We will first demonstrate the dichotomy of interest by showing what Biot's theory predicts if it is applied to heterogeneous reservoirs. The main issues with up-scaling in poroelasticity occur for the low frequency asymptotics, and so we limit discussion to this regime here. For low frequencies, all the wavelengths are long, thereby covering large regions of the heterogeneous medium, and so up-scaling is an issue that must always be addressed in this limit.