Effects of pore-level reaction on dispersion in porous media

The Darcy-level consequences of the transport of reactive tracers is analyzed by detailed pore-level modeling, based on a network model. Moments of the residence-time distribution of the conservative process (reversible reactions) are useful for investigation of the spreading of tracers, even when complete evaluation of the residence-time distribution is not available. We carry out simulations to show how reaction terms have to be included in the convection-dispersion equation to correctly predict the Darcy-level effects of reversible reactions at the pore-level. In the case of spatially homogeneous rate constants, the value of the dispersion coefficient corresponds to that of a nonreactive tracer. Spatial heterogeneities of the rate constants give rise to a dispersion coefficient that depends on the strength of the disorder in the reaction rates and the dispersion coefficient depends nonlinearly on the mean flow velocity. The effects of reaction can be summarized in terms of two dimensionless groups, the Damkohler number Da and the variance of the rate constant distribution. For Da⪢1, a macroscopic convection-dispersion-reaction equation offers a valid description of transport, even for spatially heterogeneous distributions of rate constants. The limit Da → 0 represents a breakdown of the macroscopic equation, though the relative error in the low-order moments of the residence-time distribution is less than 20% for 0.1 <Da < 1. A binary distribution of the rate constant at its percolation threshold yields the maximum value of the dispersion coefficient. Plots of the Darcy-level Peclet number, ULD∥, with respect to the length of the system, L, reaches an asymptotic value at a length much larger than the typical pore length. This indicates the presence of a correlation length much larger than the pore length.

[1]  C. Baudet,et al.  Transfer matrix algorithm for convection-biased diffusion , 1986 .

[2]  S. Redner,et al.  Introduction To Percolation Theory , 2018 .

[3]  John F. Brady,et al.  Anomalous diffusion in heterogeneous porous media , 1988 .

[4]  Wilkinson,et al.  Hydrodynamic dispersion in network models of porous media. , 1986, Physical review letters.

[5]  Stephen Whitaker,et al.  Dispersion in pulsed systems—II: Theoretical developments for passive dispersion in porous media , 1983 .

[6]  P. Sharratt,et al.  Deactivation of a supported zeolitic catalyst: diffusion, reaction and coke deposition in stochastic pore networks , 1986 .

[7]  M. Sahimi,et al.  Dispersion in Flow through Porous Media , 1982 .

[8]  K. Sorbie,et al.  The inclusion of molecular diffusion effects in the network modelling of hydrodynamic dispersion in porous media , 1991 .

[9]  Muhammad Sahimi,et al.  Dispersion in flow through porous media—I. One-phase flow , 1986 .

[10]  Stephen Whitaker,et al.  Dispersion in pulsed systems—I: Heterogenous reaction and reversible adsorption in capillary tubes , 1983 .

[11]  John H. Cushman,et al.  Nonlocal Reactive Transport with Physical and Chemical Heterogeneity: Linear Nonequilibrium Sorption with Random Kd , 1995 .

[12]  Wilkinson,et al.  Transport and dispersion in random networks with percolation disorder. , 1988, Physical review. A, General physics.

[13]  R. Aris.  On the dispersion of a solute in a fluid flowing through a tube , 1956, Proceedings of the Royal Society of London. Series A. Mathematical and Physical Sciences.

[14]  Francesco Dondi,et al.  Statistical analysis of gas chromatographic peaks by the Gram-Charlier series of type A and the Edgeworth-Cramer series , 1981 .

[15]  Jan Åke Jönsson,et al.  Chromatographic theory and basic principles , 1989 .

[16]  Peter K. Kitanidis,et al.  Analysis of one‐dimensional solute transport through porous media with spatially variable retardation factor , 1990 .

[17]  John F. Brady,et al.  Nonlocal dispersion in porous media: Nonmechanical effects , 1987 .