Frictional Pressure Loss Research Articles

CFD analyses and correlation of pressure losses on the shell-side of concentric, helically-coiled tubes heat exchangers

This paper presents and discusses the results of Computational Fluid Dynamic (CFD) analyses for calculating the friction pressure losses of isothermal flows of liquid sodium, water, and helium gas, on the shell side of annular heat exchangers (HEXs) of concentric, helically coiled tubes. The analyses covering wide ranges of HEX geometrical parameters and flow Reynolds numbers, varied the number of HEX coils from 4 to 16, and examined the effect of refining the numerical mesh grids on the results. Expressing the friction factor in terms of an effective HEX porosity, a weighted average of the areal and volume porosities, collapses the friction factor results on a single curve for developing a continuous dimensionless correlation. The developed correlation, which agrees with the CFD results for 5.0<Re<107 to within ±6%, is given as:f=(58/Re)+(0.315/Re0.02).For low Re flow in helically coiled tubes HEXs, the friction pressure losses increase proportional to the mass flux, G, but inversely proportional to De2. For high Re flow, these losses increase proportional to the mass flux to the 1.98 power, G1.98, and inversely proportional to the equivalent hydraulics diameter to 1.02 power, De1.02. For low Reynolds flows (Re⩽20), the HEX pressure losses are ∼10% lower than in open annuli, but become higher with increased Reynolds number to as much as 97% at Re=107.

Inlet effects on vertical-downward air–water two-phase flow

This paper focuses on investigating the geometric effects of inlets on global and local two-phase flow parameters in vertical-downward air–water two-phase flow. Flow visualization, frictional pressure loss analysis, and local experiments are performed in a test facility constructed from 50.8mm inner diameter acrylic pipes. Three types of inlets of interest are studied: (1) two-phase flow injector without a flow straightener (Type A), (2) two-phase flow injector with a flow straightener (Type B), and (3) injection through a horizontal-to-vertical-downward 90° vertical elbow (Type C). A detailed flow visualization study is performed to characterize flow regimes including bubbly, slug, churn-turbulent, and annular flow. Flow regime maps for each inlet are developed and compared to identify the effects of each inlet. Frictional pressure loss analysis shows that the Lockhart–Martinelli method is capable of correlating the frictional loss data acquired for Type B and Type C inlets with a coefficient value of C=25, but additional data may be needed to model the Type A inlet. Local two-phase flow parameters measured by a four-sensor conductivity probe in four bubbly and near bubbly flow conditions are analyzed. It is observed that vertical-downward two-phase flow has a characteristic center-peaked void profile as opposed to a wall-peaked profile as seen in vertical-upward flow. Furthermore, it is shown that the Type A inlet results in the most pronounced center-peaked void fraction profile, due to the coring phenomenon. Type B and Type C inlets provide a more uniform distribution of the void fraction profile with a reduced coring effect.

A Review of Prediction Methods for Two-Phase Pressure Loss in Mini/Micro-Channels

Previous methods and correlations for predicting two-phase frictional pressure loss in mini/micro-channels are reviewed and compared. The empirical correlations are classified into four groups of modeling approaches: Homogeneous equilibrium models (HEMs), separated flow models (SFMs), direct empirical correlations, and flow pattern specific correlations. In order to examine the characteristics of the predictive methods for two-phase pressure loss in mini-channels and to assess the accuracy of the previous models and correlations, extensive experimental data and correlations that are available in the open literature are collected. The 1175 and 1304 experimental data for the two-phase pressure drop for condensing and boiling flows, respectively, are gathered from 15 papers and reports. The results present that the size of the channel significantly influences the pressure drop. The comparison demonstrates that Cicchitti et al.’s two-phase viscosity model is recommended for predicting two-phase pressure loss when the HEM is used. In general, the SFM with the two-phase multipliers of Muller–Steinhagen and Heck and Kim and Mudawar outperforms others for channel diameters of less than 3[Formula: see text]mm.

Dynamic Numerical Microchannel Evaporator Model to Investigate Parallel Channel Instabilities

A fully dynamic model of a microchannel evaporator is presented. The aim of the model is to study the highly dynamic parallel channel instabilities that occur in these evaporators in more detail. The numerical solver for the model is custom-built and the majority of the paper is focused on detailing the various aspects of this solver. The one-dimensional homogeneous two-phase flow conservation equations are solved to simulate the flow. The full three-dimensional (3D) conduction domain of the evaporator is also dynamically resolved. This allows for the correct simulation of the complex hydraulic and thermal interactions between the microchannels that give rise to the parallel channel instabilities. The model uses state-of-the-art correlations to calculate the frictional pressure losses and heat transfer in the microchannels. In addition, a model for inlet restrictions is also included to simulate the stabilizing effect of these components. In the final part of the paper, validation results of the model are presented, in which the stability results of the model are compared with the existing experimental data from the literature. Next, a parametric study is performed focusing on the stabilizing effects of the solid substrate properties. It is found that increasing the thermal conductivity and thickness of the solid substrate has a strong stabilizing effect, while increasing the number of microchannels has a small destabilizing effect. Finally, representative dynamic results are also given to demonstrate some of the unique capabilities of the model.

MHD design analysis of an annular linear induction electromagnetic pump for SFR thermal hydraulic experimental loop

The design variables of an annular linear induction electromagnetic pump (ALIP) for SFR thermal hydraulic experimental loop were analysed magnetohydrodynamically. The theoretical model of ALIP was configured for magnetohydrodynamic (MHD) analysis. Mathematical equations for the developed pressure, generated by Lorentz electromagnetic force and hydraulic efficiency were derived. The developed pressure was found to be a function of design variables, including the geometrical variables of pump core length, inner core diameter and flow gap, and the electromagnetic ones of turns of coils, frequency and input current. The developed pressure from the MHD analysis was compared and identified with the developed pressure derived by an equivalent circuit method leading to Laithewaite’s standard design formula for a linear induction electromagnetic pump. The design characteristic of the electromagnetic pump was analyzed according to the change of the pump’s geometric and electromagnetic variables, taking into account hydraulic friction pressure loss in the narrow annular gap of the pump. The design specification of ALIP with a flow rate of 900L/min and a developed pressure of 4.5bar was drawn from the characteristic analysis of the variables.

Equivalent circulating density modeling of Yield Power Law fluids validated with CFD approach

A numerical and experimental analysis is conducted on the flow of Newtonian and non-Newtonian fluids in annuli. A numerical model is presented that accurately estimates the annular frictional pressure losses with and without the inner pipe rotation. The numerical model is validated using a CFD software. Experiments are conducted at a 27 m long flow loop using various fluids that can be characterized as Yield Power Law (YPL). The results of the experiments are compared with the results obtained with the numerical model. Today, the most drilling fluids show YPL behavior. The proposed numerical model can calculate the equivalent circulating density while circulating YPL fluids accurately. The model is validated with a CFD software and compared with experimental results, the published experimental results and with the slot approximation. The results obtained from the numerical model shows good agreement with the experiments and also with the experimental results from the literature. The comparisons between the models indicate that the slot approximation can result in large errors especially when the diameter ratio is low, meaning the diameter of the inner pipe is significantly smaller compared to outer pipe. The numerical model is coupled with a stability criterion that determines the onset and offset of the transitional flow between laminar and turbulent regions of YPL fluids. Various degrees of eccentricity are analyzed in terms of pressure profile and flow stability with the proposed method. This study contributes to a better understanding of flow in annuli. The results obtained from this study are useful to predict the transition and the annular frictional pressure loss profiles more accurately than existing methods. Potential applications include risk avoidance and optimized operations.

Performance Modeling and Analysis of a Hollow Fiber Membrane System

A mathematical model was developed for performance of hollow fiber membrane filtration system by considering both frictional and kinetic pressure losses along the fiber. The model was solved numerically as a whole and analytically with the kinetic term omitted with constant driving pressure as the primary control parameter. Numerical simulations first deuctivity (exit velocity) of a hollow fiber was greatly affected by the radius of the fiber. The axial velocity reached a plateau value rapidly along a fiber of a small diameter while increased linearly along a fiber of sufficiently large radius. For given membrane materials (resistance) and fiber length, an optimal diameter of the fiber can be determined to maximize exit velocity.monstrated that the kinetic pressure loss in the hollow fiber was negligible compared to the frictional pressure loss for the current hollow fiber membranes. It was further demonstrated that the prod

Limitations in the Use of the Equivalent Diameter

This paper deals with the inaccuracy assessment of the friction pressure loss estimation based on Darcy formula combined with an equivalent hydraulic diameter and a friction factor valid for circular pipes when applied to a square rod bundle. The assessment has been done by comparing the analytical and semi-empirical predictions with two different CFD codes results: CFX and NEPTUNE_CFD. Two different analytical approaches have been considered: the whole-bundle and sub-channel approaches, both for laminar and turbulent flow conditions. Looking at results, it is reasonable to assume that an error in the range of 11% - 23% is likely when using equivalent diameter in the laminar regime. In the case of turbulent regime, the equivalent diameter works better and the error is in the range between a few percent and ~12%.

Calibration of friction pressure losses during hydrofrac

Calibration of friction pressure losses during hydrofrac

Modeling and Experimental Study of Solid–Liquid Two-Phase Pressure Drop in Horizontal Wellbores With Pipe Rotation

Determining pressure loss for cuttings-liquid system is very complicated task since drillstring is usually rotating during drilling operations and cuttings are present inside wells. While pipe rotation is increasing the pressure loss of Newtonian fluids without cuttings in an eccentric annulus, a reduction in the pressure loss for cuttings-liquid system is observed due to the bed erosion. In this study, cuttings transport experiments for different flow rates, pipe rotation speeds, and rate of penetrations (ROPs) are conducted. Pressure loss within the test section and stationary and/or moving bed thickness are recorded. This study aims to predict frictional pressure loss for solid (cuttings)–liquid flow inside horizontal wells using computational fluid dynamics (CFD) and artificial neural networks (ANNs). For this purpose, numerous ANN structures and CFD models are developed and tested using experimental data. Among the ANN structures, TrainGdx–Tansig structure gave more accurate results. The results show that the ANN showed better performance than the CFD. However, both could be used to estimate solid–liquid two-phase pressure drop in horizontal wellbores with pipe rotation.

Selectivity and Mass Transfer Limitations in Pressure-Retarded Osmosis at High Concentrations and Increased Operating Pressures.

Pressure-retarded osmosis (PRO) is a promising source of renewable energy when hypersaline brines and other high concentration solutions are used. However, membrane performance under conditions suitable for these solutions is poorly understood. In this work, we use a new method to characterize membranes under a variety of pressures and concentrations, including hydraulic pressures up to 48.3 bar and concentrations of up to 3 M NaCl. We find membrane selectivity decreases as the draw solution concentration is increased, with the salt permeability coefficient increasing by a factor of 2 when the draw concentration is changed from 0.6 to 3 M NaCl, even when the applied hydraulic pressure is maintained constant. Additionally, we find that significant pumping energy is required to overcome frictional pressure losses in the spacer-filled feed channel and achieve suitable mass transfer on the feed side of the membrane, especially at high operating pressures. For a meter-long module operating at 41 bar, we estimate feedwater will have to be pumped in at a pressure of at least 3 bar. Both the reduced selectivity and increased pumping energy requirements we observe in PRO will significantly diminish the obtainable net energy, highlighting important new challenges for development of systems utilizing hypersaline draw solutions.

The Effects of Drillstring-Eccentricity, -Rotation, and -Buckling Configurations on Annular Frictional Pressure Losses While Circulating Yield-Power-Law Fluids

Summary An experimental study followed by comprehensive flow modeling is presented. The experiments were conducted on a horizontal annulus with drillstring under compression, considering the influence of rotation on frictional pressure losses of yield-power-law (YPL) fluids. Flow through various buckling configurations with and without drillstring rotation was investigated. Correlations of critical Reynolds numbers are presented that predict the onset and offset of transition from laminar- to turbulent-flow regions in concentric and eccentric annuli. A broad model of flow of YPL fluids is proposed for concentric, eccentric, and buckled configurations. The model includes the effects of rotation in laminar, transitional, and turbulent flow. A 91-ft inner pipe was rotated while applying axial compression during flow. At the no-compression case, eccentricity of the inner pipe is varied as the drillstring rotated. The aim for such a design was to simulate actual drilling operations. The test matrix involves flow through sinusoidal, transitional, and helically buckled drillstring. The effect of pitch length is investigated. Helical modes with two different pitch lengths were tested. Eight distinct YPL fluids were used to examine the dependence of pressure losses on fluid parameters. In the theoretical part, a stability criterion is modified to determine the onset of transitional flow of YPL fluids and a correlation is proposed for practical purposes. In addition, pressure-loss-prediction models are presented for the flow of YPL fluids through concentric, eccentric, free, and buckled configurations of the drillstring, with and without rotation. The proposed models are compared with data from the literature and the experiments. It has been observed that increasing eccentricity and rotary speed causes an earlier transition from laminar to turbulent flow. Results suggest reduced pressure losses with an eccentric pipe. In addition, buckled configurations showed a further decrease of frictional pressure losses as the compression increases. In the helical mode, two pitch lengths are compared, and decreasing the pitch length resulted in a decrease in pressure losses. Rotation tests are conducted with free and buckled configurations. Rotation in the free-drillstring mode showed an increase in pressure losses as the rotary speed of the drillstring increases. Amplified vigorous motion of the drillstring is visually observed as the drillstring is buckled while rotating. Rotating the drillstring while buckled showed a further increase in pressure losses compared to rotating in free mode. This additional increase in pressure losses is attributed to the more-dynamic motion of the drillstring. Distinct differences of pressure losses in the effects of buckling and rotation are observed in laminar, transitional, and turbulent flow. Significant differences are measured in the transition region.

Comparative Analysis of the Pressure Loss from the Circulation of Drilling Fluid During Microhole Drilling with the Use of Coiled Tubing

The choice of fluid-circulation conditions is of great importance in microhole drilling (MHD) conducted with coiled tubing (CT) as the drill string because of the long length and small bending radius of the tubing coiled on the reel, which result in high circulation friction pressure loss (CFPL). A model for calculating CFPL in flexible CT has been constructed by combining a power-law fluid flow equation and the Dean Number. The calculations have revealed patterns of change in the CFPL during MHD. The CFPL in CT, whether reeled or in downhole, increases steeply with an increase of drilling fluid flow rate, decreases slowly with increasing CT inner diameter, and rises linearly with an increase in CT length. The total CFPL over the entire CT decreases slowly with decreasing CT length when the CT is run downhole from the reel. Deep MHD is suitable only for low drilling-fluid flow rates when the inner diameter of CT is large. Suitable ranges of drilling-fluid flow rate and CT inner diameter have been determined for various drilling depths. The research will provide a basis for selecting CT and drilling-fluid circulation parameters for MHD.

Ultra-deepwater blowout well control analysis under worst case blowout scenario

Because of the high frictional pressure losses in kill lines in ultra-deep water wells, it is challenging to control the blowout under worst case blowout scenarios. The operational parameters need to be carefully controlled to avoid exceeding the operational limitations such as breaking the formation or exceeding available pump pressure limit. In this study, dynamic kill simulations of multiphase flow are carried out to evaluate the operational parameters during the kill process. The simulations account for transient changes including frictional pressure losses, u-tube effect and fluid density variations. By optimizing the operational sequence with regards to, kill mud density, pump flow rate, pump down staging, relief well drillstring and trajectory, blowout can be controlled without exceeding the operational window. This paper shows that 10,390 bbls of the kill mud, 8000 psi pump pressure limit, optimum flow rate arrangement, and minimum 270 min required to get full kill mud return to the sea floor during the well kill operation. Through the aid of advanced transient software models, assessment of the required capacity to kill a blowout enables development of realistic contingency plans to ensure that well control can be re-established in case of an ultra-deep water worst blowout scenario.

Frictional pressure loss of drilling fluids in a fully eccentric annulus

It is common practice when drilling oil and gas wells to assume that the drillstring is placed concentrically in the annular space with either the open hole or previous casing strings in order to predict annular frictional pressure losses. The assumption of such a concentric annulus is, however, a considerable simplification that may not properly reflect the majority of drilling applications in the field. In fact, with an increasing number of deviated/horizontal and extended reach wells being drilled, a fully eccentric annulus is actually present in a large section of the wellbore.In this study, we apply experimental, analytical, and numerical approaches to investigate the impact of drillpipe eccentricity on the annular pressure loss while circulating non-Newtonian drilling fluids. The length of the experimental section of a flow loop was 27.74 m (91′) and it consisted of 0.0245 m (1″) steel drillpipe and 0.0571 m (2.25″) acrylic casing with the inner diameter of 0.0508 m (2″). Drillpipe was placed at the bottom of the casing, thereby simulating a fully eccentric annulus. Four Yield Power Law (YPL) drilling fluids were tested in this flow loop. Annular pressure loss for a wide range of laminar flow rates was recorded for each fluid. A numerical model based on a finite difference approach was developed to estimate the annular pressure loss. Subsequently, the experimental data was compared with the proposed model and also with several other widely used analytical and numerical approaches previously reported in the literature. The obtained results show that in the laminar flow regime, the annular frictional pressure loss in a fully eccentric annulus is considerably less than a concentric annulus, on occasions by less than 50%. In general, all the applied models under-estimated the effect of eccentricity on pressure loss. However, the novel proposed model showed the least discrepancy with the experimental data. Furthermore, it was found that the difference between the estimated and experimental results increases with increasing fluid yield stress. This suggests that models and/or correlations that are developed to correct for the eccentricity effect for fluids with negligible yield stress (for instance Power Law fluids) are not suitable to estimate the pressure loss for YPL fluids with elevated yield stress.

A New Model to Determine the Two-phase Drilling Fluid Behaviors through Horizontal Eccentric Annular Geometry, Part B: Frictional Pressure Losses Estimation

Drilling with aerated muds is becoming more often used in underbalanced drilling operations. One of the major challenges that has to be faced in such operations is the estimation of the physical behavior of aerated fluids inside the annulus. In this study, experiments have been conducted at METU Multiphase Flow Loop using air-water mixtures with various in-situ flow velocities of 0–120 and 0–10 ft/s, respectively. This study aims to develop a model to estimate the frictional pressure losses for two-phase flow through horizontal eccentric annular geometry. In order to estimate the frictional pressure losses, three different methods were developed: (i) definition of new friction factors by using experimental data; (ii) modification of Lockhart-Martinelli pressure loss correction factor; and (iii) modification of Beggs and Brill model by changing the equation constants. The comparison of the developed models with experimental data has shown that frictional pressure losses can be estimated with a reasonable accuracy.

Model inference using the Akaike information criterion for turbulent flow of non-Newtonian crude oils in pipelines

The friction factor is a crucial parameter in calculating frictional pressure losses. However, it is a decisive challenge to estimate, especially for turbulent flow of non-Newtonian fluids in pipes. The objective of this paper is to examine the validity of friction factor correlations adopting a new informative-based approach, the Akaike information criterion (AIC) along with the coefficient of determination (R 2). Over a wide range of measured data, the results show that each model is accurate when it is examined against a specific dataset while the El-Emam et al. (Oil Gas J 101:74–83, 2003) model proves its superiority. In addition to its simple and explicit form, it covers a wide range of flow behavior indices and generalized Reynolds numbers. It is also shown that the traditional belief that a high R 2 means a better model may be misleading. AIC overcomes the shortcomings of R 2 as a trade between the complexity of the model and its accuracy not only to find a best approximating model but also to develop statistical inference based on the data. The authors present AIC to initiate an innovative strategy to help alleviate several challenges faced by the professionals in the oil and gas industry. Finally, a detailed discussion and models’ ranking according to AIC and R 2 is presented showing the numerous advantages of AIC.

Experimental Study on Pressure Drop of Aluminum-Oxide/Water Nanofluids

In this experimental work, frictional and local pressure losses were investigated for aluminum-oxide/water nanofluids flowing inside a circular smooth pipe, sudden contraction and expansion pipe sections, 45 and 90 deg elbows in turbulent regime. The aluminum-oxide/water nanofluids used in the experiments have volume concentrations of 1, 2, and 3%; and they have nanoparticle dimensions of 30–40 and 40–80 nm. Also, the density and viscosity of the nanofluids were determined. This study shows that aluminum-oxide/water nanofluids cause a proportional increase in frictional and local pressure losses for turbulent flow. Accordingly, the traditional equations for the friction factor and the pressure loss coefficient fail to accurately estimate the pressure drop for turbulent flows of nanofluids. New empirical equations of the friction factor and the pressure loss coefficient were formulated in the turbulent flow.

Frictional Pressure Losses of Fluids Flowing in Circular Conduits: A Review

Summary Fluids are pumped through circular conduits in various operations in the petroleum industry. These fluids may be Newtonian or non-Newtonian, clean or proppant-laden, polymer-based or surfactant-based, single-phase or multiphase, drag-reducing, and others. They are pumped through straight and coiled tubing under laminar- or turbulent-flow conditions. Calculation of frictional pressure losses for these circumstances is crucial for the success of the operation. A simple Darcy-Weisbach (Darcy 1857) equation is widely used to calculate frictional pressure losses in pipes. However, a unique term, friction factor, has to be determined. Enormous numbers of correlations are available to determine the friction factor. These correlations vary in complexity and applicability and have their own positive and negative features. In addition, several parameters included in the correlations have to be identified, and they vary from one correlation to another. The task at hand is determining the proper correlation. Estimating the friction factor is not an easy task, and it can be very confusing. Inaccurate estimation may lead to erroneous results and failure of operations. This study provides a comprehensive review of the friction-factor correlations and presents how to select the most-suitable correlation for specific conditions. It discusses the parameters involved in friction-factor calculation and how to define them. The authors compare and question the applicability, accuracy, and limitations of each correlation to propose the most-accurate ones. An innovative, user-friendly, and step-by-step code using the most widely used and accurate correlations can then be developed to predict the friction factor. The present study is an effort to simplify the friction-factor challenge. It aims at providing the most-accurate friction-factor correlations to overcome the complexity faced when calculating frictional pressure losses. In conclusion, it summarizes the state of the art in the field of fluids and hydraulics in the oil and gas industry.

Structural mechanical and thermal hydraulic aspects on the behaviour of crack like leaks in piping

The evaluation of fluid flow rates through crack-like leaks in pressurized components of NPPs plays an important role for leak-before-break considerations. When using available simplified methods for the estimation of critical discharge flow rates, a suitable friction factor has to be chosen. Guidelines are given in the German code KTA 3206 based on investigations of leak rate experiments summarized in this paper. The frictional pressure loss in different leak flow approaches has to be chosen consistently in order to obtain comparable results with different models.Thermal hydraulic and structural mechanical analyses were performed for a postulated leak in the pressurizer surge line (SL) of a PWR Konvoi type under design basis accident conditions. The leak was postulated in form of a through-wall crack in circumferential direction. The size of the leak was calculated in the framework of Finite Element calculations with the code ADINA using an analysis model of a cooling loop of Konvoi type. With the calculated leak size, an ATHLET calculation was conducted, also examining the influence of the consideration of a variable leak size depending on the system pressure and mechanical loads. In the investigated case, the implication of the decreasing leak size, especially on the course of the remaining system pressure, cannot be neglected. The reduction of the leak area amounts in the transient examined to ca. 25% after about 1 h due to both the system pressure and temperature decrease and leads therefore also to an approximately 23% smaller leak rate. These results are dependent on the assumed position of the leak.Concerning the determination of the leak rates as critical flow-through rates with simplified methods good agreement has been achieved although the approaches differ considerably in parts. Relevant influence factors are the inflow losses in the crack channel, the consideration of the hydraulic diameter in connection with the leak area and the assumptions on the flow resistance coefficient due to the roughness of the crack surfaces.