Drainage-imbibition

Iliuta I, Hamidipour M, Larachi F. Non-equilibrium thermomechanical modeling of liquid drainage/imbibition in trickle beds. AIChE J. 2012 58 3123. 

The Great Assumption of percolation modellers is that some property (usually "pore radius" for drainage-imbibition) of the bonds (or sites) of the network is... 

Interpretation for irreducible water saturation assumes that the rock is water-wet or mixed-wet (water-wet during drainage but the pore surfaces contacted by oil becomes oil-wet upon imbibition). If a porous medium is water-wet and a nonwetting fluid displaces the water (drainage), then the non-wetting fluid will first occupy the larger pores and will enter the smaller pores only as the capillary pressure is increased. This process is similar to the accumulation of oil or gas in the pore space of a reservoir. Thus it is of interest to estimate the irreducible water saturation that is retained by capillarity after the hydrocarbon accumulates in an oil or gas reservoir. The FFI is an estimate of the amount of potential hydrocarbon in... 

The capillary pressure PC(S) exhibits a marked hysteresis phenomenon when the liquid is alternately withdrawn (drainage) and introduced (imbibition) into the particulate bed. Consequently, capillary pressure changes as a result of variations in saturation do not follow a unique functional relationship. In fact, the suction is always higher on the drainage side of the imbibition-drainage cycle (M8). In Fig. 7 the suction curve starts at zero when S = 1. 

Nguyen et al. [205] designed a volume displacement technique that was used to measure the capillary pressures for both hydrophobic and hydrophilic materials. One requirement for this method is that the sample material must have enough pore volume to be able to measure the respective displaced volume. Basically, while the sample is filled wifh water and then drained, the volume of water displaced is recorded. In order for the water to be drained from fhe material, it is vital to keep the liquid pressure higher than the gas pressure (i.e., pressure difference is key). Once the sample is saturated, the liquid pressure can be reduced slightly in order for the water to drain. From these tests, plots of capillary pressure versus water saturation corresponding to both imbibitions and drainages can be determined. A similar method was presented by Koido, Furusawa, and Moriyama [206], except they studied only the liquid water imbibition with different diffusion layers. 

Here k is the permeability of the dry medium and J(S[) characterizes hysteresis behaviour in the trickling regime. It should be noted at this level that Eqn. (5.2-12) was derived by these authors from available data on two-phase imbibition and drainage curves, implicitly identified to the trickling flow regime in trickle-beds. The J function may be multi-valued and depends on the history of the flow, however Grosser et al. [22] as well as Dankworth et al. [23] assume it to be single-valued. 

A constricted tube model is used to analyze viscous and capillary effects associated with foam flow in porous media. The foam moves through the pore structure as single layer, continuous bubble trains. Capillary resistance stems from the drainage and imbibition surfaces as well as the internal lamellae structure. 

To access the importance of Fg in Equation 53 and to determine how this quantity changes from non-dispersed flow to foam flow, a transient gas permeability test was performed and the results presented in Figure 11. In particular, drainage and imbibition tests were first conducted to reach a final drainage state with Ql being fixed at 0.53 pl/s. The measured permeability corresponded to the lower curve in Figure 11. Here again, the dependence on gas... 

Figure 10. Axial pressure profiles observed at steady state for initial drainage experiment (no prior imbibition) and final drainage experiment (after a number of successive drainage and imbibition experiments).

Figure 12. Permeability curves at different liquid rates. In both cases, shut-off of liquid injection to cell results in a constant permeability (dotted line) after long periods of time. Data correspond to different displacement histories , second imbibition O, third drainage A, fourth drainage , third imbibition , drainage with succeeding tests being conducted at increasing Qg s A imbibition with Qg decreasing in succeeding tests.

Data from Fulcher et al. (1985) showed that above 5.5 mN/m, IFT seemed to have little effect on k or k,. Chen and Chen (2002) observed that as water/ oil IFT was reduced, both water and oil relative permeabilities were increased, their end points were raised, and residual saturations were decreased. These observations were obvious only when the IFT was below 0.1 mN/m. The imbibition curves were different from the drainage curves, even when the IFT was reduced below 0.02 mN/m. 

Fig. 1-4. Capillary phenomena (imbibition and drainage) in pores with dilleienl emss section shapes bill identical pore cross sectional area.

The modified unitary approach of Philip (1977a), supplemented by adsorption terms presented by Iwamatsu and Horii (1996), provides a means of calculating equilibrium liquid-vapor interfaces for various chemical potentials during drainage and imbibition. Four major steps are discerned during the transition from adsorption to capillary-dominated imbibition (Fig. 1-6). At low matric potentials,... 

Although it is unclear whether slit snap-off during drainage occurs at the same chemical potential as for imbibition, we have adopted a similar expression for simplicity. In any case, we expect effects of slits emptying at lower chemical potentials to have a minor influence on the upscaling scheme due to the presence of a distribution of slit spacing in a sample. 

To calculate unsaturated hydraulic conductivity A"(p) we have to take into consideration the spontaneous filling (snap-off) of the slit and the central pore for imbibition and the spontaneous redistribution of liquid for drainage. These aspects are extensively discussed in Film Adsorption on Rat Surfaces and in Slit-Shaped Pores and Capillarity and Pore Shape . The unsaturated conductivity before slit filling is given as ... 

The saturation will increase monotonically with y with s = 0 at y = 8S, and s = 1 at y = 8g(. In principle, we then expect the results of Chung et al. [120] for the condensation to apply to the evaporation. However, since the available experimental results for pc (drainage versus imbibition) show a hysteresis, and also due to the lack of symmetry in Kr((s)/Krg, we do not expect a complete analogy. 

Imbibition The displacement of a non wetting phase by a wetting phase in a porous medium or a gel the reverse of drainage. 

Using the theory of hydrostatic foam stability [21, 26], the behaviour of foams in contact with fabrics was studied [181]. Under these conditions, the drainage of liquid from the foam occurs under the influence of the following processes 1) suction of liquid due to capillarity of high-dispersion foams 2) imbibition of foam by the capillary structure of fabrics. The production of foams with a controlled structure allows to achieve a more uniform application of a dye to a fabric. Foamer formulations were developed containing surfactants and a water-soluble polymer, which allow to achieve a minimum initial syneresis rate up to 10 m/s [182]. 

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