Look for the Delta H vap for each solvent - the enthalpy of evaporation, this will tell you how much energy (heat) is needed to boil a mol of the solvent.
Heat needed to boil, must be removed to condense, 1:1.
You should also look for the heat capacity of the solvents that you have, this will give you the thermal mass of the reaction mix.
Using these numbers will give you a heat balance, in theory.
Problem with theory: solvents can interact with eachother, and with the reaction elements ... if they are a good solvent, then for sure, they do! It is probably best to start with pue theory, as the interactions cannot be easily modelled as what is in the reaction changes over time (as A + B moves to more AB and some A and some B).
The rate of evaporation of a solvent in a reactor depends on several factors, such as the temperature, pressure, surface area, and air flow. To calculate the rate of evaporation, you need to know the following information:
The volume and density of the solvent in the reactor
The vapor pressure and latent heat of vaporization of the solvent at the operating temperature
The overall heat transfer coefficient and effective heat transfer area of the reactor
The log mean temperature difference between the solvent and the cooling medium
The relative evaporation rate of the solvent compared to a standard solvent (such as n-butyl acetate)
One possible method to calculate the rate of evaporation is as follows:
Calculate the mass of the solvent in the reactor by multiplying the volume and density
Calculate the amount of heat required to vaporize the solvent by multiplying the mass and latent heat of vaporization
Calculate the amount of heat transferred from the solvent to the cooling medium by multiplying the overall heat transfer coefficient, effective heat transfer area, and log mean temperature difference
Calculate the time required to evaporate the solvent by dividing the heat required by the heat transferred
Calculate the rate of evaporation by dividing the mass of the solvent by the time required
Alternatively, you can use a science-based tool that can estimate the rate of evaporation based on the vapor pressure, boiling point, and relative evaporation rate of the solvent. You can find such a tool in this web page: Determining Solvent Evaporation Rates Faster with Science-based Tool.
Here are some references that explain more about this topic:
[How To] Calculate Rate of Distillation in a Batch Reactor1: This article provides an example case study on how to calculate the rate of distillation in a batch reactor using some basic data and equations.
Determining Solvent Evaporation Rates Faster with Science-based Tool2: This article explains how to use a science-based tool to estimate the rate of evaporation based on some key parameters of solvents.
5.6A: Overview of Rotary Evaporation3: This article gives an overview of rotary evaporation, a technique that uses reduced pressure and rotation to increase the rate of evaporation.