Analysis of stresses around a sand arch shows that a failure criterion exists. When a critical flow rate is reached the arch will collapse, leaving behind a greater cavity. Field test data can consistently be described by this theory. Extending the stress analysis to cylindrical wellbores shows that a plastically strained zone develops in poorly cemented rocks, when the well is drilled. During production this zone increases with the flow rate until the entire layer is fluidized. When injecting, fracture conditions may be reached before the material returns to an elastic state of stress. The stress analysis can be used to estimate the strength of the rock near the wellbore.
L'analyse des contraintes autour d'une arche de sable montre l'existence d'une condition de stabilite critique. Quand le debit de fluide atteint un niveau maximum, l'arche s'ecroule, provoquant une plus grande cavite. Cette theorie est verifiee par des resultats d'essais effectues sur un puits reel. L'extension de cette analyse à un trou cylindrique montre que l'on aura une zone plastiquement deforme autour du puits quand on fore dans une formation mal cimentee. En production cette zone croît avec le debit jusqu'à ce que la formation entière s'ecoule comme un fluide. En injection les conditions de fracturation peuvent être atteintes avant que la formation ne soit revenue à l'etat elastique. Cette theorie peut aussi être utilisee pour obtenir indirectement une valeur de la resistance de la roche autour du puits.
Die Analyse von Spannungen um ein Gewölbe aus Sand zeigt, daß ein Bruchkriterium existiert. Wenn eine kritische Strömungsrate erreicht ist, bricht das Gewölbe und hinterlaßt einen größeren Hohlraum. Feldtestdaten können mit dieser Theorie widerspruchsfrei beschrieben werden. Wendet man die Spannungsanalyse auf zylindrische Bohrlêcher an, dann zeigt sich, daß in schlecht zementiertem Gestein eine plastisch deformierte Zone entsteht, wenn der Brunnen gebohrt wird. Wahrend der Produktionsphase erweitert sich diese Zone entsprechend der Strömungsrate, bis die gesamte Schicht verfluessigt ist. Bei Injektion können die Bruchbedingungen erreicht werden, bevor das Material wieder zu einem elastischen Spannungszustand zurueckgekehrt ist. Die Spannungsanalyse kann genutzt werden, um die Festigkeit des Gesteins in Bohrlochnahe abzuschatzen.
The purpose of drilling a well in petroleum exploration is to locate and produce hydrocarbons on a commercial basis. Before the drill penetrates the down hole strata, there will be horizontal and vertical stresses, caused by the weight of the overlying strata and tectonic activity. As the drilling bit makes the hole, the vertical and horizontal stresses will be changed around the wellbore. This paper describes stress analyses performed on a poorly consolidated layer of rock around a well. The main purpose of this work, when it started several years ago, was to investigate the sand problem occurring in poorly consolidated sandstones when oil and gas is produced. Recently, a more general stability analysis has been made and this analysis has also served as a basis for the investigation of hydraulic fracture initiation pressures. The sand problem is normally experienced as sand influx from the formation into the production string. Flow of formation fines together with the produced fluids is often experienced during normal production. Such particle flow will not be a serious problem because the particles are small and small in quantity. Particle flow starts to be a real problem only when load bearing grains are removed from the formation, which will result in a reduction in the load carrying capacity and a potential failure of the formation. Formation of sand arches behind perforation openings is a mechanism that can stabilize a poorly consolidated sand and prevent it from flowing into the well. Sand stability by arching was first treated by Terzaghi (1936) in his trap door experiment, demonstrating that arching was a real and stable phenomenon. Later Hall and Harrisberger (1970) made an experimental study on arches in relation to maximum sand free production rates. Stein et al. (1974) and Stein (1977) assumed that the maximum flow rate an arch can withstand is proportional to the shear modulus G for the sand. The G modulus they obtained from accoustic and density logging data. Tippie and Kohlhaas (1974) and Cleary et al. (1979) made laboratory studies of the arching phenomenon and its relation to flow rate and confining stress levels. Tixier et al. (1974) treated the prediction of sanding from an interpretation of the mechanical properties log. Coates and Denoo (1981) introduced a refinement of the method presented by Tixier et al. Typical for these works is that they are based on empirical relations derived from experimental data and field operations. A theoretical study of the stresses around a sand arch, supported by laboratory work, has been made by Bratli and Risnes (1981). The laboratory investigation showed there existed a limit to the load imposed by the. fluid drag forces that a given arch can sustain.
