On the second‐order correction to velocity covariance for two‐dimensional statistically isotropic porous media

Second‐order perturbation theory has recently been applied to flow and transport in statistically isotropic porous media. The second‐order head correction has been found to be important in the velocity covariance and thus also in transport. This result was obtained by using numerical integration on the second‐order correction for velocity covariance with the higher‐order head fluctuation. The present paper is a continuation of previous studies and aims at deriving an analytical, closed‐form expression for the second‐order correction term involving higher‐order head fluctuation in lognormal statistically isotropic media with exponential log conductivity correlation. The higher‐order correction for velocity covariance is found to be most significant in the transverse direction, a result that is consistent with previous analysis.