We examine the classical Bischoff-Aris pore diffusion problem with a first-order surface reaction and identify three controlling regimes. The first two of these are well known for over 60 years and correspond to the limiting cases of phi(s)(2) much less than 1, phi(2) much less than 1 and phi(s)(2) much less than 1, phi(2) much greater than 1, respectively. (Here, phi(s)(2) and phi(2) are the Thiele moduli based on transverse and longitudinal diffusion times and are defined by phi(s)(2) = 2k(s)r(p)/D-m, phi(2) = 2k(s)L(2)/r(p)D(m), where r(p) is the pore radius, L is the pore length, D-m is the molecular diffusivity and k(s) is the surface rate constant.) In the first limiting case (phi(s)(2) much less than 1, phi(2) much less than 1) the concentration gradients are negligible in both the transverse and longitudinal directions, the pore effectiveness factor is close to unity (eta approximate to 1) and the rate constant (k(upsilon)) based on unit pore volume is related to the surface rate constant by k(upsilon) approximate to 2k(s)/r(p). In the second limiting case (phi(s)(2) much less than 1, phi(2) much greater than 1) the concentration gradients are negligible in the transverse direction but exist in the longitudinal direction, the pore effectiveness factor is given by eta approximate to 1/phi and the observed rate constant (k(upsilon)) is related to the surface rate constant by k(upsilon) approximate to (1/L)root<(2k(s)D(m)/r(p))over bar>. The third limiting regime which we identify in this work corresponds to the limit in which the characteristic reaction time being much smaller compared to both the transverse and longitudinal diffusion times (phi(s)(2) much greater than 1, (2)(phi) much greater than 1). In this mass transfer controlled regime (which corresponds to a fast surface reaction with both transverse and longitudinal concentration gradients), we show that the pore effectiveness factor is given by the asymptotic formula eta approximate to Delta'/phi. Delta' = (4/phi(s))[(1/pi)ln(2 phi(s)(2)/3 pi) + 0.251] and the observed rate constant is a logarithmic function of the surface rate constant, i.e, k upsilon approximate to (4D(m)/r(p)L)[(1/pi)ln(4k(s)r(p)/3 pi D-m) + 0.251]. We also examine various simplified one-dimensional models used in the literature and show that these models do not describe the mass transfer controlled (fast reaction) regime accurately. We derive analytical expressions for the local Sherwood number and propose a one-dimensional two-phase model with position-dependent mass transfer coefficient that has the same qualitative features as the two-dimensional model.