# Inferring Relative Permeability from Resistivity Well Logging

Inferring Relative Permeability from Resistivity Well Logging Introduction Permeability is a chattel of a spongy medium that measures the capacity of a substance to transmit fluids. Generally, permeability that is applied in petroleum industry is steady in Darcyâ€™s flow equation which compares pressure gradient, flow rate and fluid properties. However, a formation has permeability regardless if the fluid is flowing or not, and as result, a straight measurement of permeability necessitates a dynamic procedure rather than a static procedure.

In the past, well logs have been used to approximate permeability through correlations that is linked to a general logged property called porosity. Perm-porosity correlations are formed from interior and changes to well log porosity. In most cases, these correlations are semilog in nature; that is in form of y = axb. The other correlations try to approximate effectual perm by including irreducible petroleum saturation approximated from Archieâ€™s equation and resistivity logs.

Majority of well logging environments are normally in static states, where incursion of mud filtrate into the permeable formations which concludes after the well is logged. One of the significant factors in geothermal reservoir engineering is steam-water relative permeability. However, it is not easier to measure steam-water relative permeability due to phase transformation and mass transfer as pressure changes. There are some physicians who argued that steam-water relative permeability can be calculated from the data of capillary pressure.

This method gives an easier and an economical approach to get steam-water relative permeability when contrasted with experimental method. The demerit side of this method is the necessity of measuring the steam-water capillary pressure that can consume a lot of time and also been difficult in most cases. Consequently, itâ€™s beneficial for scientists and engineers to have a technique in order to conjecture steam-water relative permeability from resistivity information as it is easier to calculate and obtain the information of resistivity from well logging.

Here is a study of a semianalytical model which is formed in order to infer relative permeability from resistivity information. The correlation betwixt resistivity index and relative permeability is derived in this way. The theory behind this is the relationship betwixt electricity flow in a conductive body and fluid flow in a porous medium. Calculation of the wetting-phase relative permeability: The conductance of a permeable medium at a water saturation of 100% is: Ga = 1/Ro (1) Where Ro = the resistivity of a water saturation of 100%

Ga = the conductance of a permeable medium at a water saturation of 100% The conductance of a permeable medium at a certain water saturation of S, is: Gw = 1/Ri (2) Where Ri = the resistivity Gw is the conductance at exact water saturation of Sw As noted from similarity theory betwixt electric flow and fluid flow, the relative permeability of the wetting phase may be calculated using the following equation: Krw = Gw = Ro = 1 (3) Ga Ri I Where I = resistivity index Krw = the relative permeability of the wetting phase.

From Archieâ€™s equation, the following equation applies: I = Ri = (Sw)? n (4) Ro Where n = the Archieâ€™s saturation exponent. When water saturate up to 100%, it is known that I=1, therefore the value of Krw =0, which means that (I) moves toward infinity as noted from the third equation. However, it is clearly known that the value (I) donâ€™t move toward perpetuity at the outstanding water saturation. Thus the value of Krw calculated in the third equation is bigger than zero, which isnâ€™t unswerving with physical surveillance.

Also, you can expect a greater value when the relative permeability of wetting phase is calculated using the third equation. This is because that the resistivity counts the average volumetric properties of the pore bodies in a porous medium whereas permeability counts the properties of pore throats. This is the reason why you can also obtain porosity through resistivity well logging but not permeability. For example, the following problem can be considered by modifying equation 3 as follows: Krw = Sw â€“ Swr 1 1 Swr I(5)

Where Swr = the residual saturation of the wetting phase. From equation 5, Krw = 1 at Sw = 100%, and Krw = 0 at Sw = Swr, which is reasonable. The fifth equation can also be expressed as follows: Krw = Sw 1 (6) I Where Sw = the normalized saturation of the wetting phase and itâ€™s expressed as follows: Sw = Sw â€“ Swr (7) 1 – Swr The relative permeability of wetting phase can be calculated using the 6 equation from the resistivity index data soon the residual saturation of wetting phase is obtained.

You should note that the residual saturation of the wetting phase may be accessed from the experimental measurement of resistivity. Calculation of the nonwetting-phase relative permeability The wetting-phase relative permeability can be calculated using the Purcell approach: Krw = (Sw) 2 + ? ? (8 Where ? = the pore size distribution index and may be calculated from the data of capillary pressure. After obtaining the relative permeability curve of the wetting phase using equation six, the value of ? may be inferred using equation eight.

The relative permeability of the nonwetting phase may be calculated after obtaining the value of ?. below is the equation: Kmw = (1 – Sw)? 1-(Sw) 2 + ? ? It can be observed that the whole relative permeability set (wetting and nonwetting phases) might be inferred from the data of resistivity index using equations six and nine. Conclusion A Darcy, the fundamental unit of permeability in Petroleum Engineering, is defined as the permeability that is required to flow 1 cc/s of a fluid of 1 cp a distance of 1 cm through a cross-sectional area of 1 sq. cm. with a pressure drop of 1 atm.

The key word is â€śflowâ€ť. Consequently, by definition the calculation of permeability must be dynamic. Even though a core without flow has a value of permeability, it not measurable without fluid flow. The correlations of permeability with porosity and water saturation are limited because of the portion of the porous media that dominates permeability; porosity and water saturation are different. Permeability is dominated by the smallest restrictions to flow, the pore throats. Porosity and water saturation are dominated by the volume within the pore bodies, not the pore throats.

Hence, correlations for permeability are inherently limited when correlating to porosity and water saturation or any other rock property that is strongly influenced by any part of the porous media other than the pore throat ( Lehr and Lehr, 2000). Work Cited American Institute of Mining, Technology and Engineering, University of California, 2010. Jay H. Lehr and Janet K. Lehr, Environmental science, Health and Technology, New York: Macmillan Press. National Petroleum Council, Impact of New Technology on U.. S Petroleum Industry, Washington: Sage Press, 2000.