Imbibition capillary pressure

Fig. 2. Modified bucket for drainage and imbibition capillary pressure measurements. 

The measured drainage and imbibition capillary pressure curves are shown in Figure 3. Although these curves are from two different samples, we assumed that they are applicable for simulation purposes. 

The "true" imbibition relative permeability function was found by using the imbibition capillary pressure, and the recovery and pressure data from 1 cc/min displacement run of Core No. 1. Figure 15 shows a comparison of "true"... 

In the course of measuring imbibition capillary pressures, Morrow (20) also determined residual non-wetting phase saturations as a function of the intrinsic contact angle. For systems which spontaneously imbibe, he found that the residual oil values in- creased as the intrinsic contact angle was increased from 0° to 62°, the limit at which spontaneous imbibition occurs. Therefore, for systems which imbibe, the best recovery should be obtained from strongly water-wet systems. 

The fractional wettability of the porous medium, defined as a measure of the fraction of the internal surface of the porous medium in contact with one fluid (13) was determined by the USBM method (14). In the USBM method for determining wettability, the logarithm to the base 10 of the ratio of areas under a secondary drainage (A3) and an imbibition capillary pressure (A2) versus water saturation curves is used to define the wettability scale. 

Figure 7. This illustrates the effect of contact angle on imbibition capillary pressures for air/liquid in Teflon cores. 9e is the contact angle on a smooth flat plate and 0 is the advancing contact angle on a roughened Teflon surface. is the displacement curvature Pi i, is the imbibition capillary pressure o is the surface tension. (Reproduced by permission from reference 103. Copyright 1978.)...

Let us consider one more physical phenomenon, which can influence upon PT sensitivity and efficiency. There is a process of liquid s penetration inside a capillary, physical nature of that is not obvious up to present time. Let us consider one-side-closed conical capillary immersed in a liquid. If a liquid wets capillary wall, it flows towards cannel s top due to capillary pressure pc. This process is very fast and capillary imbibition stage is going on until the liquid fills the channel up to the depth l , which corresponds the equality pcm = (Pc + Pa), where pa - atmospheric pressure and pcm - the pressure of compressed air blocked in the channel. 

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. 

Wettability Index (W), (based on the U.S. Bureau of Mines wettability test), in which the forced (pressure) imbibition of water is compared to forced imbibition of oil via capillary pressure curves. The wettability index varies from -oo for complete oil-wetting, to zero for neutral, to +°° for complete water-wetting. For practical purposes, W usually varies between about -1.5 and +1.0. 

This is more than adequate to set news inks at commercial levels of ink application. Capillary imbibition is thus the predominant ink setting mechanism since spreading and bulk diffusion are much slower processes. However, two complications arise in this simplistic model. Implicit in the model is the assumption that the capillaries are connected to an inexhaustible supply of liquid. This is not the case, and it would be more reasonable to assume that as the larger capillaries drain the oil from the surface of the paper differential capillary pressures in the interconnected network drain the vehicle into progressively smaller capillaries emptying the larger ones (see Figure 1). These differential pressures can be expressed as ... 

Figure 5. (a) Primary drainage and (b) primary imbibition two-phase (water/PCE) capillary pressure-saturation curves for water-, intermediate-, and... 

The imbibition and drainage capillary pressure curves were measured for two samples from the same outcrop as Core No. 1. One of the samples was used without semi-permeable plate for the measurement of primary and secondary drainage. The maximum acceleration subjected to this core sample was corresponding to 20 psi capillary pressure. The other rock sample was used with a semi-permeable plate in the centrifuge drainage bucket and was subjected to a maximum rotational speed corresponding to 4.5 psi and then the speed was decreased in steps to trace the imbibition curve. The time given for each step was thirty hours. 

There are a variety of simple and inexpensive techniques for measuring contact angles, most of which are described in detail in various texts and publications and will be mentioned only briefly here. The most common direct methods (Fig. 17.4) include the sessile drop (a), the captive bubble (b), the sessile bubble (c), and the tilting plate (d). Indirect methods include tensiometry and geometric analysis of the shape of a meniscus. For solids for which the above methods are not applicable, such as powders and porous materials, methods based on capillary pressures, sedimentation rates, wetting times, imbibition rates, and other properties, have been developed. 

From capillary pressure measurements for sphere packings (11), the imbibition pressure at 70% wetting phase saturation is given by ... 

The integration of equation 15 is used to obtain the area under the individual curves (Ai for secondary drainage and A2 for forced imbibition). A limit of final saturation or capillary pressure must be chosen to provide consistent results. Wettability is defined as... 

Where surfactant is introduced to the reservoir via some carrying fluid, the relevant capillary pressure curves are from imbibition, both spontaneous and forced. Porous plate/membrane desaturation [26], flow or centrifuge effluent production [27, 28] and direct measurement of saturation in the porous media [29] are capable of measuring the complete imbibition curve. When used with reservoir-like fluids, the results from these methods reflect the wettability state of the porous rock. When surfactant is introduced, these methods should also be able to see the impact of wettability alteration. Two of these methods, the porous plate/membrane and the direct measurement of saturation methods require no modeling to be accurate for laboratory use. 

Summary. The Amott, USBM, Spontaneous Imbibition Index, imbibition rate, and capillary pressure are all displacement methods applicable to porous media and the possible evaluation of wettability alteration by surfactants. However, these methods must be complemented by more fundamental studies using contact angles or adhesion studies (Wilhelmy), etc. to meld the understanding of surface interactions with the macroscopic displacement of fluids. To comprehend how a surfactant alters the contact angle on a flat surface provides only part of the information to predict how the surfactant will interact in porous media. To measure only the fluid displacement in porous media provides little information on surface interactions. NMR and/or cryomicroscopy could help span this gap. Cryomicroscopy can directly look at pore surfaces, but for the moment, it is difficult and time consuming to use. Both techniques provide more of a qualitative measure of wettability than quantitative, but they are tools that can complement and help bridge between more fundamental measurements and quantitative displacement methods. 

Here, fa is dimensionless time, f is time, is porosity, k is permeability, Oo/w is interfacial tension, IFT, fi , is viscosity of water, and L is block dimension (length). They assumed that gravity effects are negligible, and that the shape of the matrix blocks, wettability, initial fluid distributions, relative permeabilities, and capillary pressures are the same. From equation 4 it is seen that the imbibition rate decreases if interfacial tension decreases. 

If the imbibition process at low IFT is governed from the beginning by capillary forces only, the oil recovery should be related to the factor a/jj.)t, as described by equation 4. The oil production in the presence of surfactant is much too high in the early stage to be scaled as a capillary-forced imbibition only [86, 93]. Due to adsorption of surfactant onto the rock surface, adsorption at the oil-water interface, and lateral displacement at the liquid-liquid interface, a gradient in the surfactant concentration is established as the water invades the pore system. At the water front, the surfactant concentration is below the CMC, and a relatively higher IFT-value will result in a relative increase in capillary pressure and higher imbibition rate. 

To prevent imbibition of the non-wetting phase, which would destroy the continuous liquid connection needed to apply equation (21.4), the maximum imposed capillary pressure must not exceed the entry pressure for the porous-disc film holder. This pressure can be estimated by Pew = 2a/rpore, where r ore is the pore radius of the porous material used. Therefore, discs with smaller pores are required for higher capillary pressures. Standard porous discs can be found with nominal pore diameters from 50 to 1 pm. Thus, when using a porous frit with pore diameters 1 pm, a typical surfactant solution (a = 30 mN/m) gives Pcmax foam films. Due to low interfacial tensions, this value can be much lower for emulsion films. Special porous... 

However, adsorption of surfactant molecules occurs also on the meniscus surface that decreases the interface tension y and therefore the capillary pressure = ly cos which is the driving force of imbibition. Considering the kinetics of impregnation, one needs to take into account the influence of surfactants on both contact angles and surface tension. 

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