Surfactants both change the wettability and lower the interfacial tension by various degrees depending on the type of surfactant and how it interacts with the specific oil. Ultra low IFT means almost zero capillary pressure, which in turn indicates little oil should be produced from capillary imbibition when the surfactant reduces the IFT in naturally fractured oil reservoirs that are mixed-wet or oil-wet. The question is then what is the transport mechanism for the surfactant to get far into the matrix and how does it scale with distance in a matrix block of a fractured reservoir?. Recent dynamic laboratory data suggest that the process is faster when a pressure gradient is applied compared to static imbibition tests. A mechanistic chemical compositional simulator was used to study the effect of pressure gradient on chemical oil recovery from naturally fractured oil reservoirs for several different chemical processes (polymer, surfactant, surfactant-polymer, alkali-surfactant-polymer flooding). The fractures were simulated explicitly by using gridblocks with fracture properties. Both homogeneous and heterogeneous matrix blocks were simulated. Microemulsion phase behavior and related chemistry and physics were modeled in a manner similar to single porosity reservoirs. The simulations indicate that even very small pressure gradients (transverse to the flow in the fractures) are highly significant in terms of the chemical transport into the matrix and that increasing the injected fluid viscosity greatly improves the oil recovery. Large-scale simulations show that the transverse pressure gradients promote transport of the surfactant into the matrix at a feasible rate even when there is a high contrast between the permeability of the fractures and the matrix. These simulations indicate that injecting a chemical solution that is viscous (because of polymer or foam or microemulsion) and lowers the IFT as well as alters the wettability from mixed-wet to water-wet, produces more oil and produces it faster than static chemical processes. These findings have significant implications for enhanced oil recovery from naturally fractured oil reservoirs and how these processes should be optimized and scaled up from the laboratory to the field.