Multiphase Saturated Rock Properties – Term Paper

Until in the recently the data available on capillary entry pressure and permeability properties of fault rocks was little. In addition, the transmissibility of fault rocks was adjusted in the absence of scientific justification. Currently, there is abundant data on the properties of fault rocks such as the capillary entry pressure, permeability as well fault thickness. Increased research on fault rock properties has facilitated complex treatment of faults in simulators [3]. Specifically, the saturated rock properties based on the real rock data to calculate the transmissibility in grid block faces which are adjacent to the fault rocks in order to account for the effects of fluid flow on faults and vice versa.

Geologic formations are regarded as capillary systems when the mechanical equilibrium in the resident fluid is dependent on capillary action as well as  gravity and hydrostatic forces . Capillary action results from the interfacial forces acting between the solid and liquid phases as well as the liquid phases. The Multiphase flow through the porous media results from the capillary action acting on liquid and solid phases. Given the arrangement of molecules at the boundary of two phases, there is energy per unit surface area associated with the interface. The description of this energy is based on the interfacial tension as well as force per unit distance inherent in phases I and j . The pressure difference existing across the boundary , which separates two immiscible fluids depends on this energy. A contact angle   at the interface of fluid-fluid-solid  is utilized in balancing the interfacial forces existing between fluid-solid and fluid-fluid interfaces

Rocks that are in their natural state, liquids composed on non-polar molecules are the non-wetting phase while water is the wetting phase. In regards to the multiphase properties of saturated rocks there is concurrent flow of liquids through the fault rocks using the Darcy’s law where there is resistance to flow of one fluid if there is an increase in second fluid phase [3]. Therefore, the  permeability in both phases  and the sum of permeability to each fluid phase is less than the rock’s intrinsic permeability. When the Darcy’s law is used in the fluid phase I,

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This implies the relative permeability of i and j is defined by the ratio of effective intrinsic permeability of the rock.

Phase Trapping

The entrapment of superfluous phases in porous media can take place in different situations during production operations, drilling, work over and completion. When there is an increase in the existing saturation in porous media or when additional immiscible phase is introduced in the porous media, it can result to relative permeability effects affecting the flow of gas, water or oil in the fault rocks. This phenomenon is called phase trapping in reference to the situation considered [1].

In Phase trapping, when the capillary pressure reduces to zero, there is no decrease in the Snw value, but reaches the non-wetting residue phase saturation (Snwr). Therefore, full recovery of oil from reservoirs bearing water-wet oil through imbibition capillary forces is difficult and impossible. This is similar to the wetting phase,  that is, using the drainage displacement mechanism to remove the wetting phase from porous medium  [1]. Capillarity has an important role in displacing one of the immiscible fluids from the other. Detailed pore structure, that is, the pore topology and pore geometry, determine the fluid-fluid interfaces formed in the porous medium [1]. The displacement of one immiscible fluid with another results from the contact of capillary forces given the geometry and size of pores are different. There are three main types of phase trapping mechanisms; these are Bypassing, Snap-Off and the Jamin Effect.


This mechanism of phase trapping occurs within the pores, throats, or at the intersection region of the throats and the pores. Generally, snap-off involves the selloidal menisci. Specific conditions and critical capillary pressures are essentially determined for simulating the processes of microscopic displacement in media with any wetta bility and structure [2]. The arrangement shapes and sizes of the throats and pores in reference to the direction of displacement phase affect the interface motions during imbibitions. Considering the square capillary through which the non-wetting phase enters the pores. The capillary pressure is determined by,


When there is an increase in the capillary pressure above the value above, then the wetting phase is pushed to the corners with decrease in the radius of the interface curvature. If there is an allowance given to the wetting phase  to flow along the flow along the corners of the pores , then there is a decrease in capillary pressure below Pcso and Pcso=2O/w

The interface pulls away from the capillary walls such that the non-wetting phase becomes a thin filament that is not supported by the walls of the capillary. In addition, the necking down becomes unstable  resulting to snapping-off of the non-wetting phase into bubbles or droplets of disconnected non-wetting phase.


The Jamin Effect refers to the resistance of the fluid flow via the capillaries because of the presence of bubbles. These bubbles delay the flow of the liquid when progressing through the capillary tubes having small diameter. The Jamin effect results from the differences in capillary pressure in two trapped globules. This effect is analyzed easily through explanation of trapped oil droplet in a water wet capillary tube.

Assuming that there is a static system having different pressure existence between two points because of capillary forces, the pressure difference should be exceeded in order for flow to take place, therefore, PA-PB should be exceeded for flow to take place [2]. In addition, the contact angle is not the same on different sides of the drop. Given that the size of the capillary tubes and radius of the capillary tubes is different, in case one drop is displaced in a particular direction then there is one receding and one advancing contact angle [1]. When the pressure difference exists between two different pores, at saturation, flow will take place as defined by the formula below:

If rA > rB then the pressure at the first capillary pore is greater than the capillary pressure at the second point. Pressure drop exists from point A to B and the gradient will have to be exceeded in order to force flow at the narrow part of capillary constriction. In order to recede the contact at point A and advance the contact point at point B, cosθA < cosθB and θA > θB . In addition, PA > PB and there is a pressure gradient existing in the direction of static flow [1].


In reference to the capillary pressure equation, if the condition of non-wetting phase invades the larger pores, there is a tendency of special trapping property of saturated rocks called bypassing. In bypassing, the main trapping mechanism during the imbibitions process is the non-wetting phase. A reservoir rock is comprised of a complex network of reuniting and branching pore elements having different geometry and sizes [3]. Therefore, any process of displacement recognizes this complex network. The simplest type of displacement under this condition is the pore doublet  [1].

In bypassing, there is invasion of a smaller throat during imbibition in the first time because the larger throats are swept away in the first process of drainage creating a higher capillary pressure [3]. The condition of bypassing happening in the larger pores of saturate rocks during the time of imbibitions is, established using the viscous and capillary forces by assuming that the pore doublet model is:

PA-Pwi= 8 μwLwV1/r12 

defining L = Lo + Lw, and assuming that  μw = μo = μ  we get:

PB-PA = –  (8 μwLV1/r12 ) + 2O Cos θ/r1

This is the same case for the second pore. Therefore, the change in pressure in the two pores combined with velocity v1 will displace oil from the small pores in the rocks and leave the water in the large pores through the mechanism of bypassing.

Reference List

[1]S. Agar and S. Geiger, Fundamental controls on fluid flow in carbonates. . [2]A. Alshawabkeh, K. Reddy and M. Khire, Characterization, monitoring, and modeling of geosystems. Reston, Va.: Geo-Institute of The American Society of Civil Engineers, 2008. [3]”Surface and Interfacial Surface Tension for Multiphase Saturated Rock | Fundamentals of Fluid Flow in Porous Media”, Special Core Analysis & EOR Laboratory | PERM Inc., 2016. [Online]. Available: [Accessed: 18- Oct- 2016].