Carbonate reservoirs are heterogeneous from pore scale to field scale. Waterflood in carbonate reservoirs often leaves behind a substantial amount of oil due to pore-scale and large-scale bypassing. Polymer flooding can improve sweep efficiency and oil production. Most EOR polymers cannot be transported through low-permeability (< 30 mD) rocks. Hydrophobically modified associative polymers (APs) associate with each other during passage through pore throats and give a larger flow resistance than conventional polymers (Flopaam) of the same molecular weight. The goal of this work is to investigate the transport of associative polymers in low-permeability carbonate reservoirs (less than 50 md). An associative polymer similar in molecular weight to Flopaam 3330 was investigated in this study. Polymer rheology and the effect of salinity were studied at 60 degrees C. Mechanical shearing and aggressive filtration were used to modify the particle size distribution in polymeric solutions and improve transport through tight cores. Single-phase polymer transport experiments were performed in outcrop Edwards Yellow and Indiana limestone cores. Mechanical shear degradation reduced the particle size and improved the transport of the associative polymer in low-permeability carbonate cores. The permeability reduction factor and the residual resistance factor were higher for the sheared AP polymers than those for the sheared Flopaam polymer. The resistance factors for the associative polymer were higher than those for Flopaam for a given shear viscosity. Coreflood experiments with AP showed the evidence of two propagation fronts: polymer concentration front and pressure gradient stabilization front due to polymer network formation and polymer adsorption. As AP polymer concentration increased, permeability reduction factor, resistance factor, residual resistance factor and polymer adsorption increased. All the coreflood experiments suggest successful polymer transport in low-permeability carbonate cores even at significantly high polymer concentrations with pre-shearing.