He also found that F varied with porosity:
For a tank of water, R0 = Rw. Therefore F = 1. Since PHIt = 1, then A must also be 1.0 and M can have any value. If porosity is zero, F is infinite and both A and M can have any value. However, for real rocks, both A and M vary with grain size, sorting, and rock texture. The normal range for A is 0.5 to 1.5 and for M is 1.7 to about 3.2. Archie used A = 1 and M = 2. In fine vuggy rock, M can be as high as 7.0 with a correspondingly low value for A. In fractures, M can be as low as 1.1. Note that R0 is also spelled Ro in the literature. In some carbonates, M seems to vary with porosity.
For rocks with both hydrocarbon and
water in the pores, he also defined the term Formation
Resistivity Index (
The value for R0 is measured in the laboratory using either a two or four electrode resistivity apparatus, with the sample 100% saturated with water of resistivity Rw. The porosity is also measured.
The core sample is then partially saturated by extraction of water with a centrifuge. The water extracted is measured to determine water saturation and resistivity Rt is measured. This step is repeated for several saturations.
Results of these tests are shown in the next twp Sections.
Electrical properties can be measured at the same time on the same core plugs as used for capillary pressure measurements. Since both measurements strongly affect the results of reservoir assessment and reservoir simulation projects, it would seem prudent to evaluate both properties in the lab before spending a lot of money on reservoir development.
Combined resistivity index and cap pressure report.
Most modern rock laboratories can perform these so-called "special core analysis" procedures. Unfortunately, many operators fail to have this work done, which is a great shame, as the data can change the calculated water saturation values quite dramatically compared to using "world-average" numbers.
Values of A, M, or N that are lower than the world-average values will increase calculated oil or gas in place.
An outline of the laboratory procedure is listed below.
1. Obtain 1-1/2 inch diameter by maximum length cylinders from core material.
2. Perform BaCl Cation Exchange Capacity measurement on sample end pieces.
3. Package with Teflon tape and stainless steel end screens if unconsolidated.
4. Extract core fluids using low temperature solvent extraction.
5. Dry samples in humidity controlled oven.
6. Determine Boyles’ Law porosity, grain density and nitrogen permeability at reservoir stress.
7. Vacuum saturate with synthetic reservoir brine.
8. Mount samples at reservoir stress and temperature (optional) in electrical conductivity/porous plate capillary pressure apparatus with water wet porous plate end piece.
9. Flush with synthetic brine at backpressure and monitor for 100% brine saturation and electrical stability.
10. Determine Formation and Cementation factor. FRw= Ro/Rw m=log FRw/log porosity
11. De-saturate using humidified nitrogen or oil in appropriate pressure steps to describe a full capillary pressure curve.
12. Monitor resistance and production volume on a daily basis at each pressure step.
13. Dean Stark extract for final water saturation verification
saturation exponent (N) from Special Core Data
NOTE: N is often lower than 2.0
quick analysis use carbonate values. Values for local situations
should be developed from special core data. Results will always
be better if good local data is used instead of traditional values,
such as those given above.
CATION EXCHANGE CAPACITY (CEC)
The multiple salinity and membrane potential methods are more direct measurements of the effect of CEC on formation resistivity and spontaneous potential.
Conductometric titration is a technique for estimating the cation-exchange capacity of a sample by measuring the conductivity of the sample during titration. The technique includes crushing the end pieces of a core sample and mixing it for some time in a solution like barium acetate, during which all the cation-exchange sites are replaced by barium (Ba++) ions. The solution is then titrated with another solution, such as MgSO4, while observing the change in conductivity as the magnesium (Mg++) ions replace the Ba++ ions.
For several reasons, but mainly because the sample must be crushed, the measured cation-exchange capacity may differ from that which affects the in situ electrical properties of the rock.
ELECTRICAL PROPERTIES FROM MULTIPLE SALINITY or C0/Cw METHOD
In conventional core analysis for
porosity, the primary measurements are bulk density (DENS or RHOB)
and grain density (DENSMA or RHOG), which give:
The excess conductivity
caused by the clay is termed (B*Qv).
Qv is a function of CEC and B is related to the mobility of the clay
cations, and that is a function of the salinity of the water in the
pores (and thus a function of water resistivity):
Example crossplot of Qv versus
In producible shaly oil sands, Qv ranges up to about
1.0 meq/cc. Shaly sands with Qv > 1.0 are generally too tight to
produce. When porosity approaches 0.00, set Qv = 0.0.
Example crossplot of M* versus Qv
A crossplot of Ct versus C0 is also made with data at various water saturations, as shown (below right). The resistivity ratio RI* for each data point is then replotted on a conventional RI vs Sw crossplot (below left), with the data grouped by salinity. Because conductance of clay exchange cations B varies with RW as in equation 6, the RI* varies with salinity and so does N*.
ELECTRICAL PROPERTIES FROM MICRO CT SCANS
With a micro CT scan image of pore size distribution, software is employed using the finite element method (FEM) to solve the Laplace equation for the electric potential field inside a digital sample for a specified potential difference at the boundaries. The electrical current field in the pores is computed and then summed-up to obtain the total current through the sample. The effective conductivity of the sample is simply the ratio of this current to the potential drop per unit length. Formation factor is then calculated as the ratio of brine conductivity to the calculated conductivity of the rock sample. Source: www.ingrainrocks.com.
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