Liquid spreading on open surfaces is a widely observed phenomenon. The physics of liquid spreading has become more complex when the surface is porous like paper or fabrics due to the evaporation of liquid and swelling of the fibers. In this study, we have performed liquid imbibition experiments on paper strips in a controlled environment with and without using hydrophobic boundaries. The experimental results are compared to the existing analytical models that account for each effect separately. The existing models were found to be inaccurate in predicting the experimental results. We developed new analytical models by modifying existing models to predict the capillary rise of liquid through paper substrate accurately. Different effects, such as the barrier (hydrophobic boundary), evaporation, and swelling, are considered simultaneously while developing the modified models to mimic the exact practical situation for the first time. We discovered that the modified models predict the experimental results more accurately than the existing models. For with and without barriers, the final models considering several effects simultaneously predict the data with a minimum accuracy range of 93% and 90%, respectively. Finally, we conducted capillary rise experiments with volatile (water) and non-volatile (silicon oil) liquids at various temperatures and relative humidity conditions to validate the analytical results.