A simple petrophysical model proposed by Waxman and Smits (WS)1 in 1968 and Waxman and Thomas (WT)2 in 1972 accounts for the results of an extensive experimental study on the effects of clays on the resistivity of shaly sands. This model has been well accepted by the industry despite a few inconsistencies with experimental results. It is proposed that these inconsistencies resulted from the unaccounted presence of salt-free water at the clay/water interface. Electrochemistry indicates that this water should exist, but is there enough to influence the results? Both a theoretical study and reinterpretation of Waxman-Smits-Thomas data show that there is. The corresponding new model starts from the Waxman and Smits concept of supplementing the water conductivity with a conductivity from the clay counterions. The crucial step, however, is equating each of these conductivity terms to a particular type of water, each occupying a representative volume of the total porosity. This approach has been named the "dual-water" (DW) model because of these two water types - the conductivity and volume fraction of each being predicted by the model. The DW model has been tested on most of the core data reported in Refs. 1 and 2. The DW concept is also supported by log data3 and has been successfully applied to the interpretation of thousands of wells. However, the scope of this paper remains limited to the theoretical and experimental bases of the DW model. The Petrophysical DW Model The purpose of this model is to account for the resistivity behavior of clayey sands. For petrophysical considerations, a clayey formation is characterized by its total porosity, ft; its formation factor, F0; its water saturation, SwT; its bulk conductivity, Ct; and its concentration per unit PV of clay counterions, Qv. The formation behaves like a clean formation with identical parameters ft, F0, and Swt but containing a water whose conductivity, Cwe, differs from the bulk formation water. Neither the type of clays nor their distribution influences the results. Since the formation obeys Archie's laws,Equation 1 The clayey sand equivalent water conductivity, Cwe, can be considered a mixture of two waters. 1. A clay water surrounds the clay particles but has a conductivity independent of the type and amount of clay. Its conductivity, Ccw, comes exclusively from the clay counterions. The volume fraction of clay water, Vcw, is directly proportional to the counterion concentration, QvEquation 2 where vQ is the amount of clay water associated with 1 unit (meq) of clay counterions. 2. The water further away from the clay is called far water. Its conductivity, Cw, and ionic concentration correspond to the salinity of bulk-formation water. The volume fraction of this water, Vfw, is the balance between the total water content and the clay water.Equation 3 The implicit assumption is that the far water is displaced preferentially by hydrocarbons.

Introduction The thermal decay time (TDT) log is based on a measurement of the rate of decay (absorption) of thermal neutrons in a formation. The principle of such logs has been described in detail elsewhere. In Ref. 4 the special features (capture gamma ray detection, Sliding Gate detection system) of the thermal neutron decay time log are described. Chlorine is by far the strongest neutron absorber of the common earth elements, and the thermal neutron decay time, T, is determined primarily by the sodium chloride present in the formation water. Like the resistivity log, therefore, the thermal neutron decay time measurement is sensitive to the salinity and amount of formation water present in the pore volume. Unlike the resistivity log, this log can be run in cased hole. Also, the thermal decay time log is relatively unaffected by drilling and completion conditions for the usual borehole and casing sizes encountered over pay zones. Consequently, when formation water salinity permits, this log can detect the presence of hydrocarbons in formations that have been cased, as well as changes in water saturation during the production life of the well. The log is thus useful for evaluating oil wells, for diagnosing production problems, and for following reservoir performance. With a version of the tool that is 1 11/16 in. in diameter, it is possible to enter a producing well through the tubing under pressure without having to kill the well.

Poupon, A., Poupon, A., Schlumberger Technical Services Clavier, C., SPE-AIME, Schlumberger-Doll Research Center Dumanoir, J., Schlumberger-Doll Research Center Gaymard, R., Schlumberger Technical Services Misk, A., SPE-AIME, Schlumberger Well Services A primary feature of this interpretation method is that it uses all the logging data in a coherent manner. The formations are analyzed for clay, shale, quartz, water, hydrocarbon content, and changes in sand-grain mineralogy. Even where hole conditions are adverse, reliable results can be achieved through extensive crosschecking for likeness. Introduction During the past 7 years methods have been developed for interpretation of clean and shaly sands using combinations of sonic, density, and neutron logs, along with resistivity and auxiliary logs. Corrections for the presence of light hydrocarbons in the formation, which affect the log readings of the sonic, density, and neutron logs, were also developed. For these methods the shale parameter values are either assumed or deduced from the log readings in adjacent shale beds. This is satisfactory as long as the shales have uniform properties. Frequently this is not so, and the log properties. Frequently this is not so, and the log analyst is faced with determining the properties of the shales occurring in the shaly sands. Intuitively it would seem that sands and shales deposited in sequence during a continuous sedimentation cycle should possess logging properties related to their common geological background. The study of neutron and density logs made in sand and shale sequences has substantiated this. From this study a conceptual model of shales and shaly sands has evolved that is consistent with geological considerations as well as logging tool responses, and in turn has led to the interpretation method described here. The method makes maximum use of all the following logs: neutron, density, resistivity,* gamma ray, SP, microresistivity, sonic, and caliper. Some of these logs may be omitted (microresistivity, sonic, caliper, and either SP or gamma ray); however, doing so decreases the reliability of the results. Formation clay content is determined from several clay indicators and the formation is analyzed for shale, quartz, water, hydrocarbon content, and changes in sand-grain mineralogy. In favorable cases an estimate of hydrocarbon density is made. The associated computer program, SARABAND, solves the interpretation, crossverifies the input data and results and determines automatically many of the required parameters. The interpretation results of main interest are listed in special tabulations and displayed on a film especially coded for easy identification. The Sand and Shale Models Fig. 1 is a neutron-density frequency crossplot generated by a computer. The plotted values of andD, are the apparent porosities from neutron and density logs. Each of the one- or two-digit numbers on the plot represents the total number of readings, over a 390-ft interval in a sand-shale sequence, having the values of N and D, corresponding to the location of the number. The distribution shown on Fig. 1 is typical of sandshale sequences. JPT P. 867

Introduction In the second of this two-part treatment of the subject, three main topics will be discussed.The interpretation techniques developed in Part I will be illustrated with an example in a Middle East well. The thermal decay time log was made with a 1 11/16-in. tool lowered through tubing. Neutron and gamma ray logs furnish the necessary porosity and shaliness data. The final results are presented as a computer-produced log.A study is made of the errors that may be tolerated in each of the following items appearing in the equation for water saturation: Slog, Sma, Sh, Sw, Ssh, øe, and Vsh. "Tolerance factors" for each enable the analyst to evaluate the accuracy of actual log interpretation.The time-lapse technique is discussed. In this method two thermal decay time logs are compared, the first one being a reference log run early in the production life of the well. This comparison provides a more accurate evaluation of changes in saturation. The degree of accuracy can be evaluated by means of tolerance factors provided as a result of the error study. Interpretation Example Gamma ray, neutron, decay time (run through tubing), and induction-log conductivity curves over an interval of a typical Middle East well are shown on Fig. 1.

This paper presents log evidence in support of the dualwater model. Included are basic studies that illustrate the model from the aspect of conductivity measurements, porosity and formation factor relationship, and the contrast to the prediction of Waxman and Smits' cation exchange capacity (CEC) model (W-S model). I 'Throughout this paper the x-plot figures are z-axis displays with an outline of the high·density areas added to reflect the data concentrations.