In Situ Access to Contaminants

understanding and exploiting physics

Control of the consequences of injecting fluid into a well depends upon sound understanding of the phenomena that occur or may be triggered by the process.  A concise summary of these should serve to indicate the complexity of a controlled injection process, while delving onto the details or presenting quantitative and mathematical descriptions could launch a nearly endless digression from the topic of soil and groundwater remediation.  As indicated by the adjacent sketch, three mechanical processes or phenomena play a major role.

, or flow into the porous medium.
  The physics of this process follow Darcy’s Law.  Of course, the particular geometry of the medium impacts magnitude of flow as do local and regional hydrology and any capillary effects established between the fluid and the walls of the pores in the medium.  If these phenomena allow fluid to pass at the rate supplied by the injection process, then a fracture will not be created, and the following two phenomena are moot.  Otherwise a fracture nucleates and propagates. Leak-off may be insignificant in some settings but in other cases may develop to a degree that arrest fracture propagation. 

Dilation, or expansion of existing space.  Modest compression and displacement of bulk media can expand the space occupied by injected fluid.  These movements can be described by the mathematics of elasticity. Magnitude of displacement depends upon net stress that occurs due to applied pressure, geometry, and in situ stress.  While displacement immediately adjacent to the fluid occurs perpendicularly, the expanding volume is accommodated by movements in all three dimensions, so stress and strain are broadly distributed around the injection location.  

Extension, or tip propgation to creation of new space.  The opening of new space requires overcoming the forces and energy that keep the solid together.  In cohesive media this is indeed a fracturing process, and the precepts of mechanical failure analysis can be applied.  The requisite rearrangement of soil grains and particles in noncohesive soil and sediment can be described by similar equations, so injected material always assumes similar form – a two dimensional, sheet-like structure with extent orders of magnitude greater than thickness.

Larry Murdoch assembled these concepts into a simple quantitative model for growth of shallow, horizontal fractures. With it, fracture propagation pressure, fracture aperture, and fracture extent can be computed with spreadsheet applications. For a copy of the publication, click here.