In this work, viscosity measurements of the quaternary mixture [0.2801CH(4) + 0.1237C(3)H(8) + 0.0829CO(2) + 0.5132 N-2] were made over the temperature range (243-423) K and at pressures up to 28 MPa, with a combined expanded relative uncertainty (k = 2) that varied between (1.6 and 2.7)%. When nitrogen was added, the change in the mixture viscosity, relative to the constituent ternary mixture, was mainly influenced by the change in the mixture molar density. Changing the mole fraction of nitrogen from 0 to 0.51 decreased the viscosity by as much as 45%. The measured viscosity data were compared with the predictions of five models: corresponding states based approaches (ECS, SuperTRAPP and PFCT), the LBC model and the LJ model. The relative deviations of the measured viscosities from those calculated by the five models exhibited a similar, systematic dependence on density. The average absolute deviations were 4.8%, 3.0%, 2.6%, 1.8% and 5.9% for the ECS, ST, PFCT, LBC and LJ models, respectively, with the LBC model providing the best representation of the data over the entire range. A friction theory (FT) viscosity model, coupled with the reference Helmholtz equations of state, was developed for the description of the viscosity of the constituent pure fluids over wide ranges of temperatures and at pressures up to 100 MPa. The average absolute deviations from the reference viscosities were 0.41%, 0.49%, 0.45% and 0.43% for methane, propane, carbon dioxide and nitrogen respectively, which is in excellent agreement with the reported uncertainty of the reference correlation models. Simple, predictive mixing rules were then used to combine these pure-fluid correlations into an improved mixture model, which provided an excellent representation of the viscosity data with an average absolute deviation of 0.90%. The current work demonstrates the value of using reference thermodynamic models to describe the repulsive and attractive pressure terms in the friction theory approach, and its potential for applications to natural gas systems.