Heterogeneous field simulation

I was simulating water injection into oil reservoir with a heterogeneous permeability/porosity field using TOUGH3-EOS8. The heterogeneous permeability/porosity fields were realized by modifying the INCON file before running TOUGH3.  It was obvious that the saturation field was heterogeneous while the pressure field seemed evenly distributed. I am confusing about this phenomenon. I think the pressure field should also be heterogeneous. Thanks for anyone who knows the reason for this problem.