1. # Rwa – Rw apparent

Rwa or Rw apparent is used to estimate the value of Rw, the resistivity of the waters filling the pores of a reservoir rock.  Rwa is derived from the most basic concepts of well log analysis, the formation resistivity factor, F and water saturation, Sw.

Archie determined that for uniform porosity F = Ro/Rw = Ro’/Rw’.  That is, for a given rock having pores filled with waters of resistivity Rw, the ratio of the rock resistivity Ro to Rw was a constant.  If one changes Rw and re-measures Ro, the ratio of the new values would equal F.  Ro is the total resistivity of the rock, 100% saturated with waters having resistivity of Rw.

Through subsequent experimentation, it was found that F = Ro/Rw = a / phi^m or that F is a function of porosity (phi in fractions) using constant ‘a’ and ‘m’ where ‘m’ is called the cementation exponent and ‘a’ is constant determined empirically.

It was also found that the apparent water saturation of a rock could be found from the following expression:

Water Saturation = Sw = (Ro / Rt)^1/n

where n=the saturation exponent, Ro is the total resistivity of the rock,100% filled with water and Rt is the measured resistivity of the target zone.

So by substitution, Sw = (Ro / Rt)^1/n = (F*Rw / Rt)^1/n = a*Rw /(phi^m)* Rt)^1/n

Or Sw = (Rw /Rwa)^1/n

where Rwa= a / (phi^m * Rt)

## Determination of Rw from Rwa

For a given uniform porosity zone with an assumed water leg, calculate Rwa.  In the water zone, the minimum Rwa will approach the actual Rw, which can then be used to calculate apparent water saturations for other intervals within the uniform porosity zone.

Typically, for first pass quick look calculations, n = 2.0, a = 1 and m = 2.0

If sands are being analyzed and pore geometry considerations are secondary to getting an ‘answer’ use a = 1.0 and m = 2.15

In sands, the rounder the grains and the better the sorting and the looser the packing of the grains the lower the value of ‘m’ with values from 1.5 to 2.0 not atypical.

In carbonates using a = 1.0 is not a bad assumption. ‘m’ will usually vary from 2.0 to 3.0

In the Western Canadian Sedimentary Basin (WCSB) typical ‘m’ would vary as follows:

Mississippian: m = 2.0

Wabamun: m = 2.10

Nisku: m = 2.2

Leduc: m = 2.3 – 2.4

Keg River: m = 2.2 – 3.2

Of course, there are exceptions to every rule.

2. It is a very common rule of thumb that permeability is a function of porosity but that assumption is a complete fallacy.

Consider a formation made up of hexagonally packed round bowling ball sized grains, the porosity of that formation would be approximately 26%. Consider another formation having hexagonally packed round 'BB' sized grains, the porosity of that formation would be approximately 26%.  Both formations have vastly different grain sizes and correspondingly vastly different pore throat sizes but still have the same porosity.

Given the same pressure differential across each of the formation, a given fluid will flow through the formation with the larger pore throats more easily than the formation with smaller pore throats.  Permeability is directly related to pore throat geometry and the tortuosity of the fluid flow path through any given rock.

Different formations can have the same porosity but because of pore throat geometry differences can have different fluid flow permeabilities. Permeability is not a function of porosity.

3. Well log data is always useful regardless of vintage or scaling.  Remember that the well log data is the only continuous depth record of the well bore. The significance being that the recorded depths on the well logs tied to the inferred reservoir characteristics based on the well log measurements provide an analyst with the best first start with respect to the analysis of a given well for hydrocarbon potential.

Don't discard older unscaled neutron and older unscaled gamma data or short normal and long normal resistivity data.  These can be digitized and re-scaled or normalized to behave with amazing consistency as compared to the more modern equivalent well logs.

4. Regards of methods used, normalization is meant to accentuate the geological response of the well logging tools and minimize adverse effects.

When in the process of normalization, it is important to keep an open mind and let the data trends present themselves and respond to what the trends suggest and not apply a preconceived notion of what the data is “supposed” to tell you. Rules of thumb and statements such as this tool “never works” have to be qualified with a “WHY”. Why does this not work or why am I using this rule of thumb.

Failure to demonstrably defend the ”WHY” implies a lack of a broad experiential database, a lack of the skill sets and tools to do a proper analysis and/or a lack of motivation on the part of the individual making those statements to resolve the questions.

In my experience, the statement “this tool never works” has, upon sufficient investigation, almost invariably turned to the statement “this tool always works”.

The limestone lateral tool was developed in the 1950’s as a porosity device but was found not to work that well and has subsequently vanished from the well logging world. The neutron log was developed in the 1940’s and is still in wide use.

Logging service companies are not going to provide a well logging tool if they cannot make money from it. Clients of the well logging companies are not going to run logging tools that do not provide valuable information.

Calibrated well logging data is always an accurate inference or reflection of the conditions of the wellbore and the formation rocks within the radii of investigation of the well logging tools. Our problem as analysts is how to we properly interpret these measurements. Maintain an objective perspective when analyzing well log data and you will resolve the “WHY”.

5. You normalize well log the data to accentuate the geologic responses while minimizing the effects of well log vintage, bore hole conditions, well logging company and well log calibration to name a few.

From experience in dealing with digital well log data from multiple wells, almost all interpretation busts or failures, aside from using the wrong interpretation procedures, can be linked back to poorly calibrated data and not doing a proper and consistent normalization prior to analysis.

Given the well log data from 100 wells in an area where there is a spread in vintage and logging company, experience would suggest that at least 1/3 of the gamma rays will be miscalibrated, 60% of the neutron data will be miscalibrated, 10-25% of the bulk density data will be miscalibrated and 5-10% of the deep resistivity and acoustic data will be miscalibrated. Of course pretty well all the SP data will be different from well to well due to the variation in drilling muds but even that can be resolved through specialized detailed analysis and normalization procedures.

Can you afford not to normalize?

6. The Well Log Analyst or Petrophysicist plays many roles within the integrated technological approach to the search and exploitation of hydrocarbon resources.

What questions do some of the main disciplines ask that the well log analyst or petrphysicist will most commonly provide answers to?

Consider the Geologist.

geological tops, depostional environments, lithology

Consider the Geophysicist.

acoustic velocity contrast, synthetic seismograms, depositional environments for modeling

Consider the Reservoir Engineer.

reservoir continuity, porosity, water saturation, permeability, net pay, areal extent

Consider the Drilling Engineer.

borehole conditions, pressures, fluids expected on drill stem testing

Consider the Production Engineer.

new wells: pressures, cement bond, perforations/packers

old wells: bypassed pay, fluid contacts, poor performance

Consider the Technological Application Development Team.

how is the log data best handled and stored?, additional computer applications required based on new insights

7. Depth measurement is the single most important aspect of capturing well log data.  If you don't know the depth of the hydrocarbons, how can you be expected to get them out of the ground.