Correction for Transient Flow in the Initial Stage of Constant-Rate Filtration

1970 ◽  
Vol 9 (2) ◽  
pp. 261-265 ◽  
Author(s):  
William Kozicki ◽  
A. R. K. Rao ◽  
Carlos Tiu
Keyword(s):  
Transient Flow ◽  
Initial Stage ◽  
Constant Rate

scholarly journals A study of the initial stage of oil spreading on calm water through methods of both instantaneous and constant rate of oil release.

1983 ◽  
Vol 16 (6) ◽  
pp. 502-507
Author(s):  
TETSUO AKIYAMA ◽  
SATORU MITSUMORI ◽  
TORU TERADA ◽  
KOZO KOIDE
Keyword(s):  
Initial Stage ◽  
Constant Rate ◽  
Calm Water

scholarly journals Porous Structure Evolution of Cellulose Carbon Fibres during Oxidation in Carbon Dioxide

2003 ◽  
Vol 21 (4) ◽  
pp. 363-371 ◽  
Author(s):  
Krzysztof Babeł
Keyword(s):  
Porous Structure ◽  
Isothermal Oxidation ◽  
Micropore Volume ◽  
Structure Evolution ◽  
Regenerated Cellulose ◽  
Porous Structures ◽  
Carbon Fibres ◽  
Initial Stage ◽  
Constant Rate ◽  
Third Stage

The isothermal oxidation of regenerated cellulose carbon fibres in the presence of CO2 or steam was described, together with the changes in the porous structures of the active fibres that evolve during different stages of the process. Three such stages were defined. In the initial stage of heating and out-gassing, changes in the porous structure were related to the violent pyrolysis that occurred. As a result, a considerable number of micropores (accessible to nitrogen) were generated together with a small number of mesopores. The next stage (principal activation stage) involved burning at a constant rate accompanied by an uniform increase in the micropore volume. In the third stage, an increased rate of oxidation was observed. This was accompanied by the development of transitional pores linked with the simultaneous limitation of micropore evolution. This stage was not efficient.

scholarly journals A Study of Cake Filtration Parameters Using the Constant Rate Process

Processes ◽  
2019 ◽  
Vol 7 (10) ◽  
pp. 746 ◽  
Author(s):  
Faiz Mahdi ◽  
Timothy Hunter ◽  
Richard Holdich
Keyword(s):  
Calcium Carbonate ◽  
Filter Cake ◽  
Cake Filtration ◽  
Initial Stage ◽  
Constant Rate ◽  
Medium Resistance ◽  
Material Sample ◽  
The Mean ◽  
Analytical Approaches ◽  
Constant Rate Process

The minerals calcium carbonate and talc were filtered under various conditions of filtrate flow rate and suspension concentration, using constant rate conditions with the aid of a peristaltic pump to draw the filtrate. Cake concentrations of between 0.41 and 0.53 v/v for calcium carbonate and 0.19 and 0.26 v/v for talc were recorded. The mean sizes of the two different minerals were very similar, but the average specific resistances obtained from the experiments were 5.9 × 1010 and 7.4 × 1011 m/kg for calcium carbonate and talc, respectively. These results do not agree with what would be predicted from an analytical equation for permeability, such as Kozeny-Carman. In addition, discontinuities were observed in all cases on the curves of filtrate volume with time for the initial stage of filtration. This behaviour is attributed to retarded packing compressibility (RPC) complicating the analysis of the filter medium resistance. RPC is an important component in determining the filter cake resistance and its functionality with cake forming pressure. It is found that there are additional effects that enhance the resistance to permeation in different cake materials, which is not recognised in the standard analytical approaches. These complexities can be related to shape, polydispersity, or agglomeration within the material sample and not to the experimental equipment or procedure. Furthermore, a complete and straightforward methodology is presented in this work for investigating the significance, or otherwise, of medium resistance on the later stages of the filtration.

The flow of polycrystalline lead under simple shear at higher temperatures

1968 ◽  
Vol 304 (1476) ◽  
pp. 1-24
Keyword(s):  
Grain Boundary ◽  
Tensile Stress ◽  
Simple Shear ◽  
Transient Flow ◽  
Boundary Migration ◽  
Grain Boundary Migration ◽  
Boundary Slip ◽  
Transition Stress ◽  
Constant Rate ◽  
Small Flow

The flow of polycrystalline lead has been investigated in detail by the method of simple shear, as used by Andrade & Jolliffe, at temperatures from 27 to 80 °C and also at 150 °C. Pre­liminary work on the variation of stable grain size with temperatures has shown that at 150 °C there are very few grains to the thickness of the metal annulus subject to shear, which is why this temperature is distinguished from the others. The range of temperature of the detailed measurements appears to be one of particular significance. The t 1/2 formula followed, as strain increases, by a t 1/3 formula, which has been shown to represent in detail the transient flow at 27 °C, has proved to be valid at all the higher temperatures and the laws governing the variation of the constants of the formulae with stress and temperature have been determined. At temperatures approaching 80 °C the flow so expressed is accompanied by a small flow linear with time, the laws of which have been determined. This linear flow has been traced to grain boundary slip, which is not involved in the t 1/2 and t 1/3 flow. Particular attention has been paid to stage III of the flow, in which the metal has the properties of a non-Newtonian fluid. The constant rate of flow has been expressed in terms of a function of the velocity and temperature which is linear with stress. It has been shown that at a certain transition stress the slope of the line changes abruptly. This transition stress is a simple function of the temperature. Photomicrographs showing the deformation of the surface grains, which with the method employed, but not with the method of tensile stress, is held to be typical of the behaviour of internal grains, have thrown some light on the processes associated with the various stages of flow. An intermittent grain boundary migration has been established at higher temperatures. The results obtained by the method of simple shear are compared with the results of tests carried out by the usual method of tensile stress with rods or wires, from which they differ in certain significant respects, such as the conditions leading to recrystallization and the accompanying effects.

Vertical Fracture Height: Effect on Transient Flow Behavior

1978 ◽  
Vol 18 (04) ◽  
pp. 265-277 ◽  
Author(s):  
R. Raghavan ◽  
A. Uraiet ◽  
G.W. Thomas
Keyword(s):  
Transient Flow ◽  
Flow Behavior ◽  
Petroleum Industry ◽  
Transient Pressure ◽  
Pressure Behavior ◽  
Constant Rate ◽  
Penetration Ratio ◽  
Fracture Height ◽  
Fractured Well ◽  
Pressure Analysis

Abstract Although a number of studies have examined the performance of vertically fractured wells, no performance of vertically fractured wells, no analytical study has examined the effect of fracture height on transient flow behavior and production capacity. The purpose of this paper is to close this gap in the knowledge about fractured well behavior. This paper presents an analytical study of the pressure behavior of a well producing at a constant pressure behavior of a well producing at a constant rate through one vertical fracture from an infinitely large reservoir with impermeable upper and lower boundaries. The fracture height is less than the formation thickness. The characteristics of the dimensionless wellbore pressure drop vs dimensionless time curves are examined for both uniform-flux and infinite-conductivity fractures. Two fracture locations (center and top) in the producing interval are considered. Curves also are presented for calculating the additional pressure drop that results because the fracture height is less than the formation thickness. Other parameters of interest examined here are (1) the ratio of vertical to horizontal permeability and (2) the ratio of fracture height to permeability and (2) the ratio of fracture height to formation thickness. The application of theoretical results to well test analysis also is discussed. Introduction Hydraulic fracturing, introduced in 1949, has provided the petroleum industry with an inexpensive provided the petroleum industry with an inexpensive way to increase the fluid production or injection capacity of wells. The success of many marginal wells can be directly attributed to hydraulic fracturing. Because of the many wells that have been hydraulically fractured, the study of the flow behavior of wells intersecting vertical, horizontal, and inclined fractures has received considerable attention. As a result of these studies, it is possible to predict and analyze pressure behavior of fractured wells and to compute production increases caused by fracture treatments. All studies on vertical and inclined fractures cited assume that the fracture extends over the entire vertical extent of the formation. Field observations, however, indicate that in Some instances this assumption is not valid. Also, the fracture height through which fluid is actually produced may not be equal to the created fracture produced may not be equal to the created fracture height. There is no discussion in the literature of the transient pressure behavior of a reservoir producing through a well with a fracture that does producing through a well with a fracture that does not extend throughout the vertical extent of the formation. This paper first examines the effect of fracture height on transient pressure behavior of a vertically fractured well producing at a constant rate. Second, we present information regarding production rate changes as a function of fracture height. Third, we delineate conditions under which it would be possible to recognize (by pressure analysis) that possible to recognize (by pressure analysis) that the thickness and fracture height are different. REMARKS ABOUT THE NOMENCLATURE In the petroleum engineering literature, the term, "a partially penetrating well," has been used to describe the situation where a well does not penetrate the entire thickness of the formation. penetrate the entire thickness of the formation. The term, "penetration ratio," has been defined as the ratio of the length of the open interval to the formation thickness. Unfortunately, this term also has been used to define the ratio of the fracture half-length to the drainage length. Among other definitions, the word "penetrate" implies "to enter or pierce; to make way into another body." In this context, using the term, "penetration ratio," to describe both situations is correct. Confusion regarding this terminology has not come up, since all studies on the pressure behavior of vertically fractured wells have assumed that the fracture extends over the entire extent of the formation. In this study, however, we need to clarify this term, even though we are examining only the pressure behavior of vertically fractured wells in an pressure behavior of vertically fractured wells in an infinite reservoir. SPEJ P. 265

The flow of polycrystalline metals under simple shear. II

1960 ◽  
Vol 254 (1278) ◽  
pp. 291-316 ◽  
Keyword(s):  
Creep Rate ◽  
Grain Growth ◽  
Simple Shear ◽  
Principal Stresses ◽  
Initial Stage ◽  
Constant Rate ◽  
Wide Range ◽  
Reverse Creep ◽  
The Moment ◽  
Experimental Findings

The flow of lead of different purities under conditions of simple shear has been investigated over a wide range of strain, at different stresses, and mostly at a temperature in the neighbourhood of 27 °C. The phenomena have been studied both with unchanged direction of stress and with the direction of stress reversed during flow. At the beginning of forward creep the t 1/3 law is strictly obeyed, within a range of strain which is determined by the purity and grain size of the lead. The region within which the t 1/3 law holds, here called stage F I, is succeeded by stage F II, during which the strain increases according to a logarithmic law, the creep rate being proportional to the increase in strain. In stage F III, which begins at a strain of about 0.3, the creep is strictly linear until the strain approaches 2.0, when rupture starts. If the stress be reversed while stage F I is in progress a creep linear with time takes place, at a rate which is twice that of the forward creep at the moment of reversal, and this constant rate continues for a time equal to that of the forward creep. This initial stage R 0 is succeeded by a stage R I which is also governed by a t 1/3 law, the constant multiplying t 1/3 being proportional to that for stage F I at the same stress. This is followed by a stage R II in which the creep rate increases according to the same law which prevailed for stage F II, and this in turn is followed by a linear stage R III characterized by the same constant creep rate as F III. If the stress be reversed at a strain so large that the t 1/3 law has ceased to be valid, the reverse creep stages are markedly affected, which emphasizes the physical significance of the t 1/3 law. A law of corresponding times is enunciated, which connects the flow in stages R 0 and R I with that in stage F I. Photomicrographs and back-reflexion X-ray photographs have shown that the t 1/3 flow is accompanied by progressive slip in the grains and local rotation of the lattice, and that in the R 0 stage slip takes place on the same slip bands as were active in the F I stage. Recrystallization and grain growth occur during stages F II and R II. In stages F III and R III there is a balance between grain break-up and grain growth, and the slip direction shows a preference for the directions of principal stresses. By considering the variation of strain rate with stress and temperature in stage III, constants have been derived which indicate that the flow in this quasi- viscous stage resembles that of a single crystal far more than that of a polycrystalline metal. The general implications of the experimental findings are discussed.

scholarly journals METHODS OF THE DETERMINATION OF THE HYDROGEOLOGICAL PARAMETERS ON THE RESULTS OF THE EXPERIMENTAL CONSTANT-RATE PUMPING TESTS FROM THE LAYERED AQUIFERS WITH OVERFLOW

2018 ◽  
pp. 50-58
Author(s):  
M. M. Burakov
Keyword(s):  
Experimental Data ◽  
Pumping Test ◽  
Piezometric Level ◽  
Pumping Tests ◽  
Hydrogeological Parameters ◽  
Flow Parameters ◽  
Initial Stage ◽  
Constant Rate ◽  
Volumetric Characteristics

The methodical aspects of the processing and interpreting the results of the experimental filtration tests of the layered strata by the constant-rate pumping tests have been developed. Determination of the filtration and volumetric characteristics of the tested pressure aquifer has been proposed on the basis of the author's method based on the results of tracking the drawdown of the piezometric level of the groundwater in the wells of the experimental cluster at the initial stage of the pumping. Methods for interpreting the experimental data of the second and third stages of the constant-rate pumping test for the calculation of the flow parameters have been proposed.

scholarly journals Information Geometry of Nonlinear Stochastic Systems

Entropy ◽  
2018 ◽  
Vol 20 (8) ◽  
pp. 550 ◽  
Author(s):  
Rainer Hollerbach ◽  
Donovan Dimanche ◽  
Eun-jin Kim
Keyword(s):  
Geometric Structure ◽  
Stochastic Systems ◽  
Power Laws ◽  
Information Geometry ◽  
Scaling Exponent ◽  
Stochastic Noise ◽  
Initial Stage ◽  
Constant Rate ◽  
Information Change ◽  
Transient Relaxation

We elucidate the effect of different deterministic nonlinear forces on geometric structure of stochastic processes by investigating the transient relaxation of initial PDFs of a stochastic variable x under forces proportional to -xn (n=3,5,7) and different strength D of δ-correlated stochastic noise. We identify the three main stages consisting of nondiffusive evolution, quasi-linear Gaussian evolution and settling into stationary PDFs. The strength of stochastic noise is shown to play a crucial role in determining these timescales as well as the peak amplitude and width of PDFs. From time-evolution of PDFs, we compute the rate of information change for a given initial PDF and uniquely determine the information length L(t) as a function of time that represents the number of different statistical states that a system evolves through in time. We identify a robust geodesic (where the information changes at a constant rate) in the initial stage, and map out geometric structure of an attractor as L(t→∞)∝μm, where μ is the position of an initial Gaussian PDF. The scaling exponent m increases with n, and also varies with D (although to a lesser extent). Our results highlight ubiquitous power-laws and multi-scalings of information geometry due to nonlinear interaction.

Reaction couples of ceramic thin films prepared by CVD

1988 ◽  
Vol 46 ◽  
pp. 798-799
Author(s):  
D.W. Susnitzky ◽  
S.R. Summerfelt ◽  
C.B. Carter
Keyword(s):  
Thin Film ◽  
Vapor Deposition ◽  
Chemical Vapor ◽  
Deposition Process ◽  
Solid State Reactions ◽  
Spatial Distributions ◽  
Diffusion Couples ◽  
Kinetics Studies ◽  
Ceramic Thin Films ◽  
Initial Stage

Solid-state reactions have traditionally been studied in the form of diffusion couples. This ‘bulk’ approach has been modified, for the specific case of the reaction between NiO and Al2O3, by growing NiAl2O4 (spinel) from electron-transparent Al2O3 TEM foils which had been exposed to NiO vapor at 1415°C. This latter ‘thin-film’ approach has been used to characterize the initial stage of spinel formation and to produce clean phase boundaries since further TEM preparation is not required after the reaction is completed. The present study demonstrates that chemical-vapor deposition (CVD) can be used to deposit NiO particles, with controlled size and spatial distributions, onto Al2O3 TEM specimens. Chemical reactions do not occur during the deposition process, since CVD is a relatively low-temperature technique, and thus the NiO-Al2O3 interface can be characterized. Moreover, a series of annealing treatments can be performed on the same sample which allows both Ni0-NiAl2O4 and NiAl2O4-Al2O3 interfaces to be characterized and which therefore makes this technique amenable to kinetics studies of thin-film reactions.

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