scholarly journals A mathematical model for identifying the fractional derivative parameter and predicting the results for the fluid flow equation in the well

2021 ◽  
pp. 72-79
Author(s):  
Темирхан Султанович Алероев ◽  
Алла Николаевна Хворова
Keyword(s):  
Mathematical Model ◽  
Fractional Derivatives ◽  
Fractured Reservoirs ◽  
Flow Equation ◽  
Oil Fields ◽  
Coefficient Of Determination ◽  
Experimental Measurements ◽  
Steady State Flow ◽  
Fluid Flow Equation ◽  
The Mathematical Model

В данной статье рассматривается идентификации параметров математической модели, основанной на дифференциальном уравнении с дробными производными. С помощью этой модели описывается установившееся течение в скважине в трещинном деформированном пласте. Рассматриваемая модель может быть использована и при разработке нефтяных месторождений с трещиноватыми коллекторами. Идентификация параметра осуществлялась с помощью оптимизации показателя качества адекватности математической модели - коэффициента детерминации. Также была представлена технология прогнозирования результатов давлений, для области, в которой не проводились экспериментальные измерения. Предлагаемая технология сопровождена расчетами. This article discusses the identification of the parameters of a mathematical model based on a differential equation with fractional derivatives. This model is used to describe the steady-state flow in a well in a fractured deformed formation. The considered model can be used in the development of oil fields with fractured reservoirs. The identification of the parameter was carried out by optimizing the quality indicator of the adequacy of the mathematical model the coefficient of determination. The technology for predicting the results of pressures was also presented, for an area in which no experimental measurements were carried out. The proposed technology is accompanied by calculations.

scholarly journals Measurement of Relative Position of Camera and Optical Beacon by Simultaneous Passive Method

2019 ◽  
Vol 8 (1) ◽  
pp. 1 ◽  
Author(s):  
Jiri Nemecek ◽  
Martin Polasek
Keyword(s):  
Mathematical Model ◽  
Relative Position ◽  
Analytical Method ◽  
Measurement Method ◽  
Position Angle ◽  
Experimental Measurements ◽  
Light Sources ◽  
Passive Measurement ◽  
Passive Method ◽  
The Mathematical Model

The paper deals with a problem of a passive measurement of the relative position of an optical beacon and an optical camera by a simultaneous analytical method. The beacon is composed of nine light sources which are arranged in space in a defined way. The proposed beacon layout enables the measurement of the beacon range and one position angle of the camera. This paper presents the mathematical model of the measurement method and the results, which were gathered on the basis of two experimental measurements. The first experiment was only indicative. The extreme results of the second experiment were as follows: the minimum and maximum absolute percentage errors of the beacon range were zero and 1.72%, the minimum and maximum errors of the position angle were 0.1 deg and 1.64 deg. The standard commercial cameras and lenses with different focal lengths were used.

scholarly journals Mathematical modelling of the drying process of sugar beet pulp with macro and microelement additions in order to improve the feed quality

2020 ◽  
Vol 180 ◽  
pp. 03020
Author(s):  
Elena Mihaela Nagy ◽  
Constantin Coţa ◽  
Zoltan Gyorgy ◽  
Teodora Deac
Keyword(s):  
Mathematical Model ◽  
Sugar Beet ◽  
Phosphoric Acid ◽  
Mathematical Modelling ◽  
Animal Feed ◽  
Hydrated Lime ◽  
Experimental Measurements ◽  
Drying Process ◽  
Beet Pulp ◽  
The Mathematical Model

In this paper a kinetic study is performed on the drying process of beet pulp with additions of macro-elements (Ca2+, Mg 2+, PO42+) from hydrated lime, hydrated dolomite lime, phosphoric acid and microelements (Co2+, Zn 2+, Fe2+, Mn2+), with the purpose of obtaining premixes with substantially improved value for animal feed. The experimental measurements made served to elaborate the mathematical model by means of which the speed with which the drying process is carried out is described, thus being able to calculate the stationing time of the material in the dryer. The equations for calculating the stationary time of the material in the dryer can be used for designing dryers (sizing them).

scholarly journals Diagnostics of the condition of sucker-rod pumping units after the analysis of dynamogram cards

2019 ◽  
Vol 298 ◽  
pp. 00137
Author(s):  
Georgy Milovzorov ◽  
Aleksei Ilyin ◽  
Pavel Shirobokov
Keyword(s):  
Mathematical Model ◽  
Control Process ◽  
Oil Fields ◽  
Centrifugal Pumps ◽  
Valve Unit ◽  
Sucker Rod ◽  
Injection Unit ◽  
Pumping Equipment ◽  
Pumping Units ◽  
The Mathematical Model

Despite of the increased share of oil wells equipped with submersible electrical centrifugal pumps, a considerable part of them is equipped and operated with sucker-rod pumping units. When operating wells with sucker-rod pumping units, different plunger pumps are used. The rod string is operated in severe environment due to long contact with highly corrosive well products and time-variant loads. Taking into account all acting loads, the diagnostics of the condition of sucker-rod pumping units is a difficult task. At the majority of oil fields in Russia, the operation of wells equipped with sucker-rod pumping units is controlled by portable and stationary dynamographs of various models. Moreover, dynamographs are used, as a rule, only to obtain images of dependence of the force on the polished piston rod upon its stroke. Based on dynamograms it is possible to find the well flow rate, pump capacity, force on the polished piston rod, etc. But one of the main problems to be solved with the help of dynamometry is the forecasting of down-hole equipment condition in the process of further operation. In this paper we overview the methods to diagnose the condition of sucker-rod pumping units based on dynamograms. The aim of the work is to develop the mathematical model to forecast the failures of down-hole pumping equipment on the results of dynamometry to automatize the control process of the unit operation. The research tasks are to analyze the existing methods for diagnosing the condition of sucker-rod pumping units, and to develop the mathematical model for forecasting the failure of the valve unit leakage. As a result, the method for forecasting the increased failure on the example of the fluid leakage in the pump injection unit is proposed. The permissible boundaries of the change in the relative force on the polished piston rod are drawn up. As a result, the failure increase is forecasted based on the frequency of the relative force on the polished piston rod getting within the interval obtained.

Investigation of Light Interaction With Transient Expanding Thick Flames

2003 ◽  
Author(s):  
Farzan Parsinejad ◽  
Hameed Metghalchi
Keyword(s):  
Mathematical Model ◽  
High Speed ◽  
Experimental Measurements ◽  
Cylindrical Chamber ◽  
Spherical Flames ◽  
Experimental Facilities ◽  
Light Beams ◽  
The Mathematical Model ◽  
Optical Behavior ◽  
Good Agreement

Optical behavior of spherical flames has been investigated using Shadowgraph method. A mathematical model has been developed to predict the intensity profile of refracted light beams interacting with a transient expanding thick flame. Experimental facilities have been built to visualize transient expanding spherical flames. Facilities include a cylindrical chamber with two end glasses for optical observation. Shadowgraph pictures of flame propagation have been taken using a high speed Charged Coupled Device camera. Flame edge has been located using the mathematical model and it has been compared to experimental measurements. Experimental results are in very good agreement with those predicted by the theoretical model.

Generalized Memristor Consisting of Diode Bridge with First Order Parallel RC Filter

2014 ◽  
Vol 24 (11) ◽  
pp. 1450143 ◽  
Author(s):  
Bocheng Bao ◽  
Jingjing Yu ◽  
Fengwei Hu ◽  
Zhong Liu
Keyword(s):  
Mathematical Model ◽  
Hysteresis Loops ◽  
Experimental Measurements ◽  
First Order ◽  
The Mathematical Model ◽  
Pinched Hysteresis ◽  
Order Parallel

A generalized memristor consisting of a memristive diode bridge with a first order parallel RC filter is proposed in this letter. The mathematical model of the circuit is established and its fingerprints are analyzed by the pinched hysteresis loops with different periodic stimuli. The results verified by experimental measurements indicate that the proposed circuit is a simple voltage-controlled generalized memristor.

scholarly journals Perbandingan Berbagai Model Matematika Pada Pengeringan Lapisan Tipis Belimbing Wuluh (Averrhoa bilimbi)

2020 ◽  
Vol 4 (4) ◽  
pp. 442-451
Author(s):  
Rival Andrea ◽  
Raida Agustina ◽  
Indera Sakti Nasution
Keyword(s):  
Mathematical Model ◽  
Thin Layer ◽  
Mathematical Models ◽  
Water Content ◽  
Predictive Value ◽  
Thin Layers ◽  
Coefficient Of Determination ◽  
Observation Data ◽  
Garden Plant ◽  
The Mathematical Model

Abstract : Belimbing wuluh merupakan salah satu tanaman buah asli Indonesia dan daratan Malaya.Belimbing wuluh (Averrhoa bilimbi) banyak ditemui sebagai tanaman pekarangan yang mudah ditanam dan tidak memerlukan perawatan khusus.Tujuan dari penelitian ini adalah menentukan model matematika pada pengeringan lapisan tipis belimbing wuluh yang terbaik menggunakan beberapa persamaan. Penelitian ini dilakukan dengan menggunakan perhitungan kadar air belimbing wuluh,perhitunganMoisture Ratio dan perhitungan persamaan model matematika, Newton, HendersonPabis, Page, Modified page, Logarithmic, Modified Hederson Pabis menggunakan Excel. Hasil penelitian menunjukkan bahwa terdapat perbedaan keenam jenis model matematika pada pengeringan lapisan tipis belimbing wuluh dengan model Newton, Henderson and Pabis, Page, Modified page, Logarithmic, Modified Hederson Pabis. Berdasarkan analisis didapat model terbaik pada pengeringan belimbing wuluh belah dua bagian yaitu model Page. Dari data pengamatan dengan prediksi model Page yang di dapat untuk belimbing wuluh belah dua bagian diperoleh nilai koefisien determinasi sebesar 0,9849 suhu 40°C, 0,9824 suhu 50°C, dan 0,9807 pada suhu 60°C. Data pengamatan dengan prediksi model Henderson and Pabis yang di dapat untuk belimbing wuluh utuh  diperoleh nilai koefisien determinasi MR prediksi sebesar 0,9696 suhu 40°C, 0,9176 suhu 50°C, dan 0,9727 pada suhu 60°C. Comparison of Various Mathematical Models in Drying Thin Layer of BilimbiAbstract : Carambola Wuluh is one of the native fruit plants of Indonesia and the mainland of Malaya. Bilimbi (Averrhoa bilimbi) is commonly found as a garden plant that is easily planted and does not require special care. The purpose of this study is to determine the mathematical model in drying the best thin layer of bilimb using several equations. This research was carried out by calculating the water content of bilimbi, calculating the Moisture Ratio and calculating the equations of mathematical models, Newton, Henderson Pabis, Page, Modified page, Logarithmic, Modified Hederson Pabis using Excel. The results showed that there were differences in the six types of mathematical models in drying thin layers of bilimbi with Newton, Henderson and Pabis models, Page, Modified pages, Logarithmic, Modified Hederson Pabis. Based on the analysis, the best model was obtained in the drying of the two-part bilimi, the Page model. From the observational data with the prediction of Page models obtained for the two-part bilimbi obtained the value of the coefficient of determination is 0.9849 at 40 ° C, 0.9824 at 50 ° C, and 0.9807 at 60 ° C. Observation data with predictions of the Henderson and Pabis model obtained for whole bilimbi obtained the predictive value of the MR coefficient of 0.9696 at 40 ° C, 0.9176 at 50 ° C, and 0.9727 at 60 ° C.

Application of Model of the Viscoelastic Body and the Fractal Analysis for the Description of Process of Flowability of Polymeric Nanocomposites

2018 ◽  
Vol 935 ◽  
pp. 150-154
Author(s):  
Z.M. Zhirikova ◽  
V.Z. Aloyev
Keyword(s):  
Mathematical Model ◽  
Carbon Nanotubes ◽  
Fractal Analysis ◽  
Fractional Derivatives ◽  
Elasticity Modulus ◽  
Viscoelastic Body ◽  
Structural Identification ◽  
Polymeric Nanocomposites ◽  
The Mathematical Model ◽  
Derivatives Of

In present work the yield process of nanocomposites polypropylene/carbon nanotubes analysis has performed within the frameworks of fractional derivatives conception and fractal analysis. The mathematical model of a viscoelastic body based on derivatives of fractional order. It has been shown that the yield stress is defined by elasticity modulus and nanocomposite structural state. The fractional exponent structural identification has performed.

scholarly journals Chimney Sweeping Robot Based on a Pneumatic Actuator

2021 ◽  
Vol 11 (11) ◽  
pp. 4872
Author(s):  
Peter Ján Sinčák ◽  
Ivan Virgala ◽  
Michal Kelemen ◽  
Erik Prada ◽  
Zdenko Bobovský ◽  
...  
Keyword(s):  
Mathematical Model ◽  
Simulation Model ◽  
Mechanical Design ◽  
Pneumatic Actuator ◽  
Robot Motion ◽  
Experimental Measurements ◽  
Sweeping Process ◽  
Real Robot ◽  
The Mathematical Model

The need of improving the quality of professions led to the idea of simplification of processes during chimney sweeping. These processes have been essentially the same for tens of years. The goal of this paper is to bring an automation element into the chimney sweeping process, making the job easier for the chimney sweeper. In this paper, an essentially in-pipe robot is presented, which uses brushes to move while simultaneously cleaning the chimney or pipeline. The problem of the robot motion was reduced using an in-pipe robot due to the environments and obstacles that the robot has to face. An approach of using a pneumatic actuator for motion is presented along with the mechanical design. The next part of this paper is focused on the mathematical model of the robot motion, as well as its simulation and testing in the experimental pipeline. The simulations were compared with the experimental measurements and a few analyses were conducted describing the simulation model and its differences with the real robot, as well as considering certain parameters and their impact on the performance of the robot. The results are discussed at the end of the paper.

Rimming Flow of a Power-Law Fluid: Qualitative Analysis of the Mathematical Model

2006 ◽  
Author(s):  
Sergei Fomin ◽  
Richard Hubbard
Keyword(s):  
Mathematical Model ◽  
Qualitative Analysis ◽  
Liquid Film ◽  
Power Law ◽  
Rotating Cylinder ◽  
Steady State Flow ◽  
Power Law Fluid ◽  
Rimming Flow ◽  
Inner Surface ◽  
The Mathematical Model

Rimming flow of the non-Newtonian fluid on the inner surface of a horizontal rotating cylinder is investigated. Simple lubrication theory is applied since the Reynolds number is small and liquid film is thin. For the steady-state flow of a power-law fluid the mathematical model reduces to a simple algebraic equation regarding the thickness of the liquid film. The qualitative analysis of this equation is carried out and the existence of two possible solutions is rigorously proved. Based on this analysis qualitative analysis, different regimes of the rimming flow are defined and analyzed analytically.

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