q921 log lec6 v1
TRANSCRIPT
Well Logging Course (1st Ed.)
1. Spontaneous PotentialA. membrane potential
B. Application
C. Log Example of The SP
1. Early Electric Log Interpretation
2. Formation Factor
3. Water saturation
4. The Porosity Exponent, m
5. The Saturation Exponent, n
6. A Thought Experiment For A Logging Application
usefulness of measuring the resistivity of earth formations the water saturation Sw
Is the desired petrophysical parameter from resistivity measurements
In this lecture the empirical basis for the interpretation of resistivity measurements is reviewed.
For many years, at the outset of well logging, it was not possible to address
the water saturation question any more precisely than whether the resistivity of a formation was high or low.
It was through the work of Leverett and Archie that it became possible to be more quantitative about the interpretation of a formation resistivity measurement and to link resistivity to
formation water resistivity, porosity (ϕ), and water saturation (Sw)
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a log of SP and formation resistivity made prior to 1935The scale “Ohms
m3” presumably refers to ohm-m.
It seems possible, noting the higher resistivity, that zone a-A contains more oil (has a lower Sw) than zone B-b.But how can
this be verified?
An early resistivity-SP log.Fall 13 H. AlamiNia Well Logging Course (1st Ed.) 6
Early SP log interpretation
The “standard” procedure at the time [for verification] was to take a core sample,
representative of the zones in question, and
to make laboratory measurements of its resistivity under different conditions of water saturation.
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Resistivity measurements of
two core samples as a function of
water saturation
for use in electric log interpretation.
Leverett experiments
M. C. Leverett was conducting experiments with unconsolidated sands, to determine
the relative permeability of oil and water (Kro & Krw)
as a function of the water saturation (Sw).
As a by-product of his research, he measured the conductivity of
the material in a sample chamber, after a calibration of the system constant,
in order to conveniently determine the fraction of kerosene and water in his permeable samples.
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Leverett conclusions
Calibration curve of Leverett’s core holder with sand pack, showing
variation of relative conductivity as a function of water saturation.
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Archie experiments
Shortly after the publication of Leverett’s work, G. E. Archie of Shell was making electrical measurements on core samples,
with the aim of relating them to permeability.
His measurements consisted of completely saturating core samples with saltwater of known resistivity Rw and relating the measured resistivity Ro of the fully saturated core to the resistivity of the water.
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Relation between water resistivity (Rw) and formation resistivity (Ro)Archie found that,
regardless of the resistivity of the saturating water, the resultant resistivity of a given core samplewas always related to the water resistivity (Rw)by a constant factor F. He called this the formation factor,
and his experiments are summarized by the following relation:
Next slide is an example of Archie work on cores from two different locations.
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the formation factor F vs. k and, almost as an afterthought, porosity, ϕExamples of
Archie attempts to correlate the electrical F with K and ϕ for water-saturated rock samples from two regions.
F vs. K and phi (phi on a much compressed scale)Fall 13 H. AlamiNia Well Logging Course (1st Ed.) 13
A summary of an exhaustive set of measurements of formation factorAlthough Archie
was searching for a correlation with K, he finally admitted that a generalized
relationship between F and K did not exist,
although one seemed to exist for porosity.
His summary graph shows the hopelessness of a F/k correlation.
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formation factor calculation
However it indicates that the F is a function of ϕ and can be expressed as a power law of the form:
the exponent m is very nearly 2 for the data considered. This empirical observation can be used
to describe the variation in F for a fixed water resistivity when the ϕ changes: the lower the porosity, the higher the resistivity will be.
The exponent m was soon named the cementation exponent, as it was observed
to increase with the cementation of the grains. In general, it was recognized that m increased
with the tortuosity of the electric path through the pore space.
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A synthesis of various resistivity/saturation experimentsThe practical application
of resistivity measurements is for the determination of water saturation (Sw).
This was made possible by another observation of Archie. He noticed that the data
of Leverett and others could be conveniently parameterized after having plotted the data in the form shown in Figure.
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water saturation vs. relative resistivity
On log–log paper, the data of water saturation versus relative resistivity plotted as a straight line, suggesting a relationship of the form:
The exponent n, called the saturation exponent, is very nearly 2 for the data considered.
From this, an approximate expression for the Sw is:
However, the fully saturated resistivity Ro (which is not usually accessible in formation evaluation), can be related to the water resistivity. So:
and with the porosity dependence, the final form is:
which can be used for purposes of estimation.
However, a more general form, is:
the constants a, m, and n need to be determined for the particular field or formation being evaluated.
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interpret a resistivity measurement in terms of water saturation (Sw)in order to interpret
a resistivity measurement in terms of water saturation (Sw), two basic parameters need to be known: the porosity φ and
the resistivity of the water in the undisturbed formation (Rw). As a starting point,
the value of the water resistivity Rw needs to be estimated. • This can be done in water zones (resistivity logs).
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Example of interpretation of resistivity measurement in terms of Sw
the value of the water resistivity Rw needs to be estimated. From zone D’ or zone C’ (water zones)
the porosity is about 28 p.u.
so F is 1/(0.28)^2, or 12.8
the apparent resistivity = 0.2 ohm-m which is assumed to be the fully water-saturated resistivity Ro,
water resistivity = 0.2/12.8= 0.016 ohm-m
the increase in deep resistivity in zone C to about 4 ohm-m correspond to a decrease in Sw
compared to zone C’ the porosity is constant at 28 p.u. The saturation in zone C:
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Example of interpretation of resistivity measurement in terms of Sw (Cont.)
zone of hydrocarbon (A) indicates the same resistivity as zone C. in zone A the porosity is much lower
and can be estimated about 8 p.u.
Thus F in zone A is 1/(0.08)2, or 156
If it were water-filled, the resistivity would be expected to be about 2.5 ohm-m compared to the 4 ohm-m observed. Thus the zone may contain
hydrocarbons, but the water saturation can be expected to be higher than in zone C.
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Effective parameters
As Archie was aware, his equations worked well in rocks that have simple, uniform pore systems filled with saline water.
Rocks with heterogeneous-pore systems, multiple-conduction mechanisms, or that are oil-wet need a more complete solution.
The problems can be considered with reference to Archie’s three equations: the relation to porosity (m), the relation to Sw (n), and the definition of formation factor (F)
is mainly an issue of clay conductivity
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The Porosity Exponent, m
Although Archie could fit his data with a single parameter, m, in general a fit of F vs. φ throughout a reservoir will require two parameters, a and m.
In practice the error caused by fitting with one parameter is often small.
In either case it would be better if the variations [of a and m] through the reservoir
could be related to some physical property, rather than relying on a general average.
Early efforts focused on finding a relation with porosity, the idea being that as porosity
decreased it was likely that the tortuosity, and hence m, increased.Many relations were developed but proved to be
specific to particular reservoirs or areas, and not generally applicable.
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the total effective m in a fractured reservoirClearer relations can be obtained
if the reservoir contains vugs or fractures. Fractures offer a straight path for current,
with minimum tortuosity.
in a fractured reservoir, if we can measure
the proportion of porosity due to fractures and
if we assume that the conductive paths through the fractures and
the intergranular porosity are in parallel, with no interaction between them,
we can calculate the total effective m.
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Methods of m Calculation
More generally, whatever the cause of the variations in m, m can be measured directly
from resistivity and porosity in a water zone, and then
assumed to be the same in the hydrocarbon zone.
Alternatively, if the water saturation can be measured
by another means in addition to resistivity, One such method
uses dielectric measurements in the invaded zone.
then either m or n can be calculated from Archie’s equation.
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saturation exponent measurement
It takes much longer to complete the type of experiment that leads to the saturation exponent (n)than to measure m. Each core sample must be measured
at several saturation states. Displacing water with oil or gas takes time,
especially in low permeability samples.
Unlike m, it is not possible to derive n from logs in a water zone.
As a result there is much less data on n, and values other than 2 are less often used.
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1st condition in which n can be significantly different than 2However, laboratory experiments
have highlighted two main conditions in which n can be significantly different than 2. The first is related to wettability.
in an oil-wet cores • the oil coats the grains and starts blocking the pore throats
when even small volumes are introduced.
• The result is a sharp increase in resistivity and a high n
• So n values much larger than 2
In a water-wet core • the water coats the grains and
provides a continuous conduction path down to water saturations of 20% or less.
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Resistivity-saturation measurements
Resistivity-saturation measurements on carbonates that have been flushed
to make them
water-wet or
oil-wet, a large increase in n
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2nd condition in which n can be significantly different than 2The second condition occurs
in rocks in which the pore space is no longer uniform but consists of an irregular mixture of different sized pores.
When oil or gas is introduced into such rocks, the water in some pore types displaced more easily
For example the oil should easily displace the water in fractures, but may not do so in vugs if they are poorly connected.
Carbonates are particularly heterogeneous, and also more likely to be oil-wet, so that for both reasons the relation between
resistivity and Sw is likely to be complicated, with n not equal to 2 and also varying with saturation.
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setup for measuring the resistivity of a homogeneous formation
It consists of a current source of intensity and a voltage-measurement
electrode M at some distance r
from the current emission at point A.
The resistivity of the homogeneous medium is Rt, so its conductivity σ is given by σ = 1/Rt . (Conductivity is usually
written as σ in measurement physics, and as C in log interpretation.)
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determining formation resistivity
the value of Rt is found to be:
The setup can be considered as a rudimentary monoelectrode measurement device for determining formation resistivity. For this device the tool constant k is seen to be 4πr ,
where r is the spacing between the current electrode and the measurement point.
Knowing the injected current and the resultant voltage, the resistivity of the homogeneous medium Rt may then be found.
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1. Ellis, Darwin V., and Julian M. Singer, eds. Well logging for earth scientists. Springer, 2007. Chapter 4