Data from Ocean Drilling Program (ODP) Legs 170 and 205 have identified systems of lateral fluid flow at the Costa Rica convergent margin: (1) an aquifer of cold seawater in the oceanic crust, (2) flow of deep-sourced fluids along conduits parallel to the decollement, and (3) vertical dewatering of compacted underthrust sediments. Numerical transport-reaction models were developed to quantify the processes of these hydrological systems. The results suggest that the lateral fluid flow in the Costa Rica subduction zone is transient (i.e., not a steadystate process). Model runs reveal that the oceanic pore water composition has been dominated by advective or diffusive connection to the lateral flow of cold seawater in the basement for the past 240 k.y. to 1 m.y. Comparing the numerical results of this study with other hydrothermal calculations also suggests that most of this water is subducted and only a small fraction is migrating upward into the overlying sediments. High-resolution propane gas data have been collected in prism sediments at Site 1254, showing a combination of upward advection (on the order of 0.4 cm/yr) due to compaction of the subducting oceanic sediments as well as lateral fluid flow with thermogenic origin. Numerical analysis shows that the lateral dewatering in the prism sediments is dominated by episodic events: the conduit at approximately 220 meters below seafloor (mbsf) has been active for approximately 2000 yr, whereas fluids have permeated the decollement zone ( approximately 360 mbsf) for nearly 4000 yr. However, shorter fluid pulses caused by seismic activity do not seem to have much impact. Finally, the downward progressing anaerobic methane oxidation reaction front, which developed between methane-rich prism sediments and sulfate-rich oceanic sediments, was analyzed. The numerical simulations show that a minimum of approximately 15 kg C/m (super 2) is oxidized within 17 k.y. of subduction (1.5 km arcward of the deformation front), probably partially provided by methane hydrates in the prism wedge.