We propose a robust multiple permeability model to account for pore size variability and filtration effects in shale reservoirs and to explain the behavior of unconventional resources such as anomalous gas oil ratios. Recent developments in technology transformed unconventional low-permeability shales into reliable energy sources. With regard to capacity, unconventional resources are found to be more abundant than conventional ones. These resources have opened new challenges and technical difficulties along with enhanced capacities. Recent advances in high precision analytical tools have revealed that pore size distribution in shale reservoirs cover a wide range. Molecules in pores with different sizes may exhibit significantly different thermodynamic behavior. Rock fluid interactions and space hindrance effects play an important role when pore sizes become close to species' molecular dimeters. This effect can result in a composition difference between pores with large and small diameters in shale reservoirs (sieving effect), with small pores mostly filled with smaller hydrocarbon molecules and large molecules residing in larger pores. To account for such a diverse behavior, this paper proposes a multiple permeability model, which divides shale media into three different permeability/porosity systems: fracture, matrix with large pores and matrix with small pores. We use a modified version of the Peng Robinson equation of state to model the equilibrium hydrocarbon distribution in large and small pores. Our thermodynamics calculations show that as pore dimeter decreases, the concentration of larger hydrocarbon molecules in those pores decreases because of size filtration. A synthetic reservoir model is used along with the multiple permeability model to analyze reservoir production behavior at different conditions. The so-called sieving effect is believed to be responsible for the anomalous production behavior (lower-than-expected or constant gas oil ratios for extended production periods). Our model is then applied to a real Eagle Ford case to history-match production data with the stimulated reservoir volume built upon the fracture microseismic data. The results show that our multiple permeability model provides a powerful tool to evaluate the complicated flow dynamics in liquid shales.