Volumetric Flow Rate Research Articles

Numerical Solution of the Newtonian Plane Couette Flow with Linear Dynamic Wall Slip

An efficient numerical approach based on weighted-average finite differences is used to solve the Newtonian plane Couette flow with wall slip, obeying a dynamic slip law that generalizes the Navier slip law with the inclusion of a relaxation term. Slip is exhibited only along the fixed lower plate, and the motion is triggered by the motion of the upper plate. Three different cases are considered for the motion of the moving plate, i.e., constant speed, oscillating speed, and a single-period sinusoidal speed. The velocity and the volumetric flow rate are calculated in all cases and comparisons are made with the results of other methods and available results in the literature. The numerical outcomes confirm the damping with time and the lagging effects arising from the Navier and dynamic wall slip conditions and demonstrate the hysteretic behavior of the slip velocity in following the harmonic boundary motion.

Wear mechanisms and material deposition of high-performance polymer composites for hydrogen compression

The transistion to renewable energy production is a main component in achieving the climate targets defined in the 2015 Paris Agreement. Power-to-gas concepts, where electrical energy is stored as hydrogen gas, require the design and operation of state-of-the-art reciprocating compressor technology to realize high pressure ratios and high volumetric flow rates for gas supply demands. The main challenges in designing machines suited for these operating conditions are high thermo-mechanical stresses acting on the piston sealing rings. High shear loads and minimal ring gap sizes demand material pairings with excellent wear resistance and sliding properties. This work investigates the life cycle limiting wear mechanisms present in the piston compressor and develops advanced concepts for piston rings in cylinder tribo-contacts. PI and PPS polymers reinforced with carbon fiber were modified with dry lubricating PTFE to fulfil the requirements of this highly stressed tribo-system. Tribo-tests were performed against steel countersurfaces with a linear oscillating tribometer in pin-on-plate configuration. The failure mechanisms were analysed utilizing scanning electron microscopy on cross-sections cut into the depth of the countersurface material with focused ion beam milling. 2D scanning transmission electron microscopy mapping supported by energy dispersive X-ray spectroscopy were performed to analyze the depth profile of the deposited tribo-layer elements on the wear track.

Odorant transport in a hagfish

Odorant transport is of fundamental and applied importance. Using computational simulations, we studied odorant transport in an anatomically accurate model of the nasal passage of a hagfish (probably Eptatretus stoutii). We found that ambient water is sampled widely, with a significant ventral element. Additionally, there is a bilateral element to olfactory flow, which enters the single nostril in two narrow, laminar streams that are then split prior to the nasal chamber by the anterior edge of the central olfactory lamella. An appendage on this lamella directs a small portion (10–14%) of the overall nasal flow to the olfactory sensory channels. Much of the remaining flow is diverted away from the sensory channels by two peripheral channels. The anterior edge of the central olfactory lamella, together with a jet-impingement mechanism, disperses flow over the olfactory surfaces. Diffusion of odorant from bulk water to the olfactory surfaces is facilitated by the large surface area:volume ratio of the sensory channels, and by a resistance-based hydrodynamic mechanism that leads to long residence times (up to 4.5 s) in the sensory channels. With increasing volumetric flow rate, the rate of odorant transfer to the olfactory surfaces increases, but the efficiency of odorant uptake decreases, falling in the range 2–6%. Odorant flux decreases caudally across the olfactory surfaces, suggesting in vivo a preponderance of olfactory sensory neurons on the anterior part of each olfactory surface. We conclude that the hagfish has a subtle anatomy for locating and capturing odorant molecules.

Synthesis of refinery hydrogen networks based on compressor performance models

Synthesis of refinery hydrogen network contributes to reductions in hydrogen consumption, production cost, and emissions. Hydrogen compressors are drivers for hydrogen distribution, which has a direct effect on the performance of hydrogen networks. The existing works focus on the hydrogen network synthesis and often use simple compressor models for easy modelling and solving, which may lead to overly ideal results. This work proposes a novel mathematical method for refinery hydrogen network synthesis considering compressor performances, incorporating both centrifugal and reciprocating compressors. The compression power vs. volumetric flowrate curves and the compression ratio vs. volumetric flowrate curves are considered for a centrifugal compressor, while the efficiency of a reciprocating compressor is correlated with the compression ratio. A mixed integer nonlinear programming model (MINLP) is formulated to minimize the total annualized cost. The developed MINLP model is examined based on two hydrogen network cases reported in literature. The results show that the minimum total annualized cost is a co-optimization of compressor type, operating points, compressor placement, and hydrogen network structure. In the two cases, compression efficiencies of centrifugal compressors range from 0.760 to 0.795 and that of reciprocating compressors are between 0.539 and 0.807. The consideration of centrifugal compressors rather than just reciprocating compressors not only improves the compression efficiencies but also simplify the hydrogen network structures. Moreover, it also brings reductions in the compression power by 2.23% and 1.97%, and decreases in the compressor investment by 7.12% and 6.87%.

Analysis of hemodynamic parameters on two-layered blood flow in a curved artery

Arterial stenosis is the thickening of the arterial wall due to the growth of aberrant tissues that prevent adequate blood flow in the human circulatory system and induces cardiovascular diseases. Mild stenosis, may lead to serious or permanent damage if remains uncured. There are differences in the curvature response and material composition between the outer layers and the core. There are several locations in blood vessels where they are curved, which affects the blood flow and shear stress. The Navier-Stokes equation in the cylindrical polar coordinate system has been extended by incorporating curvature term in two-layered blood flow along the axial direction with appropriate boundary conditions. Mathematical expressions for hemodynamic parameters such as velocity profile, volumetric flow rate, pressure drop, and shear stress have been calculated analytically in the case of a curve artery with stenosis. Moreover, we have analyzed the effect of stenosis on different hemodynamic parameters with the variation of core and peripheral-layer viscosity and curvature. Flow quantities are affected by the habitancy of stenosis and stipulate different blood flow behavior in both layers in the case of curved artery. This modeling technique may help researchers in medicine, mathematical biology, and bio-engineering.

Novel insights into acetylation kinetics in a continuous Flow milli-reactor for chemo-enzymatic separation of silybin A/B

The separation of silybin A (SilA) and B (SilB) diastereomers in optically pure compounds is challenging due to their very similar physical and chemical properties. However, such separation is crucial for evaluating the biological activity of the diasteroisomers SilA and SilB, which show very different performance in pharmacological applications like treating prostate cancer, liver diseases, and Alzheimer’s disease. The most common isolation method is based on high-performance liquid chromatography, but it is slow and has a yield in pure SilB of hundreds of milligrams per day. An alternative chemo-enzymatic separation method, utilizing an immobilized lipase CALB catalyst to stereoselectively acetylate silybin B (1b), offers advantages in terms of higher productivity, selectivity, and scalability, particularly when applied in flow reactors. This study delves into the kinetics of Sil acetylation catalyzed by Novozym 435 in a continuous flow milli-reactor, investigated at various temperatures, volumetric flow rates, and Sil initial concentrations. It is noteworthy that, at the current state of the art, there is a lack of kinetic studies on this reaction, emphasizing the novelty and significance of this work. The kinetic and fluid dynamic parameters were estimated using a non-linear regression analysis of experimental data. The examined reaction showed a null apparent activation energy, explaining the temperature insensitivity of the final acetylated silybin B (1b) concentration. Furthermore, the decrease in steady-state concentrations of the acetylated products with increasing volumetric flow rates indicated that the reaction was occurring in a kinetic regime. Interestingly, a maximum starting Sil concentration was identified, above which there was no favorable impact on conversion.

A simple hydrodynamic model for clay

Laboratory description of clay normally distinguishes the scale of atoms from the scale of clay particles and aggregates. Contemporary constitutive models for clay tend to ignore this scale separation, and rather focus on phenomenology. By considering scale separation, this paper introduces a robust physics-based phenomenological constitutive model for clay that qualitatively captures their broad spectrum of rate-dependent mechanical features. The model is derived using the thoroughly rigorous hydrodynamic procedure. While some imagine that by considering rigour and physics, their models would get complicated, the resulting set of equations reveal a surprising degree of simplicity. The derivation strongly benefits from the principle of two-stage irreversibility, which describes energy flow within the material from the continuum scale down to the atomistic micro-scale, through the meso-scale of clay aggregates. While thermal and meso-related temperatures capture atomistic and clay aggregate fluctuating motions, a sink term from the latter to the former underpins the direction of the energy flow. The model’s standout feature is in pinpointing new transport coefficients that drive both volumetric and shear plastic flows in a thermodynamically coupled manner. A novel scheme is then proposed to calibrate these coefficients from conventional steady-state observations. Thanks to the formulation the model shows a remarkable level of predictiveness, despite being relatively simple mathematically. In particular, the model readily explains the broad spectrum of rate-dependent phenomena during transient loading, along with creep and relaxation processes. Given the generality of hydrodynamics, it is anticipated that the new model could be expanded to capture fluid-solid transitions between liquid-like soft mud and plastic-like stiff clay responses, contingent on water content variations.

DEVELOPMENT OF ADVANCED WATER/LIBR ABSORPTION CHILLER WITH CONDENSATION HEAT RECOVERY FOR SIMULTANEOUS COOLING AND HEATING APPLICATIONS

A prototype of an advanced single-stage water/LiBr absorption chiller with a design cooling capacity of 40 kW was developed. The prototype is designed to operate in a simultaneous cooling and heating mode by recovering condensation heat. This paper presents and discusses the newly developed advanced chiller prototype and the modified multifunctional test rig for prototype characterization in different operation modes. The test rig has four external heat carrier loops to characterize and validate the prototype during the simultaneous cooling and heating operation. External and internal temperature sensors and volumetric flow rate measuring devices are installed in the prototype. The design conditions of the advanced absorption chiller are chilled water inlet/outlet temperatures of 12/7 °C, driving hot water and cooling water (absorber external loop) inlet temperatures of 100 °C and 30 °C, respectively, and produced hot water inlet/outlet temperatures of 40/55 °C. The prototype also operates as a conventional absorption chiller to provide only cooling by rejecting the absorber and condenser heat to cooling water (heat rejection medium). Finally, developing such absorption chillers improves overall performance and provides dual useful outputs (cooling and heating).

Theoretical models for predicting ventilation performance of vertical solar chimneys in tunnels

Solar chimney as a reliable renewable energy system has been primarily utilized for building ventilation, but its application in the tunnel is rarely explored. This study develops theoretical models to predict the ventilation performance of vertical solar chimney in urban tunnel. Five temperature distribution types within the chimney cavity are analyzed, including uniform, vertically linear, horizontally semi-parabolic, two piecewise semi-parabolic in the depth direction, and three-dimensional parabolic profiles. The theoretical models consider the effect of chimney configuration, tunnel geometry, glazing materials, and solar radiation intensity on airflow rate through solar chimney. Validation against experimental data and numerical simulation shows that considering three-dimensional temperature distributions results in an average 11 % deviation from validation data, outperforming assumptions of uniform (29.3 % deviation) or lower-dimensional profiles. The volumetric flow rate through solar chimney exponentially decreased with h/w and h/d that the optimum ratio of h/d is 10. The airflow rate linearly increased with 0.14 power of glazing absorptivity. This analysis provides technical guidance for optimizing solar chimney design in tunnels, enhancing natural ventilation, and reducing energy consumption for mechanical ventilation systems.

Electrochemical treatment of azo dye wastewater by dynamic flow diaphragm system: Response surface methodology optimization and energy consumption analysis

In this experiment, the degradation process of azo dye wastewater was studied based on the diaphragm double chamber electrochemical reactor, taking the mono azo dye amaranth as an example. Through the circulation flow of appropriate volume of wastewater in the cathode and anode chamber, the simultaneous action of cathode and anode was realized, and the degradation and decolorization efficiency of azo wastewater was improved while reducing energy waste. The optimal reaction conditions optimized by response surface methodology were as follows: the voltage was 20.74 V, the plate spacing was 4.89 cm, and the cycle speed was 60.66 rad / min. The optimal decolorization rate was 99.66 %. The energy consumption analysis of the dynamic flow diaphragm system electrochemical method and the static flow diaphragm system electrochemical method for the treatment of azo dye wastewater was compared and analyzed. In addition, the possible degradation process of azo dye wastewater by dynamic flow electrochemistry was inferred by ultraviolet spectroscopy and mechanism prediction analysis. The experimental results show the great potential of the dynamic flow membrane system process in the treatment of azo dyes.

Oscillating flow of Jeffrey fluid in a rough circular microchannel with slip boundary condition

By utilizing the perturbation method, approximate analytical solutions for velocity and volumetric flow rate are provided for oscillating flow of Jeffrey fluid in a rough circular microchannel with slip boundary condition. Meanwhile, the impact of relevant parameters on the flow is analyzed theoretically and graphically. A particular interest is given to the effect of slip length b¯ on velocity and volumetric flow rate at various angular Reynolds numbers Re. The key findings show that the velocity grows at low angular Reynolds number (Re=1) and reduces at high angular Reynolds number (Re=50) with increasing slip length b¯. As for the volumetric flow rate, it demonstrates a gradual growth pattern with slip length at Re=1. However, there is a slight initial rise followed by a decline as the slip length b¯ increases atRe=50. Moreover, an analysis is conducted on how wall roughness ε and wave numbers kaffect the volumetric flow rate across varying angular Reynolds numbers Re and slip lengths b¯. Observations reveal that larger values of parameters ε and k lead to reduced volumetric flow rates at Re=1, irrespective of the slip length. At Re=50, a decline in volumetric flow rate is induced by an increase in wall roughness ε for smaller slip lengths. Conversely, the inverse outcome holds when slip lengths are larger. Higher wave numbers k correlate with elevated volumetric flow rates, independent of the slip length. In light of the applications of oscillating flow and Jeffrey fluid in biomedical research, particularly in the study of human physiological systems such as blood flow, these findings are of significant importance.

Synthesis of Cs3Cu2I5 Nanocrystals in a Continuous Flow System.

Achieving the goal of generating all of the world's energy via renewable sources and significantly reducing the energy usage will require the development of novel, abundant, nontoxic energy conversion materials. Here, a cost-efficient and scalable continuous flow synthesis of Cs3Cu2I5 nanocrystals is developed as a basis for the rapid advancement of novel nanomaterials. Ideal precursor solutions are obtained through a novel batch synthesis, whose product served as a benchmark for the subsequent flow synthesis. Realizing this setup enabled a reproducible fabrication of Cs3Cu2I5 nanocrystals. The effect of volumetric flow rate and temperature on the final product's morphology and optical properties are determined, obtaining 21% quantum yield with the optimal configuration. Consequently, the size and morphology of the nanocrystals can be tuned with far more precision and in a much broader range than previously achievable. The flow setup is readily applicable to other relevant nanomaterials. It should enable a rapid determination of a material's potential and subsequently optimize its desired properties for renewable energy generation or efficient optoelectronics.

Numerical Modelling and Mathematical Modelling of Non-Contact Gripper for Maximum Negative Pressure and Grasping Area

The aim of this paper is to provide a mathematical relationship between the geometrical parameter (cone radius), input parameter (volumetric flow rate) and constraint condition (gap height) with the grasping parameters for non-contact gripper. The cone mill Bernoulli gripper is taken as the reference model. The grasping parameters are negative pressure and grasping area. Thus, to provide the mathematical relation four different cone radius, three volumetric flow rates and three gap heights are taken. With the help of statistical tool (MINITAB) the mathematical relationship is established. A standard full factorial design is chosen to provide the regression equation. With the help of interaction graph the effect of individual parameters on grasping are established. Key Words: Non-contact gripper, Bernoulli, Automation, Grasping area, Negative pressure, Face Radius (FR).

Numerical analysis of polyphenol oxidase inactivation in non-Newtonian characteristic liquid food with high viscosity during radio frequency treatment

Enzymatic browning is one of the main problems in the food industry, especially in juice and jam processing. An efficient approach to reduce enzymatic browning is to inactivate key polyphenol oxidases (PPO) that cause color reactions. Radio frequency (RF) treatment has advantages of volumetric heating and no chemical residue, making it one of the most potential treatments to replace traditional heating for pasteurization. In this study, a finite element model was established using the commercial software, COMSOL, to investigate the feasibility and effectiveness of PPO inactivation in non-Newtonian characteristic liquid food with high viscosity during pilot-scale RF treatments. The PPO was represented by the tyrosinase, and four concentrations of carboxymethylcellulose (CMC) solutions were considered to have high viscosity and non-Newtonian characteristics for liquid food. The results showed that the relative residual enzyme activity rapidly decreased to 1.2% when the target temperature increased to 70 °C during a batch RF enzyme inactivation. Meanwhile, the simulated and experimental trends were consistent with an acceptable RMSE value. The low-concentration CMC solutions (0.5% and 1.0%) with shorter heating times may be more suitable for developing the batch RF enzyme inactivation technology. During continuous-flow RF enzyme inactivation, the F-value increased with an increase in the solution concentration but sharply decreased with an increase in the volumetric flow rate. The exponential function could be used to describe the relationship between the relative residual enzyme activity and the volumetric flow rate of the CMC solution after RF treatment. The optimal volumetric flow rates for reducing the activity of PPO in 0.5%, 1.0%, 1.5%, and 2.0% CMC solutions to 20% were 426.13, 467.87, 552.05, and 566.07 mL/min, respectively. This study can provide valuable information for inactivating enzymes in non-Newtonian characteristic liquid food with high viscosity.

Influence of corrugated tube structure and flow rate on the hydrogen absorption performance of metal hydride reactor and structural optimization

The metal hydride bed (MHB) reactor is an effective instrument for storing hydrogen. However, thermal stress causes the cooling tube expansion inside the MHB. The long-term effects will lead to the failure of the cooling tube. To absorb the thermal stress and reduce the deformation of the cooling tubes, this article establishes an MHB reactor with corrugated cooling tubes to study its hydrogen absorption performance. The results prove that some parameters are adversarial and flow rate patterns are complex (such as extreme flow rate and insufficient flow rate) in the hydrogen absorption process of the corrugated tube MHB reactor, which makes it impossible to optimize the structure of the corrugated tube through the gradient method. Under the condition of a fixed corrugated tube volume of 3×10−6m3 and a cooling water volumetric flow rate of 0.5×10−4m3/s, the structural parameters of the corrugated tube are optimized by the Monte Carlo algorithm. According to the optimized results (N=8, ro=4.25 mm, ri=3.98 mm, do=3.17 mm, di=4.33 mm), the hydrogen absorption efficiency of the corrugated tube MHB reactor (reaction fraction 0.758) is 1.36 times that of the straight tube (reaction fraction 0.557) at 560 s. Thus, the corrugated tube can reduce thermal stress and improve the heat transfer effect. This research is beneficial in improving long-term stability, enhancing operational efficiency, and reducing the volume and weight of large MHB reactors.

Heat transfer analysis in particulate flow of Williamson fluid with electric double layer effects

This research is conducted to investigate the heat transfer analysis in a two-phase fluid model under the impact of an electric double layer and magnetic field through two types of geometries with porous media. The Darcy model is used to capture the effect of porous medium. The perturbation technique is employed to produce the analytical solution of fluid and particulate velocities, temperature distribution, volumetric flow rate, and stream function. The computational revealed that the two-phase model produces 32 and 36% greater heat transfer as compared to the single-phase model by considering convergent and divergent channels, respectively. It is observed that the divergent channel provides 4% more heat transfer as compared to the convergent channel. The present study will offer valuable insights into the electric double-layer dynamics of two-phase fluid through complex configurations, such as biomedical engineering. The current two-phase model is also very important and applicable in electrofluidic dynamic and biomedical engineering where biomedical electronic devices such as two-phase lab-on-chip may be engineered.

An In Silico Modelling Approach to Predict Hemodynamic Outcomes in Diabetic and Hypertensive Kidney Disease

Early diagnosis of kidney disease remains an unmet clinical challenge, preventing timely and effective intervention. Diabetes and hypertension are two main causes of kidney disease, can often appear together, and can only be distinguished by invasive biopsy. In this study, we developed a modelling approach to simulate blood velocity, volumetric flow rate, and pressure wave propagation in arterial networks of ageing, diabetic, and hypertensive virtual populations. The model was validated by comparing our predictions for pressure, volumetric flow rate and waveform-derived indexes with in vivo data on ageing populations from the literature. The model simulated the effects of kidney disease, and was calibrated to align quantitatively with in vivo data on diabetic and hypertensive nephropathy from the literature. Our study identified some potential biomarkers extracted from renal blood flow rate and flow pulsatility. For typical patient age groups, resistive index values were 0.69 (SD 0.05) and 0.74 (SD 0.02) in the early and severe stages of diabetic nephropathy, respectively. Similar trends were observed in the same stages of hypertensive nephropathy, with a range from 0.65 (SD 0.07) to 0.73 (SD 0.05), respectively. Mean renal blood flow rate through a single diseased kidney ranged from 329 (SD 40, early) to 317 (SD 38, severe) ml/min in diabetic nephropathy and 443 (SD 54, early) to 388 (SD 47, severe) ml/min in hypertensive nephropathy, showing potential as a biomarker for early diagnosis of kidney disease. This modelling approach demonstrated its potential application in informing biomarker identification and facilitating the setup of clinical trials.

Response Time Dynamics of a Membrane-Based Microfluidic Gas Sensor

Practical gas–liquid interfacing is paramount in microfluidic technology, particularly in developing microfluidic gas sensors. We have created an easily replicable membrane-based closed microfluidic platform (MB-MP) to achieve in situ gas–liquid contact for low-resource settings. We have fabricated the MB-MP using readily available materials like double-sided tape or parafilm without conventional soft lithographic techniques. The response characteristics of the MB-MP are studied using CO2 as the model gas and bromothymol blue dye as the sensing material. The dye’s color change, indicative of pH shifts due to CO2 absorption, is captured with a digital microscope and analyzed via the ImageJ software package v1.54g. The response shows saturation and regeneration parts when cycled between CO2 and N2, respectively. Experiments are conducted to investigate the response characteristics and saturation rate under different conditions, including changes in volumetric flow rate, gas stream velocity, and dye solution volume. We observe experimentally that an increase in volumetric flow rate decreases the delay and increases the saturation rate of the response, surpassing the impact of the gas stream’s increased velocity. Furthermore, increasing the dye volume results in an exponential decrease in the saturation rate and an increase in the delay. These insights are essential for optimizing the platform’s response for point-of-use applications.

Multi-objective topology optimization design of silicon carbide metal oxide semiconductor field effect transistors power module liquid-cooled heatsink for electric vehicles

Silicon carbide (SiC) metal oxide semiconductor field effect transistors (MOSFETs) is gradually replacing silicon-based insulated gate bipolar transistor (IGBT) as the switching devices in electric vehicle power inverters due to its higher operating temperatures, switching speeds, and frequencyies. However, the high switching frequency of SiC MOSFETs can increase the losses of the power inverter, resulting in an increase in the temperature, which will limit the performance of power inverters. The improvement of power module performance is mainly controlled by optimizing its control methods during operation and improving its cooling system. Currently, the liquid-cooled heatsink used in power modules have disadvantages such as large flow resistance and poor heat dissipation performance. In order to enhance the performance of the heatsink, this study first established a three-dimensional finite element model of SiC MOSFETs power module based on a pin fin heatsink. The accuracy of the model was verified by numerical and experimental methods. Secondly, based on numerical analysis, a multi-objective topology optimization method for the power module liquid-cooled heatsink is proposed. This method takes heat exchange and fluid dissipation energy as the objective function and uses weight factors to adjust the influence of each on the objective functions. Additionally, the temperature distribution of the heatsink is considered to optimize its performance. Finally, the numerical results show that the topology-optimized heatsink exhibits better performance at high coolant volumetric flow rates. When the coolant volumetric flow rate is 14 L/min, the pressure drops of topology-optimized heatsink is reduced by 63.94 % and the junction temperature of the power module is reduced by 0.24 % compared with the pin fin heatsink. This topologically optimized heatsink could be helpful to improve the performance of existing power module heatsinks.

UPDATED MATHEMATICAL MODEL OF THE TRUNK PIPELINE SECTION WITH LOOPING IN CASE OF LEAKAGE

Pipeline transport is the main method of moving volumes of oil and oil products, as it has several advantages, for example, quality safety and high throughput. At the same time, it also has some disadvantages, which can include the difficulty of increasing throughput without high capital investments and possible leaks and unauthorized tie-ins into pipelines, which are sometimes difficult to identify. Looping is one of the main ways to increase the throughput of the existing pipeline system, when the need to increase the volume of oil and oil products supplies requires the construction of several parallel pipelines — looping. At the same time, the basic mathematical model for calculating the section of the trunk oil pipeline with looping does not fully cover all the physical processes associated with the distribution of flows in the parallel section, which arise due to turbulences in the connection nodes, as well as head loss along the length of the jumpers. Taking into account the resulting flow redistributions, it becomes difficult to detect a potential leak, since any of the detection methods can not solve the problem with high accuracy with determining the leak coordinate with an unknown distribution of fluid flow rates in a parallel section. As part of the study, an updated mathematical model of the oil export pipeline section with looping was developed, which took into account the presence of a potential leak in the parallel section. Mathematical modeling was carried out on the basis of the assumption of a known coordinate, the effect of leakage on the redistribution of flows in a parallel section was estimated. To assess the impact of the leak, various coordinates and volumetric flow rates were set, based on the calculation results, graphs of the flow rate in looping versus its length and internal diameter were plotted. The study is the initial phase of developing a hydraulic location leak detection system for the oil export pipeline section with looping. The need to refine the mathematical model for determining the flow rate in the parallel section is an urgent and necessary task, the solution of which will allow identifying potential leaks with reliable accuracy.