We consider a stochastic pressure equation with log-normal coefficient and infinite dimensional noise. Using a white noise framework, we study spatial and stochastic regularity of solutions of the stochastic pressure equation. We first establish that a particular class of weighted chaos spaces can be characterized by Gaussian Sobolev type norms in the random argument. Then, we use these results to prove that the solution of the stochastic pressure equation has the classical regularity in the spatial variable and a stochastic regularity on this class of weighted chaos spaces.