The Study of Spontaneous Co-Current and Counter-Current Imbibition in Heavy Oil Fractured Reservoirs with the Focus on their Distinctions in Numerical Simulation Methods
Authors: Hamidpour Esmaeil , Fathollahi Sadegh , Mirzaei-Paiaman Abouzar , Bardestani Majid , Kamalifar Hadis 
Published: December 2018

Abstract
Simulation of fractured reservoirs is an old headache in oil industry, especially for reservoirs located in southern west of Iran. The situation is much more complex when dealing with heavy oil. Most of the simulation results are not reliable due to the many uncertainties in the data related to fractured reservoirs, especially characterizing the flow of heavy fluids in fractures. Consequently, the oil administration is unable to forecast a near-to-reality future of reservoirs. Due to the long run time and technical constraints in single porosity method which is used for fractured reservoirs, a much faster dual porosity algorithm is suggested for simulation of fractured reservoirs. Till now, the single porosity method is used to validate the corresponding dual porosity algorithm.
Oil production in fractured reservoirs is controlled by special mechanisms e.g. capillary imbibition, gravity drainage and etc. Capillary imbibition can be occurred co-currently, counter-currently or both together. These two are different significantly in both their rate of imbibition and their ultimate oil recoveries. Counter-current imbibition is slower than co-current imbibition and the ultimate oil recovery is also lower in some extent. This is due to the difference in their boundary condition and relative permeability. Both of co/counter-current imbibition can be occurred in water injection around a matrix block. Counter-current imbibition is more active when dealing with heavy reservoir fluid. Hence, studying the effect of simultaneous counter-current spontaneous imbibition (COUCSI) and co-current spontaneous imbibition (COCSI) in heavy oil reservoirs is necessary.
We have come to the point that for having systematic evaluations of simulating methods each mechanism should be introduce to the simulator exclusively. To do this, there should be a thorough understanding of the process and consequently expected behaviors of the model should be specified in full details. Therefore, first of all some recent experimental researches are investigated carefully. Then to see the dimensions of the errors related to simulations, a carefully designed model is used to see the performance of the simulator in accounting of oil production under capillary imbibition mechanism. Two matrix blocks are set one above each other and also they are surrounded by fractures. The water then is injected from the bottom and liquids will be produce from the top in a way that constant voidage requirement is met. By this constraint, total pressure drop is negligible and the viscous displacement is of no significance. Accordingly, the process is controlled by capillarity. After full description of single porosity model and understanding its capability in simulating water injection controlled by capillarity, then an equivalent dual porosity model is generated and compared to the single porosity simulation.
Finally the equation that is developed for relating the counter-current relative permeability to the co-current relative permeability (Bentsen, 2013) is used to improve the results of the dual porosity method.