Experimental analysis of drag reduction in the pipelines with response surface methodology Hamid Reza Karami a,n , Mohammad Keyhani b , Dariush Mowla c a Department of Mechanical Engineering, University of Alberta, Edmonton, Canada b Department of Chemical Engineering, Faculty of Engineering, Razi University, Kermanshah, Iran c School of Chemical and Petroleum Engineering, Shiraz University, Shiraz, Iran article info Article history: Received 9 September 2015 Accepted 30 November 2015 Available online 8 December 2015 Keywords: Drag reduction luid flow Friction factor Response Surface Methodology (RSM) Statistical analysis Nomograph abstract Obtaining fundamental variables has critical importance in solving engineering problems, and analysis of experimental data aids more-efficient experimentation. Drag reduction in pipelines is particularly useful in efforts to reduce energy losses. In the present study, statistical procedures are used to analyze some drag reduction experimental data to determine the degree to which each variable and its interactions with the others contribute to drag reduction. The experiments in this study incorporate parameters such as Reynolds number and temperature of fluid, concentration of different drag reducing agents and re- lative roughness of pipes. A proposed model has been developed by applying response surface metho- dology to historical data. The statistical analysis shows that the model is statistically acceptable (R 2 ¼96.78%). Results of analysis show that 95% of variation in the friction factor can be described only by Reynolds number and concentration of drag reducing agent and their interactions. Finally for operational applications, a nomograph has been presented to evaluate friction factor simply. & 2015 Elsevier B.V. All rights reserved. 1. Introduction Adding drag reducing agents (DRAs) to a turbulent fluid flow greatly decreases friction losses. Accurate determination of prac- tical friction losses in dilute drag reducing solutions has been addressed by many researchers. Most studies focus on determin- ing effective parameters for drag reduction (De Gennes, 1986; Hamouda and Moshood, 2007; Joseph et al., 1986; Karami and Mowla, 2012; Lumley, 1969; Mowla and Naderi, 2006; Mysels, 1949; Toms, 1948; Wyatt et al., 2011). Virk (1975) published a comprehensive study on drag reduc- tion for water flow and proposed relationships for a fanning fric- tion factor. He investigated the performance of different polymer solutions and found a trend to a maximum drag reduction (MDR) asymptote in all cases. Based on some experimental data, Karami and Mowla (2013) obtained a generalized mathematical model for the friction factor of DRAs in crude oil pipelines. The correlation predicts the drag reduction under different operating conditions such as tempera- ture, flow rate, pipe diameter and roughness, as well as different concentrations of various types of DRAs. Gallego and Shah (2009) developed a generalized friction pressure correlation for coiled and straight tubing on the basis of the energy dissipation of eddies in turbulent flow fields and shear- rate-dependent relaxation time. They found that their model in straight tubing correlated better than previous models. Also, Shah et al. (2006) developed new correlations for pre- dicting friction factor values as a function of the solvent’s Reynolds number for both straight and coiled tubing using the data for an optimum concentration of polymeric fluid. Based on the elastic properties of polymers, Sher and Hetsroni (2008) proposed a mechanistic model for turbulent drag reduction using additives, and compared their results with Virk (1975) experiments. Based on the experimental data obtained for different operat- ing conditions, Mowla and Naderi (2004) proposed a mathema- tical model for predicting drag reduction by a given polymer for a two phase flow. Their model could also be used for calculating friction and maximum drag reduction as a function of DRA concentration. As far as we know, there are no statistical analyses of experi- mental parameters on drag reduction, although these investiga- tions have the potential to increase the efficiency of experiments. When several input variables potentially influence important process specifications, engineering statistics are applied to de- termine the relations and specifications of the system (Myers et al., 2009). Design of experiment (DOE) and, particularly, response surface methodology (RSM) are two main engineering-statistics Contents lists available at ScienceDirect journal homepage: www.elsevier.com/locate/petrol Journal of Petroleum Science and Engineering http://dx.doi.org/10.1016/j.petrol.2015.11.041 0920-4105/& 2015 Elsevier B.V. All rights reserved. n Corresponding author. E-mail address: hamidrez@ualberta.ca (H.R. Karami). Journal of Petroleum Science and Engineering 138 (2016) 104–112