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Early- and Late-Time Prediction of Counter-Current Spontaneous Imbibition, Scaling Analysis and Estimation of the Capillary Diffusion Coefficient
被引:6
|作者:
Andersen, Pal Ostebo
[1
]
机构:
[1] Univ Stavanger, Dept Energy Resources, N-4021 Stavanger, Norway
关键词:
Counter-current spontaneous imbibition;
Universal scaling;
Early- and late-time solutions;
Interpretation of experimental recovery data;
WETTABILITY LITERATURE SURVEY;
OIL-RECOVERY;
WATER-WET;
POROUS-MEDIA;
MODEL;
MATRIX;
FLOW;
D O I:
10.1007/s11242-023-01924-6
中图分类号:
TQ [化学工业];
学科分类号:
0817 ;
摘要:
Solutions are investigated for 1D linear counter-current spontaneous imbibition (COUSI). It is shown theoretically that all COUSI scaled solutions depend only on a normalized coefficient lambda(n)(S-n) with mean 1 and no other parameters (regardless of wettability, saturation functions, viscosities, etc.). 5500 realistic functions lambda(n) were generated using (mixed-wet and strongly water-wet) relative permeabilities, capillary pressure and mobility ratios. The variation in lambda n appears limited, and the generated functions span most/all relevant cases. The scaled diffusion equation was solved for each case, and recovery vs time RF was ana-lyzed. RF could be characterized by two (case specific) parameters RFtr and lr (the cor-relation overlapped the 5500 curves with mean R-2 = 0.9989 ): Recovery follows exactly RF = T-0.5 (n) before water meets the no-flow boundary (early time) but continues (late time) with marginal error until RFtr (highest recovery reached as T-0.5 (n) ) in an extended early-time regime. Recovery then approaches 1, with lr quantifying the decline in imbibition rate. RFtr was 0.05 to 0.2 higher than recovery when water reached the no-flow boundary (critical time). A new scaled time formulation Tn = t/TTch accounts for system length L and magnitude D of the unscaled diffusion coefficient via a = L-2/D, and Tch separately accounts for shape via lambda(n). Parameters describing lambda(n) and recovery were correlated which permitted (1) predicting recovery (without solving the diffusion equation); (2) predicting diffusion coefficients explaining experimental recovery data; (3) explaining the challeng-ing interaction between inputs such as wettability, saturation functions and viscosities with time scales, early-and late-time recovery behavior.
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页码:573 / 604
页数:32
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