SPE Journal
Volume 16, Number 4, December 2011, pp. 856-863

SPE-109506-PA

Analysis of a Model for Anomalous-Diffusion Behavior of CO2 in the Macromolecular-Network Structure of Coal

View full textPDF ( 1,429 KB )

DOI  More information 10.2118/109506-PA http://dx.doi.org/10.2118/109506-PA

Citation

  • Mazumder, S., Vermolen, F., and Bruining, J. 2011. Analysis of a Model for Anomalous-Diffusion Behavior of CO2 in the Macromolecular-Network Structure of Coal. SPE J.  16 (4): 856-863. SPE-109506-PA. http://dx.doi.org/10.2118/109506-PA.

Discipline Categories

  • 6.8 Fundamental Research in Reservoir Description and Dynamics
  • 6.7 Reserves Evaluation
  • 6.6 Reservoir Monitoring/Formation Evaluation
  • 6.3 Fluid Dynamics

Keywords

  • Coal, CO2 sequestration, superdiffusion, stress-dependent diffusion, irreversible thermodynamics

Summary

This paper gives an analysis of the Thomas and Windle model (Thomas and Windle 1982) to determine its usefulness for describing anomalous diffusion of CO2 in coal and its relation to matrix swelling. In addition, a finite-element description for this model is derived. For reasons of easy reference, a shortened derivation of the Thomas and Windle model is presented, which was originally derived to describe diffusion in polymers. proposed by Hui et al. (1987a, 1987b). Because the cumulative sorption showed t α behavior with α > 0.5, the behavior was described as enhanced diffusion or even superdiffusion. Analysis of the model equation shows no evidence for superdiffusion even if non-Fickian behavior is observed [i.e., there is (1) an initial phase in which the coal surface gets saturated with a slope > 0.5 in a log-log plot of cumulative sorption vs. time, (2) an intermediate phase that shows the typical square-root-of-time behavior of an ordinary diffusion process, and (3) a final phase with a slope < 0.5 toward equilibrium]. The cumulative mass is for all times less than what would have been obtained for pure diffusion in a particle characterized by a rubber diffusion coefficient. The slow saturation at the surface masks a process where fast stress-induced diffusion dominates, which indeed can be faster than Fickian. The cumulative sorption rates give behavior similar to the Rückenstein model (Rückenstein et al. 1971), but the advantage of the Thomas and Windle model is that it can also calculate the resulting coal-swelling effects.

© 2010. Society of Petroleum Engineers

View full textPDF ( 1,429 KB )

History

  • Original manuscript received: 17 August 2007
  • Meeting paper published: 30 October 2007
  • Revised manuscript received: 27 June 2010
  • Manuscript approved: 8 July 2010
  • Published online: 7 December 2010
  • Version of record: 23 December 2011