Artykuł poświęcony jest metodom określania wydatku krytycznego w odwiertach pionowych i poziomych eksploatujących ropę naftową i gaz ziemny w stanie pseudoustalonym i nieustalonym. Podano szereg zależności do ustalania wydatku krytycznego dla rozmaitych konfiguracji, tj. rodzaju odwiertu (poziomy/pionowy), charakteru dopływu medium złożowego (pseudoustalony/nieustalony) oraz rodzaju medium (gaz ziemny/ropa naftowa) opracowanych przez rozmaitych autorów, poświęcając szczególną uwagę metodzie Chaperon – jako jedynej mającej podstawy teoretyczne. Podano zaproponowane przez autorów bardzo proste wzory, które mogą służyć do orientacyjnej oceny wielkości wydatku krytycznego, i losowo porównano wyniki z otrzymanymi za pomocą metody Chaperon, stwierdzając dającą się zaakceptować rozbieżność wyników, pomimo że w modelu Chaperon w przypadku odwiertu poziomego przyjmowano inne założenia odnośnie do kształtu obszaru drenowanego przez odwiert i charakteru przepływu. Zależności te wykorzystywane są do interpretacji zachowania ciśnienia przy radialnym dopływie ropy naftowej i gazu ziemnego do odwiertu pionowego i poziomego. Podane zależności oparte są na powszechnie znanych wzorach wiążących ciśnienie denne ruchowe w odwiercie z natężeniem dopływu medium złożowego. W artykule zestawiono rozmaite korelacje służące do określania wydatku krytycznego proponowane przez rozmaitych autorów opracowane przy przyjęciu rozmaitych założeń. Rozbieżności wyników poszczególnych korelacji dla tego samego zestawu danych proponowanych przez różnych autorów mogą dochodzić do kilkuset procent, co uzmysławia złożoność zagadnienia zawadniania się odwiertów eksploatacyjnych i trudność realistycznego opisu tego zjawiska. Korelacje podane w tekście artykułu opracowano na podstawie modeli analogowych lub na podstawie badań laboratoryjnych.
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The article discusses the methods used for evaluation of the critical flow rate in vertical and horizontal wells in case of oil or natural gas flow. The transient and pseudo-steady flow is considered. Various relations used for evaluation of critical flow rate for vertical/horizontal wells proposed by several authors have been provided. Special attention has been paid to Chaperon model which is the only one having the theoretical foundation. Very simple equations which can be used for evaluation of critical flow rate, based on well-known and generally accepted equations relating the bottom hole pressure and flow rate have been proposed. Those equations relate the pressure behavior in oil and gas wells assuming the radial flow in the reservoir. Relations for vertical and horizontal wells have been provided. They can be used for approximate evaluation of critical flow rate which is the highest flow rate not causing inflow of water into oil or gas well. Of course there are discrepancies between results given by Chaperon and the proposed methods but they are not very large and are acceptable from the technical point of view. One should remember that in case of the horizontal wells the Chaperon model assumes rectangular shape of drainage area while the methods proposed in this paper use the circular drainage area and radial flow. It should be noted that the critical flow rates evaluated using various methods provided in literature and listed in this article yield results which may differ by several hundred percent for the same set of input data – this indicates the complexity of the problem of water inflow to the production wells. Equations proposed by various authors are based on the analog models or results of the laboratory experiments.
An unsteady flow and heat transmission of ionized gases via a horizontal channel enclosed by non-conducting plates in a rotating framework with Hall currents is examined using electro-magnetohydrodynamic (EMHD) two-fluid heat flow. The Hall current impact is taken into account by assuming that the gases are totally ionized, the applied transverse magnetic field is very strong. For temperature and velocity distributions in two-fluid flow regions, the governing equations are solved analytically. For numerous physical parameters such as the Hartmann number, Hall parameter, rotation parameter, viscosity ratio, and so on, numerical solutions are visually displayed. It was discovered that an increase in temperature in the two regions is caused by the thermal conductivity ratio. It was also realized that an increase in rate of heat transfer coefficient at the plates is caused by either the Hartman number or the Hall parameter.
Hall currents are used to investigate MHD unsteady two fluid flows and heat transport of plasma along a straight channel of conducting plates. In the two liquid zones, the velocity and temperature fields for the case of conducting side plates are obtained by solving the governing equations using a two-term series under the specified conditions. The distribution profiles are graphically resolved and examined. The distributions are thought to be dependent on the electron-to-total pressure ratio. The flow and heat transfer factors are also influenced by other parameters such as the Hartmann number, Hall parameter, rotation parameter, thermal conductivity and viscosity ratio.
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Trapezoidal-shaped hydrographs are typical of anthropized rivers, as this form is generally associated with the release of water from hydropower dams. To investigate how such unnatural waves can affect bedload rate, preliminary fume experiments were performed in Krakow, Poland, looking at bedload transport rate, bed shear stress and bed morphology. In addition, close-range bed surface photogrammetry was used to investigate bed changes due to the passage of the food wave. Three scenarios, having the same water volume but different wave magnitudes, were tested. The lowest wave showed almost no sediment transport and no visible changes in bed morphology, while higher waves changed the bed morphology, creating erosion and accumulation zones. The highest wave was characterized by an 8-shaped hysteresis of the bedload rate with a peak during the wave maximum. The lag time between the maximum bedload rate and the wave plateau was longer than expected due to zero-slope conditions.
This paper investigated the problems and impacts of transient flow in pipeline systems due to pump power failure. The impact of different protection devices was presented to assure surge protection for the pipeline system. A model via Bentley HAMMER V8.0 Edition was employed to analyse and simulate hydraulic transients in the pipeline system, and protection alternatives were studied. Surge protection included using only an air vessel, using an air vessel and two surge tanks, and employing five air vessels and vacuum breaker. The obtained results for pressures, heads, and cavitation along the pipeline system were graphically presented for various operating conditions. Using five air vessels with vacuum breaker valve as surge protection proved to be more effective and economical against pump power failure. Changing the flow density did not have a significant impact on the pressures. For protection with an air vessel; it was concluded that the value 40% of the original diameter for inlet pipe diameter of air vessel, and the value of 2/3 of original pipe diameter were critical values for the transient pressures. Cast iron pipes proved to be the best pipe material for all studied volumes of the air vessel. For protection with an air vessel and two surge tanks; as the inlet pipe diameters increased the maximum pressures increased and the minimum pressures decreased. Regression analyses were performed obtaining equations to predict the pressures according to the inlet pipe diameter, the area of surge tank, and the pipe diameter.
The stretching sheets with variable thickness may occur in engineering applications more frequently than a flat sheet. Due to its various applications, in the present analysis we considered a three dimensional unsteady MHD nanofluid flow over a stretching sheet with a variable wall thickness in a porous medium. The effects of radiation, viscous dissipation and slip boundary conditions are considered. Buongiorno’s model is incorporated to study the combined effects of thermophoresis and Brownian motion. The dimensionless governing equations are solved by using MATLAB bvp4c package. The impact of various important flow parameters is presented and analysed through graphs and tables. It is interesting to note that all the three boundary layer thicknesses are diminished by slip parameters. Further, the unsteady parameter decreases the hydromagnetic boundary layer thickness.
An unsteady flow and melting heat transfer of a nanofluid over a stretching sheet was numerically studied by considering the effect of chemical reaction and thermal radiation. The governing non-linear partial differential equations describing the flow problem are reduced to a system of non-linear ordinary differential equations using the similarity transformations and solved numerically using the Runge–Kutta–Fehlberg fourth–fifth order method. Numerical results for concentration, temperature and velocity profiles are shown graphically and discussed for different physical parameters. Effect of pertinent parameters on momentum, temperature and concentration profiles along with local Sherwood number, local skin-friction coefficient and local Nusselt number are well tabulated and discussed.
Pressure pipes made of selected plastics are widely used in current water supply systems. Unfortunately, the theoretical basis for modeling transient flows in these pipes has not been clarified yet. For simplified one-dimensional numerical modeling, a model is commonly used in which the total deformation of the pipe walls is expressed by the sum of instantaneous and retarded deformations. One of the main problems lies in the correct experimental determination of the creep function defining the properties of the polymer. The influence of other parameters on which the numerical solution of the method of characteristics is based is the subject of the research presented in this paper.
Developments in construction engineering (new materials, construction techniques) facilitate the design of very flexible, light structures with low damping which unfortunately results in higher susceptibility of these structures to wind action. It is therefore necessary to use more accurate scientific tools in the engineering phase of these structures. Analytical methods for considering wind effects on structures encounter difficulties with respect to mathematical formulations of aerodynamic forces. In this paper a 2D numerical model has been described which considers the fluid domain with respect to a cylindrical obstacle. This 2D model has been discretized using the finite volume method, and numerical simulations have been undertaken in order to describe the unsteady flow conditions within the analyzed domain. The simulations have been performed with boundary conditions characterizing the flow past a cylindrical obstacle. The results have been compared with the literature data from similar experiments. On the basis of the flow characteristics obtained, as well as the spatial distributions of the flow parameters, a model for further 3D analyses was selected. Next, a 3D numerical study of unsteady flow forces acting on a slender cylinder has been analyzed. Toward the end, a two-way fluid solid interaction approach has been utilized, which incorporates a computational fluid dynamics approach combined with computational solid dynamics.
In order to improve the performance of the shell and tube heat exchanger, a porous baffle and a splitter bar are employed in this research. Through the arrangement of the porous baffle in the tube-side inlet and the splitter bar in the tube, the flow distribution of liquid in the heat exchanger is improved. PIV technology is used to investigate the unsteady flow in the tube-side inlet and the outlet of different models. The porous baffle significantly improves the flow of fluid in the shell and tube heat exchanger, especially by eliminating/minimizing the maldistribution of fluid flow in the tube-side inlet. The performance of the arc baffle is better than that of the straight baffle. The splitter bar has a minimal effect on the flow field of the tube-side inlet, but it effectively improves the flow in the tube bundle and restrains the vortex generation in the tube-side outlet.
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Authors presents the integration of a one-dimensional continuity equation of a new flow model, along the trajectories of liquid planes. That was made possible by expressing the fluid velocity u with partial derivatives of the function ζ - a function which expresses the position of liquid planes in the flow relative to the positions they occupied when the fluid was at rest. Consequently, the one-dimensional continuity equation has become integrable. This work was signaled in previous authors articles with a description of the process of obtaining formulas, that showing partial derivatives of the function ζ - by integrating a one-dimensional continuum equation along the fluid plane trajectory. In addition, this work is a complement of the previous works, in which the integral of the one-dimensional continuity equation along the straight lines x = const and t = const in the rectangular coordinate system x,t were derived. This work also includes the integral of the differential equation of liquid plane trajectories expressing the function η, which keeps a constant value along these trajectories. In addition, the content of the work consists a necessary explanations and, on the end, additional proof of the derived equations.
Using the results of their earlier work the authors examine in details the issue of velocity of movement of flow front in one-dimensional transient flow. The authors identify the physical meaning of the symbols used and fragments of equations, as well define the basic properties and restrictions of the velocity of spread of the one-dimensional transient flow.
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Korzystając z wyników wcześniejszych swoich prac Autorzy rozpatrują szczegółowo zagadnienie prędkości przemieszania się czoła jednowymiarowego przepływu nieustalonego. Autorzy dokonują identyfikacji sensu fizycznego używanych symboli i fragmentów równań, a także określają podstawowe własności i ograniczenia prędkości rozprzestrzeniania się jednowymiarowego przepływu nieustalonego.
For some time, work has been underway aimed at significant simplification of the modelling of hydraulic resistance occurring in the water hammer while maintaining an acceptable error. This type of resistance is modelled using a convolution integral, among others, from local acceleration of a liquid and a certain weighting function. The recently completed work shows that during efficient calculations of the convolution integral, the effective weighting function used does not have to be characterised by large convergence with a classical function (according to Zielke during laminar flow and to Vardy-Brown during turbulent flow). However, it must be a sum of at least two or three exponential expressions so that the final results of the simulation could be considered as satisfactory. In this work, it has been decided to present certain analytical formulas using which it will be possible to determine the coefficients of simplified effective weighting functions in a simple direct way.
An analysis is presented to investigate the unsteady magnetohydrodynamic (MHD) mixed convection boundary-layer flow of a micropolar fluid over a vertical wedge in the presence of thermal radiation and heat generation or absorption. The free-stream velocity and surface temperature are assumed to be oscillating in magnitude but not in the direction of the oncoming flow velocity. The governing equations have been solved by two distinct methods, namely, the finite difference method for the entire frequency range, and the series solution for low frequency range and the asymptotic series expansion method for the high frequency range. Numerical solutions provide a good agreement with the series solutions. The amplitudes of skin friction and couple stress coefficients are found to be strongly dependent on the Richardson number and the vortex viscosity parameter. The Prandtl number, the conduction-radiation parameter, the surface temperature parameter and the pressure gradient parameter significantly affect the amplitudes of skin friction, couple stress and surface heat transfer rates. However, the amplitudes of skin friction coefficient are considerably affected by the magnetic field parameter, whereas the amplitudes of heat transfer rate are appreciably changed with the heat generation or absorption parameter. In addition, results are presented for the transient skin friction, couple stress and heat transfer rate with the variations of the Richardson number, the vortex viscosity parameter, the pressure gradient parameter and the magnetic field parameter.
W artykule przedstawiono analizę numeryczną niestacjonarnego pola przepływowego w modelu turbinowego uszczelnienia labiryntowego w rzeczywistych warunkach pracy dla dwóch różnych struktur uszczelnienia labiryntowego z okładziną o strukturze plastra miodu oraz ze ścianą gładką. Oprócz strat przecieku, obszar ten jest szczególnie istotny z uwagi na zjawisko generacji hałasu szerokopasmowego powstałego w wyniku turbulentnych zjawisk przepływowych. Wyniki przedstawiono jako wielkości akustyczne w funkcji częstotliwości. Pozwoliło to na określenie częstotliwości głównych, przy których zaistniały ich szczytowe wartości. Dodatkowo porównano zmianę bezwymiarowej wartości przecieku w czasie. Wyniki obliczeń wskazały wpływ zastosowanej struktury uszczelnienia na tłumienie fluktuacji ciśnienia oraz wartości przecieku przy różnych prędkościach obrotowych wirnika.
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This work aims to perform detailed time-dependent flow analysis of gas turbine stage model equipped with tip labyrinth seal against honeycomb or smooth land, in order to identify the noise generated aerodynamically. Two different sealing structures were investigated – honeycomb structure and smooth land. The main scopes of this investigation were evaluation of unsteady flow field behaviour, indication regions were the vorticity and broadband noise is generated. Also an impact of the sealing structure on the flow behind the rotor was checked. To evaluate results, acoustic pressure – p’ and Sound Pressure Level (SPL) values were used. Discharge coefficient, as a measure of non-dimensional leakage has also been inquired and compared. The results shown an influence of honeycomb structure, and rotational velocity of rotor on pressure fluctuations and noise damping.
An unsteady MHD two-layered fluid flow of electrically conducting fluids in a horizontal channel bounded by two parallel porous plates under the influence of a transversely applied uniform strong magnetic field in a rotating system is analyzed. The flow is driven by a common constant pressure gradient in a channel bounded by two parallel porous plates, one being stationary and the other oscillatory. The two fluids are assumed to be incompressible, electrically conducting with different viscosities and electrical conductivities. The governing partial differential equations are reduced to the linear ordinary differential equations using two-term series. The resulting equations are solved analytically to obtain exact solutions for the velocity distributions (primary and secondary) in the two regions respectively, by assuming their solutions as a combination of both the steady state and time dependent components of the solutions. Numerical values of the velocity distributions are computed for different sets of values of the governing parameters involved in the study and their corresponding profiles are also plotted. The details of the flow characteristics and their dependence on the governing parameters involved, such as the Hartmann number, Taylor number, porous parameter, ratio of the viscosities, electrical conductivities and heights are discussed. Also an observation is made how the velocity distributions vary with the rotating hydromagnetic interaction in the case of steady and unsteady flow motions. The primary velocity distributions in the two regions are seen to decrease with an increase in the Taylor number, but an increase in the Taylor number causes a rise in secondary velocity distributions. It is found that an increase in the porous parameter decreases both the primary and secondary velocity distributions in the two regions.
We consider the time dependent Hartmann flow of a conducting fluid in a channel formed by two horizontal parallel plates of infinite extent, there being a layer of a non-conducting fluid between the conducting fluid and the upper channel wall. The flow formation of conducting and non-conducting fluids is coupled by equating the velocity and shear stress at the interface. The unsteady flow formation inside the channel is caused by a sudden change in the pressure gradient. The relevant partial differential equations capturing the present physical situation are transformed into ordinary differential equations using the Laplace transform technique. The ordinary differential equations are then solved analytically and the Riemann-sum approximation method is used to invert the Laplace domain into time domain. The solution obtained is validated by comparisons with the closed form solutions obtained for steady states which have been derived separately and also by the implicit finite difference method. The variation of velocity, mass flow rate and skin-friction on both plates for various physical parameters involved in the problem are reported and discussed with the help of line graphs. It was found that the effect of changes of the electric load parameter is to aid or oppose the flow as compared to the short-circuited case.
The paper aims to analyze the heat transfer aspects of a two-layered fluid flow in a horizontal channel under the action of an applied magnetic and electric fields, when the whole system is rotated about an axis perpendicular to the flow. The flow is driven by a common constant pressure gradient in the channel bounded by two parallel porous insulating plates, one being stationary and the other one oscillatory. The fluids in the two regions are considered electrically conducting, and are assumed to be incompressible with variable properties, namely, different densities, viscosities, thermal and electrical conductivities. The transport properties of the two fluids are taken to be constant and the bounding plates are maintained at constant and equal temperature. The governing partial differential equations are then reduced to the ordinary linear differential equations by using a two-term series. The temperature distributions in both fluid regions of the channel are derived analytically. The results are presented graphically to discuss the effect on the heat transfer characteristics and their dependence on the governing parameters, i.e., the Hartmann number, Taylor number, porous parameter, and ratios of the viscosities, heights, electrical and thermal conductivities. It is observed that, as the Coriolis forces become stronger, i.e., as the Taylor number increases, the temperature decreases in the two fluid regions. It is also seen that an increase in porous parameter diminishes the temperature distribution in both the regions.
An unsteady boundary layer free convective flow and heat transfer of a viscous incompressible, microploar fluid over a vertical stretching sheet is investigated. The stretching velocity is assumed to vary linearly with the distance along the sheet. Two equal and opposite forces are impulsively applied along the x-axis so that the sheet is stretched, keeping the origin fixed in the micropolar fluid. The transformed highly non-linear boundary layer equations are solved numerically by an implicit finite difference scheme for the transient, state from the initial to the final steady-state. To validate the numerical method, comparisons are made with the available results in the literature for some special cases and the results are found to be in good agreement. The obtained numerical results are analyzed graphically for the velocity, the microrotation, and the temperature distribution; whereas the skin friction, the couple stress coefficient and the Nusselt number are tabulated for different values of the pertinent parameters. Results exhibit a drag reduction and an increase in the surface heat transfer rate in the micropolar fluid flow compared to the Newtonian fluid flow.
In this paper, 3D numerical analysis of unsteady flow forces acting on the thermowell of steam temperature sensor is presented. According to that purpose, the CFD+CSD (computational fluid–solid dynamics) approach has been used. The nonstationary of fluid acting on the thermowell such as: Strouhal frequency, amplitude of pressure, structure of vortex, peak of pressure, field of pressure, field of velocity, etc. are studied analytically and numerically. There have been examined two cases of flow with changing both temperature, pressure and mass flow rate (operating daily and night in the unit with capacity of 380 MWe). In accordance with the standards ASME PTC 19.3 TW-2010 the possibility of entry into resonance has been examined.
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