Mud solid and filtrate invasion are the most common causes of formation damage during overbalanced drilling (OBD), which is a method of drilling in which the wellbore pressure remains greater than formation pressure. During the past ten years, underbalanced drilling operations (UBD), which can be defined as a drilling method in which the wellbore pressure is less than formation pressure, has been growing due to their applications such as prevention of lost circulation, reduction of filtration lost in naturally fractured and mature reservoirs.

It is very difficult to always maintain the underbalanced conditions in drilling and completion operations during bit changing and tripping operations. In these cases due to the non-existence of internal and external mud cake, there will be high amount of mud solid and filtrate invasion into the formation.

Besides these, the potential of formation damage still exist during UBD due to Counter-current Spontaneous Imbibition (COUCSI) process. In this case, for water-based muds the original water phase pressure in the reservoir is less than the irreducible water saturation. Therefore the capillary pressure and wettability characteristics of the formation can result in water invasion from the drilling fluid into the formation.

The main goal of this study is modeling of this process for a vertical and horizontal well in a conventional reservoir, which are being derilled using a water-based mud system in an underbalanced mode, investigating the effects of some factors such as amount of underbalanced pressure difference and exposure time. In addition, the amount of invaded water and invasion distance are discussed too. The numerical modeling and resulting governing system of partial differential equations, the descretized forms and initial and boundary conditions are presented.

Based on this numerical modeling, it is shown that for high capillary pressure values, the amount of water invasion increases. Moreover, for lower underbalanced differential pressure and higher exposure times, water invasion and invasion distance increases too.

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