While it is common knowledge that the values of Archie's parameters ‘a’, ‘m’ and ‘n’ may vary for sandstone reservoirs at different conditions ? consolidated/unconsolidated, water-wet/oil-wet, pore geometry, degree of sphericity, clay content and in-situ depositional environment ? the values of a = 1, m = 2 and n = 2 have been linked historically with Archie's equations. Statistically, these values were assumed as the population mean when used in calculations, but the magnitude of errors associated with their use is often neglected. This study shows how a sample of data drawn from experimental and analytical methods determine Archie's parameters. Well logs from sandstone reservoirs are used to draw statistical inferences about the population characteristics of Archie's parameters in sandstone reservoirs. This also shows the magnitude of relative error possible when m = 2 and n = 2 are used to compute water saturation and formation resistivity factors. Introduction The 1942 landmark publication by Gus Archie titled, "The Electrical Resistivity Log as an Aid in Determining Some Reservoir Characteristics "(1) introduced new parameters relevant to describing reservoirs using well logs and set standard parameters for the identification of permeable zones within a reservoir. Basically, Archie's experiments involved measuring the porosity and electrical resistivity of numerous shale-free sandstone cores from the Gulf Coast by saturating them with brine of salinities ranging from 20 to 100,000 ppm of NaCl. Archie's work established the following relationships: Equation (1) (Available In Full Paper) where Ro is the resistivity of the rock fully saturated with brine and Rw is the formation water resistivity. F is termed the formation resistivity factor and is a measure of the effect of formation on the path of electrical current traveling through the electrolytic brine in the rock pore system. The plot of F against porosity (Φ) on log-log scales revealed a linear trend equivalent to: Equation (2) (Available In Full Paper) The ‘m’ parameter represents the trend's negative slope. In deriving the above expression, Archie force-fitted a line to his formation resistivity factor against porosity data such that F = 1.0 at 100% porosity. A replica of Archie's original plot using clean sandstone cores is shown in Figure 1. This was however deemed unnecessary as other research works revealed that when a line is fitted to formation resistivity factor against porosity, the intercept at 100% porosity would not always derive one, but can be greater or less than one. Winsauer et al.(2), for example, duplicated Archie's experiments with sandstone cores from a wide range of reservoirs and arrived at: Equation (3) (Available In Full Paper) Thus, the general form of Archie's formation resistivity factor is expressed as: Equation (4) (Available In Full Paper) Winsauer first referred to Archie's ‘m’ parameter as the cementation factor, while ‘a’ would later be referred to as the tortuosity factor. Archie, again, considered partially saturated hydrocarbon bearing shale-free sandstones and proposed a second factor called the resistivity index (I) that would further increase the rock's resistivity. He expressed this as: Equation (5) (Available In Full Paper) FIGURE 1: Plot of formation resistivity factor against porosity (Available In Full Paper)

Ground water contamination has been a major consideration in the in the Oil and gas industry of the United States and indeed the world. Previous works have shown the reduction of cost and increased quality in intermediate cementing by the use of sodium metasilicate to replace the existing bentonite slurry system being used. The use of admixtures of 50:50 Class H (or Class C): Pozzalon with 2% bentonite have functioned effectively worldwide for nearly 50 years as lightweight slurries for situations where heavier completion cements posed a risk of exceeding low fracture gradients in a particular well bore. Pozzolanic materials are lightweight, and effectively combine with calcium hydroxide that is liberated during the hydration of Portland cement. Historically, the 2% bentonite has been utilized to assist in the specification of relatively high water-to cement ratios, and therefore lighter slurry density, without the generation of excessive free water as the cement progresses through the setting process. The bentonite has performed well in meeting this requirement, but two things remain elusive: first, its presence in typical cement slurries reduces the effectiveness of a given concentration of most commercially available fluid loss additives. Second, while the 2% (by weight of cement) volume may seem of no consequence, the shipping costs associated with moving tons of the material over a long period of time can be significant.This study was carried out to determine whether or not there were other commercially available materials that could substitute for bentonite and yield improved slurry qualities at the same or reduced cost. Extensive testing of 50:50 slurries revealed that small quantities of sodium metasilicate (on the order of 0.5% by weight of cement) could effectively replace bentonite. Free water was controlled to the same degree, and a synergy with a commonly available fluid loss additive was discovered, allowing either a) less total fluid loss additive for a given fluid loss control tolerance, or, b) better fluid loss control for a given concentration of fluid loss additive and c) current studies have also shown the possibility of wellbore water and formation water interaction being reduced due to increased strength of the slurry system being used.The testing procedure is summarized, and relative economics associated with the systems are discussed.

The essence of this work is to show students how to reduce landfill dumps in onshore drilling and cementing operations by close looped monitoring of additives. While liquid additives are used in offshore & international cementing operations, land-based operations use a bulk-drybatch-mixed process. Additives control cement volumetric yield, thickening time, compressive strength, free water, rheology, and fluid loss control. Computerized closed-loop control of liquid additives 1) allow unused, uncontaminated cement to be hauled off location after an operation, 2) promote environmental responsibility by reducing the volume of waste cement hauled to a landfill, and 3) provide better quality control of slurries pumped "on-the-fly" due to better distribution of additives in the slurry and tighter computerized tolerances. Students are challenged to always work towards environmentally friendly processes and use of flow regime equations to vary viscosity. Laboratory tests are carried out to verify the predictions made through the regime equations. Surface slurries utilizing liquid sodium silicate in API Class C Cement were designed to meet or exceed Texas Railroad Commission Rule 13 requirements for "zone of critical cement" "extended cement" systems. Slurries were tested for thickening time, free water, compressive strength, and rheology for various combinations of weight, water, yield, additive concentration, and adherence to TRRC (Texas Railroad Commission) Rule 13 specifications.