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By A. A. Venghiattis

A rational approach to the selection of the appropriate perforator to use in each specific zone of an oil well is presented. The criteria presently in use for this choice bear little resemblance with actual down-hole condilions. These environmental conditions affect the elastic properties of rocks. One of these elastic properties, acoustic velocity, is suggested as the leading parameter to adopt for the choice of a perforator because, being currently measured in the natural location of the formation, it takes into account all of the effects of compaction, saturation, temperature, etc., which are overlooked in the laboratory. Equations and curves in relation with this suggestion are given to allow the prediction of the depth of perforation of bullets and shaped charges when an acoustic log has been run in the zone to be perforated. INTRODUCTION When an oil company has to decide on the perforator to choose for a completion job, I wonder if it is really understood that, to date, there is no rational way of selecting the right perforator on the basis of what it will do down-hole. This situation stems from the fact that the many varieties of existing perforators, bullets or shaped charges, are promoted on the basis of their performance in the laboratory, but very little is said on how this performance will be affected by subsurface conditions such as the combination of high overburden pressure and high temperature, for example. The purpose of this paper is to show the limitations of the existing ways of evaluating the performance of perforators, to show that performances obtained in laboratories cannot be extended to down-hole conditions because the elastic properties of rocks are affected by these conditions and, finally, to suggest and justify the use of the acoustic velocity of rocks, as the parameter to utilize for the anticipation of the performance of a perforator in true down-hole environment. EVALUATING THE PERFORMANCE OF A PERFORATOR It is natural, of course, to judge the performance of a perforator from the size of the hole it makes in a predetermined target. Considering that the ultimate target for an oilwell perforator is the oil-bearing formation preceded in most cases by a layer of cement and by the wall of a steel casing, the difficulties begin with the choice of an adequate experimental target material. For obvious reasons of convenience, the first choice that came to the mind of perforator designers was mild steel. This is a reasonable choice for the comparison of two perforators in first approximation. Mild steel is commercially available in a rather consistent state and quality, and is comparatively inexpensive. The trouble with mild steel is that it represents a yardstick very much contracted; minute variations in depth of penetration or hole diameter and shape may be significant though difficult to measure. The penetration of projectiles in steel being a function of the Brinell hardness of the steel (Gabeaud, O'Neill, Grun-wood, Poboril, et al), it is often difficult to decide whether to attribute a small difference in penetration to a variation on the target hardness or to an actual variation on the efficiency of the projectile. Another target material which has been widely used for testing the efficiency of bullets or shaped charges in an effort to represent a formation—a mineral target as opposed to an all-steel target—is cement cast in steel containers. This type of target, although offering a larger scale for measuring penetrations, proved so unreliable because of its poor repeatability that it had to be abandoned by most designers. The drawbacks of these target materials, and particularly their complete lack of similarity with an oil-bearing formation, became so evident that a more realistic target arrangement was sought until a tacit agreement was reached between customers and designers of oilwell perforators on a testing target of the type shown on Fig. 1. This became almost a necessity about seven years ago because of the introduction of a new parameter in the evaluation of the efficiency of a perforator, the well flow index (WFI). The WFI is the ratio (under predetermined and constant conditions of ambiance, pressure and temperature) of the permeability to a ceitain grade of kerosene of the target core (usually Berea sandstone) after verforation. to its vermeabilitv before perforation. The value of this index ;or the present state if the perforation technique varies from 0 to 2.5, the good perforators presently available rating somewhere around 2.0 and the poor ones around 0.8, There is no doubt that, to date, the WFI type of test is by far the most significant one for comparing perforators. It is obvious that a demonstration of a perforator

By Edward A. Barrett, Launa Mallett, Charles Vaught, Kathleen M. Kowalski, Michael J. Brnich, Lynn L. Rethi, Robert Randolph, William J. Wiehagen

The goal of the Pittsburgh Research Laboratory's training research is to explore the relationship between valid instruction and improved worker performance. Studies summarized in this paper include: (a) the development and assessment of training techniques that strengthen miners' ability to act competently in emergencies; (b) investigations of classroom simulations that enhance the perceptual, judgment and decision making skills of workers confronted with mine hazards; and (c) field studies of the linkages between financial investments in occupation at skills training and measurable outcomes.' The authors maintain that better ties between training and performance will aid long-term human resource development. The best way to establish this connection is through the use of objective and reliable data.

By Thomas M. Barczak, Ron Smith

Steel liner plates, which are bolted together to form a shell, are commonly used to provide temporary protective linings in the tunneling industry to ensure the stability of the tunnel and safety of the workers until more permanent ground reinforcement can be installed. As the ground deforms to try and close the opening, the liner plate is radially stressed, and by deforming redistributes these loads back to the surrounding insitu earth. Grouting behind the plates is done to fill any voids and ensure uniform contact to the strata around the back of the plates. Another function of the liner plate in some applications is to act as a platform or structure for the mining machine to react against in order to develop the necessary forward thrust to be able to excavate the face. In this case, the liner plates are loaded axially as a horizontal column of bolted liner plate rings, creating a jacking force against the liner plate assembly. In general, the buckling strength of the plate sections determines the jacking force capacity. Historically, the jacking force capacity of tunnel liner plates has been theoretically determined by some simplistic equations developed from tests of single liner plates. Recently, full-scale tests on a complete circular section of bolted liner plate ring segments have been conducted in the NIOSH Safety Structures Testing Laboratory using the unique Mine Roof Simulator to apply controlled loading in a manner that simulates the real world environment. Due to the unique size and capacity of the Mine Roof Simulator, these are believed to be the first full-scale tests conducted on the jacking force capability of tunnel liner plate rings. These tests indicate that the previously used theoretical equations tend to over predict the jacking force capacity of these tunnel liner plates. Unanticipated deformations in the field have been observed at loads below these theoretical design loads, therefore, a more accurate determination of the jacking force capability was needed. This report summarizes the full-scale test results, examines design parameters that impact the jacking force capability, and develops new mathematical models to improve the prediction of design loads.

By M. MacLaughlin, J. Whyatt

A case study is presented that relates statistical descriptions of joint sets to the distribution of local wedge failures along the crest of a catch bench at the Yellowstone Talc Mine. The fracture sets and bench width were mapped by teams of geological engineering students from Montana Tech under the direction of Dr. Mary MacLaughlin. The students analyzed the fracture data, conducted physical property tests, and used a beta version of a NIOSH program “Bwedge” to predict the distribution of surviving bench widths. In the course of this analysis the students developed evidence of software performance issues that, unfortunately, frustrated their analysis. These have now been addressed and a full analysis completed. The analysis confirms the validity of the student mapping program and provides insight into the effects of blasting and excavation practices on the bench. It also provides a tool for exploring the pattern of bench crest failure that would result from variations in both bench geometry and blasting practices.

By William Gleason

Despite a global slowdown in most mining sectors, Caterpillar, the world?s largest mining equipment maker continues to forge ahead with new, and improved offerings to the global mining industry. On Nov. 10, as part of its Loading and Hauling Mining Focus Session at its Tinaja Hills proving grounds south of Tucson, AZ, Caterpillar unveiled to customers and media its two latest mining products, the 994K wheel loader and 6020B hydraulic shovel. The Caterpillar 994K wheel loader builds on a nearly 25-year history of the 994 model but with one noticeable difference ? the 994K is bigger ? much bigger. Weighing in at 239,142 kg (527,218 lb) the 994 K is up to 20 percent larger and comes with up to 30 percent increase in payload capacity. This behemoth of a machine is currently being tested at Caterpillar?s Tucson Proving Grounds, Anglo Gold Ashanti?s Cripple Creek and Victor gold mine in Colorado and Taseko?s Gibraltor copper and molybdenum mine in British Columbia, Canada.

By R. G. Gürtunca, J. A. Breslin

This paper briefly describes the progress in mine safety in the United States, with emphasis on recent events that have followed since the explosion at the Sago Mine in January 2006. Legislation following the mine accidents last year and areas of work carried out by the National Institute for Occupational Safety and Health (NIOSH) related to the accidents are discussed. American coal production in 2006 was 1,150 million short tons. Most of this coal is consumed domestically, with annual exports of coal about 50 million tons. One third of annual production is produced at surface mines and the rest from underground. This coal is produced by about 82,000 miners working at 1,400 coal mines. Major improvements in coal mine safety have been made in the US since the Federal Mine Safety and Health Act of 1977. The fatal injury rate in underground coal mines between 1977 and 2004 was reduced by 47.8% to 0.036. The annual number of fatalities dropped from 112 to 14 during that period. Likewise, the non-fatal days-lost injury rate was reduced by 42.6% from 10.87 to 6.24. The improvements in mine safety during this period can be seen in the graph of underground coal mine explosion fatalities and injuries from 1980 to present, which is shown in Figure 1. Between 1984 and 1993 (9 year period) there were 5 explosions and one major mine fire, for a total of 55 fatalities. Over the seven year period from 1993 to 1999 there were no fatalities from coal mine fires and explosions. However, in the six years since 2000 there have been 5 explosions and one fire, which have caused 37 fatalities. [ ]

Pillars with width to height ratios of less than 1.0 are frequently created in underground hard rock mines. The strength of slender pillars can be estimated using empirically developed equations. However, the equations can provide variable results when the width-to-height ratios approach 0.5. This paper investigates some of the issues affecting pillar strength at low width-to-height ratios in hard brittle rock. The investigation includes an evaluation of empirical pillar strength data presented in the literature and observations of pillar performance in underground limestone mines in the eastern United States, supplemented by numerical modeling in which failure processes and sensitivity of slender pillars to variations in rock mass properties are evaluated. The results showed that the strength of slender pillars is more variable than that of wider pillars. The numerical model results demonstrated the increasing role of brittle rock failure in slender pillar strength. The absence of confinement in slender pillars can result in a fully brittle failure process, while wider pillars fail in a combined brittle and shearing mode. The onset of spalling in slender pillars occurs at or near the ultimate strength, while this is not the case for wider pillars. Slender pillars are shown to be more sensitive to the presence of discontinuities than wider pillars, which can partly explain the increased variability of slender pillar strength. Two examples are presented, which illustrate failure initiation by brittle spalling and the sensitivity of slender pillars to the presence of discontinuities.

By L. F. Elkins

Water coming into wells with bottom water present in the Fosterton field, when their oil recovery was only 0.1 to 1.5 per cent of oil in place below the lowest perforation, confirms lack of shale barriers to vertical flow which also are not apparent in cores and electric logy. Low contrast of vertical and horizontal permeability, high mobility ratio betweerz oil and water zone and pos.rible rate effects due to gravity Combine to prevent easy analysis of water invasion pattern and efficiency by analogy or intuition. Theoretical analysis of performance including these factors using a new direct nurnerical .solution of potential distribution in a network led to unanticapted indications that water would under-run the entire oil reservoir with low volumetric coverage if supplied through natural influx or peripheral water injecfion below the oil-water contact. An unusual pattern of water injection is to he adopted in this recently unitized pool to provide more uniform water flooding in that two-thirds of the oil reservoir not underlain by bottom wafer. INTRODUCTION The Fosterton field, Southwestern Saskatchewan, Canada, was discovered in Jan., 1952. It produces at a depth of 3,100 ft from a pinch-out of the Roseray sand at the Lower Cretaceous-Jurassic unconformity. The field, covering 2,500 acres, contains 54 wells on 40-acre spacing. Development was essentially complete in June, 1954, but significant production did not start until May, 1955, when a pipeline outlet became available. Within one year rapid in- creases in gas-oil ratio and early encroachment of water created operating problems in the down-structure eastern half of the field and raised serious questions about reservoir performance and ultimate recovery. This paper describes the unusual behavior of water encroachment—on both well and reservoir bases—and the analyses made to interpret it. The field was unitized July 1, 1958, for water flooding. A somewhat unconventional

By B. G. Meyburgh

SYNOPSIS As a result of a test programme over a period of approximately ten years and a decision to extend the uranium plant, it was decided to design and erect the first full-scale Purlex Plant in the Republic of South Africa. The plant at Buffelsfontein G.M. Co. Ltd. was commissioned in August, 1968, and to date has produced results superior to those predicted in the original estimates. The capital expenditure was R678 000 for a plant capable of treating 1 600 gallons per minute of pregnant solution. Compared with the conventional resin ion exchange process, it has been found that the saving in production costs is 21 cents per pound U3O8 produced. The amine loss is 10 parts per million, which is equivalent to a total organic loss of 250 parts per million. The uranium loss in the raffinate is less than 0.001 g/l U3O8. The final product is of a high quality and it is probable that it is pure enough to convert to the fluoride directly.

By William Reininger

Microtunneling provides a necessary solution for multiple utility crossings associated with the New York Metropolitan Transportation Authority Capital Construction Company?s (MTACC) Eastside Access Project for the Long Island Rail Road. Construction of four TBM tunnels and their approach structures at the eastern end of the project in Sunnyside, Queens required significant modification and expansion of the railroad infrastructure at this location. Maintenance of railroad traffic during project construction is a principal requirement. As a consequence fourteen (14) utility crossing segments are being installed under active traffic by microtunneling methods. Microtunnels were installed in a variety of conditions including depths, types of soils and construction restraints.

By M. Felsenthal

Engineers are frequently faced with the problem of having to predict oil recovery from a solution gas drive reservoir in the early life of a field. This is often the time when actual laboratory or field-derived gas-oil permeability (kg/k0) data are not yet available. Although excellent collections of k0/k0 data for various types of rocks may be found in the literature,1,2,3 a need exists for a more detailed correlation of k0/k0 data with core properties such as porosity, permeability, clay content or pore-size distribution. It is the purpose of this article to present this type of correlation for sandstone material. The correlation is based on laboratory tests performed on over 300 core samples from 19 reservoirs in the United States and Canada. EXPERIMENTAL Cores were analyzed by routine procedures, using samples of conventional size (7/8-in. diameter, 7/8-in long) cut parallel to the bedding planes. Air permeability was measured at 1.67 atm mean pressure in a Hassler-type apparatus. Porosity was determined with the aid of a Ruska bulk volume meter and a Boyle's Law rock volume meter, An evaporation method' was used to evaluate irreducible water saturations. Core samples were saturated with 25,000 ppm NaCl brine. The brine was reduced to the irreducible saturation, and the remainder of the pore space was filled with kerosene. This was followed by multiphase flow tests using the so-called "dispersed feed" technique.5 n this technique, gas and oil (kerosene and kerosene-saturated air) were dispersed with the aid of a porous Alun-durn feed head, the face of which contained a waffle-shaped system of Lucite-lined grooves. Oil entered the back side of the feed head and emerged at the raised areas of the front face. Gas was introduced directly into the system of grooves at the front face. The gas-oil mixture then entered the test core which was kept in capillary contact with the feed head. Permeabilities were determined from rate and pressure measurements and saturations from weights. All determinations were performed at equilibrium or steady-state conditions. Pore-size distributions were determined on selected samples by a mercury injection technique.6 GENERAL CORRELATIVE TRENDS When examining data from a given reservoir, it was noted that k0/k0 vs saturation curves became generally less steep as specific air permeability increased, a development that has a favorable effect on oil displacement efficiency by solution gas drive. This trend has also been reported by others in the literature.' An effect of porosity on k0/k0 data was also noted. This effect was not generally discernible in a study of relative permeability data for a given reservoir but became apparent when data for sandstone reservoirs of similar lithology but differing average porosity were compared. For instance, in a comparison of argillaceous and/or calcareous sandstones from 11 reservoirs ranging in average porosities from 14 to 28 per cent, a definite trend was noted, indicating that for a given permeability k0/k0 curves became less favorable (i.e., steeper) as porosity increased. A similar trend was observed for a group of comparatively clean sandstones from five reservoirs ranging in average porosities from 15 to 21 per cent. For a given permeability and porosity, comparatively clean sandstones gave more favorable k0/k0 curves than argillaceous and/or calcareous sandstone or chert reservoirs. The laboratory studies also showed that least favorable k0/k0 curves were exhibited by shaly sandstone, conglomerate, and sandstone containing carbon inclusions. Table 1 lists the various source reservoirs classified by lithology types. To facilitate a correlation of k0/k0 data with core characteristcis, it was found expedient to work with

By William Brundan

INTRODUCTION The Srisailam Left Bank Canal (SLBC) Tunnel Scheme is part of the Alimineti Madhava Reddy Project in Andhra Pradesh, South India. This scheme has been planned since 1983 and will provide irrigation facilities to drought-ridden areas in Andhra Pradesh. Water will be transferred from the Srisailam Reservoir during the monsoon months to 0.3 million acres of farmland and will also provide drinking water to villages en-route. The paper will address the design and onsite assembly of the Robbins Double Shield TBMs for Tunnel-1 of the SLBC tunnel scheme from planning to start-up of the machines. Also, it will provide a current status of the project and describe the advantages of a site assembly. Problems encountered to date and the solutions adopted will also be described. The project comprises over 50 km of tunnels and involves construction of the world?s longest tunnel without intermediate access. The TBM tunnels at 43.9 km in length and 10.0 m diameter will cross the Amrabad plateau, containing a wild life sanctuary and India?s largest tiger reserve, the Rajiv Gandhi. Jaiprakash elected to excavate the tunnel using two tunnel boring machines, rather than by drill and blast, in order to alleviate surface disturbances to environment and the tiger reserve, wild life sanctuary, and protected forestry areas. The Project was awarded to the Main Contractor Jaiprakash Associates Ltd with The Robbins Company as the Tunnel Boring Machine (TBM) supplier in August 2005. The Robbins Company supplied the TBMs along with two continuous conveyor systems and all spares and consumables to complete the tunnel excavation.

By T. M. Barczak, S. C. Tadolini

Pumpable roof supports provide an alternative approach to secondary support in underground mining. Unlike all other supports that are either partially or fully prefabricated prior to being transported into the mine, the pumpable support is fabricated in place in the mine entry. This reduces the underground material handling efforts and thus the injuries historically associated with in-mine support construction. On-site fabrication also facilitates application of the support in areas that are inaccessible to transportation equipment such as scoops or rail cars, making it ideal for many bleeder applications. One of the main advantages of the pumpable support is that it fully bridges from the mine floor to the roof, thereby eliminating the requirement of “topping off” the support with wooden wedges or crib blocks that soften most other support responses. This report examines the development of modern pumpable roof support technology and provides a full description of the performance capabilities of each of the support products now on the market.

By L. T. Stanley

A method is described whereby the behavior of the front is approximated when gas is injected into a thick reservoir having reasonably homogeneous properties. The method is applied to the Abqaiq field of Saudi Arabia. The producing member is the Arab-D, a high-permeability calcarenite which has no continuous betlding planes. Field performance indicates the injected gas to be partially miscible with the reservoir oil because gas volume factors experienced are lower than those predicted by the gas law. Eqlrilibril~m calculations confirnz ihis and also show that the volume factor may vary appreciably, depending on the relative quantities of oil and gas in contact in the reservoir; consequently, volutnetric balances are made for the purpose of determining the behavior of the gas volume factor during injection history. The effect of gravity segregation on position and shape of the gas front is approximated by dividing the producing section into three zones vertically and tracing the movement of the average interface in each zone, with counterflow of oil and gas taking place betweell zones behind the front. This results in a gas front that advances more rapidly along the top of [he formation than along the base, producing an "umbrella" effect in cross section that becomes more pronounced as the front progresses. The calculations cover the gas-injection period of Abqaiq field history through 1958, and the position of the gas front is plotted at one-year intervals. Finally, some comparisotls between the calcrlated fronial position and the gas-oil contact as Measured by neutron logs are made. INTRODUCTION Fig. 1 is a structure contour map of the Abqaiq field. For analytical purpcses, the field has been divided into two areas designated A and B, as shown on the map. Gas injection into Area A was begun in early 1954 into two wells located near the crest of the structure on the north-south axis of the anticline. During the period covered by this paper, the average injection rate has been 122 MMscf/D with a maximum sustained rate of 160 MMscf/D. The reservoir pressure has been maintained at 2,450 psig since start of gas injection. The reservoir originally was undersaturated but, prior to pressure maintenance, the pressure was drawn below the bubble point in most of the Area A section, creating an in-place free-gas saturation of 8 per cent at the crest of the structure. The average critical gas saturation is 13 per cent established by laboratcry core tests. That the entire reservoir remained below critical gas saturation prior to gas injection is borne out by the fact that none of the crestal wells have exhibited high gas-oil ratios during production history. The Area A reservoir is a carbonate section about 200-ft thick having average porosity and permeability of the order of 22 per cent and 500 md, respectively. The productive horizon is the Arab-D member of Jurassic age and is encountered at an average depth of

By Isaac A. Zlochower

A number of ignition incidents involving mining and farm equipment have illustrated the surprising danger of drilling, cutting, or otherwise penetrating sealed compartments or frames that are filled with metal scrap for ballast. The presence of chemically-reactive metals (or electrochemically-active pairs), such as zinc in galvanized steel, can produce hydrogen from moisture in the steel scrap, and the resulting pressure, due to the internally-generated hydrogen, can produce an easily-ignited gas jet when the sealed component is penetrated.

By M. K. Larson, J. P. Dunford, E. G. Zahl, T. M. Brady

Researchers at the Spokane Research Laboratory of the National Institute for Occupational Safety and Health, Spokane, WA, have collaborated with three Western longwall coal mines in an on going effort to develop technologies that will aid in providing safe and stable working areas. The goal of the research described here is to develop a stress monitoring system that will provide immediate information to mine managers for making daily safety decisions as areas of poor ground are mined through. Initial work has focused on answering preliminary questions regarding the reliability and use of stress change patterns. Research is concentrated on monitoring horizontal stress because horizontal stress is transmitted over long distances through stiff strata, thus allowing an extended length of entry to be monitored. This paper presents an explanation of the concept, key results from field tests at two mine sites, and a proposed process for implementing a monitoring system. System design layouts, instrument use, data collection and interpretation methods, and processes to present findings to mine staff are described. Additional validation and correlation with actual failure mechanisms are required before this approach can be recommended at ongoing operations. However, initial results indicate that this approach shows promise in mines prone to bumps and roof falls associated with large stress changes. In particular, analyses of measured changes in horizontal stresses appear useful.

This paper on the relation of Granite and Sedimentary Contacts to Victorian Mining will, it is hoped, be of interest to members of the Institute.The broad fact that gold often occurs' at or near the junction of granite with sedimentary silurian or metamorphic rocks has been noted by some Victorian geologists, miners, and prospectors; but the fuq practical value -of the fact does not seem to have been fully realised by prospectors. Glancing at the Geological" Map of Victoria, one can see that many of our goldfields 'are situated at or near the junction of granite with Palceozoic sedimentary formations, and that some of our alluvial fields are on granite. Many prospectors are possessed of this knowledge but when prospecting a contact locality, they would be just as likely to confine their search for auriferous matrices to spots a quarter of a mile on the sedimentary side, as on the actual contact line of two formations.

By V. S. Tuman

In the first part of this paper, an estimate is made of the magnitude and extent of the thermal stresses which result from mud circulation. Our study is made for the period of relaxation, i.e., when the drilling operations are terminated and mud circulation is discontinued. In the second part, we have shown how the thermal stress can affect the wave propagation. An example is worked out for a Carbondale sandstone (Illinois basin). It is concluded that, in extreme cases when differential temperature is about 100°F, the travel time will be affected by about 2 microsec/ft. For more refined permeability studies, such corrections would be desirable. MAGNITUDE AND EXTENT OF THERMAL STRESSES RESULTING FROM MUD CIRCULATION When geological beds are penetrated by boreholes, it is observed that the formation temperatures increase with depth; however, the temperature profile varies considerably from place to place. During drilling operations, mud pumped from a pit at atmospheric temperature absorbs heat from the lower beds. As a result, the drilling fluid returning to the surface is at a higher temperature than the surrounding beds. The temperature gradient in a well depends on the rate of mud circulation and other factors; normally, this temperature gradient is smaller than the natural gradient in the formations. (See Fig. 1.) The temperature difference between the mud column and the surrounding beds gives rise to therma1 stresses (which are also important in the phenomenon of fracturing), and it is expected that they will affect the transit time of the sonic front in velocity logging.1 It is evident chat beds near the surface will undergo various cycles and will have a complicated dynamical and thermal-stress history. A limestone bed which is just penetrated will act as a source of heat, warming up the cold mud pumped down a few minutes earlier from the surface pit. The same limestone bed a week later will act as a sink, absorbing heat from the drilling mud which has already warmed up sufficiently to be at a higher temperature than the bed in question. No doubt a large section of the hole will undergo a heat treatment, which will make the calculation of the exact magnitude of the thermal stresses very difficult. In the solution of wellbore thermal equation, it is assumed that the rock around the wellbore is elastic and isotropic, and that the system is radially symmetrical. A complete dynamical solution of the thermal stresses set up at different horizons during the drilling operations would require a comprehensive history of the mud circulation, the surface temperature of the pit and the number of hours in which mud was not circulated. CONDUCTION OF HEAT AND THERMAL EQUATION OF STATE