An Analytical Scaling Method for Spontaneous Imbibition in Gas/Water/Rock Systems
- Kewen Li (Stanford U.) | Roland N. Horne (Stanford U.)
- Document ID
- Society of Petroleum Engineers
- SPE Journal
- Publication Date
- September 2004
- Document Type
- Journal Paper
- 322 - 329
- 2004. Society of Petroleum Engineers
- 5.6.5 Tracers, 1.2.3 Rock properties, 5.3.2 Multiphase Flow, 5.5.2 Core Analysis, 5.1 Reservoir Characterisation, 5.6.4 Drillstem/Well Testing, 5.4.2 Gas Injection Methods, 4.6 Natural Gas, 1.10 Drilling Equipment, 5.5.3 Scaling Methods, 5.9.2 Geothermal Resources, 5.3.1 Flow in Porous Media, 6.5.2 Water use, produced water discharge and disposal, 4.3.4 Scale, 1.6.9 Coring, Fishing
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A method was developed to scale the experimental data of spontaneous water imbibition (cocurrent) for gas/water/rock systems. In this method, a dimensionless time was defined with the effects of relative permeability, wettability, and gravity included. The definition was not empirical but based on a theoretical derivation. Using this dimensionless time, experimental data from spontaneous water imbibition in different rocks with different size, porosity, permeability, initial water saturation, interfacial tension, and wettability might be scaled. The scaling model proposed in this study for gas/water/rock systems was verified experimentally for different rocks (Berea, chalk, and graywacke from The Geysers) with significantly different properties; it was also verified experimentally at different initial water saturations in the same rock. The scaling results from this study demonstrated that the cocurrent spontaneous water imbibition in gas/water/rock systems could be scaled and predicted.
Spontaneous water imbibition is an important mechanism during water injection or aquifer invasion into highly fractured reservoirs. The amount and the rate of water imbibition from the fracture into the matrix by spontaneous imbibition are essential to the understanding of reservoir performance. The process of spontaneous water imbibition is controlled by the properties of the porous medium and the fluids, and by their interactions. These parameters are porosity, permeability, pore structure, matrix size and shape, boundary condition, fluid viscosity, initial water saturation, wettability, interfacial tension, relative permeability, and gravity. Li and Horne1 derived an equation to correlate the imbibition rate and the recovery by considering almost all of these variables.
Scaling spontaneous water imbibition is important for the evaluation of the production performance because so many factors are involved. To scale the experimental data successfully, it may be necessary to consider the effects of all the significant factors. Scaling has been investigated widely in oil/water systems but rarely in gas/liquid systems.
It has been a challenge for a long time to scale the experimental data of spontaneous imbibition in gas/liquid systems. Ignoring the effects of relative permeability, wettability, and gravity in the dimensionless time might be the reason. Natural gas/water/rock systems are usually strongly liquid-wet. However, this does not imply that there are no significant differences among different gas/water/rock systems in terms of wettability. Gravity may also play an important role in some cases.
Dimensionless time used frequently to scale spontaneous-imbibition data is defined as follows:
where tD=the dimensionless time, k=the rock permeability, f=the porosity, s=the interfacial tension between oil and water, t=the imbibition time, µm=the geometric mean of water and oil viscosities (Ma et al.2) or the water viscosity (Mattax and Kyte3), and La=the characteristic length defined as follows:
where Vt=he bulk volume of the matrix, Ai=the area open to imbibition in the ith direction, and dai=the distance traveled by the imbibition front from the open surface to the no-flow boundary. Mattax and Kyte3 used only the water viscosity in the scaling group, but a condition for scaling was that the viscosity ratio in the laboratory tests be equal to that in the reservoirs. The scaling method represented by Eq. 1 was verified experimentally by Zhang et al.4 in strongly water-wet oil/water/rock systems using Berea sandstone core samples.
Later Tong et al.5 also verified that the spontaneous water imbibition at mixed wettability for recovery (OOIP) of mineral oil of different viscosities could be correlated satisfactorily by using µm. However, the scaling method represented by Eq. 1 was rarely verified experimentally in rocks with different wettability.
Zhou et al.6 proposed another scaling group of dimensionless time with mobility terms of both wetting-phase and nonwetting-phase included. The reported scaling results of recoverable recovery were improved by using the proposed dimensionless time, although still scattered.
Zhang et al.4 mentioned that the geometric mean of the wetting-phase and nonwetting-phase viscosities did not scale results in gas/liquid/rock systems. Eq. 2 was modified from the shape factor suggested by Kazemi et al.7 As pointed out by Zhang et al.,4 when the dimensionless time defined in Eq. 1 was used to scale the experimental data in gas/liquid systems, the results were scattered significantly.
To scale the experimental results of spontaneous oil imbibition in gas/oil systems, Wang8 calculated the average value of oil and gas viscosities using a different approach than the geometric mean. The average viscosity is defined as: µm=µo3/4µa1/4, where µo and µa are defined as the viscosities of oil and air, respectively. This empirical approach may have limited application, as stated by Wang.8
One can see from the previous literature review that the dimensionless time defined in Eq. 1 (Ma et al.2) cannot be used to scale the experimental data in gas/liquid/rock system.
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