Environmental Impact Assessment of Petrochemical Industry using Fuzzy Rapid Impact Assessment Matrix

Introduction

Modern petroleum engineers have used many equations to describe the physics behind the fluid flow through porous media. Under ideal situations these equations, which form the basis of modern software, yield accurate results. However, ever so often engineers are faced with challenging problems that seemingly defy physics: be it a well test problem, a history matched simulation model, or even a tool as simple as the material balance. Upon further investigation, engineers have to concede to the simple explanation that the assumptions behind those equations were violated. Even further discomforting is the admission that engineers have not yet properly characterized the physics behind the fluid flow through porous media.

Darcy’s pioneering work is at the heart of all equations related to porous media. Often engineers use it without question. Forchheimer  demonstrated the departure from linearity for high velocity flows. However little has been said about the validity of Darcy Law at low velocities. Considerable amount of work  has already been published in this area outside of petroleum, but it has not seeped through the petroleum engineering literature.

Darcy’s law

Darcy’s Law is based on the experimental observation that the apparent fluid velocity is proportional to the applied pressure gradient on a porous medium. This observation is analogous to flow of fluid through pipes, capillaries (Poisseuille’s Law) and also to that of flow of current through a resistive conductor. Wyckoff, separated Darcy’s original constant of proportionality into permeability (a property of the porous medium) and viscosity (a property of the fluid.

Following sections discuss some of the well-known departures from Darcy’s Law.

Post Darcy flow effect: Forchheimer made observations that the Darcy’s Law deviated from linearity for high velocities. He attributed this to the inertial losses. He proposed a velocity squared term to account for this non-linearity. Even in 1901, Forchheimer noted that some experimental data does not fit his newly proposed quadratic flow equation. He then proposed the addition of a cubic term to describe those data. Due to the less than proportional increase in flow velocity with respect to applied pressure gradient, this effect has shown a significant influence on well performance . This effect is generally termed as Non-Darcy flow; however in this study we will refer to it as Post-Darcy flow. Later studies [8-10] have published the impact of Post-Darcy flow on fractured gas wells. The literature already has effectively dealt with Post-Darcy flow and the reader is suggested to consult elsewhere for a more comprehensive treatment of the subject.