I have also used EES for this purpose, Frankly speaking, for LiBr-H2O system transient analysis is quite difficult. First go for steady state modelling. There is a lake of resources available for transient state analysis. So go for steady state analysis.
I suggest you to search for dynamic simulation that deal with the start up operation of the absorption chiller, may be these articles can help you with your mathematical model to introduce them to EES.
A simple way is to simulate many steady state conditions, and after you can take them as oututs and using another program for a quasi steady analysis. The otehr program can be a small code in matlab or fortarn. Moreover, if you have TRNSYS, you can couple EES and TRSNYS...