Efficient Quantification of Uncertainties Associated with Reservoir Performance Simulations Dongxiao Zhang, The University of Southern California The efficiency and accuracy of a stochastic approach depend on how many (N) terms are required to approximate the underlying random field. In general, with the decrease of the correlation scale (η/L) the critical number of terms (Nc) increases exponentially in order to retain the same level of energy while the required energy level (Ec) decreases exponentially if a certain accuracy in the final solution is desired (a). The net outcome is that with the decrease of η/L, to maintain a certain accuracy Nc increases only slightly (b). 1.00
45
2
40
σY=1.0
45
Ec w/ convergence criterion
35
35 0.90
2
σ Y=1.0
30
30 0.85
20
0.80
.
25
Nc
25
EC
Nc
N c w/ convergence criterion
40
0.95
20 15
15 0.75
10
10 0.70
5
Nc w/ 90% energy criterion
0 0.1
(a)
0.2
0.3
0.4
η/L
0.65 0.5
0.6
0.7
5 0 0.1
(b)
0.2
0.3
0.4
η /L
0.5
0.6
0.7
