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Formation Resistivity Factor

Formation Resistivity Factor 2016-10-25T11:54:45+00:00

Fundamentals of Fluid Flow in Porous Media

 

Chapter 2

Formation Resistivity Factor

Porous media consist of mineral, rock fragments and void space. The solids with exception of certain clay minerals (such as shaly sands where clay shales produce electrical conductivity) are nonconductive. Generally the electrical property of a rock depends on void space geometry and the fluids that occupy the void space. The fluid of interest for petroleum engineers are oil, gas and water. Oil and gas are nonconductor and water is conductive when contains dissolved salts.  Water has electrolyte conductivity, because electricity conducted by movement of ions. The resistivity term, as the reciprocal of conductivity, is used to define the ability of a material to conduct current:
Resistivity term to define ability of material to conduct current

Where:

  • r = resistance, ohm
  • R = resistivity of, ohm-cm
  • A = Cross section area, cm2
  • L = Length, cm

“Formation Resistivity Factor” is the most fundamental concept in considering electrical properties of rock:
Formation Resistivity Factor Equation

Where:

  • Ro = Resistivity of fully water saturated rock
  • Rw = Saturating water resistivity

It is only defines for porous matrices of negligible electrical conductivity. It is evident that F is always greater than unity in the absence of electrical conductive layers. The formation resistivity factor measure the influence of pore structure on the resistance of sample. In the absence of a conductive mineral layer the electrical current can flow only through the fluid in the rock interconnected pores. This implies that F is related to the porosity of the rock. The influence of pore structure on the electrical conductivity may be divided into two contributions: the reduction of the cross section which is available for conduction and the orientation and length of conduction path (Figure 2‑29). For isotropic disordered media, the ratio of the cross section available for conduction to the bulk cross section is equal to the bulk porosity, i.e. F is inversely related to porosity:

Figure 2‑29.II:
Figure 2-29ii Equations

Figure 28.III:
Figure 28iii Equation

Where T is defined as tortuosity.

The Influence of Pore Structure on the Electrical Conductivity
Figure 2-29: The Influence of Pore Structure on the Electrical Conductivity

Measurements showed that F varies more than just in inverse proportion to porosity. The first relationship between F and Φ was suggested by Archie (1942):
Relationship between F and Phi by Archie (1942)

Where m is “cementation exponent” and its value is usually between 1.3 to 2.5 for various types of rocks. For clean and uniform size sands: a = 1 and m = 2. More general form of the Archie’s law is:
General Form Archies Law

Where a is an intercept. Generally a logarithmic plot of F versus Φ is used to find a and m value for a special sample (Figure 2‑30).

According to the presented formula it can be shown that the following variables have effects on the resistivity of natural porous media:

  • Temperature
  • Water salinity
  • Porosity
  • Pore geometry
  • Formation stress
  • Rock composition
  • Degree of cementation
  • Type of pore system inter-crystalline
  • Sorting and Packing (in particulate system)

The last six factors have effect through the influence on the conduction path. Confinement or overburden pressure may cause a significant increase in resistivity by blocking of some conduction paths and reduction in the cross sections which are available for flow.  This usually occurs in rocks with low porosity or that are not well cemented.  Older data was collected using measurements in unconfined core samples.  So to have the same condition as in the reservoir resistivity measurements and formation factors determination under confining pressures are recommended for improved analysis.

Formation Resistivity Factor vs. Porosity
Figure 2-30: “Formation Resistivity Factor vs. Porosity

Several generalized relationships have been reported to relate F and Φ. The widely used ones are:

Equation Investigator Year Comments
F = 0.62Φ-2.15 Winsauer et al 1952 data from 30 samples – 28 sandstones core plugs, one limestone plug, and one unconsolidated sand sample
F = 1.45Φ-1.54 Carothers 1968 Data from 793 sandstone reservoirs
F = 1.13Φ-1.73 Timur et al 1972 Data from 1833 sandstone samples
F = 2.45Φ-1.08 Porter and Carothers 1970 1575 F-φ data points from 11 wells from offshore California-Pliocene and four wells from offshore of Texas-Louisiana Miocene
F = 1.97Φ-1.29 Porter and Carothers 1970 720 F-φ data points from 11 wells from offshore California-Pliocene and four wells from offshore of Texas-Louisiana Miocene
F = 1.00Φ-2.04 Carothers 1968 Data from 188 carbonate samples
F = 1.00Φ-2.5 Schlumberger and Shell 1979 For compact rocks, low porosity and non-fractured carbonate
F = 1.97Φ-(1.87 + 0.019 / Φ) Schlumberger and Shell 1979 For compact rocks, low porosity and non-fractured carbonate
F = 1 + 1.03(Φ-1.73 – 1) Pérez-Rosales 1982 analytical relationship

 

References

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