Linear and nonlinear solutions for one‐dimensional compaction flow in sedimentary basins

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Abstract
We consider the effects of assuming linearity in solving the moving boundary problem that describes one‐dimensional groundwater flow in compacting sedimentary basins. The linear problem in which specific storage and hydraulic conductivity do not vary can be solved analytically. This solution should be applied to geological problems with caution because of the implications of assuming that specific storage is constant over the range of stresses typical of sedimentary basins. A nonlinear equation in which specific storage and hydraulic conductivity vary with effective stress describes compaction flow more realistically. This equation can be solved accurately by a numerical method. Solutions to the nonlinear equation show that the solution to the linear equation can significantly overpredict excess heads in compacting basins. Large excess heads develop by compaction in sediments of lesser conductivity and over a smaller conductivity interval than suggested by the linear solution. The nonlinear solutions predict that geopressured zones should develop in shaly basins undergoing rapid sedimentation but fail to explain the abrupt transition from hydrostatic to near‐lithostatic pressures observed in these basins. The transition is better explained as the result of a facies change or a discontinuity in conductivity caused by diagenetic reactions than a decrease in hydraulic conductivity during compaction.