Upscaling of Permeability Field of Fractured Rock System: Numerical Examples

Table 1

Flux across the exit boundary for the different fractures and mesh scenarios.

	2 fractures	10 fractures	40 fractures	800 fractures
Reference (fine mesh)	1.238536𝑒−03	1.140093𝑒−03	1.784033𝑒−03	4.037607𝑒+00
Upscaled (2×2)	1.2060398𝑒−03	1.1671849𝑒−03	1.7678765𝑒−03	4.0482439𝑒+00
Upscaled (5×5)	1.2279665𝑒−03	1.1480335𝑒−03	1.6639357𝑒−03	4.0201914𝑒+00
Upscaled (10×10)	1.2305291𝑒−03	1.1357165𝑒−03	1.6719508𝑒−03	4.0624327𝑒+00
Upscaled (20×20)	1.2377141𝑒−03	1.1567826𝑒−03	1.7251369𝑒−03	4.0636998𝑒+00
Upscaled (40×40)	1.2329549𝑒−03	1.1414539𝑒−03	1.7356198𝑒−03	4.0958317𝑒+00
Upscaled (60×60)	1.2330102𝑒−03	1.1364853𝑒−03	1.7344252𝑒−03	3.9842654𝑒+00
Upscaled (80×80)	1.2312922𝑒−03	1.1368569𝑒−03	1.7406374𝑒−03	4.0324003𝑒+00
Upscaled (100×100)	1.2368716𝑒−03	1.1353105𝑒−03	1.7651864𝑒−03	4.0198896𝑒+00
Upscaled (160×160)	1.2354428𝑒−03	1.1366243𝑒−03	1.7682102𝑒−03	3.9614817𝑒+00
Upscaled (200×200)	1.2376183𝑒−03	1.1376407𝑒−03	1.7735081𝑒−03	4.0495773𝑒+00
Upscaled (240×240)	1.2366092𝑒−03	1.1380291𝑒−03	1.7735767𝑒−03	3.9653353𝑒+00
Upscaled (300×300)	1.2393249𝑒−03	1.1413561𝑒−03	1.7762217𝑒−03	3.9176552𝑒+00
Upscaled (400×400)	1.2368358𝑒−03	1.1370930𝑒−03	1.7671836𝑒−03	3.7225614𝑒+00
Upscaled (500×500)	1.2378015𝑒−03	1.1405213𝑒−03	1.7877663𝑒−03	4.0850977𝑒+00