1 / 9

Continuous Time Random Walk Model

Continuous Time Random Walk Model. Primary Sources: Berkowitz, B, G. Kosakowski, G. Margolin, and H. Scher , Application of continuuous time random walk theory to tracer test measurents in fractured and heterogeneous porous media , Ground Water 39 , 593 - 604 , 2001 .

umay
Download Presentation

Continuous Time Random Walk Model

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript

  1. Continuous Time Random Walk Model Primary Sources: Berkowitz, B, G. Kosakowski, G. Margolin, and H. Scher, Application of continuuous time random walk theory to tracer test measurents in fractured and heterogeneous porous media, Ground Water39, 593 - 604, 2001. Berkowitz, B. and H. Scher, On characterization of anomalous dispersion in porous and fractured media, Wat. Resour. Res.31, 1461 - 1466, 1995. Mike Sukop/FIU

  2. Introduction • Continuous Time Random Walk (CTRW) models • Semiconductors [Scher and Lax, 1973] • Solute transport problems [Berkowitz and Scher, 1995]

  3. Introduction • Like FADE, CTRW solute particles move along various paths and encounter spatially varying velocities • The particle spatial transitions (direction and distance given by displacement vector s) in time t represented by a joint probability density function y(s,t) • Estimation of this function is central to application of the CTRW model

  4. Introduction • The functional form y(s,t) ~ t-1-b (b > 0) is of particular interest [Berkowitz et al, 2001] • b characterizes the nature and magnitude of the dispersive processes

  5. Ranges of b • b ≥ 2 is reported to be “…equivalent to the ADE…” • For b ≥ 2, the link between the dispersivity (a = D/v) in the ADE and CTRW dimensionless bb is bb = a/L • b between 1 and 2 reflects moderate non-Fickian behavior • 0 < b < 1 indicates strong ‘anomalous’ behavior

  6. Fitting Routines/Procedures • http://www.weizmann.ac.il/ESER/People/Brian/CTRW/ • Three parameters (b, C, and C1) are involved. For the breakthrough curves in time, the fitting routines return b, T, and r, which, for 1 < b < 2, are related to C and C1 as follows: • L is the distance from the source • Inverting these equations gives C and C1, which can then be used to compute the breakthrough curves at different locations. Thus C and C1 should be constants for a ‘stationary’ porous medium

  7. Fits

  8. Fits

  9. Conclusions • CTRW models fit breakthrough curves better

More Related