A permeation measuring system with a nickel membrane of 30 m thickness was installed near the mid plane of the spherical tokamak, QUEST. Hydrogen permeation through the membrane heated at fix temperatures (422 - 506 K) was measured during short pulse (< 1 s) and long pulse (1 hour) plasma discharges. After the membrane was heated to a required temperature, hydrogen plasma was discharged using a 2.45 GHz or 8.2 GHz RF system. Significant plasma-driven permeation was observed even for very short plasma discharges (e.g. 0.1s). Numerical calculations with the use of diffusion equation under recombination boundary conditions were conducted to simulate the transient permeation behavior. The numerical calculations were also used to estimate diffusion coefficient and recombination coefficients of membrane material. Temperature dependence of both the coefficients was explained by the Arrhenius law. A one hour long permeation curve was also numerically reproduced using the same set of parameters except an increasing recombination coefficient on the plasma side of the membrane.