# Combining Advective Transport Equations for Two Solutes: Help Needed!

• nikokampman
In summary, the conversation discusses the desire to combine two advective transport equations for solutes into a single equation. The equations involve concentration, time, distance, velocity, dispersion coefficient, and flux terms. However, it is mentioned that it may not be possible to combine the equations and solve for the concentrations simultaneously. The person is seeking help with determining the appropriate mathematical rules to use.
nikokampman
I want to combine the advective transport equation for two solutes such that

dC1(z)/dt=D(d2C1(z)/dz2)-v dC1(z)/dz + J1

and

dC2(z)/dt=D(d2C1(z)/dz2)-v dC2(z)/dz + J2

where C is the concentration in the fluid, t = time, z = distance, v = velcity, D = dispersion coefficient, and J is a flux term for C to the fluid

I want to combine to yield

d(C1/C2)/dt = ?

I can't work out the specific form of the chain rule or quotient rule I need to use... can anyone please help me? Be most appreciated!

I don't think that that can be done. One must solve for the concentrations separately.

## 1. How do you combine advective transport equations for two solutes?

To combine advective transport equations for two solutes, you first need to determine the individual advective transport equations for each solute. Then, you can combine them by adding or subtracting the equations, depending on the direction of flow. This will allow you to solve for the combined advective transport equation for both solutes.

## 2. What is the purpose of combining advective transport equations for two solutes?

The purpose of combining advective transport equations for two solutes is to model the transport of multiple solutes in a fluid or porous medium. This allows for a more comprehensive understanding of the overall transport processes and can provide more accurate predictions of solute concentrations at different locations.

## 3. What factors should be considered when combining advective transport equations for two solutes?

When combining advective transport equations for two solutes, it is important to consider the flow rate, direction of flow, dispersion coefficients, and initial concentrations of each solute. These factors can greatly impact the combined equation and should be carefully evaluated to ensure accurate results.

## 4. Are there any limitations to combining advective transport equations for two solutes?

Yes, there are limitations to combining advective transport equations for two solutes. One limitation is that it assumes the solutes are transported independently of each other, which may not always be the case. Additionally, it may not be applicable in all types of flow conditions or for highly reactive solutes.

## 5. Can combining advective transport equations for two solutes be applied to real-world scenarios?

Yes, combining advective transport equations for two solutes can be applied to real-world scenarios. It is commonly used in environmental and engineering applications to model the transport of contaminants in groundwater or wastewater systems. However, it is important to carefully consider the limitations and assumptions of the combined equation for each specific scenario.

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