Decomposition of Rock Deformation During Proppant Embedment
Authors: Yaoyang Li , Guangqing Zhang , Pengxu Xie , Jue Wang 
Published: August 2024

ABSTRACT:
The deep-formation rock has various deformation modes such as viscosity, elasticity and plasticity under the action of complex geo-stress, high temperature and high pore pressure. These deformation modes increase the proppant embedment depth at different stages and affect the long-term conductivity of the fracture. A servo-controlled triaxial compression test machine and a linear variable displacement transducer (LVDT) are used to carry out the uniaxial loading and unloading creep test in this paper. The viscoelastic, viscoplastic, elastic, and plastic strains of rock are separated. The results show that the momentary plastic deformation of rocks accounts for 30%-50% of the momentary deformation of rock, and a composite creep model considering the momentary plastic strain can reflect the creep characteristics more accurately. A composite viscoelastic-plastic model of rock has been set up to describe the elastic, plastic, and viscous deformation characteristics of rock during the deformation process. This model has higher accuracy in distinguishing the elastic, plastic, and viscous deformation characteristics during the loading history of rock. The conclusions of this paper can guide the evaluation of the long-term conductivity of in-situ hydraulic fractures.

1. INTRODUCTION
Creep is one of the inherent properties of rocks, especially in deep reservoir rocks subjected to high stress, high temperature, and other conditions; it is easier to show the creep due to the development of bedrock joints and fractures, which plays a crucial part in the long-term effective proppant support and artificial reservoir reconstruction effect. At present, the research on rock elastoplastic viscous deformation separation mainly includes the laboratory single and triaxial stage loading and unloading creep experiments and the theoretical research on the establishment of multi-component (elastic element, plastic element, and viscous element) combination model based on the experimental results (Liu et al., 2020 and Zhang et al., 2020). A nonlinear viscous element of the unsteady parameter Burgers model was proposed, which can be used to describe the three stages of creep characteristics of rocks (Han et al., 2018). a nonlinear empirical power function creep model was proposed that can reflect the rheological characteristics of deep soft rocks under different stresses based on the results of large-scale true triaxial creep experiments in the mudstone (Chen et al., 2009). At the same time, some scholars consider rock damage in the creep model, which is used to describe the accelerated creep stage of hard rock (Hu et al., 2009). some scholars connected the empirical model of viscosity coefficient decay as a power function with time with the Kelvin model. They established an improved viscoplastic model that can describe the accelerated creep characteristics under different confining pressures (Liu et al., 2017). Other scholars established a nonlinear viscoelastoplastic creep constitutive model with the parameter unsteady, which can describe rocking unsteady creep based on the creep results of sandstone in the Chongqing area under different confining pressures (Liu et al., 2018). ROBERTS et al. conducted triaxial compression, tensile, and cyclic tensile creep tests on salt rock and studied the influence of different loading methods and stress paths on the creep and dilatation characteristics of salt rock (ROBERTS et al.,2015). SINGH et al. obtained the elastic modulus and viscosity coefficient of salt rock during uniaxial compression using acoustic emission technology based on the Maxwell model. They predicted the uniaxial creep behavior of salt rock according to these parameters (SINGH et al., 2018). BOUKHAROV et al. analyzed three typical processes in the rheological curve of brittle rocks. They used the stress-triggered Hooke body and strain-triggered nonlinear sticky pot element in series to describe the unsteady creep process (BOUKHAROV et al., 1995).