Underbalanced drilling is one of the drilling techniques which relies on reservoir fluid influx. After more than 2 decades of the invention of the underbalanced drilling technology, the calculation of the fluid influx into the wellbore is yet to be improved. A knowledge of the fluid influx into the wellbore while drilling is required for accurate hydraulic modelling for designing a successful underbalanced drilling operation.

In this paper, the influx from the reservoir is defined by applying a transient mathematical solution with the possibility of incrementing the wellbore length in time. The mathematical model allows for permeability variation along the wellbore length leading to the possibility of formation evaluation while drilling. The results, through few examples, show that permeability is directly affecting the influx magnitude while drilling.

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