Approbation of the mathematical model of a multiphase flow meter using the example of predicting the flow rate of a gas condensate well under various technological modes

This study experimentally analyses the binding characteristics of analytes mixed in liquid samples flowing along a micro-channel to the receptor fixed on the wall of the micro-channel to provide design tools and data for a microfluidic-based biosensor. The binding or detection characteristics are analyzed experimentally by counting the number of analytes bound to the receptor, with sample analyte concentration, sample flow rate, and the position of the receptor along the micro-channel length as the main variables. A mathematical model is also proposed to predict the number of analytes transported and bound to the receptor based on a probability density function for Brownian motion. The coefficient in the mathematical model is obtained by using a dimensionless mathematical model and the experimental results. The coefficient remains valid for all different conditions of the sample analyte concentration, flow rate, and the position of the receptor, which implies the possibility of deriving a generalized model. Based on the mathematical model derived from mathematical and experimental analysis on the detection characteristics of the microfluidic-based biosensor depending on previously mentioned variables and the height of the micro-channel, this study suggests a design for a microfluidic-based biosensor by predicting the binding efficiency according to the channel height. The results show the binding efficiency increases as the flow rate decreases and as the receptor is placed closer to the sample-injecting inlet, but is unaffected by sample concentration.

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Low-cost flow-rate estimate in separate layers along gas wells from temperature and pressure profiles

The APPEA Journal ◽

10.1071/aj12024 ◽

2013 ◽

Vol 53 (1) ◽

pp. 285

Author(s):

Emile Barrett ◽

Imran Abbasy ◽

Chii-Rong Wu ◽

Zhenjiang You ◽

Pavel Bedrikovetsky

Keyword(s):

Thermal Conductivity ◽

Mathematical Model ◽

Flow Rate ◽

Low Cost ◽

Pressure Sensors ◽

Gas Wells ◽

Production Rates ◽

Pressure Profiles ◽

Temperature And Pressure ◽

The Mathematical Model

Estimation of rate profile along the well is important information for reservoir characterisation since it allows distinction of the production rates from different layers. The temperature and pressure sensors in a well are small and inexpensive; while flow meters are cumbersome and expensive, and affect the flow in the well. The method presented in this peer-reviewed paper shows its significance in predicting the gas rate from temperature and pressure data. A mathematical model for pressure and temperature distributions along a gas well has been developed. Temperature and pressure profiles from nine well intervals in field A (Cooper Basin, Australia) have been matched with the mathematical model to determine the flow rates from different layers in the well. The presented model considers the variables as functions of thermal properties at each location, which is more accurate and robust than previous methods. The results of tuning the mathematical model to the field data show good agreement with the model prediction. Simple and robust explicit formulae are derived for the effective estimation of flow rate and thermal conductivity in gas wells. The proposed approach has been applied to determine the well gas rate and formation thermal conductivity from the acquired well pressure and temperature data in field A. It allows for recommending well stimulation of layers with low production rates.

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Mathematical model of a steam turbine condenser

Bulletin of the National Engineering Academy of the Republic of Kazakhstan ◽

10.47533/2020.1606-146x.83 ◽

2021 ◽

Vol 80 (2) ◽

pp. 41-46

Author(s):

N. G. Borissova ◽

◽

M. D. Shavdinova ◽

Keyword(s):

Mathematical Model ◽

Vapor Pressure ◽

Steam Turbine ◽

Flow Rate ◽

Cooling Water ◽

Calculation Methods ◽

Turbine Condenser ◽

Passport Data ◽

Steam Turbine Condenser ◽

The Mathematical Model

The paper analyses the existing calculation methods for steam turbine condenser. The refined methods for calculating the condenser have also been considered. The dependency of the vapor pressure in the condenser on the temperature of the cooling water and the steam flow rate into the condenser have been considered. It can be seen from the obtained dependencies that the calculation of the condenser according to the ARTI and HEI (USA) methods coincides with the passport data. It is recommended to use the ARTI and HEI (USA) techniques for equipment diagnostics, and to use the KTP and USTU-UPI techniques when studying ways to increase the efficiency of the condenser. The mathematical model of the KG2-6200 condenser has been tested at the Almaty СHPP-2.

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Nozzle-Shaped Electrode Configuration for Dielectrophoretic 3D-Focusing of Microparticles

Micromachines ◽

10.3390/mi10090585 ◽

2019 ◽

Vol 10 (9) ◽

pp. 585 ◽

Cited By ~ 2

Author(s):

Krishna ◽

Alnaimat ◽

Mathew

Keyword(s):

Mathematical Model ◽

Microfluidic Device ◽

Flow Rate ◽

Electric Potential ◽

Performance Metrics ◽

Volumetric Flow Rate ◽

Electrode Configuration ◽

Electrode Length ◽

The Mathematical Model ◽

Applied Electric Potential

: An experimentally validated mathematical model of a microfluidic device with nozzle-shaped electrode configuration for realizing dielectrophoresis based 3D-focusing is presented in the article. Two right-triangle shaped electrodes on the top and bottom surfaces make up the nozzle-shaped electrode configuration. The mathematical model consists of equations describing the motion of microparticles as well as profiles of electric potential, electric field, and fluid flow inside the microchannel. The influence of forces associated with inertia, gravity, drag, virtual mass, dielectrophoresis, and buoyancy are taken into account in the model. The performance of the microfluidic device is quantified in terms of horizontal and vertical focusing parameters. The influence of operating parameters, such as applied electric potential and volumetric flow rate, as well as geometric parameters, such as electrode dimensions and microchannel dimensions, are analyzed using the model. The performance of the microfluidic device enhances with an increase in applied electric potential and reduction in volumetric flow rate. Additionally, the performance of the microfluidic device improves with reduction in microchannel height and increase in microparticle radius while degrading with increase in reduction in electrode length and width. The model is of great benefit as it allows for generating working designs of the proposed microfluidic device with the desired performance metrics.

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Sea Water Pump Station Basin Mathematical Hydraulic Model Test (CFD Analysis)

Volume 5: Polar and Arctic Sciences and Technology; CFD and VIV ◽

10.1115/omae2009-79245 ◽

2009 ◽

Author(s):

Sadegh Barzegar ◽

Alireza Elhami Amiri ◽

Pooyan Rahbar ◽

Mehdi Assadi Niazi

Keyword(s):

Mathematical Model ◽

Free Surface ◽

Model Test ◽

Flow Rate ◽

Sea Water ◽

Water Pump ◽

Pumping Station ◽

Water Pumping ◽

Pump Station ◽

The Mathematical Model

Background and aim: A sea water intake, with original design of the six drum screen and twenty sea water pump intake with very different flow rate connected to header bay. The capacity of Origin Sea water intake including huge pump station and drum screen is 200,000 m3/hr. The purpose of the mathematical hydraulic model test of the sea water pumping station is to verify that the basin allows a good operating condition for each pump. To ensure a good operating condition for each pump, the design of the seawater basin has to insure: • A correct filter working; • Low transversal velocities; • A flow without vortex. Method and material: The mathematical model of the basin allows to know the flow and to verify: • The main dimensions of the pumping station; • The distance between the inlet ducts and the filters; • The distance between the filters and pump chambers. Result: in the first basin, the flow patterns no problems. Only swirl at the exit of culverts and near the free surface, and two areas where the flow has no velocity were observed. In the downstream other filters, we observe also a circulation that generates a tangential velocity. Conclusion: The mathematical model of the sea water pumping station has allowed calculating three cases (without and with filter stopped) for the low water level and nominal flow rate. In most difficult case, we observe some recirculation, mainly near the free surface, without more influence on principal flow. In the three cases, the distribution of the flow rate between the drum screens is uniform; the gap is inferior to 2%. At the entry of the pump chambers, the velocity fluctuations and the angle are low. Consequently, the secondary flows in pump chambers will be limited.

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Experimental and Theoretic Research on Solar Power Membrane Distillation

Advanced Materials Research ◽

10.4028/www.scientific.net/amr.97-101.2300 ◽

2010 ◽

Vol 97-101 ◽

pp. 2300-2305

Author(s):

Hong Jiang Cui ◽

Pei Ting Sun ◽

Ming Hai Li

Keyword(s):

Mathematical Model ◽

Mass Flow Rate ◽

Mass Flow ◽

Flow Rate ◽

Thermal Efficiency ◽

Solar Power ◽

Membrane Distillation ◽

Working Fluid ◽

Air Gap Membrane Distillation ◽

The Mathematical Model

Air gap membrane distillation experiments of different temperature and mass flow rate of working fluid were done for the use of solar power and setting up the mathematical model of AGMD’ heat and mass transfer. The calculation correctness of mathematical model was discussed and the thermal efficiency of membrane distillation system was calculated. The results showed that the experimental flux of membrane distillation reached 49kg/m2•h and the biggest relative error is less than 9% between results of experiment and mathematical model calculation. The mathematical model can be used to forecast the process parameters of membrane distillation. The highest thermal efficiency of this system is 68% and the main influencing factors of thermal efficiency are temperature and mass flow rate of working fluid.

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The Design and Analyses of Magnetorheological Fluid Throttle Valve

Advanced Materials Research ◽

10.4028/www.scientific.net/amr.383-390.1208 ◽

2011 ◽

Vol 383-390 ◽

pp. 1208-1214

Author(s):

Rong Wu ◽

Wen Xiang Lin ◽

Wen Tang

Keyword(s):

Mathematical Model ◽

Computational Model ◽

Flow Rate ◽

Electromagnetic Induction ◽

Fluid Model ◽

Scientific Research ◽

Magnetorheological Fluid ◽

Research Field ◽

Throttle Valve ◽

The Mathematical Model

Magnetorheological (MR) Fluid is an intellectual material with comprehensive prospect. In recent years, it is widely attended in the scientific-research field. Flow rate computational model of the MR throttle valve is derived by using Binham fluid model. The mathematical model of electromagnetic induction intensity for the MR throttle valve is established. The designed magnetorheological throttle valve is simple, compact and has some creativity. Proposed use of magnetorheological hydraulic components presents a problem.

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Evaluation of a Close Coupled Slotted Orifice, Electric Impedance, and Swirl Flow Meters for Multiphase Flow

Volume 2, Fora: Cavitation and Multiphase Flow; Fluid Measurements and Instrumentation; Microfluidics; Multiphase Flows: Work in Progress ◽

10.1115/fedsm2013-16112 ◽

2013 ◽

Cited By ~ 2

Author(s):

Gerald Morrison ◽

Sahand Pirouzpanah ◽

Muhammet Cevik ◽

Abhay Patil

Keyword(s):

Multiphase Flow ◽

Flow Rate ◽

Swirl Flow ◽

Response Curves ◽

Flow Meter ◽

Two Phase ◽

Flow Meters ◽

Mixture Density ◽

Wide Range ◽

Impedance Sensor

The feasibility of a multiphase flow meter utilizing closely coupled slotted orifice and swirl flow meters along with an impedance sensor is investigated. The slotted flow meter has been shown to exhibit well behaved response curves to two phase flow mixtures with the pressure difference monotonically increasing with mixture density and flow rate. It has been determined to have less than 1% uncertainty in determining the flow rate if the density of the fluid is known. Flow visualizations have shown that the slotted orifice is a very good mixing device as well producing a homogenous mixture for several pipe diameters downstream of the plate. This characteristic is utilized to provide a homogeneous mixture at the inlet to the swirl meter. This is possible since the slotted orifice is relatively insensitive to upstream and downstream flow disturbances. The swirl meter has been shown to indicate decreased flow rate as the mixture density increases which is opposite to the slotted orifice making the solution of the two meter outputs to obtain density and flow rate feasible. Additional instrumentation is included. Between the slotted orifice and swirl meter where the flow is homogenous a custom manufactured electrical impedance sensor is installed and monitored. This array of instrumentation will provide three independent measurements which are evaluated to determine which system of equations are robust enough to provide accurate density and flow rate measurement over a wide range of gas volume fractions using a very compact system.

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