Abstract

This work develops a general rate law for magnesite dissolution in heterogeneous media under variable flow and length conditions, expanding the previous work under one particular flow and length conditions (Wen and Li, 2017). We aim to answer: 1) How does spatial heterogeneity influence the time and length scales to reach equilibrium? 2) How do relative timescales of advection, diffusion/dispersion, and reactions influence dissolution rates under variable flow and length conditions? We carried out 640 Monte-Carlo numerical experiments of magnesite dissolution within quartz matrix with heterogeneity characterized by permeability variance and correlation length under a range of length and flow velocity.

A rate law Rhete = kAT(1-exp(τeq,m/τa))(1-exp(- Lβ))^α was developed. The former part is rates in equivalent homogeneous media kAT(1-exp(τeq,m/τa)), depending on rate constant k, magnesite surface area AT, and relative timescales of reactions τeq,m and advection τa. The latter term (1-exp(- Lβ))^α is the heterogeneity factor χ that quantifies the deviation of heterogeneous media from its homogeneous counterpart. The term has a scaling factor, called reactive transport number β=τa/(τad,r+τeq,m), for domain length L, and the geostatistical characteristics of heterogeneity α. The β quantifies the relative timescales of advection at the domain scale τa versus the advective-diffusive-dispersive transport time out of reactive zones τad,r and reaction time τeq,m. The χ is close to 1 and is insignificant under long residence time conditions (low flow velocity and / or long length) where the residence time is longer than the time needed for Mg to dissolve and transport out of reactive zones (τad,r+τeq,m) so that equilibrium is reached and homogenization occurs. In contrast, χ deviates from 1 and is significant only when β is small, which occurs at short length or fast flow where timescales of reactive transport in reactive zones are much longer than the global residence time so that reactive transport is the limiting step. These findings demonstrate that dissolution rates in heterogeneous media reach asymptotic values in homogeneous media at “sufficiently” long lengths.

Citation

Wen, H. and Li, L. (2017): Magnesite Dissolution Rates Across Scales: Role of Spatial Heterogeneity, Equilibrium Lengths, and Reactive Time Scales. 2017 American Geophysical Union Fall Meeting, New Orleans, LA, 11-15 Dec .

This Paper/Book acknowledges NSF CZO grant support.