></svg> and JRC(lower)</td></tr><tr class="fig-image" id="b"><td><object data="https://static-preview.hindawi.com/articles/geofluids/volume-2021/6612378/figures/6612378.fig.008b.svgz" name="6612378.fig.008b" type="image/svg+xml"></object></td></tr><tr class="fig-caption"><td><b>(b) </b>Relationships between <svg height="9.49473pt" id="M124" style="vertical-align:-0.2063999pt" version="1.1" viewbox="-0.0498162 -9.28833 6.21949 9.49473" width="6.21949pt" 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="M452 333C452 398 425 448 375 448C329 448 235 404 140 292H138L229 683C233 701 234 712 225 712C208 712 149 686 66 677L64 652H97C135 652 140 651 129 598L38 167C23 96 29 57 44 33C60 7 98 -12 132 -12C169 -12 232 3 290 41C383 102 452 223 452 333ZM365 316C365 199 308 87 239 49C221 39 200 35 183 35C137 35 99 70 112 163C116 191 123 215 129 233C190 316 290 392 330 392C348 392 365 372 365 316Z"></path></g></svg> and JRC(lower)</td></tr></table>

<div>Variations in Forchheimer coefficients versus roughness of lower surfaces.</div>

Geofluids

fig8

Figure 8

Figure 8: Effect of Lower Surface Roughness on Nonlinear Hydraulic Properties of Fractures 