Using a Monte Carlo simulation in three dimensions, we studied the variation of the root-mean-square (rms) displacement (R rms ) of polymer chains with time and the rates of their mass transfer (j) as a function of biased field (B), polymer concentration (p), chain length (L c ), porosity (p s ), and temperature (T). In homogeneous/annealed system, the rms displacement of the chains shows a drift-like behavior, R rms ∼ t, in the asymptotic time regime preceded by a subdiffusive power-law (R rms ∼ t k , with k < 1/2) at high p. The subdiffusive regime expands on increasing L c and p but reduces on increasing T or B. In quenched porous media, the drift-like behavior of R rms persists at low barrier concentration (p b ) and high T. However, at high P b and/or low T, chains relax into a subdrift and/or subdiffusive behavior especially with high p or long L c . Flow of chains is measured via an effective permeability (σ) using a linear response assumption. In annealed system, σ increases monotonically with B at high T and low p but varies nonmonotonically at low T, high p and high L c . We find that σ decays with L c , σ ∼ L -a c , where a depends on B, p and T with a typical value a ≃ 0.43-0.64 for p = 0.1-0.3 at B = 0.5. Further, σ decays with p, σ ∼ - Cp with a decay rate C sensitive to T and B. In quenched porous media, even at low p b and high T, σ varies nonmonotonically with bias, i.e., the increase of a is followed by decay on increasing the bias beyond a characteristic value (B c ). This characteristic bias seems to decrease logarithmically with barrier concentration, B c ∼ - Klnpb. The prefactor K depends on the chain length, K 0.35 for shorter chains (L c = 20, 40) and 0.15 for longer chains (L c = 60). Scaling dependence of a on L c similar to that in annealed system is also observed in porous media with different values of exponent a. The current density shows a nonlinear power-law response, j ∼ B δ , with a nonuniversal exponent δ 1.10-1.39 at high temperatures and low barrier concentrations.