Proposed Model For Shale Compaction Kinetics: Forward Depositional Model
Authors: Smith James Edward , Smith-Rowland Edward Millard 
Published: February 2023

Over geologic time wind, rain and snow combine to disintegrate,dissolve or react with land and vegetation, and to move altered solids lower as required by gravitational forces. The finest solids are deposited in low, less turbulent areas, such as lake bottoms and continental shelves. They sometimes stack up to thicknesses of kilometers, and begin compacting. These sediment sections are called shales, and as initially deposited in water, shales can have porosities up to 50-80{\%} water, As they are buried, many alteration products from oil to slate are produced due to overburden and temperature increasess, making them important to study. Besides initial mechanical compaction, other mechanisms can contribute to reduction of porosity. A preceeding paper showed that an important process is pressure solution of some part of the shale minerals. Without naming the mineral(s) involved, it postulated that the greater the product of the water and pore interfaces, the faster the reaction would proceed. This term is $ \varphi^{4m/3}(1-\varphi)^{4n/3}$ , where $\varphi$ is porosity and m and n are numbers close to unity. The large exponents, 3/4, recognize that the reaction occurs at the molecular scale at which the surfaces are rough. A second term, $\exp^(-E/RT)$ , indicates that the reaction is impeded by a quantum energy barrier, E, with diminished impeding power as increased available thermal energy, represented by the absolute temperature, T, becomes available at greater depths in the Earth. These two factors combine to allow porosity $\varphi$ to reduce with time, or equivalently for the fraction of solids, $(1-\varphi)$, to increase with time,$\left. \frac{\partial(ln(1-\varphi) ) }{\partial t } \right |_{\sigma} = (\varphi )^{4m/3}( 1-\varphi )^{4n/3}Ae^{-E/(RT)}$. The current development recognizes that this equation provides snapshots, at all times during the burial, of the sediments at each depth. A time-depth history for a shale section, known in detail, would allow determination of the parameters m, n, E and a lumped proportionality constant A. Lacking this known history, a constant rate of solids deposition, r, can be assumed and these parameters can then be determined. This has been done here for six shale sections, and for a wide range of deposition rates. Satisfactory results were obtained over this range of r's using the previously determined m and n, and porosity and temperature profiles, presently varying only A and E. The present porosity profiles necessarily incorporate any overpressure or underpressure conditions that may have existed in the past or currently, as the net difference between overburden and pore pressure is a primary driving force for pressure solution. The derived activation energy E is close to that for pressure solution of $SiO_2$, which may comprise 20-50{\%} of shales.Experiments are suggested to clarify the pressure solution mechanism. The roles of horizontal forces and pH are discussed. An approximate method for re-casting horizontal forces as a vertical gravitational equivalent force is illustrated for the Macran 2 section.