What is developed in this paper is the cumulative fluid flow across the resistance existing at the wellbore. This is the skin effect that is encountered that is treated here for both positive and negative skin.
Essentially, what is reproduced are work curves where the cumulative fluid produced vs dimensionless time are related to the different values for the skin effect.
In treating with the negative skin in connection with the cumulative fluid produced, it has been learned that the mathematical model that designates such a skin to exist at the wellbore cannot apply, but what is attained is an effectively increased wellbore radius beyond the well bit size that shows the influence of fracturing or any remedial work performed on the well. Thus, the matrix of the sand is effected to evidence discontinuity in the pressure drop for the fluid flowing toward the well; and for the increased effective wellbore radius to the wellbore proper, the flowing pressure is essentially constant. Thus, the mathematical model indicates an open network can exist in the region of the well if the flow is radial and such is shown by the Lord Kelvin effect in pressure buildup.
The basis for this work is the Laplace transformation published by van Everdingen and Hurst, for which the present paper is an extension of the necessary work curves, incorporating the mathematics for the skin effect. The skin effect is also the joint undertaking of these authors published separately in the literature.