Elastoplastic Modelling of Sand Production Using Fracture Energy Regularization Method
Bibliographic record
Abstract
Abstract This paper extends the capacity of the current sand production models by eliminating the influence of artificial conditions and numerical mesh on localization and deformation response in the sanding model. Past studies indicate strong size effects when using classical elastoplastic models. To rectify this deficiency, a fracture energy regularization method is implemented in the numerical model. The model incorporates both the geomechanical aspects (e.g. rock elastoplastic deformation and rock disaggregation), as well as the transport aspects (e.g. the role of seepage on rock deformation and solid release). The model employs a Mohr-Coulomb flow theory of elastoplasticity with friction hardening/cohesion softening. Emphasis is given on calibration procedure and validation of the enriched model through back analysis of triaxial and uniaxial compression tests. Next, the model is used to compare the numerical predictions with laboratory data on sand production. The comparison incorporates the stress and deformation, as well as the sand volume. The calibration study shows that friction hardening and cohesion softening can satisfactorily reproduce numerically the weak sandstone response to various loading conditions. Further, computation results of strain softening material illustrates that a fracture energy regularization strategy enables the model to exhibit mesh invariance of the energy dissipation. Introduction Sand production involves two distinct stages. These are:mechanical degradation of the intact sandstone rock to loose particles by the stress concentration around the wellbore; andthe transport of the loose particles by hydrodynamic forces to the wellbore. An effective sand production model must be adequately equipped with the tools that simulate the phenomena associated with both degradation and seepage forces. One such model is discussed in this paper with an emphasis on modelling of the degradation process and a detailed description of the elastoplastic model calibration. As it has been discussed in the literature, rock mechanical degradation is related to the development of micro-cracks as failure localizes in narrow bands at post-peak strength. Development of the micro-cracks violates the continuum mechanics assumption leading to spurious influence of the numerical mesh on the formation response(1–7). This mesh dependency is separate from the small numerical error, which should tend to zero with mesh refinement. As a result of the mesh dependency, the numerical model looses its objectivity and needs to be rectified. Recognition of the deficiencies of the standard continuum theory in the modelling of deformation discontinuity has led to the development of various enrichment methods. De Borst(8) compared the performance of several of these techniques. The common approach in all these methods is the introduction of some sort of length scale that must be built into the constitutive model. Mesh independence for localization problems can be obtained in a pragmatic fashion by scaling the softening rate in inverse proportion to the element size. This approach was described by Crook et al.(7) and is based on the work of Pietruszczak and Mroz(5) and Bazant and Oh(6). The basic idea in this method is that fracture energy, which is the energy dissipated due to the formation of micro-cracks, must not differ for numerical meshes of various size.
Fetched live from OpenAlex and de-inverted. Abstracts are not stored in this database: the inverted indexes are 8.6 GB of the frame’s 9.3 GB of text, and the host has 13 GB free.
How this classification was reachedexpand
Full frame distilled prediction
Teacher imitationNot calibrated prevalence, not ground truth. Human validation pending. Learned from the 10,348 direct Codex labels and 10,348 direct Gemma labels. Candidate is the union of thresholded teacher heads; consensus is their intersection. These outputs are machine_predicted_unvalidated and are not human labels or direct frontier model labels.
Codex and Gemma teacher scores by category
| Category | Codex | Gemma |
|---|---|---|
| Metaresearch | 0.000 | 0.000 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.000 | 0.000 |
| Bibliometrics | 0.003 | 0.001 |
| Science and technology studies | 0.000 | 0.000 |
| Scholarly communication | 0.000 | 0.000 |
| Open science | 0.000 | 0.000 |
| Research integrity | 0.000 | 0.000 |
| Insufficient payload (model declined to judge) | 0.000 | 0.000 |
Machine scores (provisional)
The two teacher heads of the student model, read on this work. A score orders the frame for review; it never asserts a category, and the validation status ships verbatim with every row.
Baseline scores from an immature model (maturity gate not passed, 7 training rounds). Scores rank; they never assert a category.
score_only:v0-immature-baseline · verbatim from the scoring run: score_only means the number may rank works, and no category label ships from itClassification
machine, unvalidatedMachine predicted; a candidate call from one teacher head, not a consensus.
How this classification was reached, model by model and score by score, is at the end of the page under "How this classification was reached".