It depends on the wettability of the porous body.  However, generally dew point is higher in porous body and bubble point is lower.  That is, within the small pores condensation might happen at pressures much higher than the conventional dew point.  For example, the dew point in a 1 nm capillary tube can be 3 times higher than the measured dew point in PVT cell (using Kelvin rule).  This coefficient is about 1.2 at 10 nm and about unity for a 100 nm capillary diameter.  Since the fluid within the pores smaller than 100 nm are assumed non-producible, therefore we can practically ignore the impact of capillarity on the PVT data. 

It depends on the wettability of the porous body.  However, generally dew point is higher in porous body and bubble point is lower.  That is, within the small pores condensation might happen at pressures much higher than the conventional dew point.  For example, the dew point in a 1 nm capillary tube can be 3 times higher than the measured dew point in PVT cell (using Kelvin rule).  This coefficient is about 1.2 at 10 nm and about unity for a 100 nm capillary diameter.  Since the fluid within the pores smaller than 100 nm are assumed non-producible, therefore we can practically ignore the impact of capillarity on the PVT data. 

Thanks a lot, Alireza for your careful answer.

We may suppose an ideal system that can produce from all pores. Another issue that remains is that how we can perform a flash calculation in the presence of porous media where Pc is active, and how we can relate the flash calculation results to the saturation (better to say, residual saturation) in porous media.

The main part of the flash calculation is mass balance, and therefore it does not change.  You just need to modify the equilibrium ratio (K-value) with respect to the capillary pressure.  Conventionally it is just a function of fugacity coefficients at both phases, while in a capillary tube the capillary pressure along with the pressures of both phases and molar density of the liquid phase come into play.  This way the phase behavior depends on the radius of the capillary media. 

Thanks a lot, Alireza.

Shall the residual saturation of liquid be considered in the gas phase VLE calculations? How can this residual phase be treated?

The impact of residual liquids must be seen in overall concentration before implementing any flash calculation.  In the case of water it may changes the pore radius, assuming it as a thin film on the rock surface.

Hope this helps.

Alireza: Could you please describe more how the impact of residual liquids can be seen in overall concentration, an how will it enter the loop of flash calculations.

Just assume all the phases as one phase within the capillary media, and calculate the overall molar fraction of each component.  Run a two phase flash and check the phase stability.  For the case of residual presence, you might find it unstable to have just two phases.  If so, run a three phase flash starting again from the calculated overall mole fractions.  Normally a three phase flash suffices, but thermodynamically you must check the stability of all phases.  This way, the residual saturation is one of the results after the phase equilibration.  You will be able to calculate the IFT also between residual liquid and other phases.

To offer some supplementary infor. from PVT measurements in lab (in general, this stage of data Collection forms the basis of further PVT calculation or simulation). The capillary pressure is normally not considered since normally it is the fresh reservoir fluid samples that are sent to PVT labs and so it is not porous media to analyse, but more like a mixed fluid phase (if Heavy oil, probably With muds or other type of contaminants present). For core labs for instance they do peform a lot core tests With porous medium). For single or multiple flash, it is the mass Conservation that Plays the key role, and for those tests performed in PVT cell like constant mass expansion, constant volume depletion, or swelling test, it is an acceptable error range in total mass and individual Component concentrations from Gas chromotography that they compare and confirm the validity of such tests. Passing these criteria, will the data be used for further PVT calculations or simulations, but they also "adjust" the PVT results manually by fine-tuning measured parameters via correlated sheet calculations, if the measured results have an error range just slightly above the red-line. 

Hope this sounds interesting, though not relevant to Your question:)

Here is the science underlying the phase equilibrium within a capillary body. I would follow up this discussion very carefully if it was my concern. However, it is generally neglected in pore scale reservoir engineering calculations since reservoir rocks have surface water even when they are strongly oil-wet; hence, tight corners where capillary effects are dominant are always filled with water and not-accessible to hydrocarbons.

At equilibrium, molecules are transferred freely across the interfacial surface. Therefore, the Gibbs’ energy (chemical potential) of every type of molecules is the same in all phases which are at thermodynamic equilibrium. This leads to equality of the fugacity of each type of compound in all phases present within the equilibrium system. It does not depend on whether the equilibrium is reached within a capillary tube, where the interface is a meniscus, or within a bulk system such as within a PVT cell with a flat interface. The chemical potential of a compound in a phase depends on the phase temperature, pressure, (molar) composition, and intermolecular interactions (in turn, a function of number, type, distance, configuration, and kinetic energy of molecules). When the interface is flat, the pressure exerted on the interface by each of the participating phases is the same. Thus, at equilibrium conditions, the pressure and temperature of the phases are the same, while they may have different compositions.  Therefore, component mass balance and equations relating the fugacity coefficients to T, p, and each phase composition (E.O.S) help construct a loop to find the equilibrium composition of each phase.

However, as the interface of equilibrium phases is curved due to surface forces (solid-fluid (surface tension) and immiscible fluid-fluid (interfacial tension) forces), capillary pressure is produced. Hence, capillary pressure is due to imbalanced molecular forces at the interface and bulk of fluid phases and solid-fluid surface. Thus, at least two fluid phases must be present within a capillary body to produce capillary pressure. The effects of interfacial forces and surface forces on capillary pressure appear as interfacial tension and interfacial curvature, respectively. The interfacial curvature is a function of solid-fluid interactions (contact angle) and the capillary radius. Therefore, capillary pressure is formulated by the interfacial tension, capillary radius, and contact angle of fluid which is in contact with the surface of the capillary body (wetting phase). The capillary pressure may be either positive or negative depending on the contact angle. As a result, there is a difference in pressure across the interfacial surface; thus, the pressure of the equilibrium phases is not the same within a capillary body. The pressure difference is called capillary pressure and defined as p(non-wetting fluid)-p(wetting fluid)=pc. For instance, when vapor and liquid are at thermodynamic equilibrium within a capillary system, liquid phase is in contact with the surface body thus is considered as the wetting phase with a contact angle of zero to 180 degree. The vapor phase pressure minus pc yields the liquid phase pressure. Thus, when transferred across the interface, molecules must overcome not only molecular configurations and interactions within the destination phase but also the pressure difference (or capillary pressure) across the interface. Therefore, the fugacity coefficient of each compound in a phase is calculated at the phase particular pressure and composition, different from those calculated when facing a flat interface where the phases’ pressure is the same. This approach triggers both liquid and gas residuals.

As Alireza explained, stability analyses help finding the number of phases present at equilibrium. Usually, water is considered as a film covered the interior surface of a capillary body, making the capillary diameter narrower. However, it may be doubtful when dealing with mixed-wet surfaces.  

Hope it is to the point.

Many thanks for your detailed explanation, Negahdar.

Many thanks for your detailed explanation, Negahdar.

Many thanks for your detailed explanation, Negahdar.

here is somehow a related research http://www.sciencedirect.com/science/article/pii/S1750583612002290?np=y

Dear Dr. Azin

PVT calculations are highly affected by capillary pressure especially in tight and shale formations where pore sizes are in the order of nanometers. Please follow the attached file in which the way of calculating K-values in the presence of Pc is somehow explained.

Regards,

Amin