Finding drying time from drying curve

This post shows how you can find the time that will take for a product to reduce its moisture content if you have a drying curve at hand.

Definition of drying rate

The drying rate $R$ is defined as:

$$R = -\frac{m_s}{A}\frac{dX}{dt}$$ Where $m_s$ is the mass of dry solid, $A$ is the area of heat/mass transfer and $X$ is humidity in mass of water per mass of dry solid. The rate also can be given in the form $R'=RA/m_s$. A drying rate curve shows $R$ as a function of $X$. To find the total drying time a simple integration is performed. But keep in mind that a drying curve is valid only for a specific equipment under specific operating conditions. 

Example

This example was taken from Seader's Book. Experimental data is provided for drying of rayon waste and it's required to estimate the drying time starting from $X=1$ to $X=0.10$.

Experimental data

A numerical integration using the average value of $R'$ between every pair of points gives a drying time equal to 5 [min]. The detailed calculation can be found on this file.