Discrete Element Modeling Results of Proppant Rearrangement in the Cooke Conductivity Cell
Authors: Mattson Earl D. , Huang Hai , Conway Michael , O’Connell Lisa 
Published: June 2014

Abstract
The study of propped fracture conductivity began in earnest with the development of the Cooke cell which later became part of the initial API standard. Subsequent developments included a patented multi-cell design to conduct four tests in a press at the same time. Other modifications have been used by various investigators. Recent studies by the Stim-Lab proppant consortium have indicated that the flow field across a Cooke proppant conductivity testing cell may not be uniform as initially believed which resulted in significantly different conductivity results. Post-test analysis of low temperature metal alloy injections at the termination of proppant testing prior to the release of the applied stress suggest that higher flow fields may be expected along the top of the proppant pack compared to the middle of the pack due to modifications made to the original Cooke cell design. To evaluate these experimental findings, a physics-based two-dimensional (2-D) discrete element model (DEM) was developed and applied to simulate stress distribution in the Cooke cell and proppant rearrangement during conductivity testing as a function of stress. Numerical simulations of the testing apparatus are critical to understanding the impact of modification to the testing cell as well as understanding key proppant conductivity issues.
The 2-D DEM model was constructed to represent a realistic cross-section of the Cooke cell with a distribution of four material properties, three that represent the Cooke cell (steel, sandstone, square rings), and one representing the proppant. In principle, Cooke cell materials can be approximated as assemblies of independent discrete elements (particles) of various sizes and material properties that interact via cohesive interactions, repulsive forces, and frictional forces. The macroscopic behavior can then be modeled as the collective behavior of many interacting discrete elements. This DEM model is particularly suitable for modeling proppant mechanical interactions subjected to an applied stress, where the experimental cell is represented as a cohesive body composed of a large number of discrete elements, and proppants can be modeled as the individual discrete particles with various sizes (following the proppant size distribution-density function used in the test) that exhibit no cohesive strength between the particles.
Initial 2-D DEM modeling results suggest that proppant rearrangement and non-uniform stress distribution can develop across the proppant pack due to square ring modifications. Compaction along the edge of the proppant pack beneath the square ring seal result in a disproportionate lower flow field along these edges as compared to the middle of the proppant pack. These results suggest that reported conductivity values determined by the Cooke cell may be biased to overestimate the actual conductivity of the proppant due to modifications to the standard Cooke cell. Such modifications should be carefully evaluated as to their consequences on determining the proppant conductivity.