WELLOG                                         PERMEABILITY


Revised 1-06-2008

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All Rights Reserved





There are numerous approaches to the measurement of permeability in formations utilizing geophysical well log data, but only a few are quantitative. The methods utilize potential, resistivity, porosity, formation factor, fluid saturation, and acoustic data derived from various logs and may be classified as follows:


View a permeability determination flow chart.


Quantitative Methods:


            Sw – F graphs for the irreducible water saturation zone.

            Sw – F effective graphs using effective porosity

            Resistivity gradients under limiting conditions


Qualitative and semi-qualitative methods:


            The SP log.


            Resistivity and Invasion


            Porosity and Formation Factor


            Acoustic amplitude logs


            Temperature Surveys


            Induced Polarization methods




A chart constructed from an empirical relationship published by Wyllie and Rose in 1950, provides reasonably accurate estimates of permeability in the irreducible water saturation zone of sandstones and shaly sands, and is based upon the general equation:



                                    K1/2 = C F Swirr + C’



Limitations and corrections of using the chart…


For gas, the K values obtained from the chart should be divided by ten. For oil gravities less than 20 API, the K derived will tend to be too low.



The chart may be used to detect the irreducible and transition zones of a common reservoir. Data points from the irreducible zone will fall along one of the lines representing C =  F x Sw; points from the transition zone will fall to the right of that line indicating a degree of water cut with production.


The C =  F x Sw values are also indicative of pore size and porosity type. Many carbonates, particularly in Canada, have been zoned in terms of C and porosity type. In sandstones, pore size is related generally to grain size, thus C values are qualitatively indicative of grain size. When plotting F and Sw data from rocks having a heterogeneous pore size distribution, data for the large and smaller pores will fall along different C =  F x Sw lines.


Some observers have found that the Timur relationship:  K = 0.136 (F)4.40/Sw2 gives more realistic estimates in certain cases.


View a chart that provides an Estimation of Permeability using the Timur equation.


Example: Given Sw = 30 percent, porosity = 15 percent      Solution:          k  = 8 mds,      C = 0.045


MOP – The Moveable Oil or Hydrocarbons Plot:


For quantitative and semi-quantitative estimates of permeability, the Wyllie, Timur, and MOP methods are the most widely used. In the MOP method, Sxo, Sw, and Sor are calculated in terms of the percent of rock volume rather than percent of pore space:



                                    Sw = (Rw/Rt)1/2


                                    Sxo = (Rmf/Rxo)1/2


                                    Sxo – Sw = Movable oil or hydrocarbons


                                    Sor = 1 – (Sxo + Sw)


The movable oil plot is quantitative only when Rmf = Rw and when the assumed “m” = 2.0 is correct. When Rmf = Rw, the correct value of m can be obtained from the relationship of the calculated Sxo and Sw in 100 percent water saturated formations.





                                    D = (Te – Tg) / (dTg/dh)




            Te = Earth temperature

            Tg = Gas temperature

            h = Depth


These values can be correlated with the gas production rates, V, as shown in the chart.




1. Construct a geothermal gradient on the temperature log.


2. Mark any point C on the temperature curve below the intersection of the geothermal gradient and above the gas entry point. Draw a line through the point C tangent to the temperature log so that its length extends over 100 feet in depth. Draw a horizontal line from the tangent point C to the geothermal gradient.


3. Read Te, 87.35 degrees where the horizontal line and the geothermal gradient intersect, and Tg, 82.40 degrees, at the tangent point C.


4. Read dTg (88.15 – 77.80); dh will be 100 feet as indicated in step 2.



Calculating using the equation above:


                                                D   = (87.35 – 82.40)/((88.15 – 77.80)/100 )= 47.826







Gas volume estimation from the temperature log chart is a plot of delta, D  , versus Gas production Rate, V, for different hole sizes.


In the preceding example, delta = 47.8 and the chart shows a production rate of 80 MCFD.





With a prior knowledge of the reservoir pressure, reservoir temperature, and the bottom hole flowing pressure, a Joule-Thomson expansion temperature can be determined from the chart.



This is the theoretical temperature of gas produced from a non-fractured reservoir. This temperature and the earth temperature at the same depth determine the extremities of the fracture index Scale 0 percent and 100 percent respectively.


Example:          Given T reservoir = 170 degrees F, P reservoir = 900 psi,  BHP F = 15 psi





1. Find the point where the reservoir pressure and reservoir temperature intersect.


2. Follow this curve to the left and down to the pressure assumed to be the bottom hole flowing pressure (BHP F = 15 psi).




When Pr and Tr do not intersect on a curve, simply parallel the nearest curve to the left and down to the assumed BHT F pressure.


3. Read the temperature of the expanded gas at this pressure (130 degrees F). This temperature is the theoretical Joule-Thomson effect.


If you still have questions about permeability ask WELLOG at info@wellog.com .