calculating electrical properties (a, m, and n)

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CALCULATING ELECTRICAL PROPERTIES (A, M, and N)

Electrical Properties Tortuosity Factor A Cementation Exponent M Saturation Exponent NVariable M Models Core Analysis Methods

ELECTRICAL PROPERTIES BASICSElectrical properties are terms used in the Archie water saturation equation,and in its shale corrected cousins, to calibrate water saturation to thephysical properties of the pore geometry of the rock. The parameters requiredare: 1: tortuosity constant A 2: cementation exponent M 3: saturation exponent N

These three terms are usually written in lower case font (a, m, n) but inkeeping with the policy of this Handbook that input parameters be capitalized,they are referred to here and elsewhere in upper case

M is defined as the slope of the best fit line drawn through a graph of formationfactor (F = R0 / RW) versus porosity, and A is the intercept of that line on the F axis.A sample of such a plot is show at the left and is discussed in more detail later inthis Chapter.

N is defined as the slope of the best fit line on a graph of resistivity index (RI = RT /R0) versus water saturation. A sample plot is shown at the left and discussed inmore detail later..

Although there is not a lot of evidence to support the assertion, N is often taken asequal to M, probably because M can sometimes be found from available log data inthe absence of core data, and N cannot.

Pore geometry in sandstones varies with lithology, grain size, sorting, shape, roughness, and shale volume. Incarbonates, it varies with pore type and how well the pores are connected. Some examples are shown below, andcombinations of these pore geometries are common. For example, fractured, moldic, intercrystalline porosity isrelatively common.

Crain's Petrophysical Handbook - CALCULATING ELECTRICAL PR... https://www.spec2000.net/14-swelec.htm

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Examples of different pore geometry models

The cementation exponent has been studied the most and the following illustrations, keyed to the pore geometryshown above, give some idea of the complexity of the problem. The two images below are from "CementationExponents in Middle Eastern Carbonate Reservoirs" by J. W. Focke and D. Munn, SPE Paper 13175, June 1987.


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Formation factor plot and M versus porosity plot for intergranular and sucrosic pore geometry.A = 1.00, M = 2.00, and do not vary with porosity.


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Similar plots for a moldic limestone. Formation factor data is scattered and M increases withincreasing porosity. A variable M method is required for a satisfactory water saturation calculation.

The equation for M is: M = 1.40 + 6.57 * PHIe where PHIe is a decimal fraction.(permeabilityregime 0.1 - 1.0 md)

The slope and intercept of the variable M plots will of course vary from one reservoir to another, and vary with thepermeability regime, which is an indicator of the connectedness of the moldic porosity.

There are a number of methods for finding and adjusting the electrical properties of rocks. The common approachesare listed here.

TORTUOSITY CONSTANT (A) FROM LOG AND RW DATAThis is easy if there is a clean water zone on the log which also tested water. The formula is: 1: A = (RW@FTlog) / (RW@FTdst)

WHERE: A = cementation exponent (unitless) RW@FTlog = RW@FT with A = 1.0 and M = 2.0 calculated from a water zone on logs (ohm-m) RW@FTdst = RW@FT from DST measured in the laboratory (ohm-m) and converted to formation temperature

Data from several wells may be averaged to obtain a good value. The parameter A varies with grain size, so wellsused should come from similar geologic settings (depth, distance from source of sediment, etc.).

CEMENTATION EXPONENT (M) FROM SPECIAL CORE DATAPlot porosity vs lab measured formation factor on log-log axes. Fit regression or eyeball line to data. Slope of line isM. Intercept at PHIe = 1 is A. The line force-fitted through F = PHIe = 1.0 is called a pinned line. Some people preferthe pinned line but most data sets do not support this approach. Strictly speaking, the line must pass through F = 1 =PHIe, so the line must be non-linear approaching this point on the graph. An example is shown below.


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Find A and M from special core data (electrical properties data) - M is slope of best fit line(pinned or free regression - your choice), A is intercept at PHIe = 1.0.

SATURATION EXPONENT (N) FROM SPECIAL CORE DATAPlot brine saturation from core analysis versus formation resistivity index (RESD / R0) on log-log axes. Draw linethrough the data to intercept at SW = 1.0. The slope of this line is N. Data from several wells may have to becombined to get a reasonable fit.


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Find N from special core data (electrical properties data). Slope is N and line must passthrough Sw = 1.0 at RI = 1.0..

CEMENTATION EXPONENT (M) FROM LOG DATAA variety of approaches are available to assess the electrical property M from log data. There is no direct method forfinding N from log data, but there is an indirect approach. If you are satisfied that A, M, and RW are correct, you cancompare the log analysis SW with the capillary pressure SW. Any difference can be repaired by adjusting N.Changing N will make no difference in a water zone, so it helps to be able to calibrate A, M, and RW in the waterzones first.

Pickett Plot MethodPickett proposed that the Archie formation factor and saturation equations be rearranged as follows: 2: log(RESD) = - M * log(PHIe) + log(A*RW@FT) 3: log(RESS) = - M * log(PHIe) + log(A*RMF@FT)

In water zones: 4: M = (log(A*RW@FT) - log(RESD)) / log(PHIe)

In invaded water or hydrocarbon zones: 5: M = (log(A*RMF@FT) - log(RESS)) / log(PHIe)

WHERE: A = tortuosity exponent (unitless) M = cementation exponent (unitless) PHIe = porosity from any source (fractional RESD = deep resistivity of rock with water and oil (or mercury) (ohm-m) RESS = shallow resistivity of rock with water and oil (or mercury) (ohm-m) RW@FT = water resistivity at formation temperature (ohm-m) RMF@FT = mud filtrate resistivity at formation temperature (ohm-m)


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COMMENTSEquation 1 represents a plot of deep resistivity vs effective porosity FROM KNOWN WATER ZONES on log-log paper.Draw a line through southwest data points. Slope of this line is M and intercept at PHIe = 1 is A*RW@FT.

Equation 2 may work in hydrocarbon zones if invasion is well developed and residual hydrocarbon is small. M will betoo high if ROS is high.

Find M and A*RW from Pickett plot

Make a separate graph FOR EACH ROCK TYPE. Typical rock types in carbonates are intergranular (clastic texture),intercrystalline (fine, medium, or coarse), vuggy (fine, medium, or large), microporosity (unconnected pores),oomoldic, and fractured zones (with any other rock type). Rock typing is usually done from sample or coredescription.

M can be made to vary by solving equation 1 or 2 for each data point instead of fitting a line through the average ofthe data set.

Shell MethodAnalysts at Shell Oil proposed a formula to vary M in carbonates with porosity. Other relationships could be found byfitting non-linear curves to the data used for the Pickett plot or by plotting individual M values versus porosity: 6: M = 1.87 + 1.9 * PHIe

Focke and Munn l MethodThe Focke and Munn paper referred to earlier shows a variety of data sets, in which M increases with porosity, asshown below: 7: M = 1.20 + 12.76 * PHIe (perm < 0.10) 8: M = 1.40 + 6.57 * PHIe (perm = 0.1 - 1.0) 9: M = 1.20 + 6.29 * PHIe (perm = 1.0 - 100) 10: M = 1.22 + 3.49 * PHIe (perm > 100)

WHERE: M = cementation exponent (unitless) PHIe = porosity from any source (fractional

Nugentl MethodAn equation proposed by Nugent uses the secondary porosity concept: 11: M >= 2 * log(PHIsc) / log(PHIxnd)


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PHIsc represents the matrix porosity and PHIxnd represents the effective porosity in the carbonate rock. Both shouldbe shale corrected as described in Chapter Seven.

Use Nugent's method in intergranular, intercrystalline, vuggy, and fossilmoldic rock types. Results are too low inoomoldic rock type.

PHIsc must be calculated with a matrix value (DELTMA) that varies with the rock lithology. This can be derived fromthe results of a two or three mineral model or sample description with DELTMA = V1 * DELTMA1 + V2 * DELTMA2 + V3* DELTMA3.

Nurmi MethodIn oomoldic porosity, Nurmi proposed the following: 12: PHIvug = 2 * (PHIxnd - PHIsc) 13: PHIma = PHIxnd - PHIvug 14: M >= 2 * log(PHIma) / log(PHIxnd)

Use Nurmi method in oomoldic rock type.

PHIsc must be calculated with a matrix value (DELTMA) that varies with the rock lithology. This can be derived fromthe results of a two or three mineral model or sample description.

Rasmus MethodThe same techniques used to derive M for various carbonate rock types can also be used to find M in fracturedcarbonates. A standard Pickett plot in water zones, or a Pickett plot using a shallow resistivity log in the invadedzone, will usually suffice. The M value so derived will be the result of BOTH fractures and the rock type in the zonecovered by the crossplot. Normally, M is chosen once for each fractured interval from Pickett plots over well-definedrock type zones or layers.

However, there is no reason to believe M is a constant in a zone because fracture intensity probably variesdramatically from foot to foot within the layer.A method proposed by Rasmus, based on secondary porosity concepts, solves this problem: 11: Md = log((1 - (PHIxnd - PHIsc)) * (PHIsc^Mb) + (PHIxnd - PHIsc)) / log(PHIe)

Mb is the formation factor exponent for the bulk matrix (un-fractured) rock and Md is the value for the combinedmatrix plus fracture, or double porosity, porosity. Mb should be determined separately in un-fractured zones ifpossible.

"META/FRF" -- Electrical Properties SpreadsheetThis spreadsheet provides a tool for summarizing Electrical Properties dara and includes crossplots to findA, M, and N.

Electrical Properties Analysis, includes crossplots to find A, M, and N. English and Metric Units


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Sample output from "META/FRF" spreadsheet for summarizing electrical properties.

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calculating electrical properties (a, m, and n)

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