Analytical solution to spontaneous imbibition under vertical temperature gradient based on the theory of spontaneous imbibition dynamics

Abstract In this work, we have theoretically studied the imbibition process related to a block in a fractured carbonate reservoir under an assumed constant, vertical temperature gradient, G T . An analytical solution to an ordinary differential equation we developed has been obtained using a computer program, and the original Washburn law normally valid for isothermal conditions of spontaneous imbibition has been found to hold true for G T equal to zero. The theoretical results of our study show that the space and time evolution of the imbibition front is strongly dependent on surface tension and dynamic viscosity of the imbibing fluid under a given temperature gradient. We have also validated our model against experimental data from a literature source based on spontaneous imbibition into a Hele Shaw Cell under longitudinal temperature gradient. The general conclusion of our study is that spontaneous imbibition in fractured carbonate reservoirs will be accelerated the higher the temperature of the injected water. This corresponds to a negative temperature gradient where the temperature of the injected water exceeds the ambient temperature of the reservoir.