Abstract
In this work, we present a novel semi-analytical framework for modelling sand production in cylindrical geometries under axisymmetric conditions and isotropic stress field. We employ the hydro-dynamic modeling of erosion simplified into a kinematic description as proposed in Kakonitis et al. (Geomech Energy Environ 35:100487, 2023b) which reduces the dynamical variables to mean porosity and plastic zone depth, i.e. purely time-dependent quantities. In the present research, we relax the negligible pressure assumption (applicable to laboratory conditions) of that work to construct a framework that applies to high pressure as well (field conditions). Additionally, we extend the kinematic formulation to incorporate the effect of variable boundary conditions (pore pressure and stresses). By developing the kinematic formulation, our aim is to offer a method that allows for fast evaluation of multitudes of plausible models against actual data. To this end, we exploit the simplicity of the proposed framework by implementing free parameter estimation through the non-linear simplex (Nelder–Mead) algorithm. This theoretical setup is applied in two cases: the first is a North Sea well erosion dataset representative of high-pressure regime and the second is an experimental hollow cylinder test on synthetic sandstone under variable external stress representative of negligible pressure. We evaluate a family of hydrodynamic and material degradation laws, and we find the best model for each case. Future directions of development of this work are also discussed.
Original language | English |
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Article number | 092904 |
Journal | Rock Mechanics and Rock Engineering |
DOIs | |
Publication status | Accepted/In press - 2025 |
Keywords
- Axisymmetry
- Degradation laws
- Elastoplasticity
- Hollow cylinder
- Hydrodynamic erosion models
- Nelder–Mead method
- Sand production