A process for the preparation of a concentrated filter cake from an admixture of partially-decomposed organic material and a polar liquid using a filter press without the input of thermal heat or superheated steam or other pressurized gas or liquid is provided by this invention. The admixture is mixed with an additional amount of the polar liquid to produce a feed slurry of the admixture having a moisture content of about 90-99% wt. The resulting slurry admixture is then introduced into the filter press having a plurality of filter plates with porous membranes secured along their outlet. The pressure condition introduced inside the filter plate chambers is increased by a pressurized gas or liquid to force the polar liquid from the admixture slurry though apertures contained in the membrane, thereby leaving a filter cake of the partially-decomposed organic material having a moisture content that is lower than the moisture content of the initial partially-decomposed organic material feed. The process and its equipment may be used to treat a variety of partially-decomposed organic material/polar liquid slurry admixtures, including high moisture peat containing water, and reduce the moisture content of the resulting peat filter cake to as low as 60% wt.