Hi,
I want to calculate non-linear gas flux and to do so I was told to
1) plot [CO2] vs Time
2) fit a polynomial curve 2nd order to the plot (quadratic function y = at2 + bt + c)
and 3) use the term b in my equation as the flux (which would be my flux at t=0 if I derive the equation to y' = 2at + b).
I am a little confused because I was originally told this is linear regression, although it seems to me this is quadratic regression, which would be a good way to calculate non-linear gas flux.
Samuel,
If you define a new variable u = t^2, then your equation becomes y=au+bt+c, which is a case of multiple linear regression. This is a very simplistic way of seeing why polynomials can be handled easily by "linear regression". perhaps the easiest way to do this is to enter the data into excel, then plot the data using a scatter plot. If you right click on the scatter plot, you should be able to access regression options, and one of these options will be for polynomials of pretty much arbitraty degree. You'll select "2", and this should give you all the regression coefficients as well as the "R^2" value in almost one step.
Hi, Gagnon
Is the nonlinear gas flow between gas flow rate and time, rather than gas flow rate and pressure? Because if the gas flow is in a stead-state, it must be linear between flow rate and time.
However, when the flow rate is small, a linear relationship of flow rate and pressure was adopted. When the flow rate is sufficiently large, the flow rate is nonlinearly related with the pressure.
So, I think you might want to know the nonlinear relationship between flow rate and pressure. If so, you can refer to one of my papers, titled "Critical hydraulic gradient for nonlinear flow through rock fracture networks: The roles of aperture, surface roughness, and number of intersections", which was published on Advances in Water Resources.
Best regards,
yours Liu
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