7.3 Archies Law (Reynolds, 1998)

Some minerals such as pyrite, galena and magnetite are commonly poor conductors in massive form yet their individual crystals have high conductivities. Hematite and sphalerite, when pure, are virtual insulators, but when combined with impurities they can become very good conductors (with resistivities as low as 0.1 m). Graphite dispersed throughout a rock mass may reduce the overall resistivity of otherwise poorly conducting minerals. For rocks that have variable composition, such as sedimentary rocks with gradational facies, the resistivity will reflect the varying proportions of the constituent materials. For example, in northern Nigeria it is possible, on the basis of the interpreted resistivities, to gauge whether a near-surface material is a clayey sand or a sandy clay. Resistivities for sandy material are about 100 m and decrease with increasing clay content to about 40 m, around which point clay becomes the dominant constituent and the values decrease further to those more typical of clay: wellformed and almost sand-free clay has a value in the range 1-10 m (Reynolds 1987a).Beberapa mineral seperti pirit, galena dan magnetit umumnya konduktor miskin dalam bentuk besar-besaran namun kristal masing-masing memiliki konduktivitas yang tinggi. Hematit dan sfalerit, ketika murni, isolator virtual, tetapi ketika dikombinasikan dengan kotoran mereka dapat menjadi konduktor yang sangat baik (dengan resistivitas serendah 0,1 m). Grafit tersebar di seluruh massa batuan dapat mengurangi resistivitas keseluruhan dinyatakan buruk melakukan mineral. Untuk batuan yang mempunyai komposisi variabel, seperti batuan sedimen dengan facies gradational, resistivitas akan mencerminkan proporsi variasi material penyusunnya. Misalnya, di Nigeria utara adalah mungkin, atas dasar dari resistivitas ditafsirkan, untuk mengukur apakah bahan dekat permukaan adalah pasir lempung atau tanah liat berpasir. Resistivitas bahan berpasir sekitar 100 m dan menurun dengan meningkatnya kandungan liat ke sekitar 40 m, sekitar yang titik tanah liat menjadi konstituen dominan dan nilai-nilai penurunan lebih lanjut untuk mereka yang lebih khas tanah liat: gramatikal dan tanah liat hampir pasir bebas memiliki nilai di kisaran 1-10 m (Reynolds 1987a).

p = acf> -ms-n Pwwhere p and Pw are the effective rock resistivity, and the resistivity of the pore water, respectively; cf> is the porosity; s is the volume fraction of pores with water; a, m and n are constants where 0.5 ~ a ~ 2.5, 1.3 ~ m ~ 2.5, and n;::::; 2.The ratio piPw is known as the Formation Factor (F).dimana p dan Pw adalah resistivitas batuan yang efektif, dan resistivitas air pori, masing-masing; cf> adalah porositas, s adalah fraksi volume pori-pori dengan air, sebuah, m dan n adalah konstanta mana 0,5 ~ a ~ 2,5, 1,3 ~ m ~ 2,5, dan n, ::::; 2. Rasio piPw dikenal sebagai Faktor Formasi (F).

The objective of most mordern electrical resistivity surveys is to obtain true resistivity models for the sub-surface because it is these that have geological meaning. The methods by which field data are obtained, processed and interpreted will be discussed later.Tujuan dari sebagian besar survei resistivitas listrik mordern adalah untuk memperoleh model resistivitas benar untuk sub-permukaan, karena inilah yang memiliki arti geologi. Metode dimana data lapangan diperoleh, diproses dan ditafsirkan akan dibahas nanti.

The apparent resistivity is the value obtained as the product of a measured resistance (R) and a geometric factor (K) for a given electrode array (see Section 7.3.2), according to the expression in Box 7.2. The geometric factor takes into account thegeometric spread of electrodes and contributes a term that has the unit of length (metres). Apparent resistivity (Pa) thus has units of ohm-metres.The tahanan jenis semu adalah nilai yang diperoleh sebagai produk dari resistensi diukur (R) dan faktor geometris (K) untuk elektroda array yang diberikan (lihat Bagian 7.3.2), sesuai dengan ekspresi dalam Kotak 7.2. Faktor geometris memperhitungkan spread thegeometric elektroda dan memberikan kontribusi istilah yang memiliki satuan panjang (meter). Tahanan jenis semu (Pa) sehingga memiliki satuan ohm-meter.

RESISTIVITY OF ROCKS and ARCHIE'S LAWFor rocks composed ofnon-conducting matrix minerals and saturated with water, an empirical relationship known asArchie's Lawis useful in analysis of electrical properties. Archie's Law is commonly writtenUntuk batuan terdiri dari non-konduktif mineral matriks dan jenuh dengan air, hubungan empiris yang dikenal sebagai Archie Lawis berguna dalam analisis sifat listrik. Hukum Archie umumnya ditulis(2-1)whereFLUIDequals the electrical properties of the fluid in the pores,Fis the porosity (ratio of void volume/total volume), andAandmare constants that depend on the geometry of the pores.For many rocks, A =about1 and m =about2.See Keller, G.V. (1982) for a broader discussion. Papers discussing various A and m values for specific rocks (shaly sands, clean sandstones, etc.) have been published in the journalGeophysics.Note: there are several versions of Archie's Law that attempt to include the effects of partial saturation (water-gas or water-oil) or mixed fluids in the pores, or, the air water mixes in the vadose zone. We will not attempt to use these formulas in this course but it is necessary to point out the fact that Equation 2-1 is not the only way in which Archie's Law is written.Archie's Law is not valid for rocks containing a significant percentage of clay. Clay provides for conductive matrix, rendering a fundamental assumption invalid. Graphite, native metals, and minerals with metallic lusters are also electrical conductors, but these are far scarcer than clays.The electrical resistivity of a fluid depends on the amount of ionic material in solution and on the temperature of the liquid. Figure 2-1 is a nomogram that allows you to compute relationships between temperature, TDS (equivalent NaCl salinity) and fluid resistivity - as well as the relationship between rock resistivity, fluid resistivity and "formation factor" (A *F-m). There are methods for calculating equivalent NaCl based on TDS involving a mixture of components but I do not have that at my fingertips (please inform me if you come across this information and I will incorporate it into my class notes). If you ever find such information is critical to your research, contact me and we should be able to find it.NOTE: Based on Figure 2-1, Archie's Law can written whereF is porosity. This is the same as equation 2.1 with A = 1.

FIGURE 2.1:Nomogram relating resistivity, formation factor, salinity and temperature. Any of these parameters may be determined if the other three are known. After Meidev (1970). This nomogram was developed for geothermal fields. Dr. Meidev is an international expert in the use of electrical resistivity in geothermal exploration.Return to Index

http://www.eeescience.utoledo.edu/faculty/stierman/EEG/notes/RR.htm

1.2 Archie's Law

Archies law refers to empirically derived equations that relate the total (or effective) electrical conductivity t of a rock sample containing water with conductivity w, to the samples porosity, , and its water saturation Sw. Knight and Endres identify the current form of Archies law as a relationship between all these parameters"Hukum" Archie mengacu secara empiris diturunkan persamaan yang berhubungan total (atau "efektif") konduktivitas listrik t dari sampel batuan yang mengandung air dengan konduktivitas w, porositas sampel, , dan itu saturasi air Sw. Knight dan Endres mengidentifikasi "bentuk saat hukum Archie" sebagai hubungan antara semua parameter

On the other hand, Gueguen identifies F=-m as Archies first law and RI=Sw-n as Archies second law. F, the formation factor, is w / o , the ratio of water conductivity to effective conductivity when the sample is fully saturated (i.e. when Sw=1). RI, the resistivity index, is o / t , the ratio of effective conductivity with Sw=1 to effective conductivity in the unsaturated sample (i.e. when (Sw