Vertical Stress Distribution in Oil-Shale Aggregate Columns During Retorting
Authors: Thigpen L. 
Published: December 2007

Abstract
This paper considers the stresses developed in an oil-shale rubble column during in-situ retorting and assesses the change of the mechanical properties of this rubble mass as a result of the properties of this rubble mass as a result of the retorting process. New data on the variation of the frictional properties of a 103-dm3/Mg grade oil shale with temperature also are presented.Solutions of the stress distributions in the column are developed in terms of the ratio of column cross-sectional area to perimeter height, the solid density of shale particles, the coefficient of friction between rubble column and wall rock, and the porosity of the rubble. Using experimentally determined relations for porosity as a function of temperature and stress, the solution implicitly accounts for the effect of material strength and bulk compressibility.Example solutions show that the vertical-stress distribution is a strong function of both the area-to-perimeter ratio and the coefficient of friction between rubble column and wall rock. Finally, these analyses may be used to give bounds on the dimensions of rubble columns for efficient in-situ retorting operations.

Introduction
Successful in-situ recovery of oil from oil-shale rubble requires that the permeability of the rubble not become too low during the retorting process. Because permeability strongly affects the costs of producing oil from shale, low values would make producing oil from shale, low values would make the process uncompetitive with fuels from alternative sources. Various studies have demonstrated that the permeability of compacting oil-shale aggregates may decrease by as much as two to three orders of magnitude for vertical stresses within the aggregate in the range of 2 to 6 MPa at temperatures ranging to 400 degrees C. These studies indicated that at higher temperatures and stresses the shale rubble column would compact to the degree that it becomes practically impermeable. Trimmer and Heard have practically impermeable. Trimmer and Heard have shown that this compaction corresponds to changes in porosity from an initial value of about 40 to 50% to a final value of about 10% for a 103-dm3/Mg oil-shale rubble with an average particle size of 0.6 cm. Thus, the pressure drop and rate of fluid flow through an in-situ retort can be expected to be influenced strongly by the temperature-dependent aggregate compaction. Therefore, to determine optimum operating conditions for the rubble in-situ extraction (RISE) process, we must understand how creep (flow of the shale) and compaction from body forces in the rubble column degrade porosity and permeability at retort temperatures. This requires determination of the changes in porosity, permeability, and mechanical properties as a permeability, and mechanical properties as a function of stress, temperature, and time.Here, we consider the vertical stress field in a retorting rubble column as the thermal wave propagates downward. The rubble is treated as a propagates downward. The rubble is treated as a column of solid particles in which porosity may vary with depth. It is well-known that the vertical stress at the bottom of bins and silos containing solid particles is much lower than the calculated vertical stress based on bulk density, bin height, and the gravitational constant. The actual vertical stress is controlled by both wall geometry and mechanical properties of the material in question. The most important properties affecting the stress are bulk density, angle of internal friction, and coefficient of friction between particles and the wall.In 1895, Janssen analyzed the stress in tall cylindrical grain silos and showed that, for a certain depth below the horizontal free surface, the ratio of the horizontal stress to the vertical stress was a constant that depended on material flow properties, which he assumed to be constant. Carley used Janssen's theory to analyze the vertical-stress distribution in a column of oil-shale rubble. In his analysis, Carley assumed the bulk density, angle of internal friction, and coefficient of friction to be constant throughout the rubble mass.
SPEJ
p. 97