Computational Fluid Dynamics (CFD) is used to investigate mass transfer from Taylor bubbles to the liquid phase in circular capillaries. The liquid phase volumetric mass transfer coefficient k L a was determined from CFD simulations of Taylor bubbles in upflow, using periodic boundary conditions. The separate influences of the bubble rise velocity, unit cell length, film thickness, film length, and liquid diffusivity on k L a were investigated for capillaries of 1.5, 2 and 3 mm diameter. The mass transfer from the Taylor bubble is the sum of the contributions of the two bubble caps, and the film surrounding the bubble. The Higbie penetration model is used to describe the mass transfer from the two hemispherical caps. The unsteady-state diffusion model of Pigford is used to describe the mass transfer to the downward flowing liquid film. The developed model for k L a is in good agreement with the CFD simulated values, and provides a practical method for estimating mass transfer coefficients in monolith reactors.