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By M. Tanaka, K. Aoki, T. Mori, H. Morioka, K. Iwano, T. Kanagawa

To estimate the detailed characteristics of the rock around the cavern during excavation, new monitoring technique for dynamic properties of the rock has been applied. In this paper, micro-seismic monitoring and AE monitoring technique are applied to the excavation of large underground rock cavern and the result was discussed to clarify the acutal behavior of EDZ around the cavern. Zur Einschätzung der Gesteinseigenschaften um die Ausschachtung herum haben die Autoren eine Technik eingesetzt, mit der die physikalischen und dynamischen Änderungen im Gestein um den Schacht während der Ausschachtung beobachtet werden. In der vorliegenden Studie wurde zur mikroseismischen Überwachung ein AE Überwachungsverfahren eingesetzt und die Autoren berichten über die Veränderungen in den Gesteinseigenschaften um die Ausschachtung herum. Dans le but d'évaluer en détail les propriétés des roches qui forment les parois des cavernes creusées, les auteurs ont utilisé une technique de mesure permettant d’observer les modifications physico-dynamiques des roches aux alentours de la caverne pendant son excavation. Dans le cadre de cet article, une technique de surveillance de l’agitation et du bruit microséismiques a été mise en œuvre et les auteurs font état de la modification des propriétés de la roche environnante.

Jan 1, 2003

By C. D. Haynes, S. C. Gambrell

The practice of roof bolting in WORLD-WIDE mining activities is very well-known, having been used extensively for over 50 years. The theory of roof bolting, however, is extremely complicated, and only recently have investigators attempted to explain the theory. Various means of stress analysis have been utilized in rock mechanics, most of which reduce rock to an isotropic, homogeneous medium that can be easily analyzed. One of the indirect research methods is the photo-elastic technique, the theory of which is widely known and needs no elaboration. This technique has been used extensively to examine the state of stress around underground openings of various shapes in certain types of strata, and under various loading configurations.'-" In-Situ Mine Roof Trusses The photoelastic technique was employed here to evaluate the state of stress above a mine opening where support is provided by the in-situ mine roof truss. This support configuration, shown in Fig. 1, has gained popularity in recent years, particularly in mines with bad roof conditions." To the authors' knowledge, no scientific determination has been made of the advantages roof trusses may offer over conventional bolting configurations comparable to roof trusses. Ordinary mine roofs usually sag or bulge downward soon after mining. Normally, after some movement the roof begins to stabilize, but the face of this bulging mine rock is usually in tension and will almost always fail unless supported. Because rock fails easily in tension, it is desirable to "preload" the roof, that is, to impress a compressive force on the mine roof to prevent bulging and subsequent tensile failure. Ordinary rock bolting installations, particularly if the bolting is perpendicular to the mine roof plane, do not produce a preloading effect. Although bolting installations squeeze the strata together and produce a beam effect desirable for support, they do not have the advantage of actual uplift. They pull down at the anchorage point with a force equal to the bolt tension which sometimes causes a separation in the plane of the anchorage detrimental to roof strength. In-situ mine roof trusses require the installation of steel tension rods in the roof of the mine much the same as conventional roof bolts, except that the rods are arranged to produce a stress pattern above the upper surface of the opening similar to that of a prestressed beam. The roof rock acts to transmit the compression force. The simplest form of truss consists of two steel rods anchored to the back of holes drilled at an angle of approximately 45 over the mine pillars. These rods are collared near the middle of the room, and the lower ends of the rods are connected by tie rods and turn-buckles. Used in this manner, a small-diameter steel rod can provide essentially the same support as a wide-flange steel beam. By tightening the turnbuckles, an uplift on the roof can be produced. Objective of the Investigation The objective of this investigation was to determine qualitatively the state of stress that exists above a mine roof after the installation of the in-situ mine roof truss vs. that of two angle roof bolts, hereafter referred to as "roof bolts," drilled and placed in the same configuration, that is, 45" above each pillar and connected together in the middle of the room by a bearing member such as a steel beam. Each state of stress was to be identified, insofar as possible, as compression or tension above the mine opening. Model Construction A photoelastic model of a mine opening was coil-structed from -in. thick PLM-4B birefringent plastic and was machined to specification shown in Fig. 2. The dimensions of the opening were chosen to simulate a width-to-depth ratio of 3 to 1. Two % -in. holes were drilled at 45" angles, as shown, to provide for the loading devices. After construction, the model was annealed at 240°F to remove stresses produced during machining.

Jan 1, 1971

Analysis of rock discontinuities, collected using a scanline method, has been undertaken at the Iron Duke open cut mine, on the southern margin of the Middleback Range in the Gawler Craton, South Australia. The iron mineralisation, which is a product of supergene enrichment of carbonate sediments, is located on the W (western) limb of a gently N plunging D2 macrosyncline. Mesofolds plunge shallowly to the NE or steeply to SE, suggesting two shortening events, of which the second produced significant macrofolds. Discontinuities include:faults and shears which display variable orientations, mainly striking WNW dipping steeply N; mesofractures or joints maintaining a well constrained orientation, dipping steeply S, subvertical striking E-W; and bedding surfaces which are folded about a gently N plunging axis. Through this example of the regional control exerted on local discontinuities, it is clear that discontinuities are not randomly distributed as often assumed in purely statistical approaches. Commonly for rocks of any age there is a distinct discontinuity pattern, reflecting the geological deformation history. If the controls exerted on local rock discontinuities can be determined and assigned a number related to their significance, the way forward is available to develop a site specifc knowledge base that can make realistic predictions for any position in a given rock mass. Such a procedure would involve assessment of the regional geology, linked to scanned discontinuities either via manual or automatic means. Recent advances in automatic scanning rock faces (eg by the I-SiTE Laser Radar) to determine discontinuities distributions, enable the rapid calculation of rock characteristics. This is a significant advance in rock engineering, providing a method of safe and quick collection of data. However it creates problems in the presence of an increase in the geotechnical data available, which should be assessed in the context of the regional geology. Although techniques are underway to analyse post-blast discontinuities, the next signifant potential advance in this area could be the integration of a knowledge based system to assess discontinuities ahead of mining, incorporating regional assessment and human intuition.

Jan 1, 2000

By E. Wolmarans

Dowding, Reynard and Associates Mineral Projects (DRAMP) was approached by the ARM/Lion Ore JV during July 2006 to conduct a feasibility study and control budget estimate for a new greenfield project for their NKOMATI Nickel mine 45 km east of Machadadorp. The scope included the evaluation and review of previous studies as well as a techno-economic trade-off on four possible comminution circuits ranging from conventional crushing and ball milling to fully autogenous milling. The following document encapsulates the thought process, decisions and the references used in selecting the final comminution route for the new 375 ktpm MMZ concentrator. Apart from the pilot test work performed, design simulations from a number of sources, performance results from a recently commissioned 100 ktpm MMZ concentrator, together with an understanding of the geology and mineralogy of the orebody and possible variations in the characteristics of the orebody over the life of mine were assessed. The results from all the above-mentioned work indicated that it would be possible to treat the MMZ ore at the desired throughputs to the desired grind sizes in a fully autogenous grinding (ABC-type) circuit. Autogenous milling is generally considered to be one of the higher risk milling circuits. This is mainly due to the fact that the ore, which is utilized as the grinding media, could be variable in terms of hardness and mineralogy/geology. Nevertheless, it is a very popular route as the cost benefits, more specifically the operating cost, are normally very attractive. This is especially the case when large low grade orebodies are evaluated. In North/South America, autogenous and semi-autogenous grinding circuits have been successfully employed during the past 20 years on large scale low grade operations. Taking all the above factors into account, the DRA/Nkomati project team recommended an autogenous circuit with the option to add steel to both the primary and secondary mills (if required) for the new operation in order to create the opportunity for significant operating cost savings. One has to bear in mind that all the new design simulations and decisions are based on previous work and potential unknown variations within the orebody will never be fully understood until the pit is operational for some time.

Jan 1, 2009

By Yves St-Amour, Vince Luongo

This paper will discuss one of the largest construction projects the City of Portland has undertaken. This phase of the Willamette River Combined Sewer Overflow (CSO)project consists of approximately 18,500 ft of tunnel in soft ground, requiring the construction of six deep shafts and jet grout ground improvement. The purpose of the project is to reduce volume of combined sewerage overflows from the drainage areas on the west side of the Willamette River. Bencor-Petrifond-Pacchiosi Joint Venture was awarded a contract to design and construct six deep circular shafts, jet grout ground improvement for three bridges and jet grout ground improvement break-in/outs for some shafts. Of the six shafts the Pumping Station Shaft was the deepest and largest, requiring a permanent ground support system with a deep jet grout ground water cut-off to 335-ft deep. The joint venture used state of the art methods and equipment to achieve its objectives and build the structures through some very difficult alluvial soils to great depths next to the Willamette River. The paper will provide a general discussion of the shaft construction and jet grout ground improvement installed for this phase of the project. It will also discuss some of the technical challenges encountered while effectively managing risk and costs, resulting in a successful project completed in a timely manner.

Jan 1, 2005

By Edward D. Graf

Once the heavy work of mining, supporting and completing an underground structure is finished, there is frequently the problem of handling unwanted water infiltration into the opening. Methods of controlling the infiltration vary from collecting and channelling the inflow to shutting off the water at the surface of the opening or within the ground formation. Discussed are various methods of controlling ground water inflow from within the structure including collector pipe systems, shotcrete, cement grout, bentonite, and various chemical grouts. Case histories illustrating some of the methods and materials will be presented.

Jan 1, 1987

By D. A. Reynolds

[A few studies on the relationship of the fusion temperature of the ash of coke to that of the corresponding coal have been made on commercial high-temperature cokes. R. J. Rose3/ in 1921 compared the' fusion temperatures of the ashes of 10 coals and. the cokes produced from them and concluded tat they were in such close agreement that either figure could be used. More recently, Quarfort4/ found that the ash of coke fused at a somewhat lower temperature than that of the original coals As the ash of a coal and that of the coke produced therefrom have the same origin their chemical composition should be identical, provided that carbonization has not altered the inorganic, or ash-forming, constituents of the coal, and such alteration seems highly improbable. However, it has been shown5/ that coke is liable to contamination by iron during crushing and preparatory to sampling. Pieters6/ found that coke ash was cantaminated in this manner up to 0.4 percent. extraneous iron would lower the ash-fusion temperature because such iron may form ferrous silicate, which is readily fusible,7/ These results provide a basis for the prediction that the ash of coke will fuse at a lower temperature than that of the corresponding coil., especially if the fine grinding of the coke was done by rubbing surfaces of iron, as in a disk pulverizer or bucking plate.]

Jan 1, 1940

By P Allen, E Gleeson, D Boakye, R Chesher, S Konopa

"An EXTENDED ABSTRACT is available for download. A full-length paper was not prepared for this presentation. Not only do epithermal gold deposits provide many challenges in estimating mineral resources, the complexities of these deposits also provide technical challenges in assessing appropriate mining and processing strategies, as well as social and environmental planning and management. The characteristics of epithermal gold deposits include being highly variable with respect to geometry and gold grade distribution, the presence of other economic contributors, mineralogy, texture, rock strength, weathering and alteration overprint. These characteristics influence the economic value of mining projects in an interlinked manner. Consequently, successful exploitation of epithermal deposits requires a holistic approach, coupled with the effective integration of geological data to meet all aspects of mine development decision-making. This paper presents examples of the key technical challenges encountered in estimating and mining epithermal deposits. It also highlights why these issues need to be addressed from the viewpoint of geology, sampling, resource estimation, mine planning, mineral processing and social and environmental planning for the true value of the mining project to be realised.CITATION:Konopa, S, Chesher, R, Gleeson, E, Allen, P and Boakye, D, 2015. Challenges in maximising the value from epithermal gold deposits, in Proceedings PACRIM 2015 Congress, pp 127–132 (The Australasian Institute of Mining and Metallurgy: Melbourne)."

Mar 18, 2015

Application of Natural Zeolite for the Removal of Diethylenetriamine (DETA) and DETA-Metal Complexes from Flotation Process Water

Sep 13, 2010

By Robert A. Bradburn

The Bureau of Mines has developed a miniature, portable two-level oxygen-deficiency alarm and produced three prototype models. Each operates from a 4.2-v dc power source, and the highest current drain of any model is 80 ma. An electrochemical cell, which produces an electrical output in proportion to the partial pressure of oxygen to which it is exposed, is used as an oxygen detector. The output of the cell is applied to an electronic circuit that detects two different levels of oxygen percentage below that of normal air, and produces distinct audible signals at these levels. The hazard alarm mode is activated when the oxygen percentage first drops below normal and produces a 500-cps "beep" tone with an intermittency of 1 cps. The danger mode produces a continuous 500-cps audible signal when the oxygen percentage drops still lower.

Jan 1, 1968

By J. A. Hudson, X. D. Pan

A rock mass responds to excavation according to the properties of the intact rock, the network of contained discontinuities and the susceptibility of the rock mass to weathering. Large deformation often occurs when one of these components causes the rock mass to have a low strength relative to the stress conditions. Analysis of such large deformations forms a significant feature of current numerical modelling in rock mechanics. A practical large deformation problem of roadways in a coal mine is described, demonstrating the requirements for improving numerical techniques. The development of a numerical model is then summarised with particular attention to several concepts pertinent to large deformation analysis in geomechanics. A numerical case study is presented in which the developed finite-element model is used and the results are compared with the in-situ measurements. Conclusions are drawn for rock engineering that are also relevant to both civil engineering and mining engineering projects

Sep 1, 1991

By W. P. Diamond, S. L. Cario, F. Garcia, J. D. Byars, T. P. Mucho

The National Institute for Occupational Safety and Health (NIOSH) has been conducting research at a Pittsburgh Coalbed longwall mine to evaluate and optimize bleeder ventilation and gob gas venthole longwall methane control systems. Gas flow into these two methane control systems was investigated using a combination of Sulphur Hexafluoride (SF6) tracer gas studies and gob venthole pressure monitoring experiments. The insights gained from this research has facilitated the development of along wall subsided strata methane control system conceptual model. This model provides the basis for design suggestions to increase the efficiency of the gob gas venthole system to permit the bleeder ventilation system to become a "safety net" for methane control.

By A. L. Foote

This is the final report of work accomplished during 1973-75 under U. S. Bureau of Mines Contract No. H0242015, "System for Handling Underground Mine Supplies and Materials." The purpose of the contract was to develop a mechanical device which could safely perform handling tasks that are normally done manually in underground bituminous coal mines. The report discusses studies leading to construct-ion of a battery-operated, three-wheel vehicle with a six-degree-of-freedom manipulator. Supportive design studies included collection and analysis of production, manual functions, and injury data on the underground bituminous coal mining industry. Transfer tasks in section storage and working places were the prime candidates for mechanical handling. Functional specifications were developed for two handling devices (one to handle existing unit loads and one to handle repackaged unit loads) and for a vehicle to mount the handling device. Design concepts for nine different handling devices were developed and a cost/benefit evaluation made for each. Detail design, capital and operating costs, and method improvement savings data were developed for two battery-operated vehicles and for two different manipulators. The three-wheel vehicle with anthropomorphic manipulator was chosen for development.

Jan 1, 1978

By E. Martinez

The effect of ultrasonic energy transmitted through a liquid on chrysotile asbestos was investigated. Ultrasonic energy was effective in fiberization of chrysotile crudes as well as standard grades of milled asbestos fibers. Treated samples of several grades of milled fibers had increased wet bulk volumes and decreased settling and filtration rates compared to untreated fibers. Ultrasonics may be a method for fiberization of chrysotile without decreasing length or use of chemical additives that alter surface properties. Cavitation of the liquid on the surface of fiber bundles is believed to be the cause of the fiberization. It was found that ultrasonic energy greatly increased the rate of precipitation of latex on asbestos. When chrysotile asbestos fibers require additional opening or fiberization, the usual method employed is some type of high speed impact or grinding to open the fibers and produce a larger surface area. These methods always cause some degradation in length due to breaking of fibers. In addition, the efficiency of mechanical methods decreases as the diameter of fiber bundles decreases. Chemical methods have been proposed and it is claimed that fiberization down to individual fibers of 200-300 A diam is possible with some wetting agents. However, large amounts of reagent are required, approximately EDWARD MARTINEZ is with Central Research Laboratories, American Smelting and Refining Co., South Plain-field, N.J. TP 63H226. Manuscript, Aug. 12, 1963. Discussion of this paper, submitted in duplicate prior to Mar. 15, 1964, will appear in SME Transactions, September 1964, and AIME Transactions, 1964, vol. 229. 50 pct of the weight of fiber treated, and some of the wetting agent remains on the surface of the chrysotile and cannot be removed by any solvent which does not destroy the asbestos.' This investigation was directed at determining whether ultrasonic energy transmitted through a liquid would be effective in fiberizing chrysotile asbestos. Samples of asbestos crudes and commercially milled fibers were treated; settling and filtration rates of treated and untreated milled fibers were obtained. EQUIPMENT A Westinghouse Corp. ultrasonic cleaning system WEHH was used in this investigation. See Table I for a breakdown of this ultrasonic unit. RESULTS AND DISCUSSION Fiberization of Chrysotile Crudes: Samples of chrysotile crudes were pulled apart with tweezers so that coarse bundles of fiber approximately 1/16 in. in diam were obtained. The bundles were put into a bottle with 200 ml of methanol and the mixture placed into the ultrasonic tank for 30 min at a power output of 1200 w. The test was repeated using water instead of methanol. During the irradiation it was noted that the surfaces of the bundles were being fiberized. The liquid eventually became cloudy with dispersed solids. Fig. 1 is an electron micrograph of the fibers, some reduced to unit dimensions, and a fine material released by the ultrasonic energy. The platy particles in Fig. 1 were identified by electron diffraction and differential thermal analysis as brucite, Mg(OH)2, which must have been intergrown in the chrysotile crudes. Electron micrographs of bulk specimens of chrysotile have shown a fine material filling the interstices between tubular fibers.2,3 Electron diffraction patterns of the fine material collected after ultrasonic treatment indicate that it is amorphous. After decanting the solution, bundles of chrysotile remained somewhat decreased in diameter. Continuing the ultrasonic irradiation of the remaining material resulted in additional fiberization. The opening of the fibers occurred in both methanol and water. Cavitation of the liquid by the ultrasonic energy is undoubtedly responsible for the fiberization. When sound waves are transmitted through a liquid at a

Jan 1, 1963

By S Colak, M Tunc, C Celik, M. M. Kocakerim

The most important parameters affecting the solubility of ulexite (sodium calcium borate) in H2SO4 were found to be reaction temperature and solid:liquid ratio, in that order. Dissolution increased with increase in temperature and stirring speed and with decrease in solid:liquid ratio, particle size and acid concentration, the last effect as a result of decreased precipitation of CaSO4 on unreacted particles. Optimum conditions, in which around 99.5% of the ulexite could be dissolved, were a reaction temperature of 60 degrees C, a solid:liquid ratio of 1:8 g/ml, an acid concentration of 8 mol/l, particle size smaller than 425 micrometres, a stirring speed of 52.33/s, a reaction time of 1 800 s, a calcining time of 3 600 s and a calcining temperature of 170 degrees C. These conditions, determined by the Taguchi method, are reproducible in a commercial production environment

Jun 21, 1905

To George Orwell the year of 1984 was the inspiration for a book. To most New Zealanders it was the year that the fourth Labour Government was elected to power. It was also the year that the review of mining legislation commenced. While Orwell's book and the election of Labour are clearly events of some historic note, one could be excused for classifying the review of minerals legislation somewhat differently in terms of its present achievements! Since the review began it has led a tortuous path through a rapidly evolving policy environment to a point three years hence where no major policies have been determined.

Jan 1, 1987

By Sergio Cattalani, David J. Kerr, Harold L. Gibson

Abstract - The Horne mine was truly a world class Cu and Au deposit. Between 1927 and 1989, it produced some 260 t of Au and 1.13 Mt of Cu from 53.7 Mt of ore that averaged 2.22% Cu, 6.1 g/t Au and 13 g/t Ag. The total value of Au and Cu production from the Horne deposit at metal prices of US$300/oz Au and US$1.00/lb Cu is an outstanding US$5.2 billion. The Horne mine was also a company builder. After optioning the property from Ed Horne (Tremoy Syndicate) in 1922, the Thomson-Chadbourne Syndicate discovered the deposit in 1923 and quickly grew to become Noranda, one of the world’s premier mining companies. This discovery fuelled exploration and, along with subsequent discoveries in the Val d’Or-Cadillac camps, led to the "economic development" of northwestern Quebec. The Horne deposit influenced and continues to influence genetic models for volcanogenic massive sulfide (VMS) deposits. Early observations at Horne contributed to an epigenetic replacement theory for VMS deposits. The most recent genetic model for the Horne, invoking sub-seafloor sulfide replacement of silicified and sericitized volcaniclastic host rocks within a graben, has subsequently been proposed for another giant VMS deposit, the Kidd Creek mine. The Horne and Kidd Creek deposits show many similarities, such as localization within synvolcanic grabens, long-lived hydrothermal activity uninterrupted by volcanism, sub-seafloor replacement sulfides, stacked sulfide lenses, zone refining, silicified footwall rocks characterized by high positive ?18O values, and association with FIII rhyolites. Notable differences between the two deposits include the lack of andesitic, basaltic or komatiitic flows at Horne, different inferred water depths, high Au content at Horne versus negligible Au, but sub-economic to economic concentrations of Sn, In and Cd at Kidd Creek.

Jan 1, 2000

By L. G. Marshall

This report describes dredging and processing of sand and gravel from a glacial-fluvial deposit in the Raccoon River valley near West Des Moines, Iowa. Preliminary cleaning and separation of the sand and gravel at the dredge site with subsequent transportation to separate plants and the production and disposal of the various grades of aggregate material are also described. The geology of the deposit is summarized. A tabulated summary of costs in units of labor, power, and supplies is included.

Jan 1, 1963

By D Craw

TheSouthern Alps in the South Island of New Zealand are currently rising rapidly as a consequence of continental collision along the Pacific-Australian plate boundary. Rapid uplift has resulted in a major thermal anomaly in the shallow crust beneath the alps. Alpine topography and associated intense precipitation, coupled with the thermal anomaly are responsible for vigorous combined topographic/convective circulation of water through the shallow crust.   Uplift is greatest in a wedge-shaped region between the Alpine Fault and an associated second-order backthrust system, the Main Divide Fault Zone, approximately 20 km to the east. The Main Divide Fault Zone is segmented into NNE and NE striking faults, which are regionally sub-parallel to the Alpine Fault, but dip northwest in the opposite direction. Reverse oblique-slip on the Main Divide Fault is in an easterly direction, with a greater component of strike-slip movement on the NE trending faults. Elevated topography in the Mt Cook region is related to thrusting of a relatively homoclinal sequence of semi-schistose rocks on top of lower-grade greywacke, which controls the position of the Main Divide. Tectonically induced fluid flow resulted in only minor alteration and hydrothermal mineralisation of fault-rocks in Alpine and Main Divide Faults, and localised deposition of quartz and/or carbonate in the immediate hangingwall.   The wedge between the Alpine and Main Divide Faults is segmented by third-order structures north of the Mount Cook region. A series of right-lateral (-085/700S) and left-lateral (-150/600SW) faults, which are synthetic and antithetic to the Alpine Fault, respectively, developed as a conjugate set during uplift. Fluid-flow in the Southern Alps is controlled by these third-order fault/fracture systems. Cu-Au mineralisation, hydrothermal veins, and surface hot spring activity are localised by third-order fault/fractures and appears to be enhanced where conjugates intersect.

Jan 1, 1995

By E. B. Brauer, W. Hurst, J. D. Clark

Because of drilling, completion, and workover practices, the permeability around a wellbore generally is different from the permeability of the formation. The zone with the altered permeability is called "skin" and its effect on the pressure or flow behavior of the well is called "skin effect". Hawkinsl has shown that the radius and the permeability of this zone are related to the skin by: If the permeability in the skin zone is less than that of the formation, the skin is positive; if it is more than that of the formation, the skin is negative. If the two permeabilities are equal, s is zero; that is, there is no skin. Van Everdingen2 and Hurst3 have given mathematical solutions to the case of a zone of reduced permeability around the wellbore. This skin effect is illustrated in Fig. 1. They treat the positive skin as a zone of reduced permeability of infinitesimal thickness around the wellbore. When applied to a well with negative skin, however, their solutions lead to the calculated flowing well pressure which is smaller than the formation pressure, i.e., an injection situation. This is a physical contradiction. In this paper, it is shown that this mathematical difficulty can be overcome by assuming an effective wellbore radius larger than the actual wellbore. Existing solutions2"4 are modified to include the effect of an enlarged wellbore radius, and thus enable the engineer to deal with negative as well as positive skins. Theoretical Development Van Everdingen and Hurst,4 through the use of Laplace transformation, obtained the following expression for transient fluid influx into a wellbore: The values for QtD, reported extensively by van Everdingen and Hurst,4 are obtained from the following integral:

Jan 1, 1970