Transient and Boundary Dominated Partial Penetration Skin Effects with Turbulent Flow in Vertical Wells of Reservoirs with Near Wellbore Damage Produced at Constant Rate and Constant Pressure Conditions
Authors: Kome M. , Amro M. 
Published: May 2017

Abstract
The increasing complexity of reservoir responses, especially with unconventional reservoirs, calls for more accurate methods of reservoir characterization and well test interpretation. Though the unconventional gas reservoirs are characterized with low flow rates, these can be high enough to exceed the laminar flow range as described by Forchheimer number given in [1]. Moreover, prolonged transient flow in such unconventional reservoirs makes the use Odehs steady state or pseudo-steady state models ([2] and [3] respectively) inappropriate. This paper investigates the combined effects of turbulence, partial penetration, wellbore storage and reservoir damage in wells, especially during the transient flow period, as an attempt to reduce erroneous estimation of reservoir parameters during well test analysis.
Many models to address the reservoir response of partial penetration wells have evolved with time as seen in the works of [2], [3], [4], [5], [6], [7] and [8]. Most of the models however, do not address the commingled effects of partial penetration with other wellbore or reservoir boundary conditions. For this reason, the combined effects of partial penetration with different wellbore and reservoir conditions are investigated. The model was developed based on the composite reservoir concept to incoporate the skin effects analogue Odeh [3] pseudo-steady state model. Flow in the reservoir is addressed in both the radial and vertical directions and by transforming the pressure diffusivity equations using the Laplace and finite Fourier transforms, a diffusivity equation analogue [6] can be derived. Turbulence flow in the reservoir was addressed using the Forchheimer model with transient turbulent flow incorporated analgue Kome [9] and modified to addressed partial penetration effect of the wellbore flowing conditions by transforming the wellbore conditions using the finite Fourier cosine and sine transforms.
With the model, the influence of each of the reservoir parameters/ wellbore flowing conditions are depicted. By considering turbulent flow during the transient phase of production, the partial penetration skin also becomes influenced by turbulence effects. By incorporation the composite reservoir model for the damage skin, the partial penetration effects does not only limit to the vertical and radial permeabilities of the undamaged zone, but also addresses the effects of alterations in vertical permeability in the skin zone. As seen in the work of Kome, 2017, the permeability conventionally derived during IARF for the transient turbulent regime is a function of the Forchheimer number hence approaches will be made as to how to elimate these effects for the partially penetrated well.
The novel model clearly shows the effects of different wellbore flowing conditions and reservoir parameters for a partially penetrated well, especially during the transient flow period and the possible errors made in the past with respect to permeability and damage skin