Solids Friction Factor Research Articles

Numerical investigation and correlation development for pressure drop in pneumatic conveying through blinded T-bends

Accurate pressure drop prediction is crucial for pneumatic conveying system design. This study numerically investigates pressure drop in gas-solid flow through pipelines with blinded T-bends using a four-way coupled Eulerian-Eulerian approach. Three-dimensional simulations were conducted for pipe diameters of 54 and 70 mm, four T-bend lengths, and fly-ash particles (25–250 μm). Pressure drop prediction is validated against experimental data. Pressure drop initially increased with particle diameter, then decreased. Pressure drop increases with increase in particle density, solid volume fraction, gas velocity, and solid loading rate but decreases with increase in pipe diameter. Increasing the blinded leg length-to-pipe diameter ratio from 0.5 to 1.5 results in an increase in pressure drop, while further increasing it to 2 leads to a decrease. This decrease is approximately 10 % for dilute flows and 40 % for dense flows. A correlation for solid phase friction factor in blinded T-bends is proposed for practical applications.

Effect of moisture content on flow behavior and resistance characteristics of dense-phase pneumatic conveying

The flow characteristic of high pressure dense-phase pneumatic conveying of pulverized coal is essential to the safe and stable operation of the gasifier. In this paper, the effects of coal moisture content on conveying behavior and resistance characteristics of dense-phase pneumatic conveying were explored. Meanwhile, a model of the additional pressure drop of particles was proposed and compared with the experimental data. The results show that though the resistance and cohesiveness increase with increasing moisture content, its influence is different in dense and dilute phase. In the dense-phase region, the coal with lower moisture content shows a larger solid mass flow rate and solid concentration; while in the dilute-phase region, the moisture content has minor effect on conveying characteristics. For the coal with lower moisture content in dense-phase region, the solid mass flow rate and solid concentration are larger, and the gas velocity has a small effect on solid friction factor, due to its smaller cohesiveness and resistance, which is showed in our experiments and inferred from our model. The additional pressure drop model was proposed for straight pipes and bends, whose parameters are probably effective than the existing parameters in this kind of model, as the deviation in the vertical rise pipe, horizontal pipe and bend pipe is controlled within ±30%, and the corresponding vertical down pipe are controlled within ±40%.

Modelling and analysis of flow of powders through long pipelines

Purpose The purpose of this paper is to focus on predicting the pressure drop in fluidized dense phase pneumatic conveying of fine particles through pipelines by modelling the solids friction factor in terms of non-dimensional parameters using experimental data of definite pipeline configuration. Finally, the model is to be tested for a different pipeline configuration. Design/methodology/approach Solids friction factor has been expressed in terms of certain non-dimensional parameters such as density ratio, solids loading ratio and mean particle diameter to pipe diameter ratio, and a certain number of coefficients and exponents. Experimental data of five conveying materials (two types of fly ash, two types of alumina and one type of cement meal) for a pipeline configuration of diameter 53 mm and length 173 m and another conveying material EPS dust for two pipeline configurations (69-mm diameter, 168-m long; 105-mm diameter, 168-m long) have been used to calculate the unknown coefficients or exponents of the mathematical model for solids friction factor. Findings The developed model gives the best results in predicting the pressure drop for the pipelines that are less than 173-m long, but the model shows a large error for the pipelines more than 173-m long. Research limitations/implications Current research will be helpful for the researchers to model the process of pneumatic conveying through long distances. Practical implications The method will be helpful in conveying powder materials through long distances in cement or brick industry, alumina industry. Social implications Fly ash piles over at the nearby places of thermal power plants. Pneumatic conveying is the best method for transporting the fly ash from the location of power plants to the nearby brick industries or cement industries. Originality/value Solid friction factor has been presented in terms of four non-dimensional parameters and evaluated the accuracy in predicting the pressure drop for two different pipeline configurations.

Review and analysis of solids friction factor correlations in fluidized dense phase conveying

ABSTRACT Few researchers have presented solids friction factor correlations for the fluidized dense phase conveying of fine particles or powders. Pressure drop for conveying can be predicted using these correlations. These correlations predict the pressure drop with minimum error margin for a definite pipeline configuration or for some specific types of conveying materials. Few researchers have applied their correlations for different pipeline configurations (of different pipeline lengths or diameters) or different conveying materials to predict the pressure drop. In this paper, different solids friction factor correlations for the fluidized dense phase conveying have been considered which are available in the literature and the behaviour of these correlations have been studied under length scale-up or diameter scale-up conditions. It has been observed that only few correlations exhibit natural pressure drop variation with change in pipeline length or pipeline diameter.

A study of energy loss due to particle to particle and wall collisions during fluidized dense-phase pneumatic transport

This paper results from ongoing research into the modelling of solids friction for fluidized dense-phase pneumatic transport of fine powders. Energy loss due to particle to particle and particle to wall collisions have been modelled. A new model for particle velocity has been introduced using numerical analysis and variable fluidized bulk density, which has shown that slip velocity decreases with an increase in the mass flow rate of air and dimensionless length. A new modified two-layer model for solids friction factor has been developed by introducing the collision effect and particle velocity model in the model of solids friction. The results of scale-up validation in larger and longer pipelines for four different products have shown that for the majority of the cases, the new model for solids friction factor has resulted in better predictions in dense-phase flow conditions compared to the predictions obtained by an existing two-layer model.

An evaluation of testing and modeling procedure for solids friction factor for fluidized dense-phase pneumatic conveying of fine powders

For the reliable design of a pneumatic conveying system, accurate estimation of solids friction factor through horizontal straight pipe is of paramount interest. Although the “straight pipe” method is fundamentally more appropriate, the “back calculation” approach provides several practical advantages for testing and modeling. However, earlier literature reports that “back calculation” approach suffers from 40 to 150% inaccuracy in prediction of total pipeline pressure drop in scale-up pipes, which had been discouraging for its use. In the present work, it has been argued that much of the criticism for the inaccuracy of back calculation method lies with the choice of its format of modeling solids friction factor. In this paper, “back calculation” method of modeling has been used by employing a “two layer” model format for solid friction factor for fly ash, ESP dust and cement. These models, when scaled up to predict the total pipeline pressure drop in larger and longer pipelines, have resulted in overall deviation from experimental data ranging from 3 to 35%, which is a significant improvement in prediction capability. The results prove that the selection of a better format of model for solids friction factor could significantly improve the reliability of “back calculation” method.

Modelling solids friction for fluidized dense-phase pneumatic conveying

Fluidized dense-phase pneumatic conveying of powders has a number of benefits in various industries such as coal-fired thermal power plants, chemical, cement, pharmaceutical, petrochemical plants, etc. However, reliable designing of fluidized dense phase pneumatic conveying system is significantly difficult due to the complex and turbulent nature of the flow. In the present work, power station fly ash was conveyed through different pipeline configurations. Governing equations were developed for the fluidized dense-phase flow in the pneumatic conveying system and were solved using Runge-Kutta-Fehlberg method (RKF45). The results revealed that the particle velocity and actual gas velocity and the ratio of the two velocities increase along the direction of flow, while an opposite trend was observed for the solids volumetric concentration. A particle velocity model has been developed using solid loading ratio and dimensionless velocity terms. This particle velocity model, when employed in the existing two-layer model format for solids friction factor, has provided improved scale-up predictions (under diameter and length scale-up conditions) compared to the original two-layer model.

A re-evaluation of design equations for the established flow region of vertical dilute-phase pneumatic conveyors

An analysis of data sets from the literature was completed for particle velocities of granular material in vertical, dilute-phase pneumatic conveyors. The generally accepted equation of motion used to describe such velocity data incorporates the solids friction factor, a variable term based on the additional pressure drop due to solids. The analysis determines that rather being a variable, the term is a constant related to the physical properties of the particle that influence its bouncing behaviour as it progresses along the pipeline. In addition, the analysis reveals that particle drag coefficients determined from the particle velocity data differ significantly from values taken from the standard drag coefficient curve. This observation was confirmed by drag coefficient measurements reported in the literature and made using particle-elutriating equipment. The drag coefficients from the pneumatic conveying experiments and the test equipment were determined under turbulent conditions, which is considered to account for the difference in values from the standard curve determined under quiescent conditions. Relationships are presented that predict the turbulence-influenced drag coefficients and the particle velocity data with good accuracy. These relationships are used to predict pressure drops for two data sets presented with the particle velocity data. The single-term pressure drop equation is used and predicts with good accuracy as well as producing the trough-shaped curve characteristic of the measured pressure drops.

On developing improved modelling for particle velocity and solids friction for fluidized dense-phase pneumatic transport systems

Pneumatic transport of fine powders in fluidized dense-phase pneumatic conveying of powders has become popular in several industries because it offers various advantages, such as reduced air flow and gas velocity, reduced pipeline sizing and wear rate, reduced size requirement of gas–solid separator unit etc. For the reliable design of a pneumatic conveying system precise estimation of the solids friction factor through horizontal straight pipes is essential, but it is a challenging task till date because of the highly concentrated, turbulent, and complex nature of the gas–solids mixture. In the present work, power station fly ash (median particle diameter: 22 μm; particle density: 2370 kg/m3; loose-poured bulk density: 660 kg/m3) and cement (median particle diameter: 19 μm; particle density: 2910 kg/m3; loose-poured bulk density: 1080 kg/m3) were conveyed through different pipeline configurations (i.e., 65-mm inner diameter × 254-m-long and 80/105-mm inner diameter × 407-m-long step-up pipeline). For the fluidized dense-phase flow in pneumatic conveying system, governing equations were developed and the same were solved using fourth-fifth-order Runge-Kutta-Fehlberg (RKF45) method. The results revealed that the particle velocity and actual gas velocity and the ratio of the two velocities increases along the direction of flow, while an opposite trend was found for the solids volumetric concentration. The particle velocity and actual gas velocity terms were then included in an existing pure dilute-phase model (for solid friction factor) to modify it, by incorporating sub-models for particle and actual gas velocities and impact and solids friction factor and make it suitable for dense-phase mode. The solids friction-factor model was then validated by comparing the experimental and predicted pneumatic conveying characteristics for different solids flow rates and by using it to predict the total pipeline pressure drops for larger and longer pipelines. The new model has shown reliable predictions in the dense-phase region.

Stability and phase space analysis of fluidized-dense phase pneumatic transport system

Fluidized dense-phase pneumatic conveying of powders is gaining popularity in several industries, such as power, chemical, cement, refinery, alumina, pharmaceutical, limestone, because of reduced gas flow rate and power consumption, decreased conveying velocities, improved product quality control, reduced pipeline sizing and wear rate, increased workplace safety etc. However, understanding the fundamental transport mechanism of fluidized dense-phase transport has only made limited progress because of the highly concentrated and turbulent nature of the gas-solids mixture. In the present work, pneumatic conveying trials were conducted with power plant fly ash (median particle diameter: 30 μm; particle density: 2300 kg/m3; loose-poured bulk density: 700 kg/m3) through 69 mm I.D. × 168 m long pipeline. The mass momentum and energy balance of the system lead to the formulation of governing equations of flow for the dense-phase pneumatic conveying, which were solved using Runge-Kutta-Fehlberg (RKF45) method for different mass flow rates of fly ash and air. The stability of the system has been established corresponding to the four critical conveying parameters: pressure drop, particle and solid velocities and solid volume fraction. The linear stability analysis for the system has been established using Lyapunov's exponent method along with Hurwitz criteria. This results of stability analysis indicate a possible change in the characteristics of dunes and transport mechanisms in the direction of flow. The system experiences drop in pressure and solids volume fraction with increasing air and solids velocity. The study has been conducted at different combinations of mass flow rates of air and solids. Two- and three-dimensional phase space portraits of critical system parameters under study (pressure drop, particle velocity, gas velocity, solids volume fraction and solids friction factor) show the bistable and multi-stable operating regions for the system.

Numerical simulation of fluidized dense-phase pneumatic conveying of powders to develop improved model for solids friction factor

Accurate prediction of the solids friction factor through horizontal straight pipes is important for the reliable design of a pneumatic conveying system, but it is a challenging assignment to date because of the highly concentrated, turbulent, and complex nature of the gas–solids mixture. Power-station fly ash was transported through different pipeline configurations. Numerical simulation of the dense-phase pneumatic conveying systems for three different solids and two different air flow rates have shown that particle and actual gas velocities and the ratio of the two velocities increases in the flow direction, whereas the reverse trend was found to occur for the solids volumetric concentration. To develop a solids friction-factor model suitable for dense-phase flow, we modified an existing pure dilute-phase model by incorporating sub-models for particle and actual gas velocities and impact and solids friction factor. The solids friction-factor model was validated by using it for scale-up predictions for total pipeline pressure drops in longer and larger pipes and by comparing experimental and predicted pneumatic conveying characteristics for different solids flow rates. The accuracy of the prediction was compared with a recently developed two-layer-based model. We discussed the effect of incorporating the particle and actual gas velocity terms in the solids friction-factor model instead of superficial air velocity.

On developing improved modelling and scale-up procedures for pneumatic conveying of fine powders

Pneumatic transport of fine powders in fluidized dense-phase mode is becoming increasingly popular in various industries, such as power, chemical, cement, refinery, alumina, pharmaceutical, limestone, to list a few, because of the reasons of reduced gas flow rate and power consumption, decreased conveying velocities, improved product quality control, reduced pipeline sizing and wear rate, increased workplace safety etc. For the reliable design of a pneumatic conveying system, it is important to accurately predict the total pipeline pressure drop. However, accurate prediction of pressure drop from an improved understanding of the fundamental transport mechanism of fluidized dense-phase flow condition has only made limited progress till now because of the highly concentrated and turbulent nature of the gas-solids mixture. Power plant fly ash (median particle diameter: 30μm; particle density: 2300kg/m3; loose-poured bulk density: 700kg/m3) was conveyed through different pipelines (69mm I.D.×168m long; 105mm I.D.×168m long; 69mm I.D.×554m long). 8 different fly ash samples were tested in a fluidizing column for their deaeration characteristics and fluidized bulk densities were determined. Governing equations of flow for the dense-phase pneumatic conveying system of fine powders were solved using Runge-Kutta-Fehlberg (RKF45) method for different fluidized bulk densities of fly ash and air flow rates. The results have shown that the particle and actual gas velocities and the ratio of the two velocities increase in the direction of flow, while a reverse trend was apparent for the solids volumetric concentration. The results were compared against the predictions obtained using existing empirical relations for particle velocity. To develop an improved model for solids friction factor, an existing reliable pure dilute-phase model has been modified for dense-phase flow condition by incorporating sub-models for particle to actual gas velocity and impact and solids friction factor. The developed solids friction factor model was validated by using it to predict the total pipeline pressure drops for larger and longer pipelines and by comparing the experimental and predicted pneumatic conveying characteristics. The results have shown improved reliable predictions and that the model is capable of addressing the gradual transition of flow mechanism from dense- to dilute-phase. The accuracy of prediction is similar (in fact better in certain scale-up cases) when compared to a recently developed two-layer based model (developed by some of the authors). The results demonstrate the importance of incorporating particle and actual gas velocity terms in the model of solids friction factor instead of the prevailing techniques that overly depend on using superficial gas velocities.

Modeling solids friction factor for fluidized dense-phase pneumatic transport of powders using two layer flow theory

Fluidized dense-phase pneumatic conveying of powders is becoming increasingly popular in various industries, such as power, chemical, cement, refinery, alumina, pharmaceutical, limestone, to list a few, due to the reasons of reduced gas flows and power consumption, improved product quality control, reduced pipeline sizing and wear rate, increased workplace safety etc. An accurate estimation of total pipeline pressure drop is of paramount importance for the reliable design of a pneumatic conveying system. However, because of the highly concentrated and turbulent nature of the gas–solids mixture, fundamentally understanding the flow mechanism and accurately predicting the pressure drop as an important design parameter has only made limited progress so far. This paper results from an ongoing investigation into developing a validated modeling procedure for solids friction factor for the accurate prediction of pressure drop and optimal operating conditions for fluidized dense-phase pneumatic conveying systems. Under the present study, a two-layer based model has been developed by separately considering the solids friction contributions of the non-suspension (dense) bed of powders flowing along the bottom of pipe and the suspension (dilute-phase flow) of particles occurring on top of the non-suspension layer. Volumetric loading ratio and dimensionless velocity have been used to model the non-suspension dune flow layer. A solids impact and friction term and dimensionless velocity have been employed to model the dilute-phase flow due their established reliability. Models have been developed using the straight-pipe conveying data of two types of fly ash, cement and ESP dust (median particle diameter: 7 to 30μm; particle density: 2300 to 3637kg/m3; loose-poured bulk density: 610–1080kg/m3). The developed models for solids friction were validated for their scale-up accuracy by using them to predict the pressure drops in five larger and longer pipelines (69mm I.D.×168m long; 105mm I.D.×168m long; 69mm I.D.×554m long, 65mm I.D.×254m long and 80/100mm I.D.×407m long pipes) and by comparing the experimental versus predicted pneumatic conveying characteristics. The two-layer model provided improved accuracy compared to existing models indicating that the model is able to adequately address the dense- to dilute-phase transition criteria.

A model of solids friction factor for fluidized dense phase pneumatic conveying

Solids friction factor is a parameter required for predicting the pressure drop in a process of pneumatic conveying. It depends upon a number of non-dimensional parameters. In this paper, experimental data for a 2m long section of a 173m long pipeline has been used to develop a mathematical model for solids friction factor. The model predicts the pressure drop with a low error margin for the 2m long pipeline. Although the model has been developed for a 2m long straight pipeline with fly ash as the conveying material, it has also been scaled-up for a 173m long straight pipeline. By scaling-up, the predicted pressure drop lies within an acceptable error margin. Since the model seems to be having less dependence upon the parameter of particle density, it predicts the pressure drop with less error margin for the experimental data of other conveying materials such as alumina and cement. The model shows high error in predicting pressure drop for the experimental data for a different pipeline configuration.

Modelling fluidized dense-phase pneumatic conveying of fly ash

This paper presents the results of an ongoing investigation into modelling important design criteria, such as minimum transport condition, straight-pipe pressure drop and solid friction factor for fluidized dense-phase pneumatic conveying of powders. Fly ash (median particle diameter: 19μm; particle density: 1950kg/m3; loose-poured bulk density: 950kg/m3) was conveyed over a wide range of flow conditions (from fluidized dense- to dilute-phase) under different conditions of pipeline diameters and lengths (viz. 43mm I.D×24m length, 54mm I.D×24m length, 69mm I.D×24m length and 69mm I.D×70m length). To define the safe minimum transport boundary, a Froude number based criteria at the pipe inlet has been used (Fri=7). The Froude number based criterion is aimed to address the requirement of different conveying velocities for different pipe diameters. Straight-pipe pneumatic conveying characteristics obtained from two sets of pressure tapings installed at different locations of pipeline have shown that the trends and relative magnitudes of the pressure drops can be significantly different depending on the location of pressure tapping points, thus indicating a change in flow mechanism along the direction of flow. A new approach of modelling solid friction factor using a volumetric loading ratio term has provided better scale-up accuracy when the model predictions were compared with experimental data. This method of modelling solid friction is aimed to address the partial filling of pipe's cross section by the dune of solids, which appears to be a better representation of the flow conditions, especially for the dense-phase pneumatic conveying of fine powders.

An Investigation into Pressure Fluctuations and Improved Modeling of Solids Friction for Dense-Phase Pneumatic Conveying of Powders

The aim of this paper is to investigate into flow mechanism with the help of pressure signal fluctuations analysis and modeling solids friction in case of solids–gas flows for fluidized-dense-phase pneumatic conveying of fine powders. Materials conveyed include fly ash (median particle diameter 30 µm; particle density 2300 kg m−3; loose-poured bulk density 700 kg m−3) and white powder (median particle diameter 55 µm; particle density 1600 kg m−3; loose-poured bulk density 620 kg m−3). These were conveyed in different flow regimes varying from fluidized-dense-to-dilute phase. To obtain information on the nature of flow inside pipeline, static pressure signals were studied using technique of Shannon entropy. Increase in the values of Shannon entropy along the flow direction through the straight-pipe sections were found for both the powders. However, drop occurred in the Shannon entropy values after the flow through bend(s). Change in slope of straight-pipe pneumatic conveying characteristics along the flow direction is another factor which provided indication regarding change in flow mechanisms along the flow. A new technique for modeling solids friction factor has been developed using a solids volumetric concentration and ratio of particle terminal settling velocity to superficial air velocity by replacing the conventional use of solids loading ratio and Froude number, respectively. The new model format has shown promise for predictions under diameter scale-up conditions.

On improving solid friction factor modeling for fluidized dense-phase pneumatic conveying systems

This paper presents results from an ongoing investigation into the modeling of solid friction factor for fluidized dense-phase pneumatic transport of powders. In spite of having the potential of being an energy economic and a better maintenance free mode of pneumatic transport, reliable design of fluidized dense-phase pneumatic conveying systems is still a difficult task due to the highly turbulent and complex nature of the flow of fine powders under high concentrations, where is it difficult to model particle–wall–air interactions. Several popular/applicable models (developed by other researchers, including one of the co-author of this paper) were evaluated to predict the total pipeline pressure loss for the dense-phase pneumatic conveying of fly ash (median particle diameter: 30μm; particle density: 2300kg/m3; loose-poured bulk density: 700kg/m3) and ESP dust (median particle diameter: 7 μm; particle density: 3637kg/m3, loose-poured bulk density: 610kg/m3) under different diameter and length scale-up conditions (viz. 69mm I.D.×168m; 105mm I.D.×168m and 69mm I.D.×554m pipes). These models are based on solids loading ratio and Froude number). A comparison between the predicted pneumatic conveying characteristics (PCC) and the experimental results showed that the models resulted in significant inaccuracy, especially under scale-up conditions of a new modeling technique has been developed using air velocity and a volumetric loading ratio term by replacing solid loading ratio and Froude number. The volumetric loading ratio term intends to address the product volume occupancy inside the pipeline, which is believed to be a better representation of flow conditions compared to mass ratio. The derived models were examined for scale-up accuracy by predicting pressure drop for different diameter/lengths of pipelines. It is found that the models have generally provided improved predictions in the dense-phase region. Whereas the existing models predicted with relative errors varying between 10 and 127% (depending on product and pipeline conditions), the new developed model resulted in predictions within 24% accuracy for a wide range of scale-up conditions, which provides better reliability and a narrower range of predictions, more suitable for industrial scale up requirements. Future work would require a more fundamental approach to understand the solid friction phenomenon for further accurate modeling.

Investigating Straight-Pipe Pneumatic Conveying Characteristics for Fluidized Dense-Phase Pneumatic Conveying

This article presents results from an investigation into the pneumatic conveying characteristics (PCC) for horizontal straight-pipe sections for fluidized dense-phase pneumatic conveying of powders. Two fine powders (median particle diameter: 30 and 55 µm; particle density: 2300 and 1600 kg m−3; loose-poured bulk density: 700 and 620 kg m−3) were conveyed through 69 mm I.D. × 168 m, 69 mm I.D. × 148 m, 105 mm I.D. × 168 m and 69 mm I.D. × 554 m pipelines for a wide range of air and solids flow rates. Straight-pipe pneumatic conveying characteristics obtained from two sets of pressure tappings installed at two different locations in each pipeline have shown that the trends and relatively magnitudes of the pressure drops can be significantly different depending on product, pipeline diameter and length and location of tapping point in the pipeline (indicating a possible change in transport mechanism along the flow direction). The corresponding models for solids friction factor were also found to be different. There was no distinct pressure minimum curve (PMC) in any of the straight-pipe PCC, indicating a gradual change in flow transition (change in flow mechanism from dense to dilute phase). For total pipeline conveying characteristics, the shapes of the PCC curves and the location of the PMC were found to be significantly influenced by pipeline layout (e.g., location and number of bends) and not entirely by the dense-to-dilute-phase transition of flow mechanism. Seven existing models and a new empirically developed model for PMC for straight pipes have been evaluated against experimental data.

Pressure drop prediction for horizontal dense-phase pneumatic conveying of pulverized coal associated with feeding to gasifier

Based on extensive bench-scale data derived from the horizontal dense-phase pneumatic conveying of pulverized coal, a correlation of solids friction factor λz was proposed in an effort to establish a model to predict the pressure drop when coal fed to the gasifier. Further, it was also an attempt to modify some public models to verify their availabilities. Then, based on the data collected from an industrial-scale horizontal pipeline under the high pressure up to 2.0MPa, the proposed model was found to be possibly among the best ones for predicting the pressure drops of the dense flow of pulverized coal. The modified Mallick and Wypych model can also provide satisfying predictions. The results suggest that the two models are both suitable for scale-up of dense-phase pneumatic conveying of pulverized coal at high pressures.

Modeling and Analysis of Solids Friction Factor for Fluidized Dense Phase Pneumatic Conveying of Powders

Pressure drop in pneumatic conveying is due to frictional interaction among gas, particle, and pipe wall. Fictional forces due to solids can be calculated using a solids friction factor. Many correlations have been proposed for predicting solids friction factor in dilute phase pneumatic conveying. These correlations are calculated based on value of the parameters calculated for a long pipeline or value of the parameter at the inlet of the pipeline. Pneumatic conveying in long pipelines suggests that some of the flow parameters are not constant along the length of the pipeline. This article presents a modeling technique for predicting solid friction factor taking into account of the local value of flow parameter. In this method, the solids friction factor is presented in terms of coefficient and exponents. The values of coefficient and exponents are predicted for fluidized dense phase conveying using different types of conveying materials. Values of coefficient and exponents are found to be different for different types of conveying materials. Variations of different parameters are studied using the calculated optimum values of coefficient and exponents. Experimental data are also used to find the possible maximum conveying distance or pipe diameter by imposing certain limiting conditions of conveying.