Sand production is an instability considered to be the result of wellbore fluid pressure reduction (drawdown) below some critical level. The model presented provides a physical mechanism for yielding front propagation away from the wellbore as sand production continues. Mass balance analysis leads to a relation between volumetric rate of sand production and the yielding front velocity. Short-term enhancement of fluid production because of simultaneous sand production depends not only on instantaneous sand flux, but also on the current radius of the yielded zone around wellbore, that is, the history of sand production for the well. Long-term enhancement is stipulated mainly by the development of a yielded, highly permeable zone around the wellbore. Competition between compact (cylindrically symmetrical) growth and channeltype morphology of yield propagation is analyzed.

Description of model

It is evident that sand production is a fundamental production enhancement mechanism without which much of the Canadian heavy oil industry would be seriously impaired. There is also evidence that sand production during a cold "primary" production phase can potentially help prepare reservoirs for EOR techniques1. However, continuous sand production is a complex process involving luid flow, stress redistributions changes in permeability, ilation and liquefaction and so on. Many first-order effects, such as sand yield and entrainment into the fluid flow, have never been addressed in conventional flow models. Thus, there is yet no means whereby the process can be studied, much less production predictions made. In previous papers2,3, we considered a new physics-based model for massive sand production. The sand production instability is caused by excessive deviatoric stress4,5 which arises in naturally stressed environments from lowering of wellbore fluid pressure below some critical magnitude at which sloughing (or liquefaction) is initiated. The goal of this new model is to investigate not only the instability initiation, but also to obtain dynamic and mass transport properties related to solid production after the appearance of a yielded zone. The model bas definite limitations arising from the simplifications necessary to make the problem analytically tractable, but most simplifications we also consider to be physically robust. A brief analytical outline of the model is given in Appendix A.

The first and perhaps obvious physical results of the model is a growing yielded zone around the wellbore during the process of sand production. Hence, a moving front between yielded and intact zones propagates radially away from the wellbore as sand production continues (Fig. 1). Second, solid component mass balance at the boundary dictates that the flowing, yielded zone porosity be higher than that of the intact stratum (dense but uncemented sand). The direction of motion of the boundary between the intact and flowing zones is opposite (away from the wellbore) to the transport direction (toward the wellbore). Of the solid mass sloughing off the intact zone surface, part increases the radius of the yielded zone, part is carried away from the boundary toward the borehole.

These physical features of the sand production process are independent of any specific details such as the type of yield criterion, fluid flow process.

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