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The capillary forces in a petroleum reservoir are the result of the combined effect of the surface and interfacial tensions of the rock and fluids, the pore size and geometry, and the wetting characteristics of the system. Any curved surface between two immiscible fluids has the tendency to contract into the smallest possible area per unit volume. This is true whether the fluids are oil and water, water and gas (even air), or oil and gas. When two immiscible fluids are in contact, a discontinuity in pressure exists between the two fluids, which depend upon the curvature of the interface separating the fluids. We call this pressure difference the capillary pressure and it is referred to by pc. The displacement of one fluid by another in the pores of a porous medium is either aided or opposed by the surface forces of capillary pressure. As a consequence, in order to maintain a porous medium partially saturated with non wetting fluid and while the medium is also exposed to wetting fluid, it is necessary to maintain the pressure of the non wetting fluid at a value greater than that in the wetting fluid. Denoting the pressure in the wetting fluid by pw and that in the non wetting fluid by pnw, the capillary pressure can be expressed as: Capillary pressure = (pressure of the non wetting phase) - (pressure of the wetting phase)

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pc = pnw - pw

That is, the pressure excess in the non wetting fluid is the capillary pressure, and this quantity is a function of saturation. This is the defining equation for capillary pressure in a porous medium.

There are three types of capillary pressure:

  • Water-oil capillary pressure (denoted as Pcwo)
  • Gas-oil capillary pressure (denoted as Pcgo)
  • Gas-water capillary pressure (denoted as Pcgw)

Capillary Pressure of Reservoir Rocks

Reservoir pore spaces can considered as bundles of interconnected capillaries of varying sizes. The capillary pressure that exists within a porous medium between two immiscible phases is a function of the interfacial tensions and the average size of the capillaries which, in turn, controls the curvature of the interface. In addition, the curvature is also a function of the saturation distribution of the fluids involved.

Electrical Conductivity of Fluid –Saturated Rocks.

Formation Factor

It is the resistivity of reservoir rock when filled with water to the resistivity of pure water.

F= Ro / Rw

Ro is the resistivity of the rock when saturated with water.

Rw is the receptivity of water.

Formation volume factor can also be expressed as….

F= C Ф (-m)

C is function of tortuosity and m is cementation factor.

Resistivity Index:

It is the ratio of resistivity of reservoir rock filed with reservoir fluid to the resistivity of reservoir rock when saturated with water.

I = Rt / Ro

Rt and Ro have usual meaning.

Effective Permeability: It is a relative measure of the conductance of the porous medium for one fluid when the medium is saturated with more than one fluid. This implies that the effective permeability is an associated property with each reservoir fluid, i.e., gas, oil, and water. As the saturation of a particular phase decreases, the permeability to that phase also decreases.

Effective permeability for the three reservoir fluids are represented by:

Kg = effective gas permeability

KO = effective oil permeability

Kw = effective water permeability

One of the phenomena of multiphase effective permeability is that the sum of the effective permeability is always less than or equal to the absolute permeability, i.e.,

Kg + ko + kw £ k

K is absolute permeability.

The effective permeability is used mathematically in Darcy's Law in place of the absolute permeability.

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