# Archie Equation Petrophysics

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INTRODUCTION

Archie Unleashed is an attempt to put the basic log analysis methodology for computing water saturation into a readable reference document. The beginning log analyst or petrophysicist should have little difficulty with the terms and concepts utilized in this paper, however, most terms are redefined in appendix A.

The basic outline of this document closely follows a previous work written for the casual interpeter in log analysis. Archie Unleashed is meant to carry that work one step further. Basic concepts are explained along with more detailed examples and explanations.

The personal computer has revolutionized the way we work and play. The kind and amount of data we work with in petrophysics can be easily handled in spread sheet programs that are under the full control of the user. The second section of Archie Unleashed examines several data sets and techniques for handling these data and defines a simple spreadsheet to do the calculations.

Section 1. The Archie Equation

-water saturation as a decimal fraction.

-Resistivity of the 100% water saturated rock.

-Resistivity of the rock-fluid system.

Equation 1.1 was empirically derived by G. E. Archie while working for Shell. This work was reported in in his famous 1942 paper. He plotted SW versus the ratio Rt/Ro (the Resistivity Index) on log-log paper, see Figure 1.1. This same technique is still used today to derive a value for n from core measurements.

The absolute value of n is commonly near 2 and is generally taken as equal to 2.00 when no laboratory determination of n is available. Accepting the convention of n = 2 allows the Archie equation to be written in the following forms:

These are equivalent expressions. Proper application will yield identical answers.

Critical Sw Values

The critical value of water saturation (Sw) is commonly taken as 50%. Sw must be less than the critical value for a zone to produce oil or gas without water production. Texture and sorting are the major factors affecting the maximum Sw before water free production.

The critical value for Sw is known to vary from about 30% to 80%. Carbonates often have a critical Sw value less than 50%, whereas sandstones may have critical Sw's well over 50%.

Predicting the critical value in low porosity carbonates, fractured carbonates, or carbonates with vugular or moldic porosity may be impossible.

Assumptions of the Archie Equation:

1. The reservoir rock is water-wet (water is the wetting fluid, the fluid in contact with the grain surfaces).

2. The reservoir rock is shale free (or the amounts are small and can be safely neglected); that is, the rock matrix is non-conductive.

3. The reservoir rock has moderate to high porosity, the higher the porosity, the better the Archie equation works.

4. The reservoir porosity is intergranular (connected) in nature.

Primary Considerations in the Archie Equation:

1. The Archie equation does not predict Sw well in low porosity rocks, particularly when porosity is less than 5%.

2. A knowledge of Sw alone may not be sufficient to predict production.

3. The Archie equation does not work well where Rw is high (fresh water). Fresh water lessens the contrast in resistivity between oil and water zones. Fresh water increases the importance or effect of conductivity along grain surfaces.

4. The Archie equation may not apply at low Sw values. In the original paper, the samples had water saturation greater than 15%.

5. n is generally greater than 2 in oil-wet reservoirs, and may reach values of 10 or more.

Guidelines For Application Of The Archie Equation:

1. The quality of the water saturation values derived from the Archie equation is no better than the quality of the well logs used.

2. If you are at wellsite, check the quality of each log run. Do not hesitate to rerun logs which do not meet quality control standards. Check especially to see that logs such as the resistivity and porosity measurements are recorded on depth with each other and with the previous surveys.

3. Choose the primary electric log as a reference. Mark intervals selected for quantitative analysis on this log. Depth. correlate the other surveys to this reference log or the Gamma ray curve from this log.

4. Select intervals with at least four feet of constant response whenever possible. Use a single representative value from the center of the zone for each porosity and resistivity measurement. This procedure minimizes thin bed and bed boundary effects on the logs.

5. Consider how to keep the interpretation simple. Analyse the most clear-cut cases first. Look for:

The obvious mineral markers (salt, anhydrite).

The cleanest, most porous, intervals.

The cleanest, water-bearing, intervals.

The cleanest, hydrocarbon-bearing, intervals.

The fluid contacts: gas/oil, oil/water.

The transition zones.

6. Tackle one unknown at a time. For example, when deriving an Rw value from logs, choose

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