**WELLOG****
PERMEABILITY**

**Revised ****1-06-2008**

**© 2007-2008 ****WELLOG**

**All Rights Reserved**

**LOGGING PERMEABILITY METHODS:**

**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**

** **

**SANDSTONE AND SHALY SAND PERMEABILITY:**

** **

**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:**

** **

** **

** K ^{1/2}
= 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}/Sw^{2}
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.**

** **

**DELTA DETERMINATION FROM TEMPERATURE LOG:**

** **

** **

** ****D**** = (Te – Tg) / (dTg/dh)**

** **

**Where:**

** **

** 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 TEMPERATURE LOG:**

** **

** **

**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.**

** **

** **

**THEORETICAL TEMPERATURE DETERMINATION (Joule – Thomson effect):**

** **

**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**

** **

** **

**Solution:**

** **

**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).**

** **

**Note: **

** **

**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 .**