# Non-Darcy binomial deliverability equations for partially penetrating vertical gas wells

• Zhibao Lu

Student thesis: Master's Thesis

### Abstract

Gas well productivity is one of primary concerns in field development and provides the basis for field development strategy. To determine the economic feasibility of a gas well, we need reliable methods to estimate its expected productivity. Well productivity is often evaluated using the productivity index, which is defined as the production rate per unit pressure drawdown. And also petroleum engineers often relate the productivity evaluation to the long time performance behavior of a well, that is, the behavior during pseudo-steady state or steady state flow. The productivity index expresses an intuitive feeling that, once the well production is stabilized, the ratio of production rate to the pressure difference between the reservoir and the well must depend on the geometry of the reservoir/well system only. Indeed, it has been long ago observed by petroleum engineers that in a reservoir with strong water drive, the productivity index of a well stabilizes in a long time. The productivity for a full penetrating vertical gas well had already been given by researchers, but for the productivity for a partially penetrating vertical gas well with non-Darcy flow different researchers had presented different solutions. Generally, there are three important factors which affect the productivity for a partially penetrating vertical gas well. The three factors are is the mechanical skin factor sm, the pseudo skin factor for partial penetration and the non-Darcy flow. In this thesis the author assume the reservoir model to be cylinder circular shape or box shape. And the pseudo skin factor sps which was used to describe the partially penetrating was cited from Dr. Jing Lu's book 'Productivity Equations for Oil Wells: New Solutions Based on Three Dimensional Models'. And the Forchheimer equation was used to describe the non-Darcy flow near the wellbore. The mechanical skin factor sm relates to penetration ratio. So the author present some gas well deliverability equations based on the above assumptions and get the general conclusions concerning the effects of non-Darcy flow on the behavior of partially penetrating vertical gas wells, and give two example to analyze how these effects combine to influence the gas well deliverability in this thesis. Key words: vertical gas well, partial penetration, point-source function, bottom water driver gas reservoir, steady-state productivity, closed boundary.
Date of Award 2012 American English Jing Lu (Supervisor)

### Keywords

• Applied sciences
• Vertical gas wells
• Petroleum engineering
• Energy
• 0765:Petroleum engineering
• 0791:Energy

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