Discrete Element Modeling Results of Proppant Rearrangement in the Cooke Conductivity Cell
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 multicell design to conduct 4 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 is 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 is to be expected along the sides and top of the proppant pack than compared to the middle of the pack. To evaluate these experimental findings, a physics-based two-dimensional (2-D) discrete element model (DEM) was developed and applied to simulate proppant rearrangement during stress loading in the Cooke conductivity cell and the resulting porosity field. Analysis of these simulations are critical to understanding the impact of modification to the testing cell as well as understanding key proppant conductivity issues such as how these effects are manifested in proppant concentration testing results. 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 represented 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 across the proppant pack results in significant non-uniform porosity distribution across the Cooke cell. Larger porosities develop along the edge of the proppant pack beneath the square ring seal and would result in a disproportionate higher 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 at high stresses and that modifications to the standard Cooke cell will affect the magnitude of this bias.
- Research Organization:
- Idaho National Lab. (INL), Idaho Falls, ID (United States)
- Sponsoring Organization:
- USDOE
- DOE Contract Number:
- DE-AC07-05ID14517
- OSTI ID:
- 1133880
- Report Number(s):
- INL/CON-13-29950
- Resource Relation:
- Conference: SPE Hydraulic Fracturing Conference,Woodland, TX,02/04/2014,02/06/2014
- Country of Publication:
- United States
- Language:
- English
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