Electrical Properties of Petroleum Reservoir Rocks
Both solid grains and vacuous space make up porous rocks. With the exception of some clay minerals, the solids are nonconductors. The shape of the voids and the fluid used to fill them determine a rock's electrical characteristics. Oil, gas, and water are the fluids of importance in petroleum reserves. Nonconductors include gas and oil.
Water is a conductor when it contains dissolved salts, such as NaCl, MgCl2, KCl normally found in reservoir water. Current is conducted in water by movement of ions and can therefore be termed electrolytic conduction. The resistivity of a porous material is defined by:
where r is resistance, [Ω], A is cross-sectional area, [m2], L is length, [m]
and resistivity is expressed in Ohm-meter (Ω.m). However, for a complex material like rock containing water and oil, the resistivity of the rock depends on:
- Salinity of the water
- Temperature
- Porosity
- Pore geometry
- Formation stress
- Composition of rock.
The resistivity of an electric current in porous rock is due primarily to the movement of dissolved ions in the brine that fills the pores of the rock. The resistivity varies with temperature due to the increased activity of the ions in solution as the temperature increases.
Due to the conductivity properties of reservoir formation water, the electrical well-log technique is an important tool in the determination of water saturation versus depth and thereby a reliable resource for in situ hydrocarbon evaluation.
Porosity and the Formation Factor:
The petrophysical researcher, Gus Archie, established that the formation factor (can be mathematically related to the porosity by incorporating two constants into an equation—"a", the tortuosity factor, which is often forced to have a value of 1 to reduce the number of variables in the equations, and "m", termed the cementation factor. These constants are related to the rock type, pore geometry, and the presence of solid conductors in the clay materials. When the porosity increases, then the formation factor decreases exponentially.
Formation Factor:
The most fundamental concept considering the electrical properties of rocks is the formation factor, as defined by Archie:
Where Ro is the resistivity of the rock when saturated 100% with water, [Ω.m], Rw is the water resistivity, [Ω.m].
The formation factor shows a relationship between water saturated rock conductivity and bulk water conductivity. Obviously, the factor depends on the pore structure of the rock.
Resistivity Index:
The second fundamental notion of electrical properties of porous rocks containing both water and hydrocarbons is the resistivity index I.
Where Rt is the resistivity of the rock when saturated partially with water, [Ω.m], Ro is the resistivity of the same rock when saturated with 100% water, [Ω.m].
Tortuosity:
Wyllie developed the relationship between the formation factor and other properties of rocks, like porosity f and tortuosity t. Tortuosity can be defined as (La/L)2,
where L is the length of the core and La represents the effective path length through the pores. Based on simple pore models, the following relationship can be derived:
a generalized Archie equation:
Where m and a are constants characterizing the rock, F is formation factor Ï„ is tortuosity of the rock, ∅ is porosity of the rock. a has values in the range 0.62-3.7 it depends on the rock type.
Cementation factor:
Archie suggested a slightly different relation between the formation factor and porosity by introducing the cementation factor:
Where ∅ is porosity of the rock, m is Archie’s cementation factor.
Archie reported that the cementation factor probably ranged from 1.8 to 2.0 for consolidated sandstones and for clean unconsolidated sands was about 1.3.
Saturation Exponent:
The famous Archie’s equation gives the relationship of resistivity index with water saturation of rocks:
Where Sw is water saturation, n is saturation exponent, ranging from 1.4 to 2.2 (n = 2.0 if no data are given).
In this equation, Rt and Ro can be obtained from well logging data, and saturation exponent n is experimentally determined in a laboratory. As a result, Archie's equation can be used to calculate in situ water saturation. Based on the material balance equation for the formation, Sw+So+Sg =1.0, the hydrocarbon reserve in place may be calculated.