Reliable evaluation of shale-play potential requires robust geological models that can simulate the generation and retention of petroleum, porosity and permeability in source rocks from first principles, and that can be implemented in basin modelling software. To be predictive, such basin models need to be calibrated against observations from real shale plays. A key control on the amount of retained petroleum is the porosity in the shale and the abundance of organic matter. Scanning electron microscopy of argon-ion milled shale samples can potentially reveal systematic variations in the amount of porosity, pore types and distributions across a range of thermal maturities. These observed variations in porosity can be used to calibrate basin modelling outputs and refine predictive models. For these reasons BP has conducted scanning electron microscopy studies of shale plays including the Eagle Ford Shale, a carbonate-rich mudstone sequence of Cenomanian to Turonian age. The results clearly show that the mean pore size decreases as thermal maturity increases and that organic matter-hosted pores are absent in low thermal maturity samples (where vitrinite random reflectance R_o <0.7) and become increasingly more abundant as thermal maturity increases). In moderately mature samples there are organic matter hosted pores that range in pore size from 5 to 500 nm. In highly mature samples, small (<50 nm) organic matter-hosted pores predominate. Our studies reveal that porosity evolution in this organic-rich, fine-grained, carbonate mudrock shows a strong correlation with increasing thermal maturity.