Hello,

I’m working on the calibration of the conductivity parameters of a 3-D steady-state flow model. I have determined max and min conductivities for each of my layers but I would like to make sure that the conductivities decrease with depth (even if their possible intervals overlap) or that kx is > or= to kz. I was thinking of using the “prior information” parameter, but I’m not sure about what syntax to use. Any suggestions would be welcomed.

Debora
Dear Debora,

I have in mind different possibilities to reach your goal:

1) Define several parameter definitions with different parameter bounds. For example, you can assign bounds with a decrease in conductivity over depth.

2) If the ratio is Kx/Kz is kept over the layer, you can provide several ratios which change over depth. Here you will need to use tied parameter when you create the definitions (e.g. Kz will be tied to Kx). The parameter is computed from the initial values assigned in the FEM file. FePEST will keep this ratio over the entire optimization.

3) Use Prior Information. The syntax of Prior Information lines in FePEST follows exactly the PEST description (see PEST Manual, section 4.2.10). An example below:

PIBL PIFAC * PARNAME + ... = PIVAL WEIGHT OBGNME

where PIBL is a character variable of the Prior Information Definition, PIFAC is a factor which affects the parameter, PARNME is the parameter name, PIVAL is a real variable to define the right-side of the PI equation, WEIGHT is the weight assigned to the article of prior information in the parameter estimation process (e.g. inverse proportional to standard deviation), and OBGNME is the observation group to which the prior observation belongs.

FePEST separates the different variables in different entry boxes for better visualization, you need just to define the equation part. Let's say you have conductivity values 100, 50, 25 and 5 decreasing over depth. In FePEST you can use PI equation to suggest that conductivity needs to decrease in depth during the optimization as follows:

1.0 * log(Kxx_1) = 2.00
1.0 * log(Kxx_2) = 1.70
1.0 * log(Kxx_3) = 1.40
1.0 * log(Kxx_4) = 0.70

Notice that factor 1.0 is required. If the parameter is log-transformed, you need to indicate it in the equation.

Thank you Carlos!

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