Study of the pressure transient behavior of directional wells considering the effect of non-uniform flux distribution

During the production,the fluid in the vicinity of the directional well enters the wellbore with different rates,leading to non-uniform flux distribution along the directional well.However,in all existing studies,it is oversimplified to a uniform flux distribution,which can result in inaccurate results for field applications.Therefore,this paper proposes a semi-analytical model of a directional well based on the assumption of non-uniform flux distribution.Specifically,the direction well is discretized into a carefully chosen series of linear sources,such that the complex well trajectory can be captured and the nonuniform flux distribution along the wellbore can be considered to model the three-dimensional flow behavior.By using the finite difference method,we can obtain the numerical solutions of the transient flow within the wellbore.With the aid of Green's function method,we can obtain the analytical solutions of the transient flow from the matrix to the wellbore.The complete flow behavior of a directional well is perfectly represented by coupling the above two types of transient flow.Subsequently,on the basis of the proposed model,we conduct a comprehensive analysis of the pressure transient behavior of a directional well.The computation results show that the flux variation along the direction well has a significant effect on pressure responses.In addition,the directional well in an infinite reservoir may exhibit the following flow regimes:wellbore afterflow,transition flow,inclined radial flow,elliptical flow,horizontal linear flow,and horizontal radial flow.The horizontal linear flow can be observed only if the formation thickness is much smaller than the well length.Furthermore,a dip region that appears on the pressure derivative curve indicates the three-dimensional flow behavior near the wellbore.

Effect of non-uniform swelling on coal multiphysics during gas injection: The triangle approach

In current dual porosity/permeability models,there exists a fundamental assumption that the adsorption-induced swelling is distributed uniformly within the representative elementary volume (REV),irrespective of its internal structures and transient processes.However,both internal structures and transient processes can lead to the non-uniform swelling.In this study,we hypothesize that the non-uniform swelling is responsible for why coal permeability in experimental measurements is not only controlled by the effective stress but also is affected by the adsorption-induced swelling.We propose a concept of the swelling triangle composed of swelling paths to characterize the evolution of the non-uniform swelling and serve as a core link in coupled multiphysics.A swelling path is determined by a dimensionless volumetric ratio and a dimensionless swelling ratio.Different swelling paths have the same start and end point,and each swelling path represents a unique swelling case.The swelling path as the diagonal of the triangle represents the case of the uniform swelling while that as the two perpendicular boundaries represents the case of the localized swelling.The paths of all intermediate cases populate inside the triangle.The corresponding relations between the swelling path and the response of coal multiphysics are established by a non-uniform swelling coefficient.We define this method as the triangle approach and corresponding models as swelling path-based ones.The proposed concept and models are verified against a long-term experimental measurement of permeability and strains under constant effective stress.Our results demonstrate that during gas injection,coal multiphysics responses have a close dependence on the swelling path,and that in both future experiments and field predictions,this dependence must be considered.

Pressure transient characteristics of non-uniform conductivity fractured wells in viscoelasticity polymer flooding based on oil-water two-phase flow

Polymer flooding in fractured wells has been extensively applied in oilfields to enhance oil recovery.In contrast to water,polymer solution exhibits non-Newtonian and nonlinear behavior such as effects of shear thinning and shear thickening,polymer convection,diffusion,adsorption retention,inaccessible pore volume and reduced effective permeability.Meanwhile,the flux density and fracture conductivity along the hydraulic fracture are generally non-uniform due to the effects of pressure distribution,formation damage,and proppant breakage.In this paper,we present an oil-water two-phase flow model that captures these complex non-Newtonian and nonlinear behavior,and non-uniform fracture characteristics in fractured polymer flooding.The hydraulic fracture is firstly divided into two parts:high-conductivity fracture near the wellbore and low-conductivity fracture in the far-wellbore section.A hybrid grid system,including perpendicular bisection(PEBI)and Cartesian grid,is applied to discrete the partial differential flow equations,and the local grid refinement method is applied in the near-wellbore region to accurately calculate the pressure distribution and shear rate of polymer solution.The combination of polymer behavior characterizations and numerical flow simulations are applied,resulting in the calculation for the distribution of water saturation,polymer concentration and reservoir pressure.Compared with the polymer flooding well with uniform fracture conductivity,this non-uniform fracture conductivity model exhibits the larger pressure difference,and the shorter bilinear flow period due to the decrease of fracture flow ability in the far-wellbore section.The field case of the fall-off test demonstrates that the proposed method characterizes fracture characteristics more accurately,and yields fracture half-lengths that better match engineering reality,enabling a quantitative segmented characterization of the near-wellbore section with high fracture conductivity and the far-wellbore section with low fracture conductivity.The novelty of this paper is the analysis of pressure performances caused by the fracture dynamics and polymer rheology,as well as an analysis method that derives formation and fracture parameters based on the pressure and its derivative curves.

An improved non-uniform fast Fourier transform method for radio imaging of coronal mass ejections

Radioheliographs can obtain solar images at high temporal and spatial resolution,with a high dynamic range.These are among the most important instruments for studying solar radio bursts,understanding solar eruption events,and conducting space weather forecasting.This study aims to explore the effective use of radioheliographs for solar observations,specifically for imaging coronal mass ejections(CME),to track their evolution and provide space weather warnings.We have developed an imaging simulation program based on the principle of aperture synthesis imaging,covering the entire data processing flow from antenna configuration to dirty map generation.For grid processing,we propose an improved non-uniform fast Fourier transform(NUFFT)method to provide superior image quality.Using simulated imaging of radio coronal mass ejections,we provide practical recommendations for the performance of radioheliographs.This study provides important support for the validation and calibration of radioheliograph data processing,and is expected to profoundly enhance our understanding of solar activities.

Robust and Reusable Fuzzy Extractors from Non-Uniform Learning with Errors Problem

Afuzzy extractor can extract an almost uniformrandom string from a noisy source with enough entropy such as biometric data.To reproduce an identical key from repeated readings of biometric data,the fuzzy extractor generates a helper data and a random string from biometric data and uses the helper data to reproduce the random string from the second reading.In 2013,Fuller et al.proposed a computational fuzzy extractor based on the learning with errors problem.Their construction,however,can tolerate a sub-linear fraction of errors and has an inefficient decoding algorithm,which causes the reproducing time to increase significantly.In 2016,Canetti et al.proposed a fuzzy extractor with inputs from low-entropy distributions based on a strong primitive,which is called digital locker.However,their construction necessitates an excessive amount of storage space for the helper data,which is stored in authentication server.Based on these observations,we propose a new efficient computational fuzzy extractorwith small size of helper data.Our scheme supports reusability and robustness,which are security notions that must be satisfied in order to use a fuzzy extractor as a secure authentication method in real life.Also,it conceals no information about the biometric data and thanks to the new decoding algorithm can tolerate linear errors.Based on the non-uniform learning with errors problem,we present a formal security proof for the proposed fuzzy extractor.Furthermore,we analyze the performance of our fuzzy extractor scheme and provide parameter sets that meet the security requirements.As a result of our implementation and analysis,we show that our scheme outperforms previous fuzzy extractor schemes in terms of the efficiency of the generation and reproduction algorithms,as well as the size of helper data.

Radial Basis Approximations Based BEMD for Enhancement of Non-Uniform Illumination Images

An image can be degraded due to many environmental factors like foggy or hazy weather,low light conditions,extra light conditions etc.Image captured under the poor light conditions is generally known as non-uniform illumination image.Non-uniform illumination hides some important information present in an image during the image capture Also,it degrades the visual quality of image which generates the need for enhancement of such images.Various techniques have been present in literature for the enhancement of such type of images.In this paper,a novel architecture has been proposed for enhancement of poor illumination images which uses radial basis approximations based BEMD(Bi-dimensional Empirical Mode Decomposition).The enhancement algorithm is applied on intensity and saturation components of image.Firstly,intensity component has been decomposed into various bi-dimensional intrinsic mode function and residue by using sifting algorithm.Secondly,some linear transformations techniques have been applied on various bidimensional intrinsic modes obtained and residue and further on joining the transformed modes with residue,enhanced intensity component is obtained.Saturation part of an image is then enhanced in accordance to the enhanced intensity component.Final enhanced image can be obtained by joining the hue,enhanced intensity and enhanced saturation parts of the given image.The proposed algorithm will not only give the visual pleasant image but maintains the naturalness of image also.

Image Non-Uniformity Correction in 3T Gd-EOB-DTPA-Enhanced Magnetic Resonance Imaging: Comparison among Different Software Versions

Background: Non-uniformity in signal intensity occurs commonly in magnetic resonance (MR) imaging, which may pose substantial problems when using a 3T scanner. Therefore, image non-uniformity correction is usually applied. Purpose: To compare the correction effects of the phased-array uniformity enhancement (PURE), a calibration-based image non-uniformity correction method, among three different software versions in 3T Gd-EOB-DTPA-enhanced MR imaging. Material and Methods: Hepatobiliary-phase images of a total of 120 patients who underwent Gd-EOB-DTPA-enhanced MR imaging on the same 3T scanner were analyzed retrospectively. Forty patients each were examined using three software versions (DV25, DV25.1, and DV26). The effects of PURE were compared by visual assessment, histogram analysis of liver signal intensity, evaluation of the spatial distribution of correction effects, and evaluation of quantitative indices of liver parenchymal enhancement. Results: The visual assessment indicated the highest uniformity of PURE-corrected images for DV26, followed by DV25 and DV25.1. Histogram analysis of corrected images demonstrated significantly larger variations in liver signal for DV25.1 than for the other two versions. Although PURE caused a relative increase in pixel values for central and lateral regions, such effects were weaker for DV25.1 than for the other two versions. In the evaluation of quantitative indices of liver parenchymal enhancement, the liver-to-muscle ratio (LMR) was significantly higher for the corrected images than for the uncorrected images, but the liver-to-spleen ratio (LSR) showed no significant differences. For corrected images, the LMR was significantly higher for DV25 and DV26 than for DV25.1, but the LSR showed no significant differences among the three versions. Conclusion: There were differences in the effects of PURE among the three software versions in 3T Gd-EOB-DTPA-enhanced MR imaging. Even if the non-uniformity correction method has the same brand name, correction effects may differ depending on the software version, and these differences may affect visual and quantitative evaluations.

FREE VIBRATION ANALYSIS AND PHYSICAL PARAMETER IDENTIFICATION OF NON-UNIFORM BEAM CARRYING SPRING-MASS SYSTEMS

To analyze a multibody system composed of non-uniform beam and spring-mass subsystems, the model discretization is carried on by utilizing the finite element method（FEM）, the dynamic model of non-uniform beam is developed by using the transfer matrix method of multibody system（MS-TMM）, the transfer matrix of non-u- niform beam is derived, and the natural frequencies are computed. Compared with the numerical assembly method （NAM）, the results by MS-TMM have good agreement with the results by FEM, and are better than the results by NAM. When using the high precision method, the global dynamic equations of the complex multibody system are not needed and the orders of involved system matrices are decreased greatly. For the investigation on the re- verse problem of the physical parameter identification of multibody system, MS-TMM and the optimization tech- nology based on genetic algorithms（GAs） are combined and extended. The identification problem is exchanged for an optimization problem, and it is formulated as a global minimum solution of the objective function with respect to natural frequencies of multibody system. At last, the numerical example of non-uniform beam with attach- ments is discussed, and the identification results indicate the feasibility and the effectivity of the proposed aop- proach.

Effect of antenna helicity on discharge characteristics of helicon plasma under a divergent magnetic field

The characteristics of the blue core phenomenon observed in a divergent magnetic field helicon plasma are investigated using two different helical antennas, namely right-handed and lefthanded helical antennas. The mode transition, discharge image, spatial profiles of plasma density and electron temperature are diagnosed using a Langmuir probe, a Nikon D90 camera,an intensified charge-coupled device camera and an optical emission spectrometer, respectively.The results demonstrated that the blue core phenomenon appeared in the upstream region of the discharge tube at a fixed magnetic field under both helical antennas. However, it is more likely to appear in a right-handed helical antenna, in which the plasma density and ionization rate of the helicon plasma are higher. The spatial profiles of the plasma density and electron temperature are also different in both axial and radial directions for these two kinds of helical antenna. The wavelength calculated based on the dispersion relation of the bounded whistler wave is consistent with the order of magnitude of plasma length. It is proved that the helicon plasma is part of the wave mode discharge mechanism.

Simulation of Corrosion-Induced Cracking of Reinforced Concrete Based on Fracture Phase Field Method

Accurate simulation of the cracking process caused by rust expansion of reinforced concrete(RC)structures plays an intuitive role in revealing the corrosion-induced failure mechanism.Considering the quasi-brittle fracture of concrete,the fracture phase field driven by the compressive-shear term is constructed and added to the traditional brittle fracture phase field model.The rationality of the proposed model is verified by a mixed fracture example under a shear displacement load.Then,the extended fracture phase model is applied to simulate the corrosion-induced cracking process of RC.The cracking patterns caused by non-uniform corrosion expansion are discussed for RC specimens with homogeneous macroscopically or heterogeneous with different polygonal aggregate distributions at the mesoscopic scale.Then,the effects of the protective layer on the crack propagation trajectory and cracking resistance are investigated,illustrating that the cracking angle and cracking resistance increase with the increase of the protective layer thickness,consistent with the experimental observation.Finally,the corrosion-induced cracking process of concrete specimens with large and small spacing rebars is simulated,and the interaction of multiple corrosion cracking is easily influenced by the reinforcement spacing,which increases with the decrease of the steel bar interval.These conclusions play an important role in the design of engineering anti-corrosion measures.The fracture phase field model can provide strong support for the life assessment of RC structures.

Effect of local thermal sensation on whole-body thermal sensation under stable non-uniform environment

To reveal the principles of human thermal responses and find out the effects of body parts on whole-body thermal sensation,through a subjective survey,experimental investigations on human responses are carried out when a single body part is thermally stimulated.Cooling airflow is sent to seven body parts,respectively.Totally 94 samples are tested.To eliminate the obvious multicollinearity of thermal sensation among different body parts,the principal component regression approach is adopted to obtain the principal components for the body parts under different experimental conditions.Through regression and analysis of principal components,the weighting factors of the seven body parts are obtained.A predictive model on whole-body thermal sensation is obtained based on the weighting factors.The results show that the different characteristics of trunk and limbs are clearly seen.The weighting factors of local thermal sensation are integrated values,and there is little difference among values of different body parts.

Threshold Voltage Model for a Fully Depleted SOI-MOSFET with a Non-Uniform Profile

A novel approximation of the two-dimensional （2D） potential function perpendicular to the channel is proposed,and then an analytical threshold voltage model for a fully depleted SOI-MOSFET with a non-uniform Gaussian distribution doping profile is given based on this approximation. The model agrees well with numerical simulation by MEDICI. The result represents a new way and some reference points in analyzing and controlling the threshold voltage of non-uniform fully depleted （FD） SOI devices in practice.

NON-UNIFORM LINEAR ARRAY CONFIGURATION FOR MIMO RADAR

Array configuration of multiple-input multiple-output （MIMO） radar with non-uniform linear array （NLA） is proposed. Unlike a standard phased-array radar where NLA is used to generate thinner beam patterns, in MIMO radar the property of NLA is exploited to get more distinct virtual array elements so as to improve pa- rameter identifiability, which means the maximum number of targets that can be uniquely identified by the radar. A class of NLA called minimum redundancy linear array （MRLA） is employed and a new method to construct large MRLAs is descrihed. The numerical results verify that compared to uniform linear array （ULA） MIMO radars, NLA MIMO radars can retain the same parameter identifiability with fewer physical antennas and achieve larger aperture length and lower Cramer-Rao bound with the same number of the physical antennas.

Numerical investigation on flow and heat transfer characteristics of corrugated tubes with non-uniform corrugation in turbulent flow

Based on finite volume method, the pressure drop and heat transfer characteristics of one smooth tube and ten different axisymmetric corrugated tubes, including two with uniform corrugation and eight with non-uniform corrugation, have been studied. A physical model of the corrugated tube was built, then the numerical simulation of the model was carried out and the numerical simulation results were compared with the empirical formula.The results show that: the friction factor decreases with the increase of Reynolds number ranging from 6000 to 57000, the value of which in the corrugated tubes with non-uniform corrugation(tube 03–10) are smaller than those with uniform corrugation(tube 01–02). The geometry parameters of tube(01) have advantages on the heat transfer enhancement in low Reynolds number flow region(from 6000 to 13000) and tube(07–08)have advantages on the heat transfer enhancement in high Reynolds number flow region(from 13000 to 57000). The vortex, existed in each area between two adjacent corrugations called second flow region, is the root of the enhancement on heat transfer in the corrugated tubes. The effectiveness factor decreases with the increasing of Reynolds number and the performances of the corrugated tubes with pitch of 12.5 mm have advantages than these of 10 mm under the same corrugation geometric parameter.

Comparative Analysis of Energy Characteristics of Two Southwest Vortices in Sichuan Under Similar Circulation Backgrounds

Based on ERA5 reanalysis data,the present study analyzed the thermal energy development mechanism and kinetic energy conversion characteristics of two extreme rainstorm processes in relation to the shallow southwest vortex in the warm-sector during a“rain-generated vortex”process and the deep southwest vortex in a“vortex-generated rain”process.The findings were as follows:(1)During the extreme rainstorm on August 11,2020(hereinafter referred to as the“8·11”process),intense surface heating and a high-energy unstable environment were observed.The mesoscale convergence system triggered convection to produce heavy rainfall,and the release of latent condensation heat generated by the rainfall promoted the formation of a southwest vortex.The significant increase(decrease)in atmospheric diabatic heating and kinetic energy preceded the increase(decrease)in vorticity.By contrast,the extreme rainstorm on August 16,2020(hereinafter referred to as the“8·16”process)involved the generation of southwest vortex in a low-energy and highhumidity environment.The dynamic uplift of the southwest vortex triggered rainfall,and the release of condensation latent heat from rainfall further strengthened the development of the southwest vortex.The significant increase(decrease)in atmospheric diabatic heating and kinetic energy exhibited a delayed progression compared to the increase(decrease)in vorticity.(2)The heating effect around the southwest vortex region was non-uniform,and the heating intensity varied in different stages.In the“8·11”process,the heating effect was the strongest in the initial stage,but weakened during the vortex's development.On the contrary,the heating effect was initially weak in the“8·16”process,and intensified during the development stage.(3)The available potential energy of the“8·11”process significantly increased in kinetic energy converted from rotational and divergent winds through baroclinic action,and the divergent wind energy continued to convert into rotational wind energy.By contrast,the“8·16”process involved the conversion of rotational wind energy into divergent wind energy,which in turn converted kinetic energy back into available potential energy,thereby impeding the further development and maintenance of the southwest vortex.

Line Patterns Segmentation in Blurred Images Using Contrast Enhancement and Local Entropy Thresholding

Finger vein extraction and recognition hold significance in various applications due to the unique and reliable nature of finger vein patterns. While recently finger vein recognition has gained popularity, there are still challenges associated with extracting and processing finger vein patterns related to image quality, positioning and alignment, skin conditions, security concerns and processing techniques applied. In this paper, a method for robust segmentation of line patterns in strongly blurred images is presented and evaluated in vessel network extraction from infrared images of human fingers. In a four-step process: local normalization of brightness, image enhancement, segmentation and cleaning were involved. A novel image enhancement method was used to re-establish the line patterns from the brightness sum of the independent close-form solutions of the adopted optimization criterion derived in small windows. In the proposed method, the computational resources were reduced significantly compared to the solution derived when the whole image was processed. In the enhanced image, where the concave structures have been sufficiently emphasized, accurate detection of line patterns was obtained by local entropy thresholding. Typical segmentation errors appearing in the binary image were removed using morphological dilation with a line structuring element and morphological filtering with a majority filter to eliminate isolated blobs. The proposed method performs accurate detection of the vessel network in human finger infrared images, as the experimental results show, applied both in real and artificial images and can readily be applied in many image enhancement and segmentation applications.

An improved binarization algorithm of wood image defect segmentation based on non-uniform background

In this study,an image binarization optimization algorithm,based on local threshold algorithms,is proposed because global and traditional local threshold segmentation algorithms cannot effectively address the problems of nonuniform backgrounds of wood defect images.The proposed algorithm calculates the threshold by the mean,standard deviation and the extreme value of the window.The results indicate that this modified algorithm enhances the image segmentation for wood defect images on a complex background,which is much superior to the global threshold algorithm and the Bernsen algorithm,and slightly better than the Niblack algorithm and Sauvola algorithm.Compared with similar models,the algorithm proposed in this paper has higher segmentation accuracy,as high as 92.6%for wood defect images with a complex background.

Experimental Study on Occupant's Thermal Responses under the Non-uniform Conditions in Vehicle Cabin during the Heating Period

The existing investigations on thermal comfort mostly focus on the thermal environment conditions, especially of the air-flow field and the temperature distributions in vehicle cabin. Less attention appears to direct to the thermal comfort or thermal sensation of occupants, even to the relationship between thermal conditions and thermal sensation. In this paper, a series of experiments were designed and conducted for understanding the non-uniform conditions and the occupant＇s thermal responses in vehicle cabin during the heating period. To accurately assess the transient temperature distribution in cabin in common daily condition, the air temperature at a number of positions is measured in a full size vehicle cabin under natural winter environment in South China by using a discrete thermocouples network. The occupant body is divided into nine segments, the skin temperature at each segment and the occupant＇s local thermal sensation at the head, body, upper limb and lower limb are monitored continuously. The skin temperature is observed by using a discrete thermocouples network, and the local thermal sensation is evaluated by using a seven-point thermal comfort survey questionnaire proposed by American Society of Heating, Refrigerating and Air-Conditioning Engineers, Inc（ASHRAE） Standard. The relationship between the skin temperature and the thermal sensation is discussed and regressed by statistics method. The results show that the interior air temperature is highly non-uniform over the vehicle cabin. The locations where the occupants sit have a significant effect on the occupant＇s thermal responses, including the skin temperature and the thermal sensation. The skin temperaWa-e and thermal sensation are quite different between body segments due to the effect of non-uniform conditions, clothing resistance, and the human thermal regulating system. A quantitative relationship between the thermal sensation and the skin temperature at each body segment of occupant in real life traffic is presented. The investigation result indicates that the skin temperature is a robust index to evaluate the thermal sensation. Applying the skin temperature to designing and controlling parameters of the heating, ventilation and air conditioning（HVAC） system may benefit the thermal comfort and reducing energy consumption.

Numerical study on non-uniform heat transfer deterioration of supercritical RP-3 aviation kerosene in a horizontal tube

The convective heat transfer of supercritical-pressure RP-3(Rocket Propellant 3)aviation kerosene in a horizontal circular tube has been numerically studied,focusing mainly on the non-uniform heat transfer deterioration along the circumferential direction.The governing equations of mass,momentum and energy have been solved using the pressure-based segregated solver based on the finite volume method.The re-normalization group(RNG)k-εturbulence model with an enhanced wall treatment was selected.Considering the heat conduction in the solid wall,the mechanism of heat transfer deterioration and the buoyancy effect on deteriorated heat transfer were discussed.The evolution of secondary flow was analyzed.Effects of the outer-wall heat flux,mass flux,pressure and tube thermal conductivity on heat transfer were investigated.Moreover,the buoyancy criterion and the heat transfer correlation were obtained.Results indicate that the poor flow performance of near-wall fluid causes the pseudo-film boiling,further leads to the heat transfer deterioration.The strong buoyancy has an effect of enhancing the heat transfer at the bottom of tube,and weakening the heat transfer at the top of tube,which results in the non-uniform inner-wall temperature and heat flux distributions.Decreasing the ratio of outer-wall heat flux and mass flux,increasing the pressure could weaken the heat transfer difference along the circumferential direction,while the effect of thermal conductivity of tube on the circumferential parameters distributions is more complicated.When the buoyancy criterion of(Grq/Grth)max≤0.8 is satisfied,the effect of buoyancy could be ignored.The new correlations work well for non-uniform heat transfer predictions.

Turbulent Variance Characteristics of Temperature and Humidity over a Non-uniform Land Surface for an Agricultural Ecosystem in China

This paper describes the application of the variance method for flux estimation over a mixed agricultural region in China. Eddy covariance and flux variance measurements were conducted in a near-surface layer over a non-uniform land surface in the central plain of China from 7 June to 20 July 2002. During this period, the mean canopy height was about 0.50 m. The study site consisted of grass （10% of area）, beans （15%）, corn （15%） and rice （60%）. Under unstable conditions, the standard deviations of temperature and water vapor density （normalized by appropriate scaling parameters）, observed by a single instrument, followed the Monin-Obukhov similarity theory. The similarity constants for heat （CT） and water vapor （Cq） were 1.09 and 1.49, respectively. In comparison with direct measurements using eddy covariance techniques, the flux variance method, on average, underestimated sensible heat flux by 21% and latent heat flux by 24%, which may be attributed to the fact that the observed slight deviations （20% or 30% at most） of the similarity ＂constants＂ may be within the expected range of variation of a single instrument from the generally-valid relations.