Elements of
Chemical Reaction Engineering
6th Edition



Home

Essentials of
Chemical Reaction Engineering
Second Edition

  Select  Chapter  >>     TOC     Preface     1     2     3     4     5     6     7     8     9     10     11     12     13     14     15     16     17     18     Appendices  
›

By Chapter Hide

  • Objectives
  • Living Example Problems
  • Extra Help
  • - Summary Notes
  • - LearnChemE Screencasts
  • - FAQs
  • - Interactive Computer Modules
  • Additional Material
  • Self Test
  • i>Clicker Questions
  • Professional Reference Shelf

By Concept Hide

  • Interactive Modules
  • -Web Modules
  • -Interactive Computer Games
  • Living Example Problems

U of M Hide

  • Asynchronous Learning
  • ChE 344
  • ChE 528

Chapter 14: External Diffusion Effects on Heteregeneous Reactions

Additional Homework Problems

CDP14-EC

  (Fracture acidizing) One technique used to increase the productivity of oil wells is to inject acid under high pressure until it fractures the porous formation. At the point of fracture, acid flows out from the well bore along the fracture slit dissolving the face of the slit as it flows. When the pressure on the well is released, the faces of the slit try to come together but a small channel usually remains where the faces have been dissolved. In addition to reacting with the slit, some of the acid "leaks off" through the side of the slit and is consumed in the porous rock. See Figure CDP11-E (Fracture acidizing).




Fracture acidizing

     
    (a) Assuming steady-state flow, derive a differential equation describing the flow and reaction of the acid in the channel assuming that the reaction is mass transport-limited to the surface for flow in a slit between two surfaces separated by a distance D,
     
   

image 11eq6.gif

     
   

As a first approximation, assume that Sh is independent of the leak-off rate.

(b) For the case of a linear leak-off rate image 11eq6a.gifsolve for the concentration profile, CA.
(c) Solve for channel thickness as a function of channel length drawing on your understanding of shrinking core analysis.
(d) Repeat part (a) accounting for the effect of leak-off on Re and Sh.

[2nd Ed. P10-15]