May 19, 2014 - Nom Geo

Using Archie’s law to find Formation Water Resistivity : Can well logs be used to detect different Groundwater zones?

Today’s question – can well logs be used to determine different groundwater zones? Here we are using Archie’s law to find formation water resistivity. I hope this article is useful. Any questions, suggestions or if it needs correction then you are welcome to leave a comment below.

Flow chart for suggested steps in performing the first part of the analysis.

Using Archie's law to find Formation Water Resistivity

In this article we examine more closely a pore pressure change we found in the previous article titled “Finding pore pressure zones using drilling parameters – The D’Exponent.

To recap, in the d’ exponent article a dip in gamma which was observed at 270 m was accompanied by negative pore pressure spikes. Because the d’ exponent method is only relating drilling performance with pore pressures some other analysis is required to understand changes in formation water, porosity and lithology.

Density Vs Gamma

Using Archie’s law to find Formation Water Resistivity seems like a simplistic approach to hydrogeology. While useful for a quick look this is a method which requires that we make a number of assumptions about the relationship between porosity and water resistivity. Here we are going to see if we can actually estimate water resistivity and salinity.

Saline water has a lower resistivity than fresh water. Hence any resistivity changes in the formation water would allow changes in water salinity to be identified. This may signify the existence of a discreet aquifer or body of water.

The only problem is that the resistivity methods assumes that the formation being tested is a clean, clay free sandstone or carbonate reservoir. In a formation containing clay which has a higher electro-chemical response, more complex empirical calculations are required to determine water resistivity. Any formation which has Interbedded or alternating sand – siltstone sequences result in frequent changes to clay content and this heterogeneity tends to mask differences in water salinity.

Methods such as the apparent resistivity method use the inverse relationship of total resistivity and porosity to variations in clay content.

The different methodologies which are available for the evaluation of the resistivity of connate water are based on the relationships between water/oil saturation, water resistivity and total resistivity as first proposed by GE Archie in 1942. This article is going to take a quick look at the Apparent Water Resistivity or Rwa Method.

The type of source data which ca be used is wireline data using gamma, density, sonic travel times and sonic porosity, micro pad resistivity (MRRS), shallow laterolog resistivity (DSLL), deep laterolog resistivity (DDLL), Spontaneous Potential (SP), temperature and importantly the drilling mud resistivity recorded in the log header as measured at surface temperature (also recorded).

The expression for apparent water resistivity Rwa is;

Rwa formula

It is possible to make the assumption that water saturation is 100% since the formation, with the exception of the coal seams is unlikely to contain any hydrocarbon saturation. As such the method offers a simple method for estimating Rwa. Once this assumption is made, it is logical to assume that the apparent water resistivity Rwa will approach the value of the actual water resistivity when clay content (Vcl) is close or equal to zero.

The method assumes that there is a derived cementation exponent (slope m) and a tortuosity factor, a. However typical values can be assumed for these parameters which will produce reasonable results.

Assumptions; Water saturation Sw = 1, m = 2.15, a = 1.0. Archie found that a value of 0.62 was also applicable for many formations, however the value of 1 has been effective for the purposes of our exercise. The value of RT = DDLL log reading.

Sonic Porosity logs are ideal for this method because they take into consideration the effects of clay on porosity.

It is important to note that this method initially calculates the “APPARENT” not the actual water resistivity. This is the resistivity which results from the influence of both water and changes to the effective porosity which is in turn influenced by clay content. Hence the results will show us changes in the apparent resistivity as influenced by the ratio of bound (highly saline) to unbound water or by changes in the permeability of the formation.

GeoNote: Bound water is that water which is immobile due to strong attractive forces between it and the pore lining minerals and clay. It is of a higher salinity, has a higher concentrations of dissolved ions and hence a much lower resistivity. In most cases it represents the original marine water which became trapped in the inter-granular spaces at the time of deposition and burial. Bound water is ubiquitous on the surfaces of clay particles.

The low gamma spike in the zone of interest is suggestive of a lower clay content.  A further hypothesis is that there is a gas saturation component in this zone. It is a pre-supposition whose validity has not been tested and which is not supported by the density data which actually shows a minor spike. While the lower clay explanation is reasonable the density spike may also be showing that another mineral is present. In this case it might be a carbonate rich horizon or a chlorite rich layer this is consistent since both calcium carbonate and chlorite clay are known to have a higher specific gravity than quartz and both are coherent with the depositional facies types. Because the chlorite (a 2:1 clay) would likely contribute to a higher(not lower) gamma reading and would negatively affect porosity the remaining coherent scenario is that of the zone being a thin, carbonate rich, low clay, porous horizon.

Our initial depth interval of interest is at 270.2-270.5 m. The graphical figure below introduces some of the log curves which assist in understanding the geological factors at play. They are Gamma (measuring potassium which occurs in clay minerals), density (density contrasts will identify coal horizons at below 1.8 g/cc or igneous intrusions at above 3.5 and Spontaneous Potential, which is a basic measurement of ionic permeability.

SP and Gamma

SP curve profiles can be correlated with depositional facies and we will return to this in a future post.

As the gamma curve is serrated, this can be used to indicate that the formation consists of alternating beds. Any pronounced gamma dip in gamma value which is not coal could be related to a sand with a lower clay content or it could be related to acid leaching of potassium out of the paleosol clays due to infiltration by acidic water from the coal seam above.

In the next image from the base of the coal seam at 254 m to the zone of interest at 270 m the resistivity curves show a separation between the MRRS pad device and both shallow and deep resistivity curves however below the ~ 270 m depth there is a distinct change suggesting a geological boundary and a change in permeability.

resistivity curves

The closeness of the DSLL and the DDLL curves throughout the depth interval of interest suggests that drilling fluid invasion is not deep, if at all. The gap between the Dual Laterolog and the Micro-focused pad MRRS which occurs from 254 to 270 m suggests that very shallow fluid invasion is occurring and some degree of permeability exists.


Because the formation sandstones are not clean, the volume fraction which is clay can be estimated by applying a calculation using log values such as density, sonic or gamma. Using the gamma log as the basis for the clay fraction estimation since the log values are accurate and straightforward the calculation spreadsheet looks like this:

Clay calculations

The clay values for the zone of interest are based on gamma so we expect to see a drop in the clay fraction proportional to the gamma log value.

In the above correlation, the clean sand gamma value was 35 API and the clay gamma value was 244 API. The upper clay value was selected as just above the maximum log values to avoid a negative value for the Ira factor.

A quick QC of the Vcl values for the entire borehole showed that numerous negative Vcl values were returned under the Larionov equation, a nonsensical result. Because this problem was avoided with the Clavier equation values the Clavier Vcl values were used.

Geo note: The clay calculation does not take into account the type of clay nor the Cation Exchange Capacity (CEC), nor the surface area of clay particles which controls the bound water volume. Clay types and their mode of intra-pore distribution is dealt with using models such as the Dual – Water model, Simandoux and derivative equations which attempt to deal with the complexity of clay effects on resistivity and water saturation in a reservoir. 


Back to apparent resistivity;

Rwa formula

Note the the calculation requires the sonic porosity log. A correction for clay which takes in the clay fraction in the following expression;

sonic porosity expression

Where Vcl is the clay fraction after Clavier.

Note that travel times used were selected to avoid “negative” porosity readings and this may reflect a flaw with the methodology. The values which were applied are;

Matrix; 71 µs /ft. (note that this is a very shallow formation)

Fluid; 209 us/ft.

Clay; 95 us/ft.

Rwa clay and Rt chart

The curve shows a peak for the apparent resistivity close to the 270.4 m mark, signifying a water zone that is distinct from the adjacent zones. The left-wards spike in clay values may be to a cleaner sandstone or it may be due to leaching of potassium by low pH waters.

The low resistivity zone which lies between 279 to 289 m is suggestive of high water salinity.  Clay distribution modes typically are either clays distributed within the pore volumes or clay which occurs in discreet layered packages as in a silt laminate interbedded with clean sands. This has an impact on permeability type and bound water ratios. So it could be lithofacies related or water flow related.

The next step is to try to ascertain the actual water resistivity Rw. The value of Rw is useful for applying Archie’s law to determine water saturation levels where hydrocarbons are likely to be found. The objective is to examine whether the method allows the discovery of zones where discreet groundwater flows can be found.


Because of the complexity of attempting to identify a clean sandstone interval to find the ideal Rwa value, the available solution is to extrapolate the Rwa trend to find the Rwa value if VCl was zero. This can be done by plotting Vcl/porosity on the x axis against Rwa on the Y axis. This will allow a trend line to be extended to the Vcl/Porosity = zero axis cross. The value of Rw will be where the Rwa trend line intersects the Vcl/ porosity = 0 point.


The results are shown below. Intervals were selected to try to achieve a unified trend for each zone. As can be seen the formation from about 270 m and below is now unified into five zones of contrasting Rw values.

Rw extrapolation chart

So far the analysis shows different values for each zone. As a final part of exercise the temperature/resistivity plots can be used to identify the NaCl salinity equivalent of the formation water for each of these zones where Rw has been estimated.

Charts for plotting the Resistivity of solution at a known temperature to find the equivalent NaCl concentration are readily available online and are published by all of the wireline logging providers. They are generally copyrighted material so no image has been included here however a quick search will find enough examples for use.

The results for Rw and NaCl salinity values are set out in the table below.
Rwa salinity final table 





Because of the inherent uncertainty in the assumptions and the departure of actual conditions from the ideal “clean” formation one needs to treat these results with care. The Rwa method seems to be inferring that different water zones exist as shown in the table above. Because of the heterogeneous set of values in the table it is possible to say that the combined pore/matrix/fluid has a different electrical response for each depth interval. The extent to which this is due solely to changes in water or whether a dual water type scenario is in play here remains uncertain.

The next post will be a continuation of analyses with this data set and more methods. There will be a new post every couple of weeks.

References and Reading – follow link to page:




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