Summary
It has been a challenge to understand why recovery by spontaneous imbibition could both increase and decrease with initial water saturation. To this end, mathematical models were developed with porosity, permeability, viscosity, relative permeability, capillary pressure, and initial water saturation included. These equations foresee that recovery and imbibition rate can increase, remain unchanged, or decrease with an increase in initial water saturation, depending on rock properties, the quantity of residual gas saturation, the range of initial water saturation, and the units used in the definitions of gas recovery and imbibition rate. The theoretical predictions were verified experimentally by conducting spontaneous water imbibition at five different initial water saturations, ranging from 0 to approximately 50%. The effects of initial water saturation on residual saturation, relative permeability, capillary pressure, imbibition rate, and recovery in gas/water/rock systems by cocurrent spontaneous imbibition were investigated both theoretically and experimentally. Water-phase relative permeabilities and capillary pressures were calculated with the experimental data of spontaneous imbibition. Experimental results in different rocks were compared.
Introduction
Spontaneous water imbibition is an important mechanism during water injection. Prediction of recovery and imbibition rate by spontaneous water imbibition is essential to evaluate the feasibility and the performance of water injection. For example, is water injection effective in the case of high initial water saturation in reservoirs? Answers to such a question may be found by investigating the effect of initial water saturation on spontaneous water imbibition.
It has been observed experimentally that initial water saturation affects recovery and production rate significantly (Blair 1964; Zhou et al. 2000; Viksund et al. 1998; Cil et al. 1998; Tong et al. 2001; Li and Firoozabadi 2000; Akin et al. 2000). However, the experimental observations from different authors (Zhou et al. 2000; Cil et al. 1998; Li and Firoozabadi 2000; Akin et al. 2000) are not consistent. On the other hand, few studies have investigated the effect of initial water saturation on recovery and imbibition rate theoretically, especially in gas reservoirs.
Using numerical-simulation techniques, Blair (1964) found that the quantity and the rate of oil produced after a given period of imbibition increased with a decrease in initial water saturation for countercurrent spontaneous imbibition. Zhou et al. (2000) found that both imbibition rate and final oil recovery in terms of oil originally in place (OOIP) increased with an increase in initial water saturation, whereas oil recovery by waterflooding decreased. Viksund et al. (1998) found that the final oil recovery (OOIP) by spontaneous water imbibition in Berea sandstone showed little variation with a change in initial water saturation from 0 to approximately 30%. For the chalk samples tested by Viksund et al. (1998), the imbibition rate first increased with an increase in initial water saturation and then decreased slightly as initial water saturation increased above 34%.Cil et al. (1998) reported that the oil recovery (in terms of recoverable oil reserves) for zero and 20% initial water saturation showed insignificant differences in behavior. However, the oil recovery for initial water saturation above 20% increased with an increase in initial water saturation. Li and Firoozabadi (2000) found that the final gas recovery in the units of gas originally in place (GOIP) by spontaneous imbibition decreased with an increase in initial water saturation in both gas/oil/rock and gas/water/rock systems. The imbibition rate (GOIP/min) increased with an increase in initial water saturation at early time but decreased at later time. Akin et al. (2000) found that the residual oil saturation was unaffected significantly by initial water saturation.
In this study, equations, derived theoretically, were used to study the effect of initial water saturation on gas recovery and imbibition rate. The equations correlate recovery, imbibition rate, initial water saturation, rock/fluid properties, and other parameters. Experiments of spontaneous water imbibition in gas-saturated rocks were conducted to confirm the theoretical predictions. The effect of rock properties on gas recovery and imbibition rate was also studied. An X-ray CT scanner was used to monitor the distribution of the initial water saturation to confirm that the initial distribution of the water saturation was uniform. In this study, we only focused on cocurrent spontaneous imbibition. It was assumed that there were no chemical reactions or mass transfer between gas and liquid.
Numerical Identification of the Filtration Capacitive Parameters in Two-Phase Petroleum Reservoirs
