Q:

Need to build a circuit resembling fluid flow through porous media

I am trying to use electronics analogy to build a model that describes fluid flow in a porous media. For example I consider voltage, current and resistance to be equivalents of pressure, flow rate and permeability (inverse of resistivity), respectively. I need some help on how to choose more elements for my circuit to accurately model the fluid flow. Since I am not an electrical engineering student and I do not have a strong background in it, I would really appreciate the answers which start from the basics and move towards more complicated explanations.
Here is a list of things I need to know how to do:

I need to be able to control the time it takes for the current to travel from one point to another point. For example if points A and B are connected with a wire and A has a higher potential and I somehow increase its potential, theoretically there should be an immediate increase in the current flowing at point B. Is there an element I can put in between which controls the response time of point B to change in potential at point A?
I need to be able to model a variable permeability condition (i.e. variable resistance). I know if I use a resistor in my circuit it will have a CONSTANT resistance, so it will not help. Also, I want the changes in resistance to be proportional to the amount of current that has been flowing through that element. Like what happens when a capacitor is being charged, dQ/dt term is proportional to Q and it exponentially decreases to zero by time. But what if I don't want it to be decreasing exponentially? What other elements can I use to force the changes to be an arbitrary function of time/flow, for example a second degree polynomial? (if it's possible at all!) Also, is there a way to do the exact opposite i.e. the resistance decreases with time?
I am not sure if it is the same as part 1 or not, but how can I model the distance between two points in space? (The further the distance the longer it takes for it to respond to changes in another point of the circuit.)

A:

It makes no sense to try to model this with electronics.  You'd need a whole lot of resistors and capacitors connected in a grid.  That would be time consuming to build, expensive, and failure prone.
Model your fluid flow on a computer.  There are various finite element modeling and solving techniques that have been applied to fluid flow for many years.  Use them.

