Pressure Drop Model Research Articles

Development of a viscosity prediction model and investigation into drag reduction in weakly magnetized waxy crude oil

The present study investigates the low magnetization of marine waxy crude oil. Through variance analysis and nonlinear regression analysis, a four-parameter and five-factor model was established to predict the magnetized viscosity of waxy crude oil. The mean absolute relative error of this model is 4.97 %, indicating its suitability for predicting the viscosity of magnetized waxy crude oil with an intensity below 100 mT. The prediction model for magnetized viscosity provides a theoretical basis for predicting key parameters in magnetization transport pressure drop and establishing the wax deposition model under magnetization conditions. By coupling the flow field and magnetic field, a pressure drop model for transporting magnetized waxy crude oil was established to predict the drag reduction effect in magnetized transportation. It is anticipated that magnetization can potentially reduce the drag rate of an oceanic oil pipeline by 8 %–10 %.

Study on Predicting Liquid Production Profile in Horizontal Wells Considering the Mechanism of Annular Flow Resistance and Water Control

The coated particle ICD water control technology has been widely used in horizontal well completion in offshore oil fields in recent years, but there is a lack of research on the simulation and prediction methods for liquid production profiles. By analyzing the dynamic inflow process of fluid, starting from the laws of momentum conservation and mass conservation, a coupled mathematical model of horizontal well reservoir wellbore pressure drop considering the mechanism of annular flow resistance was established, and solved through programming. Based on the actual well data of a certain block in an offshore oilfield, a horizontal well reservoir production model was established. The calculation results of the example show that the annular flow resistance and water control technology can effectively control the balanced liquid production of horizontal wells, thereby increasing the anhydrous oil recovery period and improving the oil recovery rate of the oilfield; The coupling model simulation and prediction method can fully reflect the mutual influence between the oil reservoir, wellbore annulus, ICD, and horizontal wellbore; The effective diameter of the ICD valve affects the changes in oil production and water content. The placement of the ICD well section has a significant effect on water control, and the compactness of the filled particles has a certain impact on pressure and water content changes.

Experimental observation and pressure drop modeling of plug formation in horizontal millifluidic hydraulic conveying.

The hydraulic conveying of glass beads is studied in a horizontal tube. At low flow rates, plugs can be observed moving across the tube, whereas pseudoplugs can be seen at higher flow rates. A statistical analysis of the plugs' and pseudoplugs' velocities and the plugs' lengths observed is conducted. A transition of the propagation speed distribution is established when the crossing over from a plug to a pseudoplug regime is reached, where the peaked plug velocity distribution turns into a uniform pseudoplug velocity distribution. On the other hand, the statistical distribution of plug lengths exhibits a log-normal mathematical shape. The interpretation of the measured pressure drop evolution with the imposed flow rate by means of an effective viscosity shows an apparent shear-thinning effect coming from the dilution of the granular material. This approach provides a predictive tool for pressure drop calculation in the pseudoplug regime.

Pressure drop model of gas-liquid phase for Venturi scrubber in fog-annular flow

Venturi scrubber is widely used in wet dust removal. Its pressure drop performance determines the dust removal efficiency. The commonly used models, most of them are empirical ones, are hard to accurately predict the friction loss between the gas core and the liquid film near the wall, the proportion of the atomized droplets to the deposited liquid film, and the gas holdup, where the influence of the throat length on throttling and the local resistance formation mechanism were not discussed. Therefore, in this study, we established a pressure drop model for Venturi based on the theoretical derivation of two-phase flow and revision of local resistance pressure drop. It uses the similar theoretical method of straight pipe for Venturi, where the iterative method was employed to calculate the liquid-phase conversion coefficient which is related to the cross-flow ratio and the gas holdup. Meanwhile, the experiments and CFD simulations were carried out to validate the model and judge whether the local resistance should be considered. The results show that if the vena contracta extends out of the throat, the unconstrained expansion flow can cause the boundary layer separation, and the fluctuation of the two-phase flow in throat can induce Kelvin-Helmholtz instability, resulting in apparent energy loss. Accordingly, the critical throat length criterion was developed, and the pressure drop model was modified with the deviation less than 17.14%. It provides a scientific basis for establishing the universal two-phase theoretical pressure drop model of Venturi scrubber.

Prediction of Conveying Resistance for a Novel Hydraulic-mechanical Hybrid Vertical Lifting System

Objective: Recently a novel hydraulic-mechanical hybrid vertical lifting system was proposed for deep-sea mining. Accurate prediction of conveying resistance is important for the engineering design of the system. Plug flow of coarse particles is the main flow regime in the system. So far rare attention has been paid to the pressure drop prediction of plug flow of coarse particles. This paper aims to investigate eight theoretical pressure drop models on the applicability to predict the pressure drop of plug flow. Methods: Eight theoretical pressure drop models were studied. In addition, a hydraulic-mechanical hybrid vertical lifting test setup was developed. The novelty of this experimental work is that plug flow of coarse particles is formed and the lifting force of the plug can be measured with the test setup. Tests were conducted with varying particle sizes, lifting speeds and plug weights. The particle size is varied among 13, 18, and 25mm. The lifting speed is varied from 0.02m/s to 0.1m/s. The plug weight varies from 5 to 10kg. The range of Reynolds number for the tested particles is between 208 and 2,000. Results: Prediction errors of eight pressure drop models are derived and compared with the experimental data collected during this study. It was found that similar prediction trends are observed for all pressure drop models under most test conditions. Except the Rose model, all models produce average prediction errors less than 15%. The average prediction error for the Rose model is 20.59%. The average prediction error for the Ergun model is 12.43%. Conclusion: From this study it can be seen that the Ergun model produces the smallest prediction error among the eight selected pressure drop models for the given experimental conditions. Therefore, the Ergun model is considered to be most applicable for the calculation of the conveying resistance for the proposed vertical lifting system.

Hydrodynamics and wet pressure drop model based on flow regimes of the novel Flow-Divided Baffle-Bridge Tray

This study introduces the Flow-Divided Baffle-Bridge Tray (FDBBT), an innovative tray design featuring hole-bridge structures at the caps’ base for pre-distribution of gas and liquid, and stepped baffles configuration at the caps’ top to minimize entrainment. The pressure drop, weep and entrainment of FDBBT were evaluated in a Φ796 mm experimental setup. Compared to the sieve tray and Glitsch V-1 valve tray, FDBBT demonstrated lower pressure drops and significantly reduced entrainment, suggesting a higher operational ceiling. Furthermore, a specialized single-cap experimental apparatus was designed to assess the lifted liquid rate and uncover gas-liquid flow regimes within the cap, namely churn flow, free-surface flow, and periodic-free-surface flow. Employing data from the single-cap experiments, complemented by CFD-assisted analysis, FDBBT's pressure drop model was established and then validated by the Φ796 mm experiments, with most deviations falling within a 5 % threshold.

Fluid Flow Study in a 3D‐Printed Heterogeneous Porous Medium Filled with Carbonate Rock Particles

AbstractA significant aspect of fluid flow in a porous medium is its properties' variation which affects velocity and pressure fields. This work evaluates fluid flow in a 3D‐printed porous medium structure filled with rocky particles. The experimental data were used to propose a pressure drop model and evaluate the accuracy of a pseudohomogeneous approximation. A porous medium with permeability of 8.95 × 10−10 m2 was used in both experiments and simulations. Parameters for the model were estimated and compared to the simulation results. The deviation between experimental and simulated pressure drop across the bed was within 6.00 % for laminar flow regimes, while for transition flow regimes more significant deviations were observed.

Predictive Model of Restart-Up Pressure Drop after Shutdown for Heavy Oil-Water Ring Transportation Pipeline.

Aiming at the problem of restart-up for a heavy oil-water ring transportation pipeline due to instability and damage of the water ring, based on the self-developed design of a small indoor loop simulation experimental device and taking four kinds of ordinary heavy oil in the Lvda oilfield as the research object, the change trend of restart-up pressure drop with time is experimentally studied when the pipeline is restarted-up after shutdown at a constant water flow. On the basis of the regression analysis of the orthogonal restart-up experimental data of four factors (oil holdup, oil viscosity, standstill period, and water cleaning superficial velocity) and mixed levels by the statistical product and service solutions statistical analysis software, a multivariate nonlinear restart-up maximum pressure drop prediction model is established. Through analysis of the characteristics of each stage of the restart-up process, an exponential decay model of restart-up pressure drop with time is created. The research results show that the variations in restart-up pressure drop with time can be divided into two stages: the attenuation stage and the equilibrium stage. The predicted value of restart-up pressure drop with time is in good agreement with the measured one, and the goodness of fit is very close to 1. The maximum restart-up pressure drop rises along with the increase in oil holdup, oil viscosity, standstill period, and water cleaning superficial velocity. The restart-up time prolongs with the increase in oil holdup, oil viscosity, and standstill period but shortens with the increase in water cleaning superficial velocity.

On the nonlinear moonpool responses in a drillship under regular heading waves

In this study, the nonlinear and viscous damping effects on the free-surface elevations of the recess-type moonpool inside a drillship are investigated. Based on a three-dimensional nonlinear potential flow (NPF3D) model, the nonlinear moonpool responses excited by regular heading waves are simulated in the time domain. To consider the vortex-shedding damping effects, induced by nonlinear moonpool responses, the pressure drop model of Chu et al. [Chu et al., “Effects of nonlinearity and viscous damping on the resonant responses in two-dimensional moonpools with a recess,” Appl. Ocean Res. 127, 103295 (2022)] is extended to three-dimensional and combined with NPF3D to form a viscous modified nonlinear potential flow model (referred to as NPF3D_V). The pressure drop model is composed of two parts in order to account for the energy loss from the first harmonic (piston-mode motions) and higher harmonics (sloshing-mode motions), respectively. The investigation focuses on the piston-mode resonance and secondary resonances of the first and second longitudinal sloshing modes. The response amplitude operators of the higher harmonics, by which the nonlinear effects are evaluated, are computed by the NPF3D_V model. It is found that the higher harmonics are noticeable at the excitation frequencies ωn0/m, where secondary resonances of the nth longitudinal sloshing mode are triggered. In addition, it is found that increasing the length of the recess can promote the nonlinear response of the moonpool significantly. For the moonpool with a long recess, the higher harmonics at secondary resonance are comparable to the first harmonics.

Advancing performance of a predictive model for pressure drop of wire gauze corrugated sheet structured packings in deep vacuum applications

A specific fluid dynamics related feature associated with application of corrugated sheet structured packings in distillation columns operated under deep vacuum conditions is that the vapour ascends through a sparsely irrigated packed bed under laminar flow conditions. In the present paper the well-known Delft Model (DM) and two ad-hoc arranged fully appropriate predictive models have been evaluated in this respect using experimental evidence obtained in total reflux vacuum distillation tests carried out with conventional and advanced geometries of a well-established wire-gauze corrugated sheet structured packing. Shortcomings and strong points of compared predictive models, which have exhibited large discrepancies with respect to relative magnitude of governing flow resistances, have been addressed, and upon a tedious elaboration the way paved for upgrading DM accordingly. As shown in present paper, a simple fundamentally sound correction of existing expressions for gas-gas interaction under laminar and turbulent flow conditions, and implementation of empirically founded expressions to account for previously unrecognized form drag related losses, occurring in case of conventional packing due to a rather sharp disrupted change in gas flow direction at transitions between packing layers, resulted in a remarkable advancement in performance of the upgraded Delft model (DM) in all cases. Yet, a further in-depth research effort is necessary to unravel true nature and scale of governing flow resistances.

A simple and accurate model to predict pressure drop in vertical gas wells

ABSTRACT Predicting pressure drop in gas wells is one of the most important issues for designing deliquification technologies and optimizing gas production. Current pressure-drop prediction methods can be divided into analytical and empirical models. Although various models have been proposed to predict pressure drop in wellbores, no model has offered stable performance over wide liquid and gas flowrate ranges. Especially for gas wells with low liquid – gas ratios, very few models have been developed specifically. In this study, a simple and accurate three-point model is developed for predicting liquid holdup in wellbores. The model is based on the liquid holdups and gas velocities at the annular – churn, churn – slug and slug – bubble boundaries and is comprehensive for calculating the liquid holdup in vertical wellbores at different liquid/gas flowrates and pressures. The proposed method was verified with 39 collected laboratory and 182 field measured data points from the literature, which have wide parameter ranges. For comparison, some widely used models in the petroleum industry were also evaluated. In validation with the laboratory data with pipe diameters of 50.8 and 101.6 mm, although the new model has an average percentage error (E3) of 220.1% in the churn flow, ranking fourth of all the evaluated models, the other five indicators in the churn flow and six indicators in the annular flow are lowest of all these evaluated models, resulting in relative performance factors (RPFs) of 0.2 and 0, respectively. In the field measured data, gas and liquid productions range between 0.34 × 104—77.6 × 104 m3/d and 1—347.8 m3/d, tubinghead pressure ranges from 0.7 to 84.7 MPa, which can cover most gas wells. The validation demonstrates that the new model still has good performance with five indicators being lowest. The RPF of the new pressure-drop model in the field measured data ranges is 0.29, still lowest of all these evaluated models, showing better performance than these widely used models in petroleum industry for vertical gas wells. This indicates that the new model can accurately predict pressure drop under different conditions in vertical gas wells.

Clogging and Unclogging of Fine Particles in Porous Media: Micromechanical Insights From an Analog Pore System

AbstractPore clogging and unclogging in porous media are ubiquitous in subsurface hydrologic processes, which have been studied extensively at various scales ranging from a single pore to porous‐medium samples. However, it remains unclear how fluid flow, particle rearrangement, and the arching effect typical of cone‐shaped pore geometry interact and how they are captured by a pressure drop model at the macroscopic scale. Here, we investigate the pore‐scale feedback mechanisms between fluid flow and pore clogging and unclogging using a fully resolved fluid‐particle coupling approach (lattice Boltzmann method‐discrete element method). We first propose to use a truncated‐cone pore to represent realistic pore geometries revealed by X‐ray images of prepared sand packing. Then, our simulations indicate that the pore cone angle significantly influences the pressure drop associated with the clogging process by enhancing particle contacts due to arching. A modified Ergun equation is developed to consider this geometric effect. At the microscale, clogging can be explained by the interparticle force statistics; a few particles in an arch (or a dome) take the majority of hydrodynamic pressure. The maximum interparticle force is positively proportional to the particle Reynolds number and negatively associated with the tangent of the pore cone angle. Finally, a formula is established utilizing fluid characteristics and pore cone angle to compute the maximal interparticle force. Our findings, especially a modified pressure drop model that accounts for pore geometry resistance, provide guidance for applying pore‐scale models of clogging and unclogging to large‐scale subsurface fines transportation issues, including seepage‐induced landslides, stream bank failure, and groundwater recharge.

Effect of guidewire on the accuracy of trans-stenotic pressure measurement—A computational study

Accurate measurement of trans-stenotic pressure drop is vital for risk stratification in coronary artery disease. Currently, in vivo pressure measurement relies mostly on a pressure guidewire inserted into the artery, which inevitably alters local hemodynamics. To precisely assess the impact of guidewire insertion on the accuracy of pressure measurement, this study conducts numerical simulations with both an idealized straight-tube model and a patient-specific model. Results with and without a guidewire model are compared and analyzed. Results from the idealized model reveal that the insertion of a guidewire shifts velocity distribution, increases resistance, and amplifies the pressure drop across the stenosis. The patient-specific model also demonstrates that the guidewire causes non-negligible flow redistribution among the arterial branches, but the influence on pressure drop remains mostly localized. An analytical model for trans-stenotic pressure drop that takes the guidewire into consideration is also proposed and validated against the 3D simulation results. It is observed that the maximum relative error is around 3.0% in the patient-specific model, indicating the effectiveness of the analytical model in physiologically accurate settings. The proposed model can be used to align computed tomography-derived fractional flow reserve values with clinically recognized FFR standards established through guidewire measurements.

EXPERIMENTAL AND THEORETICAL CHARACTERIZATION OF TWO-PHASE FLOW DISTRIBUTION IN UNBALANCED FLOW NETWORKS

This study investigates the two-phase flow distribution of R-1234yf into two-branched channels. The effect of unbalanced pressure drop and tube diameter on the flow distribution was especially characterized and modeled. The experiments were conducted for a mass flux ranging from 393 kg/m<sup>2</sup>s to 1179 kg/ m<sup>2</sup>s, and the inlet quality was fixed at 0.2. The flow distribution was mainly governed by the pressure drop ratio between two branched channels. The mal-distribution under the unbalanced pressure drop condition was mitigated by increasing mass flux, whereas sustained mal-distribution was observed under unbalanced tube diameter conditions. Correspondingly, a theoretical representation of the phenomenon based on the principle of minimum entropy production was developed and adopted to predict two-phase flow distribution in an unbalanced flow network. The characteristics of the experimental data were clearly and quantitatively reflected in the prediction results. Under the unbalanced pressure drop condition, the predictions agreed well with the experimental data, maintaining the maximum deviation within ± 30%, whereas it exceeded ± 30% under the unbalanced tube diameter condition. The analysis of such theoretical formulation suggests the necessity of appropriate pressure drop models of flow impact, contraction, and merging at the outlet channel, which are compatible with the extremization of entropy production for further improving the prediction accuracy without compromising its generality.

Vertically downward gas-liquid flow: Void fraction and pressure drop

Using an air-water mixture and 34 mm ID pipe, a series of pressure drop and void fraction measurements were collected. The observed flow regimes were falling film, annular, bubbly, cap bubble, slug, and churn flows. The temporal fluctuations of void fraction and pressure drop measurements were firstly studied using signals visualization and PDF. It was revealed that both signals can be used to identify the flow regimes. A new flow pattern map is proposed based on the Froude number, calculated using the mixture velocity of the two phases, and the ratio of gas-to-liquid superficial velocities. The behaviors of the total and frictional pressure drops were studied and the influence of the superficial velocities as well as the flow regimes were identified. The experimental results were compared to four existing vertically downward frictional pressure drop models, none of which provided accurate predictions.

Droplet formation of yield stress fluids in asymmetric parallelized microchannels

The microemulsion method is limited due to low productivity. Using Carbopol gel (0.05 %, 0.13 %, 0.2 %) and mineral oil as dispersed phase and continuous phase respectively (3 ≤ Qd ≤ 8, 2 ≤ Qc ≤ 350), the numbering-up of YSFs droplets in asymmetric parallel microchannels are experimentally studied. Ca*(10-3-10) and Cac (10-4-10-2) are introduced to divide the two-dual droplet flow pattern which is conducive to production. It is found that yield stress mainly acts on the necking stage of droplet formation, so the continuous phase flow can be increased to shorten the necking time and improve the size uniformity. The influence of rheology on droplet morphology makes the existing multiphase flow pressure drop model no longer applicable. Therefore, a correction pressure drop model of Carbopol slugs and prediction models of droplet size and generation frequency are proposed. This study provides a reference for the high-throughput production of YSFs droplets in microchannels.

Pressure drop prediction in a pneumatic conveying system with different curvature radius pipes for conveying particles

To investigate the system pressure drop distribution when conveying particle using different curvature radius pipes for the pneumatic conveying system, this paper measured the particle velocity distribution, particle-particle collision characteristics, collision energy loss, minimum pressure drop gas velocity, system pressure drop distribution, and power dissipation for R/D = 3.75, R/D = 5, and R/D = 6.25 pipes. Subsequently, the artificial neural network technique is used to predict the pressure drop of the pneumatic conveying system. It is found that the pressure drop of the system is lower when using the pipe with R/D = 6.25 for conveying particles. Compared to the pipe with R/D = 3.75, the reduction in power dissipation is 3.18 and 5.27% for conveying pellets when using R/D = 5 and R/D = 6.25 pipes, respectively. In addition, the energy loss of the system can be effectively reduced when using the pipe with R/D = 6.25 for conveying particles, which is more beneficial for the particles move in the pipe. The pressure drop model built with artificial neural network can predict the pressure drop value of the system more accurately within ±1.5%.

Modeling single-phase transverse flows in a PWR rod bundle at low Reynolds number

In normal functioning conditions, the primary component of the flow within the rod bundle of a PWR core is in the axial direction, along the rods. However, in accidental situations, such as the refilling or reflooding phase during a Loss of Coolant Accident, or a Steam Line Break accident, transverse flows may significantly affect thermal-hydraulic properties in the core. Such effects have received little attention in system codes such as CATHARE, particularly in anisotropic rod structures at low Reynolds numbers. Here, we develop macroscopic pressure drop models for flows spanning from the creeping regime to unsteady vortex shedding. The averaged model is a generalized Darcy–Forchheimer equation with an apparent permeability including a rotation matrix and a non-linear dimensionless coefficient. The constitutive relations for the intrinsic permeability matrix are derived from polynomial regressions based on results obtained from microscale numerical simulations at different flow directions and Reynolds numbers. We finally test our approach in a case where transverse flow is imposed through a differential of inlet velocities and validate by comparing results from CATHARE with those obtained from a finite element toolbox.

Construction and application of flow pressure drop model of perforated well considering pressure loss of perforation hole

Perforating well is one of the main production wells in reservoir development. Perforating effect directly affects well production, so the optimization of perforating parameters has attracted wide attention. Because pressure difference serves as the driving force for fluid flowing from formation to wellbore, it is important to understand the composition of production pressure difference in perforating well, which can guide the optimization of perforating parameters and the evaluation of perforating effect. In order to clarify the composition of production pressure difference during the production process of perforated wells, a pressure drop model pressure drop model is established based on fluid mechanics theory, which includes a pressure drop model of formation and a pressure drop model of perforation hole. The pressure drop model of formation is firstly constructed based on the Darcy's law and the equivalent resistance method, and the pressure drop model of perforation hole is built by the fluid tube-flow theory. Secondly, the numerical calculation method is adopted to realize the coupling solution of models, and the accuracy of this model is verified by comparison of the Karakas-Tariq model. Finally, the effects of formation physical properties and perforating parameters on flow pressure drop are discussed. The results show that there is a difference of more than 2 orders of magnitude between the pressure drop generated in perforation hole and flow pressure difference, and pressure drop of perforation hole can be neglected in practical applications. Comparing with medium–high permeability reservoirs, optimizing perforation parameters in low permeability reservoirs has a more significant impact on flow pressure drop. Among perforating parameters, perforation length and perforation density have great influence on flow pressure difference, while perforation diameter and phase angle have relatively little influence. These results have certain guiding significance for optimizing perforating parameters in different permeability reservoirs.

Model and Analysis of Pump-Stopping Pressure Drop with Consideration of Hydraulic Fracture Network in Tight Oil Reservoirs

The existing pump-stopping pressure drop models for the hydraulic fracturing operation of tight oil reservoirs only consider the main hydraulic fracture and the single-phase flow of fracturing fluid. In this paper, a new pump-stopping pressure drop model for fracturing operation based on coupling calculation of the secondary fracture and oil-water two-phase flow is proposed. The physical model includes the horizontal wellbore, the fracture network and the tight oil reservoir. Through the numerical simulation and calculation, the wellbore afterflow performance, the crossflow performance between the main hydraulic fracture and the secondary fracture, the fracturing fluid leakoff and the oil-water replacement after termination of pumping are obtained. The pressure drop characteristic curve is drawn out by the bottom-hole flow pressure calculated through the numerical simulation, and a series of analyses are carried out on the calculated pressure drop curve, which is helpful to diagnose the -oil-water two-phase flow state and the fracture closure performance under the control of the fracture network after hydraulic fracturing pumping. Finally, taking a multi-stage fractured horizontal well in a tight oil reservoir in the Junggar basin, China as an example, the pump-stopping pressure drop data of each stage after hydraulic fracturing are analyzed. Through the history fitting of the pressure drop characteristic curve, the key parameters such as fracture network parameters, which include the half-length of main hydraulic fracture, the conductivity of main hydraulic fracture and the density of secondary fracture, the fracture closure pressure are obtained by inversion, thus, the hydraulic fracturing effect of fractured horizontal well in tight oil reservoirs is further quantified.