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By J. C. Martin

Stmplified equations are developed for the flow of fluids in gas drive reservoirs in which the effects of gravity can be neglected. The results show that the pressure distribution is governed by a nonlinear heat flow type of equation, and the saturation distributions are related to the pressure by the same equations QS those developed by Muskat for the average pressure and saturations in gas drive reservoirs. Unrler certain conditions the equation for the pressure can be approximated by the linear form of the heat flow equatlon. This equation tk analogous to the equation for the pressure in single-phase compressible flow The analysis reveals that the equation for the pressure in n~ultiphase flows can be obtained directly from the equation for the pressure in slngle-phase flows by simply replacing the single-phase compressibility by the total compressibility and the single-phase mobility by the sum of the mobilities of all the fluids present. Perrine's method of pressure buildup analysis for multiphme flows is based on these same substitutions. Thus, the development presented in this paper constitutes a theoretical justification for Perrine's method of pressure buildup analysis. One of the most difficult problems associated with the production of oil is the determination of the flow of the fluids within the reservoirs. One purpose of this paper is to present the development of simplified equations for the flow in gas drive reservoirs. The other purpose is to present some of the needed theoretical foundation for the methods currently being used in the analysis of multiphase pressure buildup data. The analysis presented in this paper makes use of a partial linearization of the equations governing multiphase flows. It is felt that the process of linearizing or partially linearizing the nonlinear equations of multiphase flows can lead to useful results since this process has proved extremely valuable in the study of other fields of science and engineering where nonlinear equations are encountered. Pressure buildup data of shut-in wells have been used for many years to estimate the static reservoir pressure. These data have also been used in studying the aver- age permeability both away from and close to the well-bores. The majority of the buildup data are obtained from wells producing two or three fluids. As yet the theoretical foundations for the methods of buildup analysis used in connection with rnultiphase buildup data have not been established. A number of methods of analysis of pressure buildup data have been developed." Most of these methods apply only to single-phase flows, and almost all of the theoretical analysis is confined to single-phase flows. Perrine' developed a method of analysis for rnultiphase flows from the method for single-phase flows of Miller, Dyes, and Hutchinson.' He did this by simply replacing the single-phase compressibility by the multiphase compressibility and replacing the single-phase mobility by the sum of the mobilities of the fluids in the rnultiphase flows. Obviously, such a procedure lacks a certain amount of theoretical justification, and such practices can lead to erroneous results. Fortunately, Perrine's results have a theoretical justification, and this justification is presented in the following discussion. It is assumed that gravitational effects and the cornpressibility of the rock can be neglected. Under these assumptions the equations governing the simultaneous flow of gas, oil and water in porous media areo* The preceding equations can be expanded into the following expressions.

By Edward A. Barrett, Roberta A. Calhoun

MORE THAN 30 MILLION EMPLOYEES each year are exposed to hazardous occupational noise, and approximately one-third of them develop permanent hearing loss (NSC, 2000). Possible explanations for the latter statistic include worker regard for noise as a mere nuisance rather than as an occupational safety and health hazard, and consequent neglect of established protective measures (e.g., hearing protection); lack of knowledge concerning noise; improper use of hearing protection; worker indifference; and inadequate training (Bauer & Babich, 2004). Many drill rigs generate high sound levels, which vary according to the type of machine, its location with respect to the physical surroundings, and the location of the sound measured around the rig. A NIOSH study measured noise output from several types of drill rigs during field investigations (Ingram & Matetic, 2003). Two types of data were recorded the actual noise generated by the drill rig at various positions around the rig and the noise to which the drill operator was exposed during the drilling cycle. For the latter, sound level measurements up to 120 dBA were recorded while hammering casing (metal on metal) in drilling a water well (Photo 1). Several types of administrative controls exist to address worker exposure to loud drill rig noise. Rotating duties to decrease exposure time and posting warning signs in high-noise work areas are two such controls. Another is the use of hearing protection. Worker use of hearing protection has been disappointing, however. One study by the University of Michigan found that construction workers used earplugs and earmuffs only between 36% and 61% of the time that they were necessary (Lusk & Kerr, 1998). In a 2001 study, OSHA reported a relatively low rate of 30.4% for use of earplugs among construction workers (Walker, 2001). Why are rates for hearing protection use so low? One explanation may be workers' lack of concern for noise in the workplace. They expect workplace noise to be a loud and in¬ evitable nuisance and, therefore, accept it as part of the job. As a result, they disregard proven measures that can protect their hearing. Other workers may use hearing protection, but do so improperly. They may misguidedly remain in high-noise areas for extended periods thinking they are protected when in fact they are not. Other reasons for low use and/or misuse of hearing protection include poor education, lack of awareness and inadequate training (Nash, 2003). To address the training issue, NIOSH developed two exercises from which drillers can learn about noise, hearing loss and hearing protection. The first is an invisible ink exercise, titled "Drill Rig Incident" (DRI) (Photo 2); the second is a 3-D slide reel training aid, "Wearing Hearing Protection Properly" (WHPP) (Photo 3). DRI is an instructor-

By Kermit G. Davis, Sean Gallagher, William S. Marras, Kimberly Kovacs

This study evaluated spinal loads associated with lifting and hanging heavy mining cable in a variety of postures. This electrical cable can weigh up to 10 kg per metre and is often lifted in restricted spaces in underground coal mines. Seven male subjects performed eight cable lifting and hanging tasks, while trunk kinematic data and trunk muscle electromyograms (EMGs) were obtained. The eight tasks were combinations of four postures (standing, stooping kneeling on one knee, or kneeling on both knees) and two levels of cable load (0 N or 100 N load added to the existing cable weight). An EMG-assisted model was used to calculate forces and moments acting on the lumbar spine. A two-way split-plot ANOVA showed that increased load (p<0.05) and changes in lifting posture (p<0.05) independently affected trunk muscle recruitment and spinal loading. The increase in cable load resulted in higher EMG activity of all trunk muscles and increased axial and lateral bending moments on the spine (p < 0.05). Changes in posture caused more selective adjustments in muscle recruitment and affected the sagittal plane moment (p < 0.05). Despite the more selective nature of trunk EMG changes due to posture, the magnitude of changes in spinal loading was often quite dramatic. However, average compression values exceeded 3400 N for all cable lifting tasks.

By Eti Purwaningsih, Widi Astuti, Erik Prasetyo

Selective-reductive leaching of manganese from low-grade manganese ore using tannic acid as a reductant in acidic media was demonstrated by XRD, SEM-EDX characterization, and batch leaching studies at room temperature. The pH change in the liquid phase before and after leaching revealed that selectivity of manganese over iron was due to the hydrolysis of iron. The acidity in the liquid phase during leaching was dictated by two mechanisms: proton-consuming reaction (manganese oxide reduction by tannic acid) and proton-producing reaction (ferric ion reduction by tannic acid to produce ferrous ion). Based on the leaching studies, the more prevalent reaction between these two was determined by initial leaching conditions: tannic acid concentration, sulfuric acid concentration, liquid-solid ratio, temperatures, and agitation time. Kinetic studies revealed that maximum recovery was attained within 6-h agitation, which indicated a product layer diffusion process.

By Gerald T. Homce, James C. Cawley

Problem: CFOI and SOII data show that 2,287 U.S. workers died and 32,807 workers sustained days away from work due to electrical shock or electrical burn injuries between 1992 and 1998. Method: The narrative, work activity, job title, source of injury, location, and industry for each fatal electrical accident were examined. A primary causal factor was identified for each fatality. Results: Electrical fatalities were categorized into five major groups. Overall, 44% of electrical fatalities occurred in the construction industry. Contact with overhead power lines caused 41 % of all electrical fatalities. Discussion: Electrical shock caused 99% of fatal and 62% of nonfatal electrical accidents. Comprising about 7% of the U.S. workforce, construction workers sustain 44% of electrical fatalities. Power line contact by mobile equipment occurs in many industries and should be the subject of focused research. Other problem areas are identified and opportunities for research are proposed. Impact on Industry: Improvements in electrical safety in one industry often have application in other industries.

In redesigning the cyanide plant at Mount Torrens, in conjunction with Mr. L. W. Grayson, the manager, several minor alterations were introduced in order to have the operations under thorough control, and these having proved serviceable may be of sufficient interest to merit a description here. The lixiviation vats, though only 8 feet in diameter, were retained, but the pipes leading away from the bottom were reduced from two inches to half-an-inch in diameter, and had a fall to the zinc boxes of about 4 feet. As these small pipes were completely filled by the solutions fiowing away from the vats, they exerted a suction equal to their fall and thus hastened the rate of flow, so that tailings containing a larger proportion of slimes could be treated than was possible where the larger pipes were used, as, there not being sufficient fiow of solution to keep the latter filled, no suction could be obtained with them. It was found that with&apos;most of the tailings treated a sufficient flow could be obtained from the half-inch pipes when the taps on, them were only one-third to half open. The lower end of each of these pipes was connected by means on indiarubber tubing with the sille hole of 11 in aspirator bottle, and to the mouth of this bottle a few feet of similar tubing was connected, so that the solutions coming through could be directed into either of the fixed tubes leading respectively to the waste water tank the strong solution zinc boxes or the weak solution zinc boxes.In working the vats, the following method was found to give good results. While filling the vats with tailings the taps were left open, so that the water might drain off into the waste water tank the surface of the tailings was carefully levelled. When the strong solution was run in at the top, the air contained in the interstices of the tailings was forced through the half-inch pipe at the bottom as a strong blast, instead of, as I believe js usual, escaping by means of channels formed by it through the tailings, and thus tending, it would appeal, to render the disposition of the tailings less even and to make.

By D. Parks, A. Miller, M. McNinch, R. Jacksha

Each year, hundreds of mine workers are involved in machinery-related accidents. Many of these accidents involve inadequate or improper use of lockout/tagout (LOTO) procedures. To mitigate the occurrence of these accidents, new safety methods are needed to monitor access to hazardous areas around operating machinery, improve documentation/monitoring of maintenance that requires shutdown of the machinery, and prevent unexpected startup or movement during machine maintenance activities. The National Institute for Occupational Safety and Health (NIOSH) is currently researching the application of Internet of Things (IoT) technologies to provide intelligent machine monitoring as part of a comprehensive LOTO program. This paper introduces NIOSH’s two phase implementation of an IoT-based intelligent machine monitoring system. Phase one is the installation of a proof-of-concept system at a concrete batch plant, while phase two involves scaling up the system to include additional sensors, more detailed safety/performance metrics, proximity detection, and predictive failure analysis.

By Kray Luxbacher, Mario Karfakis, Erik Westman, Peter Swanson

Three-dimensional velocity tomograms were generated to image the stress redistribution around an underground coal longwall panel to produce a better understanding of the mechanisms that lead to ground failure, especially rockbursts. Mining-induced microseismic events provided passive sources for the three-dimensional velocity tomography. Surface-mounted geophones monitored microseismic activity for 18 days. Eighteen tomograms were generated and high-velocity regions correlated with high abutment stresses predicted by numerical modeling. Additionally, the high-velocity regions were observed to redistribute as the longwall face retreated, indicating that velocity tomography may be an appropriate technology for monitoring stress redistribution in underground mines.

By Donald P. Tuchman, Justin R. Patts, Emanuele G. Cauda, Andrew B. Cecala, Elaine N. Rubinstein

Video techniques for monitoring exposure, such as NIOSH’s “Helmet-CAM,” employ both real-time dust monitors and mobile video cameras to assess workers’ respirable dust exposures. Many real-time personally worn dust monitors utilize light scattering sensing elements, which are subject to measurement biases as a function of dust type (size, composition, shape factor) and environmental conditions such as relative humidity. These biased and inaccurate dust measurements impair the monitor’s ability to properly represent actual respirable dust concentrations. In the testing described, instrument mass concentration data was collected using three different types of commonly used commercial off-the-shelf personal dust monitors and compared to a reference standard. This testing was performed in a calm air (Marple) dust chamber in which three units of each make and model (for a total of nine monitors) were used for each test. Equivalency factors (EF, a multiplier to match the Thermo TEOM 1400a reference instrument) ranged between 0.746 and 1.879 across all dusts and environmental conditions tested, and between 0.821 and 1.519 on the ISO test dust.

By M. Sadegh Safarzadeh, Stanley M. Howard

The two-dimensional predominance area (Kellogg) diagram (PAD) surfaces bounding the three-dimensional Cu-As-S-O system were constructed at 900 K. The computations employed gases As4O6(g), O2(g), and SO2(g) as the independent coordinate species to generate diagrams of As4O6(g) − O2(g),O2(g) − SO2(g), and As4O6(g) − SO2(g), while the third gas (As4O6, O2, or SO2) was fixed. The results indicate that there is no shared boundary between enargite (Cu3AsS4) and copper sulfate (CuSO4); however, at PO2 < 10−6 atm, PAs4O6 < 10−10 atm, and PSO2 > 10−4 atm, CuSO4 is the stable phase at 900 K. The chemical driving force for oxidation of intermediate phases between enargite and copper sulfate is substantial except for basic sulfate (CuO · CuSO4).

By Tyler Acorn, Brandon Wilson, Jeff Boisvert

Scenario-level uncertainty is a representation of large-scale differences encountered when considering ultimate mining pits optimized over various subsets of stochastic realizations. Accounting for scenario-level uncertainty allows mine plans to be assessed against several probabilistic subsurface interpretations. Scenario-level uncertainty is found through clustering stochastic geostatistical realizations and optimizing final pits across the realizations in each cluster. Where these pits are geometrically different, plans for each scenario differ. Knowing these differences allows the value of each planning alternative to be assessed based on the value and relative probability of each scenario. These results also facilitate the use of formal decision-making frameworks for planning, leading to optimization that better represents the full statistical characterization of the deposit. An example utilizing this approach evaluates both infrastructure placement and drilling program requirements. In both cases, scenario-level uncertainty improves initial plans by limiting opportunity costs and identifying additional potential.

By L. McWilliams, L. D. Patts, J. D. Noll, S. E. Mischler

Elemental carbon (EC) is currently used as a surrogate for diesel particulate matter (DPM) in underground mines since it can be accurately measured at low concentrations and diesels are the only source of submicrometer EC in underground mines. A disadvantage of using EC as a surrogate for DPM is that the fraction of EC in DPM is a function of various engine parameters and fuel formulations, etc. In order to evaluate how EC predicts DPM in the underground mining atmosphere, measurements of total carbon (TC; representing over 80% of the DPM) and EC were taken away from potential interferences in four underground metal/non-metal mines during actual production. In a controlled atmosphere, DPM mass, TC, and EC measurements were also collected while several different types of vehicles simulated production with and without different types of control technologies. When diesel particulate filters (DPFs) were not used, both studies showed that EC could be used to predict DPM mass or TC. The variability of the data started to increase at TC concentrations below 230, µg/m3 and was high (>+20%) at TC concentrations below 160 µg/m3, probably due to the problem with sampling organic carbon (OC) at these concentrations. It was also discovered that when certain DPFs were used, the relationship between DPM and EC changed at lower DPM concentrations.

By Martin Herrenknecht

After the successful breakthrough at the end of 2006 of both TBMs into the multifunctional site Faido (MFS), in the middle of 2007 the two tunnel boring machines resumed the 12 km long section between Faido and Sedrun. In the roughly a 10 month interval both approximately 465 m long tunnel boring machines were partly dismantled, pushed through the 2.5 km long MFS, rebuilt for the new larger diameter of 9.5 m and reassembled to be ready for operation. In the rebuilding phase, improvements were made to the equipment, especially as a result of experience gained from the previous 14 km long drive in the section Bodio and taking into account the latest information regarding the upcoming 14 km section Faido. Both TBM drives are currently in the rock formations of the Lucomagno gneiss, which stretch over a section of 3.5 km from the MFS Faido to the predicted Piora Syncline. This section is divided into two fold axes of the Chièra Synform, where the Lucomagno gneiss pass from a sub-horizontal into vertical bedding. The drives, with current rock overburdens exceeding 1,500 m and, as known from the excavation phase of the MFS, in part highly disturbed rock formations, are characterized by the locally intense rock squeezing conditions with large convergences in the vicinity of the driving TBM as well as backwards due to the interaction of the two drives. High expenditure for the support measures, reduced driving performances together with extensive extra work associated with deadlines and increased costs are the result. In the paper the previous experience with the TBM drives in the section Faido and the challenges still awaiting us are presented and discussed.

By Sebastiaan Peelman

NdFeB permanent magnets are the best available magnets used in many technology applications. However, at their end-of-life (EoL) most of magnets and the contained REEs are lost during the recycling of the bulk metals. The REEs are classified as the most critical raw materials in the European Union, and recycling of REEs from EoL products will reduce their criticality and contribute to the sustainability of REE. Various technological routes have been reported, but most of the methods are effective for highly concentrated magnets or magnet scrap, which is greatly dependent on expensive pre-dismantling processes. This paper presents various innovative metallurgical solutions to the effective REE recovery from current industrial practice for WEEE recycling, including the ferrous scrap from WEEE shredder products and shredder residues from computer hard disk drives. Both hydrometallurgical and combined hydro- and pyrometallurgical REE recovery routes are developed after demagnetization and physical upgrading.

By Ashis Bhattacherjee, Rahul Upadhyay, Nearkasen Chau, Aditya Kumar Patra, Dhanjee Kumar Chaudhary

Heavy earth-moving machineries used in open-pit mines intensively expose the drill operators to whole-body vibration and shocks and thus to musculoskeletal disorders. The roles of an individual, machine, and rock-related factors in their exposure remain poorly understood. This cross-sectional study investigated their role among 39 drill operators from Indian iron ore mines. It shows that 70% of the operators were exposed to high levels of vibration, above the limit values recommended by ISO 2631-1. Multiple linear regression models showed that the whole-body vibration and shock exposures were strongly associated with operator’s age, drill machine model, rock’s hardness, uniaxial compressive strength, and density. The role of body mass index was close to significance (p = 0.08). Univariate analyses found that drill’s age, seat pad thickness, and seat backrest height were also strong predictors. These results help in identifying risky operators, materials and occupational situations, and in implementing appropriate prevention and intervention to reduce and monitor the exposures and health risk.

By W. R. Reed, J. A. Organiscak

Haul trucks have the potential to generate large amounts of respirable dust. This respirable dust has been shown to be a health hazard to personnel, especially if it has a high silica content. Lack of dust sampling data from haul trucks prompted the completion of a study to quantify respirable dust concentrations. These field studies were conducted measuring instantaneous respirable dust at stationary locations from passing haul trucks at a stone quarry and at a coal mine site. Fugitive dust levels from haul trucks were analyzed to characterize dust dispersion. This analysis indicates safe following distances for haul trucks and other heavy equipment to avoid overexposure of respirable dust from the lead haul truck.

By Steven Putt

Seismic While Drilling (SWD) is a newly developed technology in the mining industry. Improving upon Measurement While Drilling (MWD) systems, SWD measures mechanical properties of the rock at incremental depths down a blast hole at a much higher resolution. SWD is also immune to common failures and inconsistencies of MWD such as operator and drill specific variation. Seismic While Drilling records the velocity and elastic modulus of the rock with centimeter accuracy in real-time. These properties measured while drilling blastholes are then used as a proxy for density which can be used for: • High resolution geologic modeling • 3D ore control • Drill and blast optimization • Drill to mill tracking One of the distinct challenges with SWD systems is the sheer volume of information acquired. With thousands of measurements per blasthole, the data can be overwhelming for even an experienced engineer. To overcome this complex challenge, the latest cloud computing and analytics models have been simplifying and organizing the data. These newer technologies can amplify an engineer’s capability by delivering actionable insights into their drilling and blasting workflows. The paper presents new results from Datacloud during recent Seismic While Drilling trials in iron ore, metallurgical coal, and hard rock mines around the world. The measurements are compared with wireline geophysical logs, core data, drill cuttings, and conventional measurement while drilling (MWD) systems to validate the technology and show how the data can be used.

Colloidal interactions play a critical role in mineral processing, including grinding, physical separation (particularly flotation), dewatering, and tailings management. Despite great energy input in comminution to liberate valuables from gangues, heterocoagulation between valuables and gangues would prevent the separation of valuables from gangues. On the other hand, selective coagulation/flocculation to increase the size of desired fine particles could enhance physical separation and dewatering, while dispersion is needed for fine grinding. To control the state of colloidal dispersions by creating favorable conditions, it is of paramount importance to study colloidal interactions in a relevant system and understand underlying mechanisms. This review summarizes recent advances in developing the-state-of-the-art techniques and novel methods of measuring colloidal forces, including atomic force microscope, surface force apparatus, zeta potential distribution measurement, quartz crystal microbalance with dissipation, and our recently developed integrated dynamic force apparatus. The basic principle of each technique was introduced first, followed by a summary of critical information derived for the relevant mineral processing systems. Finally, the pros and cons of each technique were discussed to emphasize the use of complementary techniques that assist in solving fundamental problems in mineral processing.

By F. N. Kissell

The machine-mounted continuous respirable dust monitor (MMCRDM) is a fixed-location area sampling device developed for possible use at the working face of an underground coal mine. This device, based on proprietary technology known as the tapered element oscillating microbalance, has evolved over the past eight years through a cooperative effort of the former Bureau of Mines, MSHA, and the Rupprecht & Patashnick Company in Albany, NY. The capability to measure respirable coal mine dust levels on a continuous basis, rather than depending solely on periodic samples obtained from the traditional coal mine dust samplers, has been a goal in the mining industry for nearly two decades. Recently, an extensive series of laboratory and underground tests was conducted by NIOSH with the cooperation of MSHA and coal operators to test the performance of the MMCRDM In preliminary laboratory testing, the MMCRDM seemed to work well. However, in every underground test, when compared to reference samplers placed close to the inlet, the MMCRDM failed to meet the 25% accuracy criterion specified in the contract under which it was developed. Two reasons explain this failure: First, in most tests the bias (the relative discrepancy between the average MMCRDM concentration and the average reference sampler concentration) was too great. Second, the variability of the samplers used for reference comparison was too large. Finally, the underground testing of the MMCRDMs showed that they are quite unreliable at this stage of development. In the majority of mine tests, no more than 10 shifts of data were taken before the MMCRDM failed to function properly. Major breakdowns, requiring the return of the MMCRDM to the factory for repairs, occurred on average every 28 days. To be considered mine-worthy, MMCRDM reliability must be substantially improved. KEYWORDS Dust, coal dust, dust instrumentation, dust sampling, dust monitoring, black lung, pneumoconiosis

By M. Mortada

Nonsteady-state flow of slightly compressible liquids in porous media of non-uniform properties has been the subject of a number of recent studies. Most of these studies considered one-dimensional flow in systems with cylindrical geometry and with the properties of the porous medium varying with radial distance only. A. Houpeurt&apos; studied the problem in its general form by examining the solutions of the differential equation, In Eq. 1, the permeability k and the porosity + are arbitrary functions of radial distance. Houpeurt concluded that, except for special forms of the functions k and the problem is not well suited for mathematical treatment, but lends itself to high-speed digital computation. Carslaw and Jaeger&apos; discussed the solution of Eq. 1 for the case in which the permeability varies as a power of the radial distance. P. Albert3 studied analytically the pseudo steady-state solutions in systems of finite radial extent and non-uniform properties. He also obtained some numerical solutions for nonsteady-state flow using a high-speed computer. William Hurst4 examined the interference pressure drop due to a point sink located in an infinite system consisting of two permeability regions in series. In this case, the permeability changed at a radial distance r from the point sink. INTERFERENCE BETWEEN OIL FIELDS IN A NON-UNIFORM AQUIFER The interference pressure drop for oil fields located in an extensive aquifer of uniform properties is discussed in a number of places in the literature. This work considers the interference pressure drop for oil fields located in a non-uniform extensive aquifer comprising two regions of different properties as shown in Fig. 1. Region I of the aquifer extends from which is the radius of Oil Field A, to ar,,, where a>1. It has permeability k,, porosity +, and effective compressibility c,. Oil Field B is located in Region II which extends from ar, to infinity and has different properties from those of Region I, but the same formation thickness h. Region II has permeability k2, porosity and effective compressibility c2. The choice of this type of aquifer should not imply that it is of frequent occurrence. It is chosen primarily to illustrate the effects of non-uniform aquifer properties on oilfield interference. It is of interest to point out that a non-uniform radial aquifer in which both the permeability and the porosity are inversely proportional to the radial distance can be treated in a manner similar to a linear aquifer of uniform properties. The situation where only the permeability varies as the inverse of the radial distance is also amenable to analytical treatment. Both aquifers behave quite differently from a radial aquifer with uniform properties so far as the water influx and the interference pressure drop are concerned. METHOD OF SOLUTION The expression for the interference pressure drop in Oil Field B due to a constant rate of water influx in Oil Field A is developed in the Appendix. This is accomplished by the simultaneous solution of two partial differential equations describing the pressure in Regions I and 11. The two differential equations are solved subject to the following conditions: (1) at r,, the pressure gradient is constant; (2) at ar the pressure and