: Laboratory studies of deforming unconsolidated reservoir sands from the Wilmington Field, CA and the Gulf of Mexico indicate that a significant portion of the deformation is both time-dependent and permanent. Furthermore, a threshold viscous compaction pressure has been identified in these sands, marking the transition from elastic to viscoplastic behavior, and which in general can be approximated by the maximum in situ effective pressure experienced by the sand at depth. Because the viscous component of deformation is significant, a standard elastic-plastic end cap model is not sufficient, and a model that includes viscoplasticity must be used. An appropriate model for unconsolidated sands can be developed by incorporating Perzyna viscoplasticity theory into the modified Cambridge clay cap model. Perzyna viscoplasticity theory simply states that pressure (and the location of the end cap) should follow a power law function of strain rate when a material is deforming viscoplastically. Hydrostatic compression tests were conducted at volumetric strain rates of 10-6, 10-5, and 10-4 per second in order to find values for the required model parameters, namely the threshold viscous compaction pressure as a function of strain rate. As a result, by using an end cap model and Perzyna viscoplasticity theory, changes in porosity in both the elastic and viscoplastic regimes can be predicted as a function of both stress path and strain rate.
1. INTRODUCTION
Inelastic porosity loss and its associated compaction and subsidence is commonly observed in unconsolidated sand and shale and weakly consolidated chalk reservoirs during production. A classic example of this is the Ekofisk field, where both field evidence and laboratory studies showed that production-induced compaction was permanent, and that the observations could be modeled with an elastic-plastic cap-type constitutive equation [1]. More recently, Chan and Zoback [2] used the modified Cambridge clay cap model to describe the deformation of unconsolidated sands from the Gulf of Mexico, and developed the DARS (Deformation of Reservoir Space) method of transferring model parameters from laboratory boundary conditions to reservoir boundary conditions in order to predict changes in porosity associated with production. Fossum and Fredrich [3] derived a unique and continuous end cap model by analyzing laboratory data from a variety of unconsolidated earth materials, and built the resulting constitutive equations into a large 3-D finite element code capable of meter-scale deformation analysis of reservoirs and aquifers. Incorporating cap-type constitutive laws into finite element models is not unique to reservoir analysis; such models are commonly used in civil engineering and soil mechanics at both the field scale [4,5] and the laboratory scale [6]. End cap elastic-plastic constitutive laws have proven to be robust and reliable predictors of the deformation of a variety of unconsolidated materials over several orders of magnitude in scale.
There are several advantages to choosing an end cap constitutive law for describing elasticplastic materials. The main advantage for geomechanical applications is that the model provides a means of quantitatively predicting changes in porosity as a function of stress under both shearing and compaction. In addition, most end cap models require solving for only a few parameters in order to be fully defined.
