Three-dimensional modeling of convection in the oceanic crust at Deep Sea Drilling Project site 504B using an integral finite difference model reasonably duplicates underpressures, surface heat flow, downhole temperature profiles, and fluid drawdown rates observed by in situ measurements in the borehole. The major constraint to produce such good fits is the permeability versus depth functions, a quantity which was actually measured in the borehole.

Pronounced ''underpressuring'' (fluid pressures less than hydrostatic) occurs throughout the convection cell if and only if a tight, nearly impermeable cap rock (chert) exists over the cell. The computed flow rates of water from the ocean through the borehole into the basalt agree closely with the measurements carried out 65, 720, and 1280 days after drilling. The model predicts an inflow rate of 50-60 L/h during the expected next occupation of the site by mid-1986. Numerical modeling has confirmed that an active hydrothermal convection cell exists in the region of hole 504B and that a very low permeability cap rock is necessary for the existence of the convection cell. Convective hydrothermal cells in the oceanic crust can explain observed periodic heat flow variations in suboceanic crust.