[Q] Analysis of unevenly spaced time series of pressure reading

Hi all! (:
I am a student collecting some pressure readings from multiple bioreactors (105) that produce biogas. Each bioreactor has three technical replica in total, and the following conditions are applied:

• Inocula: either no inocula; Sample A, community 1; Sample B, community 1; Sample C, community 1; Sample A, community 2; Sample B, community 2; or Sample C, community 2. Total of 7 conditions.
• Feed: either no feed; feed 1, feed 2, feed 3, or feed 4. Total of 5 conditions. (3 rep * 5 * 7 = 105)

All readings are collected with a manometer with range (-1. 30) Bar with 0.% accuracy. The readings are collected at (semi) irregular intervals of about 2 h during working hours (9-17) for six days. And no measurement is collected outside working hours.

Plotting the data with a scatter plot Y=Pressure X=Δt in minutes, I observe that the pressure is growing (or decreasing, depending on the biological process at hand) similarly to a sigmoid function.

I have read a couple of papers by Andreas Eckner and by Irina Rish about modelling unevenly spaced time series but they seem to focus mainly on data projection. However, I am interested in estimating the duration of the lag phase and the maximal rate.

Which would be the correct approach? I would be very grateful if someone could point me in the right direction. And I apologize in advance for any mistake or lack of clarity! I am just approaching the fascinating world of independent research and loving the learning process so far!

Cheers :)