Characterization of Spontaneous Water Imbibition Into Gas-Saturated Rocks
- Kewen Li (Stanford U.) | Roland N. Horne (Stanford U.)
- Document ID
- Society of Petroleum Engineers
- SPE Journal
- Publication Date
- December 2001
- Document Type
- Journal Paper
- 375 - 384
- 2001. Society of Petroleum Engineers
- 5.5 Reservoir Simulation, 5.3.2 Multiphase Flow, 4.1.2 Separation and Treating, 5.2.1 Phase Behavior and PVT Measurements, 5.9.2 Geothermal Resources, 6.5.2 Water use, produced water discharge and disposal, 5.8.6 Naturally Fractured Reservoir, 5.3.1 Flow in Porous Media, 4.1.5 Processing Equipment, 5.6.4 Drillstem/Well Testing, 5.5.2 Core Analysis, 5.6.5 Tracers, 5.4.1 Waterflooding, 5.4 Enhanced Recovery, 5.5.8 History Matching, 4.3.4 Scale, 1.6.9 Coring, Fishing
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A method has been developed to characterize the process of spontaneous water imbibition into gas-saturated rocks. Water relative permeability and capillary pressure can be calculated simultaneously from water imbibition data using this method. A linear relationship between imbibition rate and the reciprocal of the gas recovery by spontaneous water imbibition was found and confirmed both theoretically and experimentally, even at different initial water saturations. There was almost no effect of initial water saturation on residual gas saturation by spontaneous water imbibition. The higher the initial water saturation, the lower the imbibition rate and the ultimate gas recovery. It was found that the capillary pressure did not vary with initial water saturation in a certain range. The capillary pressure and the water relative permeability calculated using the new method was consistent with the experimental results measured using other techniques. The method developed in this paper is also of importance for scaling up experimental data.
Many oil and gas reservoirs are developed by water injection or are associated with active aquifers. The reinjection of produced water into geothermal reservoirs, which are usually highly fractured, is also a practical solution to the problems of reservoir pressure decline and environment pollution. Spontaneous water imbibition phenomena exist in most of these reservoirs except those that are not water-wet; it is an important process driven by capillary forces. The study of spontaneous water imbibition is essential to predict the production performance in these reservoirs developed by waterflooding, especially in highly stratified formations and fractured reservoirs where the amount and rate of mass transfer between the matrix and the fracture influence the recovery and the production rate.1-5 It is also possible to determine the wettability of the rock-fluid systems from spontaneous water-imbibition measurents.6 Because the spontaneous imbibition is a capillary pressure-dominated process, the imbibition rate is significantly dependent on the properties of the porous media, fluids, and their interactions. These include permeability7 and relative permeability of the porous media, pore structure, matrix sizes, shapes and boundary conditions,2,5,8,9 fluid viscosities,7,10,11 initial water saturation (Swi),12-15 the wettability of the rock-fluid systems,6,7 and the interfacial tension between the imbibed phase and the resident phase.7,16 Most of the studies in the literature focused mainly on oil-water-rock systems. There are many naturally fractured gas reservoirs positioned over active aquifers.17 The water coning in these gas reservoirs often results in excessive water production, which may kill a well or severely curtail its economic life because of water handling costs.18 The understanding of the mechanisms that govern spontaneous water imbibition in gas-water-rock systems is important to the development of naturally fractured gas reservoirs with active aquifers.17-19 Few methods, however, are available for characterizing the process of spontaneous water imbibition into gas-saturated rocks. The method used usually is the Handy equation,20 that is, the weight or the volume of the imbibed water is proportional to the square root of the imbibition time:
where A and Nwt=the cross-section area of the core and the volume of water imbibed into the core, respectively; f=the porosity, µw=the viscosity of water and t=the imbibition time; kw, Pc, S wf are usually defined as the effective permeability of water, the capillary pressure, and the water saturation, respectively.13,20 These definitions of kw, P c, and Swf may not be physically clear. For example, is Swf the water saturation behind or in front of the water imbibition front? It will be seen from the derivation in the next section that S wf=the water saturation behind the imbibition front, while kw=the effective permeability of water phase at a water saturation of Swf. Similarly, Pc=the capillary pressure at Swf.
There are three main disadvantages to using the Handy equation20 to characterize spontaneous water imbibition. First, effective water permeability and capillary pressure cannot be calculated separately from a spontaneous water imbibition test. Second, the straight line between the square of weight gain and the imbibition time often does not go through the origin, as it is supposed to. Third, the relationship between the square of weight gain and the time is not a straight line during the later period of water imbibition, or even in the early period in some cases. Additionally, the amount of water imbibed into porous media is infinite when imbibition time approaches infinity, which is physically impossible. The reason for this may be because the gravity was not considered in deriving the Handy equation.20
Aronofsky et al. 1 suggested an empirical form of the function of time relative to production from the matrix volume:
where R=the recovery in terms of recoverable resident fluid by water imbibition, ?=a constant giving the rate of convergence, and t=the production time.
As pointed out by Kazemi et al.,5 the equation proposed by Aronofsky et al.1 appeared to work well for history matching but did not generally reflect the physics of flow correctly. Using a numerical simulation technique, Chen et al.21 demonstrated that the Aronofsky et al.1 exponential relationship (Eq. 2) was only valid for cases with constant diffusion coefficients. Conducting water imbibition tests in the core samples from fissured oil fields, Iffly et al.22 showed that it was difficult to obtain the relationship between the recovery and dimensionless time with Eq. 2.
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