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Production scheduling of open pit mining is a key area as it deals with the management of operating cash flows of mining companies. The efficiency of long-term schedules is usually assessed with economic criteria such as net present value (NPV), discounted cash flow rate of return (DCFROR) and payback period, which are not sufficient on their own for revealing the complex picture of the decision-making process.This paper offers a thorough analysis of the most important contemporary criteria of long-term production scheduling, as way to provide the mining practice with a new approach to the decision-making process. The list of criteria includes technological, economic and probabilistic ones. A detailed case study is provided aiming to illustrate the applicability of the criteria for comparing the scheduling approaches regarding the economic interests of a mineÆs owner and contractor. The results obtained can be used for revealing new trends in the current methodology of open-pit production scheduling optimisations.

Sep 26, 2011

By Eduardo Vitral

The present study focuses in the simulation of pattern formation by ion beam sputtering on a material surface. This process is responsible for the appearance of unexpectedly organized patterns, such as ripples, nanodots and hexagonal arrays of nanoholes. A numerical analysis of preexisting patterns is proposed to investigate surface dynamics, based on a model derived from a Kuramoto-Sivashinsky anisotropic equation, in a two dimensional surface with periodic boundary conditions. While deterministic, its highly nonlinear character gives a rich range of results, making it possible to describe accurately different patterns. A finite-difference semi-implicit splitting scheme is employed on the discretization of the governing equation. Simulations were conducted with realistic coefficients related to physical parameters (anisotropies, beam orientation, diffusion). The study dealt with a random and a monomode 1D structure initial condition in order to understand how the shape and wavelength of the initial pattern evolve with time. Ripples and hexagonal patterns were observed in the results, being physically consistent with the phenomenon. Moreover, the Method of Manufactured Solution has been used as verification of the developed numerical scheme.

Aug 16, 2017

By J. M. Mwase

The platinum group metal (PGM) industry is currently reliant on the crush-mill-float-smelt-refine route to process PGM ores. However, there are many instances where this route would not be feasible. An alternative process route has been developed which involves heap bioleaching to extract base metals followed by heap reclamation and a water wash step, leading into heap cyanide leaching to extract precious metals. This process was evaluated through test work on samples of Platreef ore using laboratory scale columns. After 304 days 75% Ni and 93% Cu were extracted in the bioleach experiment at 65°C, and after 60 days 58% Pt, 99% Pd and 90% Au in the follow-up cyanide leach experiment at 50°C. A preliminary process flow sheet has been developed around this. Analysis via a mineral liberation analyser showed that the remaining Pt was in the form of the mineral sperrylite, which appeared to be slow leaching in cyanide in comparison to the other mineral types. Analysis of cyanide effluent solution showed high levels of thiocyanate, which present an environmental risk for disposal and high consumption of cyanide. Further studies to develop the process for commercial application in the South African PGM industry are outlined.

Jan 1, 2014

By S. A. Kubyshkin, A. A. Agafonov, A. L. Shakhnin, S. M. Sukharzhevsky, A. A. Komlev, N. V. Vorob’ev-Desyatovskii, A. Pichugina

Cyanidation of gold ore results in formation not only of Na[Au(CN)2], but also cyanometallate complexes of some transition metals. During subsequent gold extraction from such solutions and pulps, using activated carbons (??), a number of problems arise. An effective solution of the problem is not possible without detailed knowledge of the interaction mechanism of transition metals cyanide complexes with AC particles. The chemical properties of AC particles and graphene, saturated with [?u(CN)n](n-1)- (n=2, 3), were studied by XPS, ESR, SQUID, and DFT. The obtained results were compared with the data on AC adsorption of anionic form of Ag(I), Au(I), Cd(II), Hg(II), Cr(III), Fe(II), Fe(III), Co(III), Rh(III), Ni(II), Pd(II), Pt(II) and Pt(IV) cyanide complexes. The adsorption of [?u(CN)n](n-1)- (n=2, 3) on AC from aqueous solutions in air is accompanied with oxidation of ?u(I) atoms. Besides, Cu(II) and Cu(III) compounds were found on AC surface. Quantum-chemical calculations confirmed the possibility of formation of Cu(I) complex with carbene-like sites of AC. The reactions of [?u(CN)n](n-1)- (n=2, 3) complexes and aromatic carbenes and their cation-radical were theoretically studied at DFT PBE level to obtain the information on adsorption of cyanometallate complexes on AC. Carbenes with different fragments were regarded as a model of activated carbons, which have free edge sites with paired o and n electrons. It was shown that [Cu(CN)2]- bounds firmly with triplet carbene, if one Cu-CN bond breaks. The dissociation process occurs through a multi-step spin-crossing mechanism to reduce total spin multiplicity of the metal-carbene complex. The behavior of transition element complexes in contact with AC in aqueous solutions is determined by the following characteristics: geometrical structure of ionic complexes; nature of ligands bonded to the central atom; concentration of reactive oxygen species in solution and its pH; nature of binding sites of AC.

Jan 1, 2018

By G. W. Luxbacher

This volume describes the use of the Penn State Mine Ventilation Simulator (PSU/MVS) to model existing mine ventilation systems and, in addition, to evaluate the effect of system modifications. Ventilation survey methods designed to insure computer input data of sufficient accuracy for simulation purposes are covered in comprehensive detail, including quantity and pressure measurement and fan performance testing. The development of input data from ventilation survey results is discussed and illustrated by the use of an actual field survey. Two programs, written in FORTRAN IV with WATFIV, are presented to calculate airway head losses from altimeter pressure measurements. An existing coal mine ventilation system is analyzed and modifications to the system are simulated and evaluated. In addition the application of the PSU/MVS to non-coal mines is briefly discussed. An extensive bibliography on ventilation surveying and simulation is included.

Jan 1, 1977

By Marco Olper

The CX-EW technology, developed by B.U.S Engitec, is improved introducing besides the battery paste electrowinning, the direct electrorefining of metallic lead (grids and poles) obtained from CX breakers. This new concept of electrorefming the antimonial lead scrap is aimed to the production of 99.99 lead and of slimes with high antimony content, avoiding gaseous emissions in melting lead scrap, and expensive and pollutant thermic refining operations. In this way, practically all lead content in the battery is available as 99.99 lead, hence with a wider market for the lead recyclers. This paper will describe the tests performed on a pilot plant scale with special reference to the relatively low energy consumption of the process.

Jan 1, 1993

By Zhang Duomo

A novel homogenous precipitation method, including microwave heating, solution conductivity controlling and freeze drying, was developed for the preparation of US nanoparticles. The effects of the precipitation conditions on the structure and morphology of CdS particles were discussed individually. It was found that under the experimental conditions the particle sizes were controllable in the range of 14nm to 100nm. Blend-type CdS was obtained from nitrate or sulphate solution and the more stable wurtzite-type US was obtained from chloride solution, which was ascribed to the coordination of C1 and Cd2+ altering the supersaturation of the solution as well as the different growth units and their connecting patterns, In the precipitation process the surface of US nanoparticles were surface modified with CH3CHSCOOH. The results demonstrate that the bifunctional thiols of thioglycolic acid modified the surface through Cd-S coordination bonding and the induced counter ion AOT-SO3 as the balance charge further increased the stability and dispersity of US nanoparticles. This surface-modified US nanoparticles had been used to prepare nonlinear optics and self-assemble catalysts.

Jan 1, 2003

By Arthur B. Yates

"The nickel deposits of Sudbury, discovered in .1885, have probably commanded as much attention as any single group of orebodies in the world. They have been the major source of the world's nickel supply since 1903, when their production first surpassed that from the Pacific Island of New Caledonia. From 1903 to 1914 the production from New Caledonia remained essentially constant, whereas that from Sudbury increased from 13,000,000 to 50,000,000 pounds a year. After 1914 the production from New Caledonia gradually dropped to about 4,000,000 pounds in 1919, where it remained until 1923. During these years the Canadian production increased steadily and since 1923 has gone up at an amazing rate to a peak of over 280,000,000 pounds in 1941. Meanwhile the New Caledonia production increased to about 10,000,000 pounds until the pressure of war raised it to roughly 14,000,000 pounds a year.The Sudbury deposits, because they have been the source of 80 per cent of the world supply of nickel, because of their economic importance to the world of metals, and because they are geologically unique in their occurrence, structure, and genesis, have attracted foremost consideration and the literature relative to their geology is voluminous. This is particularly true in regard to genesis.There is a significant and interesting parallel in time between the advancement of the science of economic geology and the great expansion of the nickel industry. The controversies regarding the fundamental classification of orebodies into generalized types were in full swing during the height of the development and expansion of the great nickel mines, and the Sudbury deposits, being the most important and the only ones of the sulphide type extensively developed, have been the chief source of information in regard to this type. The observations and the conclusions drawn thereon from numerous studies of the various mines of the district have not only influenced, but are the essence of, this chapter of the science."

Jan 1, 1954

By B. Arsenault

Aluminum coatings can provide galvanic cathodic protection for several metals and alloys, In order to be a suitable protective solution on structural components, the mechanical integrity of the component must be preserved, In particular, fatigue properties are a challenge for thermal-spray protective coatings on mechanical structures, To address the issue of the fatigue integrity of 7075 aluminum alloy with an arc-sprayed protective coating, different surface preparations prior to arc spraying were considered, In the present work, a feasibility study was performed using laser ablation as a surface-preparation technique before or during arc spraying of coatings, This was collaborative effort between the LERMPS laboratory in France, the National Research Council Canada and the Royal Military College of Canada, Both fatigue and adhesive properties of aluminum coatings were evaluated in relation to substrate-surface-preparation techniques including laser ablation (Protal® process), grit blasting and shot peening. Results indicate that a combination of key conditions, including the use of nitrogen as the arc spray gas, shot peening, and proper laser energy density for ablation, provide high fatigue resistance of metallic coated 7075 alloy substrates. Specimens prepared under these conditions show a similar fatigue resistance to uncoated substrates.

Jan 1, 2005

By E. Ben-Awuah, H. Askari-Nasab, N. Al Habib

Open pit mines are getting deeper with time and transportation expenses are increasing because of the increasing haulage distance. In-pit crushing and conveying (IPCC) is getting popular in deeper open pit mines as a suitable alternative to truck haulage because it offers a lower operating cost due to shorter haulage distance and less truck requirement. Semi-mobile in-pit crusher, currently the most popular IPCC system, is relocated every two to five years and the short-term plan needs to be updated accordingly. Short-term planning with IPCC is an area of research that has not been explored extensively yet and hardly any model can generate short-term extraction sequence considering an IPCC in place. This research work proposes a mixed integer programming model to generate short-term production plan within a time horizon of 12 months. The objective of the model is to optimally allocate shovels to minimize cost of material handling and maximize revenue subject to meeting plant requirement, maximum allowable tonnage variation and IPCC location constraints to achieve production and NPV targets set by strategic plan. The proposed model has been implemented in a hypothetical case study for verification. The comparison of results between scenarios with and without IPCC is expected to justify the use of IPCC in large open pit mines from a short to medium term perspective. A semi-mobile IPCC system with one relocation is considered in the case study.

Feb 1, 2023

By M. K. Larson, J. K. Whyatt

Proper employment of numerical stress analysis design tools is based on the demonstrated ability of a model to capture key elements of the geologic site model and accurately simulate how these elements interact with a mine design. While these tools have progressed markedly, they are, at heart, a gross simplification of the abundant complexity of a natural setting and its response to mining. A generic deep longwall site model was developed that includes aspects of the geology of deep coal mines in the Wasatch Plateau and Book Cliffs coal fields of Utah. The site model contains a set of common features and observations of how these features typically respond to mining. This site model was the basis for evaluating use of empirical, boundary element and volume element stress analysis tools to analyze the distribution of stress around a deep longwall panel. More specifically, this evaluation examined shifting of stress to panel abutments and gob, distribution of stress in the abutment and deformation and failure of bridging strata. Measurements of abutment stress changes at two sites in the Wasatch Plateau region were used to illustrate model calibration. Overall, these comparisons highlight the considerable differences between methods. Volume element tools can incorporate considerable detail and have fewer underlying assumptions, but this detail carries a considerable computational cost. Boundary element tools are much more efficient. However, this efficiency comes at the cost of added assumptions. These assumptions were challenged by the presence of a strong sandstone unit in the overburden, leading to boundary element results that depart significantly from volume element results. Empirical rules are the simplest, but are even more burdened by assumptions, many of which are implicit in underlying cases. Insight into the nature and impact of underlying assumptions in each method is essential to the proper use of results in mine design.

Jan 1, 2009

By V Chamberlain, M Appeah Owusu, M Aniawu-Asumakah, A Anyimadu, R Peattie

This is an integrated geology and plant improvement study arising from the heterogeneity seen in mineralogy and gold association at the Obuasi goldmine in Ghana. This heterogeneity comes from the two ore types mined, the one being a sulphide ore, mainly composed of gold-bearing arsenopyrites. This gold is refractory and exhibits a strong relationship between gold and As. The other is quartz veins, that are high grade and free milling. The installed circuit consists of comminution – Gravity -Flotation – BIOX – Leaching and Adsorption processes. The opportunity tested involved improved mass pull - related flotation recovery of Au in the Sulphide stream; while balancing the need for a minimum Sulphide grade for the Bio-oxidation process, occasioned by the removal of 25 to 30 % of the (quartz) stream through preconcentration by Ore sorting. The current circuit is then utilized for the sulphide route, while a smaller grind-gravity circuit is utilised for the quartz stream in a relatively inexpensive way, followed by a common leaching and adsorption circuit. Added advantages of the strategy includes faster recovery of gold from the quartz stream, with less consumption of reagents from saving on flotation and BIOX reagents for this stream. Screening and Ore sorting was successfully tested with laser technology, achieving over 98% separation of quarts (containing up to 40% of the gold). The plant schedule of Ore, the suggested circuit design for the Ore sorting, the results obtained from the different flotation regimes, as well as consequent financial modelling have been presented and discussed in this paper. This illustrates the opportunity that arises out of a detailed analysis of material versus installed circuits, even if the gains in pre-concentration do not necessarily involve rejection of gangue material. An added opportunity for future investigation, briefly discussed but not tested in this paper, would be to maintain current mass pulls but with increase in throughput (by the space created by the sorted material). This will of course require the mining ability. It could also add LOM value by altering the cut-off grade.

Nov 10, 2020

By C. A. Jeffrey, K. Pearson

Abstract - The Croft diorite in central England belongs to a suite of Caledonian igneous rocks collectively known as the South Leicestershire diorite complex. Although the intrusions occupy separate outcrops, they are linked at depth to form a single pluton, buried beneath a cover of Triassic sediments (Le Bas, 1972; 1982, Allsop and Arthur, 1983). Both the Caledonian diorites and the overlying sub-Triassic unconformity have been affected by a complex history of alteration and mineralization which can be subdivided into four stages: (1) deuteric effects, caused by the release of volatiles during magmatic cooling; (2) albitization through sodic enrichment; (3) formation of lowtemperature laumontite, analcime and calcite veins with associated wall-rock alteration to prehnite and pumpellyite; and (4) sub-Triassic unconformity-hosted base metal, manganese and palygorskite mineralization. Zeolite mineralization occured some 200 Ma later than the intrusion itself, during post-Triassic times, as indicated by the presence of a single vein of laumontite and microcrystalline calcite which cross-cuts the sub-Triassic unconformity surface and enters the overlying Triassic sediments. Evidence from fluid inclusion work indicates that two fluids were involved in the deposition of the zeolite veins. One fluid was initially of relatively high temperature (~100°C to 320°C) and low salinity (~0.2 to 5.9 wt% NaCl equiv.), and was probably meteoric in origin, whereas the other was of relatively low temperature (~41°C to 165°C) and high salinity (~0.4 to 16.72 wt% NaCl equiv.), and is interpreted to represent a basinal brine. During Triassic rifting, thinning and fracturing of the crust, with the possible rise of associated magmas (Halliday and Mitchell, 1984), could have increased permeability and heat flow, initiating the circulation of hydrothermal fluids. Triassic unconformity-hosted base-metal mineralization in Central England is similar to other Triassic-Jurassic mineralization in Europe (Mitchell and Halliday, 1976).

Jan 1, 1997

By C. A. Jeffrey, K. Pearson

The Croft diorite in central England belongs to a suite of Caledonian igneous rocks collectively known as the South Leicestershire diorite complex. Although the intrusions occupy separate outcrops, they are linked at depth to form a single pluton, buried beneath a cover of Triassic sediments (Le Bas, 1972; 1982, Allsop and Arthur, 1983). Both the Caledonian diorites and the over-lying sub-Triassic unconformity have been affected by a complex history of alteration and mineralization which can be subdivided into four stages: (1) deuteric effects, caused by the release ofvolatiles during magmatic cooling; (2) albitization through sodic enrichment; (3) formation of low-temperature laumontite, analcime and calcite veins with associated wall-rock alteration to prehniteand pumpellyite; and (4) sub-Triassic unconformity-hosted base metal, manganese and palygorskite mineralization. Zeolite mineralization occured some 200 Ma later than the intrusion itself, duringpost-Triassic times, as indicated by the presence of a single vein of laumontite and microcrystallinecalcite which cross-cuts the sub-Triassic unconformity surface and enters the overlying Triassic sediments. Evidence from ?uid inclusion work indicates that two ?uids were involved in the deposition of the zeolite veins. One ?uid was initially of relatively high temperature (~100°C to 320°C) and lowsalinity (~0.2 to 5.9 wt% NaCl equiv.), and was probably meteoric in origin, whereas the other wasof relatively low temperature (~41°C to 165°C) and high salinity (~0.4 to 16.72 wt% NaCl equiv.),and is interpreted to represent a basinal brine. During Triassic rifting, thinning and fracturing of the crust, with the possible rise of associated magmas (Halliday and Mitchell, 1984), could have increased permeability and heat ?ow, initiating the circulation of hydrothermal ?uids. Triassic unconformity-hosted base-metal mineralization in Central England is similar to other Triassic-Juras-sic mineralization in Europe (Mitchell and Halliday, 1976).

Jan 1, 1997

By R. Melley, P. Wissner

The paper looks at the basic theory of tri-bological wear and the role played by the lubricant and its additives. It presents the argument that the “real cost of lubrication” is not the purchase price of the oil or grease, but rather the costs associated with not using the correct lubricant. A number of examples are presented, covering oils, greases and additives, in which a detailed evaluation of the application has shown that when all of the benefits of using the best lubricant/additive are evaluated, the savings achievable greatly surpass the incremental cost of the superior lubricant. One of the emerging classifications of costs in industry today are those associated with environmental protection. Two of the examples used describe the replacement of more conventional lubricants with environmentally acceptable products, compounded to compete in all aspects of serviceability, but which have the added bonus of being not only biodegradable but also of being of low toxicity.

Jan 1, 1997

By Robert R. Unterberger

The purpose of this paper is to summarize the research of the past sixteen years on three distinct methods of probing into solid rock. The first method is to use radar of the appropriate frequency. The second method is to use sonar. The third method is of recent vintage and uses techniques of nonlinear sonar also known as parametric sonar. The first two concepts, that of radar and sonar, are common to most people. Very few have heard of nonlinear sonar. Each of the probing techniques were investigated in order to overcome deficiencies in the former technique. Each has its advantages and disadvantages. It should be emphasized that all of these techniques for probing (or seeing) into rock are used in mines, and generally speaking not from the surface. Only in very special cases, such as certain very dry parts of Egypt or Peru, or, for example, the surface of the moon, will these probing techniques work from the surface. The reason for the development of these probing techniques has been to alert miners to possible hazards ahead of mining. Such hazards may be (1) old (unknown) boreholes connected with high pressure water zones above, (2) fractures that might connect to the Gulf of Mexico above the mine, (3) water-filled fractures that threaten the safety of miners, or (4) the discovery of dry faults ahead that can disrupt the planning of future operations.

Jan 1, 1983

By C. L. Karr

Establishing suitable control of pH, a requirement in a number of mineral and chemical industries, poses a difficult problem because of inherent nonlinearities and frequently changing process dynamics. Researchers at the U.S. Bureau of Mines have developed a technique for effectively controlling such systems. This technique successfully combines the process control capabilities of fuzzy logic and the search capabilities of genetic algorithms. Fuzzy logic offers an effective mechanism for handling nonlinearities, while genetic algorithms can provide fuzzy logic controllers with real-time adaptive capabilities. This Bureau-developed technique is applied to a laboratory acid-base neutralization experiment. Nonlinearities in the laboratory system are associated with the logarithmic pH scale and the changing process dynamics are due to alterations in pH and buffering capacity input solutions. Results indicate fuzzy logic controllers augmented with genetic algorithms offer a powerful alternative to conventional process control techniques in such nonlinear, rapidly changing systems.

Jan 1, 1992

By R. E. Chaney

This report summarizes the research on the Strategic and Critical Materials Program tasks conducted at the Idaho National Engineering Laboratory (INEL) between Mdy 1983 and April 1984. The work is divided into two areas: 1. Production Technologies - Tasks directed at developing advanced extraction technologies ? Biologically-Assisted Minerals Processing ? Metal/Gas Reactions and Thermal Plasmas ? Dehydration of Aluminum Chloride Hexahydrate. 2. Conservation/Substitution Technologies - Tasks directed toward establishing the technical processing base which will permit the use of advanced materials ? Joining of Rapidly Solidified Alloys (RSA) ? Joining of Silicon Nitride-Based Ceramics ? Nondestructive Evaluation of Ceramic and RSA Joints and Materials.

Jan 1, 1984

By A. Bieg, M. Samson, Z. Bell, A. Zinsser, J. Schuyler

As the world progresses toward the renewable energy transition, the demand for minerals increases exponentially. According to the International Energy Agency (IEA) 2021 Net Zero by 2050 Report, critical mineral production needs to grow six times to combat climate change. It’s estimated that four to seven percent of global greenhouse gas (GHG) emissions come from the mining sector’s Scope 1 and 2 (direct and indirect) emissions. Including Scope 3 (upstream, downstream, and embedded) emissions, the sector accounts for 28% of global GHG emissions. In a typical mining operation, diesel fuel is the biggest source of direct GHG emissions, and haulage is often the main source of diesel emissions. Large haul trucks have been the industry standard for over 50 years and offer flexibility, relatively low capital cost (especially with equipment lease options), and guaranteed technology with known maintenance. The challenge will be to justify their continued use when there are more economical options that lead to significant reductions in GHG emissions. The purpose of this study is to compare five haulage options in terms of GHG emissions, using the methodology defined by the Greenhouse Gas Protocol Scopes 1, 2, and 3 (Category 2). Additionally, this analysis compares operating and capital costs associated with the five haulage options (emerging and proven technologies): 1) Diesel-Electric Haul Trucks, 2) Battery-Electric Haul Trucks, 3) Fuel Cell Haul Trucks, 4) Railveyor, and 5) Conveyor. This analysis looks at the emissions and costs associated with operating the equipment (fuel and electricity), the embedded emissions and costs associated with the construction and installation of the equipment itself, and the associated infrastructure (roads, powerlines, and rail).

Feb 1, 2023

By E. D. Glass, R. C. Hessing

The volume of gas in storage reservoirs may be compuled from estimates of hydrocarbon pore volume and gas density. However, both are dificult 10 estimate accurrately. Further, no adequate method has been presented for estimating reservoir performance during operation for Volumetric gas-storage reservoirs. Normally, gas-storage reservoirs exhibit small pressure gradients in the area conr(zilliitg the storage wells, even under conditions of maximum injection or withdrawal. A zone of low permeability usally surrounds, and is in communication with, tile permeable zone which causes the storage reservoir to exhibit a definite pressure lag, as evidenced by lack of pressure stabilization after extended periods of shut-in. An analysis is presented for determining pore volume and gas in place, and for predicting future reservoir behavior of such reservoirs. The mathematical development is presented and a solution is shown for an operating storage reservoir. INTRODUCTION Depleted gas reservoirs arc often used for gas storage. The reservoir usually contains a permeable area in which numerous storage wells arc located. The permeable zone permits high deliverability and injectivity with relatively small pressure loss. However, pressure equilibrium may not be attained even after long periods of shut-in because of the fact that the permeable zone is in communication with an adjacent tight section. Most of these gas-storage reservoirs are sand lenses, such as ancient beaches or offshore bars. The areal geometry of these reservoirs is normally such that flow in the tight zone will be approximately linear, and the solutions presented here should apply. DISCUSSION For purposes of this paper, a gas-storage reservoir is considered to consist of a volume of permeable rock in communication with tight rock, all of which is surrounded by an impermeable barrier. Pressure gradients across the permeable zone are small due to low flow resistance and well density. Hence, the permeable zone is considered to be at a uniform pressure which is only a function of time as gas is injected or withdrawn. The tight zone is considered to be linear with uniform permeability and porosity, and the pressure in the tight zone is a function of both position and time. l'wo solutions for flow in this system are used to define the reservoir and determine its properties. The first solution is for an infinite linear tight zone in communication with the permeable zone. The expression for constant gas-withdrawal rate is Eqs. I and 2 ore superposed to account for varying rates of production or injection and are used to fit gas-storage field reservoir history. The solution for the infinite case, Eq. 1, is first applied to field data for early times following a shut-in period. Constants BDa and c are ohtained by a least-squares fit of pressure and rate data. After the pressure wave from gas injection or withdrawal reaches the external boundary of the tight zone, the infinite solution will no longer apply and pressure behavior should be more nearly represented by Eq. 2 for a gas reservoir in communication with a finite linear tight zone. The values of the constants found from curve-fitting Eq. 1 to the early time data may then be used in Eq. 2 that only the coefficient- L containing the unknown