Energy & Fuels, Vol.23, 2149-2156, 2009
Calculation of Viscosity Scaling Groups for Spontaneous Imbibition of Water Using Average Diffusivity Coefficients
Spontaneous imbibition is an important driving mechanism for oil recovery in fractured water-wet reservoirs. Reliable scaling relationships have to be used to scale laboratory test results to the field. This work addresses the scaling law described by Ma et al. (J. Pet. Sci. Eng. 1997, 18, 165.), with emphasis on the fluid viscosity term. Oil recovery curves versus time are generated using a mathematical expression, which has been shown to reproduce laboratory results very well for spontaneous imbibition of water into chalk cores (Standnes, D. C. J. Pet. Sci. Eng. 2006, 50, 151.). The expression includes an average constant diffusivity coefficient, which is calculated as an average value over the water saturation range. Calculated oil recovery rates versus time are then scaled using the Ma et al. scaling law describing mass transfer between matrix blocks and fractures. This law includes a geometrical mean term of the fluid viscosities found empirically to account for variation in oil and water viscosities. Excellent scaling is obtained for differences in rock sample size, oil viscosity (keeping water viscosity equal to 1.0 mPa s), and matched fluid viscosities. These results are in line with reported results in the literature. Oil recovery curves versus time are then calculated for different constant values of the oil viscosity (2, 4, 10, 22, and 43 mPa s) varying water viscosity from 1.0 mPa s to 500 times the oil viscosity for each oil viscosity value. Scaled oil recovery curves versus time show that the viscosity scaling group should be changed from the geometrical mean of the fluid viscosities to mu(0.82)(w)mu(0.18)(o) [for viscosity ratios (ratio of water to oil viscosity) above unity] to obtain reasonable good scaling in line with experimental results reported by Fischer and Morrow (paper presented at the Eighth International Symposium on Reservoir Wettability and Its Effect on Oil Recovery, Houston TX, May 16-18, 2004). Oil recovery curves versus time are then calculated for different constant values of the water viscosity (2, 4, 10, 22, and 43 mPa s). The oil viscosity is varying from matched to 500 times the water viscosity for each water viscosity value. The results show that the viscosity scaling group should change from the geometrical mean of the fluid viscosities to approximately mu(0.58)(w)mu(0.42)(o) (viscosity ratios below unity) to obtain reasonable good scaling. The same procedure is then applied to calculate the viscosity scaling group to be used to obtain good scaling for imbibition of water into gas-saturated rock samples. The results show that the viscosity scaling group in this case should be equal to mu(0.95)(w)mu(0.05)(gas) to scale the calculated gas recovery versus time curves properly. Many of the results presented here are in accordance with experimental results, but many also need further comparison to experimental data to assess their correctness.