Experimental study of the effects of a multistage pore-throat structure on the seepage characteristics of sandstones in the Beibuwan Basin:Insights into the flooding mode

To investigate the relationship between grain sizes, seepage capacity, and oil-displacement efficiency in the Liushagang Formation of the Beibuwan Basin, this study identifies the multistage pore-throat structure as a crucial factor through a comparison of oil displacement in microscopic pore-throat experiments. The two-phase flow evaluation method based on the Li-Horne model is utilized to effectively characterize and quantify the seepage characteristics of different reservoirs, closely relating them to the distribution of microscopic pores and throats. It is observed that conglomerate sandstones at different stages exhibit significant heterogeneity and noticeable differences in seepage capacity, highlighting the crucial role played by certain large pore throats in determining seepage capacity and oil displacement efficiency. Furthermore, it was found that the displacement effects of conglomeratic sandstones with strong heterogeneity were inferior to those of conventional homogeneous sandstone, as evidenced by multiple displacement experiments conducted on core samples with varying granularities and flooding systems. Subsequently, core-based experiments on associated gas flooding after water flooding were conducted to address the challenge of achieving satisfactory results in a single displacement mode for reservoirs with significant heterogeneity. The results indicate that the oil recovery rates for associated gas flooding after water flooding increased by 7.3%-16.4% compared with water flooding alone at a gas-oil ratio of approximately 7000 m^(3)/m^(3). Therefore, considering the advantages of gas flooding in terms of seepage capacity, oil exchange ratio, and the potential for two-phase production, gas flooding is recommended as an energy supplement mode for homogeneous reservoirs in the presence of sufficient gas source and appropriate tectonic angle. On the other hand, associated gas flooding after water flooding is suggested to achieve a more favorable development effect compared to a single mode of energy supplementation for strongly heterogeneous sandstone reservoirs.

Modified Sadowski formula-based model for the slope shape amplification effect under multistage slope blasting vibration

Blasting operations,which are crucial to open-pit mine production due to their simplicity and efficiency,require precise control through accurate vibration velocity calculations.The conventional Sadowski formula mainly focuses on blast center distance but neglects the amplification effect of blasting vibration waves by terraced terrain,from which the calculated blasting vibration velocities are smaller than the actual values,affecting the safety of the project.To address this issue,our model introduces the influences of slope and time into Sadowski formula to measure safety through blast vibration displacement.In the northern section of the open-pit quartz mine in Jinchang City,Gansu Province,China,the data of a continuous blasting slope project are referred to.Our findings reveal a noticeable vibration amplification effect during blasting when a multi-stage slope platform undergoes a sudden cross-sectional change near the upper overhanging surface.The amplification vibration coefficient increases with height,while vibration waves within rocks decrease from bottom to top.Conversely,platforms without distinct crosssectional changes exhibit no pronounced amplification during blasting.In addition,the vibration intensity decreases with distance as the rock height difference change propagates.The results obtained by the proposed blast vibration displacement equation incorporating slope shape influence closely agree with real-world scenarios.According to Pearson correlation coefficient(PPMCC)analysis,the average accuracy rate of our model is 88.84%,which exceeds the conventional Sadowski formula(46.92%).

Multistage hydraulic fracturing of a horizontal well for hard roof related coal burst control:Insights from numerical modelling to field application

Multistage hydraulic fracturing of horizontal wells(MFHW)is a promising technology for controlling coal burst caused by thick and hard roofs in China.However,challenges remain regarding the MFHW control mechanism of coal burst and assessment of the associated fracturing effects.In this study,these challenges were investigated through numerical modelling and field applications,based on the actual operating parameters of MFHW for hard roofs in a Chinese coal mine.A damage parameter(D)is proposed to assess the degree of hydraulic fracturing in the roof.The mechanisms and effects of MFHW for controlling coal burst are analyzed using microseismic(MS)data and front-abutment stress distribution.Results show that the degree of fracturing can be categorized into lightly-fractured(D≤0.3),moderately fractured(0.3<D≤0.6),well-fractured(0.6<D≤0.9),and over-fractured(0.9<D≤0.95).A response stage in the fracturing process,characterized by a slowdown in crack development,indicates the transition to a wellfractured condition.After MFHW,the zone range and peak value of the front-abutment stress decrease.Additionally,MS events shift from near the coal seam to the fractured roof layers,with the number of MS events increases while the average MS energy decreases.The MFHW control mechanisms of coal bursts involve mitigating mining-induced stress and reducing seismic activity during longwall retreat,ensuring stresses remain below the ultimate stress level.These findings provide a reference for evaluating MFHW fracturing effects and controlling coal burst disasters in engineering.

Characteristics and demographic factors of traditional Chinese medicine constitution types among elderly individuals in China:A national multistage cluster random study Author links open overlay panel

Objective To reveal the distribution characteristics and demographic factors of traditional Chinese medicine(TCM)constitution among elderly individuals in China.Methods Elderly individuals from seven regions in China were selected as samples in this study using a multistage cluster random sampling method.The basic information questionnaire and Constitution in Chinese Medicine Questionnaire(Elderly Edition)were used.Descriptive statistical analysis,chi-squared tests,and binary logistic regression analysis were used.Results The single balanced constitution(BC)accounted for 23.9%.The results of the major TCM constitution types showed that BC(43.2%)accounted for the largest proportion and unbalanced constitutions ranged from 0.9%to 15.7%.East China region(odds ratio[OR]=2.097;95%confidence interval[CI],1.912 to 2.301),married status(OR=1.341;95%CI,1.235 to 1.457),and managers(OR=1.254;95%CI,1.044 to 1.505)were significantly associated with BC.Age>70 years was associated with qi-deficiency constitution and blood stasis constitution(BSC).Female sex was significantly associated with yang-deficiency constitution(OR=1.646;95%CI,1.52 to 1.782).Southwest region was significantly associated with phlegm-dampness constitution(OR=1.809;95%CI,1.569 to 2.086).North China region was significantly associated with inherited special constitution(OR=2.521;95%CI,1.569 to 4.05).South China region(OR=2.741;95%CI,1.997 to 1.3.763),Central China region(OR=8.889;95%CI,6.676 to 11.835),senior middle school education(OR=2.442;95%CI,1.932 to 3.088),and managers(OR=1.804;95%CI,1.21 to 2.69)were significantly associated with BSC.Conclusions This study defined the distribution characteristics and demographic factors of TCM constitution in the elderly population.Adjusting and improving unbalanced constitutions,which are correlated with diseases,can help promote healthy aging through the scientific management of these demographic factors.

Comprehensive evaluation of chemical breakers for multistage network ultra-high strength gel

Polymer gels have been accepted as a useful tool to address many sealing operations such as drilling and completion,well stimulation,wellbore integrity,water and gas shutoff,etc.Previously,we developed an ultra-high strength gel(USGel)for medium to ultra-low temperature reservoirs.However,the removal of USGel is a difficult problem for most temporary plugging operations.This paper first provides new insights into the mechanism of USGel,where multistage network structure and physical entanglement are the main reasons for USGel possessing ultra-high strength.Then the effects of acid breakers,encapsulated breakers,and oxidation breakers(including H_(2)O_(2),Na_(2)S_(2)O_(8),Ca(ClO)_(2),H_(2)O_(2)+NaOH,Na_(2)S_(2)O_(8)+NaOH,and Ca(ClO)_(2)+NaOH)were evaluated.The effects of component concentration and temperature on the breaking solution were studied,and the corrosion performance,physical simulation and formation damage tests of the breaking solution were carried out.The final formulation of 2%-4%NaOH+4.5%-6%H_(2)O_(2) breaking solution was determined,which can make USGel completely turn into water at 35e105C.The combinations of“acid t breaking solution”,“acid+encapsulated breaker”and“encapsulated breaker+breaking solution”were evaluated for breaking effect.The acid gradually reduced the volume of USGel,which increased the contact area between breaking solution and USGel,and the effect of“4%acid+breaking solution”was 23 times higher than that of breaking solution alone at 35C.However,the acid significantly reduced the strength of USGel.This paper provides new insights into the breaking of high-strength gels with complex network structures.

Multistage Triaxial Behavior of Shallow Landslide Hazard Site Soil of Rangamati Sadar Area, Bangladesh

The soil samples were collected from a shallow landslide hazard site of the Rangamati Sadar in Bangladesh to determine the shear strength properties of the soil. Multistage triaxial consolidation undrained test has become worldwide more accepted to determine the shear strength parameters. Multistage triaxial undrained tests were performed on five samples taken from five different depths of boreholes. Samples were evaluated under two natural conditions and three remolded situations. Samples were consolidated before shearing at confining pressures from 50 kPa to 1200 kPa. All the test results are discussed in terms of deviator stress versus axial strain, mean effective stress versus deviator curves, stress ratio versus axial strain, and excess p. w. p. versus axial strain curves. The samples consolidated at low effective stress first displayed peak positive values of excess p. w. p., followed by increased strains due to sample bulging failure, and only a few samples formed a shear surface failure. The strength parameters were estimated using the maximum deviator stress as the failure criterion i.e. the overall value of the cohesion is 20 kPa and the friction angle is 34°. Hence, the critical state line has been constructed and the critical state parameters have been calculated. The critical state stress ratio M was calculated to be 0.036. The shear strength of soil is one of the significant mechanical properties that are thoroughly used to assess the landslide and liquefaction potentiality of the soil.

Multistage Stochastic Programming Model for the Portfolio Problem of a Property-Liability Insurance Company

The current portfolio model for property-liability insurance company is only single period that can not meet the practical demands of portfolio management, and the purpose of this paper is to develop a multiperiod model for its portfolio problem. The model is a multistage stochastic programming which considers transaction costs, cash flow between time periods, and the matching of asset and liability; it does not depend on the assumption for normality of return distribution. Additionally, an investment constraint is added. The numerical example manifests that the multiperiod model can more effectively assist the property-liability insurer to determine the optimal composition of insurance and investment portfolio and outperforms the single period one.

Multistage Extension and Age Dating of the Xiaoqinling Metamorphic Core Complex,Central China

Abstract There are two extensional systems in the Xiaoqinling metamorphic core complex (XMCC). One is the detachment fault system developed along the peripheries of the XMCC, which extended in an ESE-WNW direction and whose upper plate moved towards the WNW. The other extensional system includes the retrograde shear zones and normal faults developed within the XMCC, which represent the collapse of the XMCC. Ar-Ar and K-Ar dating shows that the extension of the detachment fault system continued from 135 to 123 Ma, i.e. in the late stage of its evolution at about 127 Ma. The collapse represented by the extensional system within the XMCC was operative during 120–106 Ma, and its main activity occurred about 116 Ma ago. These suggest that the XMCC experienced two extensional stages in its evolution, i.e., the syn-orogenic regional extension and post-orogenic collapse extension.

Microstructure Design of High-Entropy Alloys Through a Multistage Mechanical Alloying Strategy for Temperature-Stable Megahertz Electromagnetic Absorption

Developing megahertz(MHz)electromagnetic wave(EMW)absorption materials with broadband absorption,multi-temperature adaptability,and facile preparation method remains a challenge.Herein,nanocrystalline FeCoNiCr_(0.4)Cu_(0.2) high-entropy alloy powders(HEAs)with both large aspect ratios and thin intergranular amorphous layers are constructed by a multistage mechanical alloying strategy,aiming to achieve excellent and temperature-stable permeability and EMW absorption.A single-phase face-centered cubic structure with good ductility and high crystallinity is obtained as wet milling precursors,via precisely controlling dry milling time.Then,HEAs are flattened to improve aspect ratios by synergistically regulating wet milling time.FeCoNiCr_(0.4)Cu_(0.2) HEAs with dry milling 20 h and wet milling 5 h(D20)exhibit higher and more stable permeability because of larger aspect ratios and thinner intergranular amorphous layers.The maximum reflection loss(RL)of D20/SiO_(2) composites is greater than-7 dB with 5 mm thickness,and EMW absorption bandwidth(RL<-7 dB)can maintain between 523 and 600 MHz from-50 to 150℃.Furthermore,relying on the“cocktail effect”of HEAs,D20 sample also exhibits excellent corrosion resistance and high Curie temperature.This work provides a facile and tunable strategy to design MHz electromagnetic absorbers with temperature stability,broadband,and resistance to harsh environments.

Bayesian synthetic evaluation of multistage reliability growth with instant and delayed fix modes

In the multistage reliability growth tests with instant and delayed fix modes, the failure data can be assumed to follow Weibull processes with different parameters at different stages. For the Weibull process within a stage, by the proper selection of prior distribution form and the parameters, a concise posterior distribution form is obtained, thus simplifying the Bayesian analysis. In the multistage tests, the improvement factor is used to convert the posterior of one stage to the prior of the subsequent stage. The conversion criterion is carefully analyzed to determine the distribution parameters of the subsequent stage＇s variable reasonably. Based on the mentioned results, a new synthetic Bayesian evaluation program and algorithm framework is put forward to evaluate the multistage reliability growth tests with instant and delayed fix modes. The example shows the effectiveness and flexibility of this method.

Charcoal Production via Multistage Pyrolysis

Interests in charcoal usage have recently been re-ignited because it is believed that charcoal is a muchbetter fuel than wood. The conventional charcoal production consumes a large amount of energy due to the prolonged heating time and cooling time which contribute to the process completing in one to several days. Wood py-rolysis consists of both endothermic and exothermic reactions as well as the decomposition of the different components at different temperature range （hemicellulose： 200-260℃; cellulose： 240-350℃ and lignin： 280-500℃）. Inthis study we propose a multistagepyrolysis which is an approach to carry out pyrolysis with multiple heating stages so as to gain certain processing benefits. We propose a three-stage approach which includes rapid stepwise heating stage to a variable target temperatures of 250 ℃, 300℃, 350 ℃ and 400 ℃, slow and gradual heatingstage to a tinal temperature of 400℃ and adiabatic with cooling stage. The multi-stage pyrolysis process can save 30% energy and the processing time by using a first temperature target of 300 ℃and heating rate of 5℃.min-1 to produce a fixed-carbon yield of 25.73% as opposed to the base case with a fixed-carbon yield of23.18%.

Experimental mass transfer coefficients in a pilot plant multistage column extractor

The volumetric overall mass transfer coefficients in a multistage column have been measured using axial dispersion model for toluene–acetone–water system. The effect of operating parameters on the volumetric overall mass transfer coefficients has been investigated for both mass transfer directions. The results show that the mass transfer performance is strongly dependent on rotor speed and mass transfer direction, although only slightly dependent on phase flow rates. In addition, empirical correlations to predict the overall mass transfer coefficients have been developed. The proposed correlations based on dimensionless numbers can be considered as a useful tool for the possible scale up of the multistage column extractor.

Experimental study on the working performance of different milling tools for multistage fracturing ball seats

To achieve the secondary production in multistage fracturing wells of tight oil,milling tools are usually used to remove the multistage fracturing ball seats to achieve production with a large diameter in later.In this paper,first of all,the working mechanism of milling tools for multistage fracturing ball seats was studied and a mechanical analysis model of single abrasive grain was established.Then,an experimental system for milling tools was developed,and the experimental tests of the flat,the blade,and the slope milling tool were conducted in order.Besides,the morphology of chips and the surface morphology of the workpiece after the experiment were analyzed.Also,the working performance of milling tools was evaluated from the perspectives of working safety,working efficiency,and wear resistance of the milling tool.The results show that the torque of the milling tool increases nonlinearly with the increase in the cutting depth of the abrasive grain and increases linearly with the increase in the cutting width.Also,the chips are irregular particles and the size is mainly from 10 to 50μm.So,the chips should be pumped up with a small pump pressure and a large displacement.Besides this,the cutting depths of the abrasive grains are from 216.20 to 635.47μm and the bottom surface of the milling tool should be eccentric to avoid the zero point of cutting speed.Furthermore,the torque of the slope milling tool is 23.8%larger than that of the flat milling tool,which is also 30.4%smaller than that of the blade milling tool.Compared with the flat milling tool,the working efficiency of the blade milling tool improves by 79.9%and the slope milling tool improves by 111.1%.Also,the wear resistance of the blade milling tool decreases by 102.7%,while the slope milling tool declines by 32.6%when compared with the flat milling tool.Therefore,the slope milling tool has the characteristics of moderate torque,stable working conditions,the highest working efficiency,and fine wear resistance,which is preferably used to mill multistage fracturing ball seats.This study provides a theoretical basis and guidance for milling multistage fracturing ball seats on-site and realizing production with a large diameter in later stages of multistage fracturing wells.

Multistage Enrichment of the Sawafuqi Uranium Deposit: New Insights into Sandstone-hosted Uranium Deposits in the Intramontane Basins of Tian Shan, China

Meso-Cenozoic intracontinental orogenic processes in the Tian Shan orogenic belt have significant effect on the sandstone-hosted uranium deposits in the intramontane basins and those adjacent to the orogen. The Sawafuqi uranium deposit, which is located in the South Tian Shan orogenic belt, is investigated to reveal the relationships between uranium mineralization and orogenies. Recent exploration results show that the Sawafuqi uranium deposit has tabular, stratiform, quasi-stratiform, and lens-like orebodies and various geological characteristics different from typical interlayer oxidation zone sandstone-hosted uranium deposits. Systematic studies of ore samples from the Sawafuqi uranium deposit using a variety of techniques, including thin section observation, a-track radiograph, electron microprobe and scanning electron microscope, suggest that uranium mineralization is closely related to pyrite and organic matter. Mineralization-related alterations in the host rocks are mainly silicification and argillation including kaolinite, illite （and illite-smectite mixed layer） and chlorite. Tree stages of mineralization were identified in the Sawafuqi uranium deposit： （i） uranium-bearing detritus and synsedimentary initial pre-enrichment; （ii） interlayer oxidization zone uranium mineralization; and （iii） vein-type uranium mineralization. The synsedimentary uranium pre-enrichment represents an early uranium enrichment in the Sawafuqi uranium deposit, and interlayer oxidation zone uranium mineralization formed the main orebodies, which are superimposed by the vein-type uranium mineralization. Combining the results of this study with previous studies on the Meso-Cenozoic orogenies of South Tian Shan, it is proposed that the synsedimentary uranium pre-enrichment of the Sawafuqi uranium deposit was caused by Triassic Tian Shan uplift, and the interlayer oxidation zone uranium mineralization occurred during the Eocence-Oligocene period, when tectonism was relatively quiet, whereas the vein-type uranium mineralization took place in relation to the strong orogeny of South Tian Shan since Miocene.

Paleoproterozoic Multistage Metamorphic Ages Registered in the Precambrian Basement Rocks at the Southeastern Margin of the North China Craton and Their Geological Implications

The Precambrian basement rocks in the Bengbu and neighboring areas, located at the southeastern margin of the North China Craton, occur as granulite terrains and xenoliths in the Mesozoic dioritic porphyry.

Variable selection-based SPC procedures for high-dimensional multistage processes

Monitoring high-dimensional multistage processes becomes crucial to ensure the quality of the final product in modern industry environments. Few statistical process monitoring(SPC) approaches for monitoring and controlling quality in highdimensional multistage processes are studied. We propose a deviance residual-based multivariate exponentially weighted moving average(MEWMA) control chart with a variable selection procedure. We demonstrate that it outperforms the existing multivariate SPC charts in terms of out-of-control average run length(ARL) for the detection of process mean shift.

Bionic Design and Analysis of a Novel Quadruped Robot with a Multistage Buffer System

Large quadruped mammals,such as ruminants,have outstanding motion ability,including running and bounding.These advanced motion abilities are related to the buffer effect of their complicated musculoskeletal systems.However,the buffer effect of most bio-robots is not satisfactory owing to the simple design of their buffer systems.In this paper,a physiological analysis of the ruminant musculoskeletal system is presented to explain the intrinsic buffer mechanism of motion.Based on the physical buffer parts of the ruminant limbs,the corresponding bionic mappings were determined.These mappings were used to guide the mechanism design of the robot multistage buffer system.The multistage buffer system includes two main buffer mechanisms:the first stage and the second stage.The buffer mechanism analysis of the first stage and multiple stages is discussed in theory to compare the effects between the normal single buffer system and the novel multistage buffer system.Then,the detailed mechanical structure of the limbs was designed based on the limb mechanism design.To further verify the superior efficacy of the multistage buffer system,the corresponding walking simulation experiments were conducted after the virtual prototype of a quadruped robot with a novel limb was built completely.Both theoretical analysis and simulation experiments prove that the bionic robot design with the novel multistage buffer system achieves better motion performance than the traditional robot buffer design and can be regarded as the design template of the robot limb.

FINITE ELEMENT SIMULATION AND OPTIMIZATION OF MULTISTAGE WARM/HOT FORMING FOR OUTER RACE

A multistage warm/hot forming is simulated for the cross grove outer race ofconstant velocity joint, using a thermo-mechanical coupled rigid viscoplastic finite element method,and specially some problem for process development and die design are analyzed. A forming testshows that computed results have good agreement with experimental results. Above obtained resultscan be applied to development of multistage warm/hot forming process and die design for outer race.

Multistage mineralization in the Haoyaoerhudong gold deposit, Central Asian Orogenic Belt: Constraints from the sedimentary-diagenetic and hydrothermal sulfides and gold

The Central Asian Orogenic Belt,as one of world-class gold economic belts,preserves a number of giant,large black shale-hosted gold deposits,while it is still debated for origin of sulfides and gold mainly due to lack of identification for multiple stages of sulfides.The Haoyaoerhudong gold deposit is hosted in a sequence of Mesoproterozoic carbonaceous and pyritic slate,phyllite,and schist that form a tight syncline along the north margin of the North China Craton.Detailed petrography of the host rocks and mineralization have defined five stages of pyrites.The earliest form of pyrite(Py_(1))occurs as fine-grained dispersed pyrite in black carbonaceous slate and medium-to coarse-grained disseminated pyrite in pyrite-rich layers,contains relative low gold and high arsenic content,indicating a syn-sedimentary or diagenetic in origin.Stage Ⅱ pyrite(Py_(2))occurs with garnet and quartz inclusions and Py_(3) occurs as pyrite veins,contains higher gold and lower As content,and are interpreted to have formed from the dissolution-reprecipitation of Py_(1) during the peak metamorphism or post-peak metamorphism.Stage Ⅳ pyrite(Py_(4))from the pyrite-quartz veins crosscut the metamorphic garnet,contains the highest gold concentrations and other trace elements,and is considered to have formed post-peak metamorphism.Abundant native gold,electrum,and maldonite occur as inclusions within Py_(4) and monazite and in fractures that crosscut garnet.While,Py_(5) with typical remobilized feature is thought to be a product of melting of former pyrites(Py_(1) to Py_(4))triggered by the large-scale Hercynian magmatism.The sedimentary/diagenetic Py_(1) have δ^(34)S values that range from +12.4‰to +16.2‰.Later generations of sulfides,including Py_(2) to Py_(5),and Ccp_(2) to Ccp_(3),have δ^(34)S values from +9.5‰to +12.7‰.Monazite with maldonite inclusions from quartz-pyrite veins yielded an intercept age of 341.3±6.6 Ma,while coarse grained monazite associated biotite along fractures in the reefs yielded an intercept age of 254.6±8.2 Ma.The paragenetic,textural,chemical,and isotopic data suggest three distinct gold producing episodes at Haoyaoerhudong gold deposit.Gold and arsenic were clearly initially concentrated in organic muds,and enriched along the structures of diagenetic arsenic-rich pyrite.Subsequently,accompanying metamorphism and deformation,gold was liberated from the dissolution of diagenetic pyrites to form the pyrite veins.Finally,accompanying transformation of pyrite into pyrrhotite,gold was released into the metamorphic fluids to become concentrated as native gold,electrum,and maldonite in pyrite-quart veins.Monazite with age of 341 Ma from quartz-pyrite veins suggests that the third major gold mineralizing event in Haoyaoerhudong occurred before the Hercynian magmatism,suggesting that the Haoyaoerhudong deposit is a typical orogenic gold deposit rather than intrusion-related deposit.

Numerical assessment on improving multistage centrifugal impeller performance by changing inlet skew angle at impeller inlet

Multistage centrifugal impellers with four different skew angles were investigated by using computational fluid dynamics.The purpose of this work is to investigate the influences of lean angle at the blade tip of the impeller inlet.Four variations of lean angles,that is,8°,10°,15° and 20°,were made at first stage impeller.Reynolds Average Navier Stokes equation was used in simulation together with a shear?stress transport(SST) k-w turbulence model and mixing-plane approach,respectively.Three dimensional fluid flows were simplified using periodic model to reduce the computational cost and time required.A good performance was expected that the secondary flow can be effectively reduced in the flow passage of the impeller without excessive increase in manufacturing cost caused by the secondary flow.The results show that secondary flow affects the main flow intricately to form vortices or having non-uniform velocity in the flow passage,which in turn results in substantial fluid energy loss not only in the impeller but also in the guide vane downstream of impeller.The numerical solutions were performed and allowed the optimum design and operating conditions to be obtained.