Correlations measured in three dimensions ( 3D ) in the Lyman-alpha forest are contaminated by the presence of the damping wings of high column density ( HCD ) absorbing systems of neutral hydrogen ( Hi ; having column densities N ( \textsc { Hi } ) > 1.6 \times 10 ^ { 17 } \mathrm { atoms } \mathrm { cm } ^ { -2 } ) , which extend significantly beyond the redshift-space location of the absorber . We measure this effect as a function of the column density of the HCD absorbers and redshift by measuring 3D flux power spectra in cosmological hydrodynamical simulations from the Illustris project . Survey pipelines exclude regions containing the largest damping wings . We find that , even after this procedure , there is a scale-dependent correction to the 3D Lyman-alpha forest flux power spectrum from residual contamination . We model this residual using a simple physical model of the HCD absorbers as linearly biased tracers of the matter density distribution , convolved with their Voigt profiles and integrated over the column density distribution function . We recommend the use of this model over existing models used in data analysis , which approximate the damping wings as top-hats and so miss shape information in the extended wings . The simple “ linear Voigt model ” is statistically consistent with our simulation results for a mock residual contamination up to small scales ( | \mn@boldsymbol { k } | < 1 h \mathrm { Mpc } ^ { -1 } ) . It does not account for the effect of the highest column density absorbers on the smallest scales ( e. g. , | \mn@boldsymbol { k } | > 0.4 h \mathrm { Mpc } ^ { -1 } for small damped Lyman-alpha absorbers ; HCD absorbers with N ( \textsc { Hi } ) \sim 10 ^ { 21 } \mathrm { atoms } \mathrm { cm } ^ { -2 } ) . However , these systems are in any case preferentially removed from survey data . Our model is appropriate for an accurate analysis of the baryon acoustic oscillations ( BAO ) feature . It is additionally essential for reconstructing the full shape of the 3D flux power spectrum .