Laboratory Investigation of Effective Stresses' Influence on Petrophysical Properties of Sandstone Reservoirs During Depletion
Authors: Belhaj H.A. , Vaziri H.H. , Islam M.R. 
Published: March 2010

Abstract
An increase in effective stresses takes place in reservoirs as a consequence of fluid production, a well-known phenomenon in both shallow and deep reservoirs. It may seem reasonable to assume that permeability and porosity decrease as pore pressure declines, since both effective radial and axial stresses become intensified during reservoir depletion. However, laboratory results show that this is not always the case. Porosity certainly decreases as a result of the compaction process, which allows the breakage of grain-to-grain cement bonds. Grain particles will become more compacted as both lateral and axial effective stresses increase. On the other hand, permeability shows no definite trend.
In this paper, a series of delicate experimental procedures were conducted to reveal some of the most intriguing phenomena in pore collapse and their impact on permeability. Sandstone samples were tested using a triaxial set-up. Based on the experimental results of this study, in weak reservoir formations, pore collapse does not occur suddenly. Rather, rocks gradually compact as grain-to-grain cement bonds break down. It was found that permeability indeed changes as effective stresses increase. However, the pathway to permeability was found to be much more complex than previously stipulated. It was discovered that enhancement or damage to permeability is not a function of pore collapse alone. Other factors, such as stress path, initial porosity, particle size, particle shape and particle distribution play a major role in determining what type of alteration in permeability occurs and to what magnitude that alteration would be.

Introduction
Traditionally, petrophysical properties data are very crucial for reserves assessment and fluid flow characterization of petroleum reservoirs. A great deal of money and effort are usually allocated in order to accurately estimate these properties. Permeability and porosity are among those properties and are by far the most important. Porosity is the key for reserves estimates while permeability is the main parameter to predict flow rates, design drawdown and, therefore, wellbore completion. Until recently, the common belief was that, once determined, these properties remain constant throughout the production life of the reservoir. Studies(1–3), including this paper, showed that this is not a realistic assumption.
During the pressure depletion process, as production from the reservoir continues, effective stresses within the reservoir increase. It is understood that the effect of reservoir stresses on porosity and permeability of the reservoir is more severe when porosity and permeability are high, although some experimental studies like Hubbert and Willis(4), Voight and St. Pierre(5) and Rosepiler(6) showed this effect is still significant, even at low porosity and permeability. It is also understood that stress paths have a large influence on horizontal and vertical permeability, and also on porosity.
The elastic uniaxial strain model is mostly used in reservoir engineering to describe production-induced changes in horizontal stress due to pore pressure decline (pressure depletion). It predicts the total horizontal stress by using overburden stress, reservoir pressure decrease and material mechanical parameters. The principal assumption in this model is that there is no lateral deformation (zero horizontal strain condition) during the depletion process.