2

I want to simulate an adsorbent bed for a chemical reactor by solving a set of partial differential equations. I want to reduce eq_1 and eq_2 to a set of ordinary differential equations via finite volume techniques for spatial terms. Ct , DL and eb are constants, i have trouble in finding a suitable model and technique in FiPy code.

Basically i want to form a 1D simulation with 100 slices where gas species i,j etc. start at x=0 and travel to the rest of the column. What type of model should i use? I have checked the exampled from FiPy code website but could not find the exact recipe that I wish.

Thanks,

eq_1

eq_2

GOKAY AVCI
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  • What have you tried so far? – alec_djinn Jan 06 '20 at 11:06
  • Have you any code available, if please post too. We can only help you if we known what you have already built. – Cobalt Jan 06 '20 at 11:26
  • Well, since i have trouble translating the closed forms of differential equations to open forms, i believe i have to do something in combination between these two samples from the codes website: To account for second order differential term something like this maybe; https://www.ctcms.nist.gov/fipy/examples/diffusion/generated/examples.diffusion.nthOrder.input4thOrder1D.html and; for 1D diffusion model https://www.ctcms.nist.gov/fipy/examples/diffusion/generated/examples.diffusion.mesh1D.html – GOKAY AVCI Jan 06 '20 at 11:32
  • What you've posed is a [convection diffusion](https://www.ctcms.nist.gov/fipy/examples/convection/index.html) problem. I don't see any need for a [4th order diffusion term](https://www.ctcms.nist.gov/fipy/examples/diffusion/generated/examples.diffusion.nthOrder.input4thOrder1D.html). As stated, though, you have 2N + 1 unknowns (v, N x q_i, N x c_i) but only N+1 (eq1, N x eq2) equations. You need N more equations to be able to solve this. – jeguyer Jan 06 '20 at 16:00
  • Thank you @jeguyer for your response. Let me elaborate more in detail: Plug flow of 2 gas system is modeled, under isothermal, isobaric conditions. interstitial gas velocity (v) is related to another constant u by v=u/e (v can be regarded as constant) At initial conditions the bed is free of gases so: at t=0 ; q_i (0,z) =0 at t>=0 ; v(0,t) = v_0 (which is known) this condition is maintained until steady state is obtained. – GOKAY AVCI Jan 07 '20 at 14:02
  • That doesn't really help. The number of equations must match the number of unknowns. If v is a known constant, then you have 2N unknowns and only N+1 equations. What are the equations for c_i? What are the equations for q_i? – jeguyer Jan 07 '20 at 16:21

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