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Influence of rock failure behaviour on predictions in sand production problems

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Abstract

The mechanical strength of rock in terms of shear or compressive failure has been previously adopted as a criterion for sand production and when used solely has been proven to overestimate the process. On the other hand, ignoring the mechanical strength behaviour of the material increases the tendency for inaccurate estimations of the erosion process. In this work, an equally proportionated inclusion of the mechanical strength and erosion-based criteria in sanding predictions is proposed and assessed by numerical models. Several rock failure models and their influences on the sanding process have been analysed, including models such as the Drucker–Prager (DP), the Drucker–Prager hardening (DP hardening), the Mohr–Coulomb (MC) and the Mohr–Coulomb softening (MC softening). Modelling outcomes show distinct differences in rock response to operating and boundary conditions (e.g. flow rate and drawdown), and predictions of sand production. It was confirmed by modelling results that despite the low magnitude of stresses and strains developed at the well face and perforation regions, post-yield hardening behaviour increases the estimation of the amount and intensity of sand production. Also, incorporating a post-yield softening behaviour increases the magnitude of stresses and strains; however, this effect is observed to have a negligible impact on sand production. The role of void ratio has been recognised as a dominant factor, as its evolution significantly determines the pattern and intensity of sand production. A more cautious selection and rigorous coupling of rock strength models in sand production modelling is therefore essential if accuracy of predictions is to be improved.

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Abbreviations

\(\tau\) :

Shear stress (N/m2 or Pa)

\(C\) :

Coefficient of internal cohesion (N/m2 or Pa)

\(\bar{C}\) :

Mobilised or variable cohesion

\(C_{0}^{\text{y}}\) :

Initial cohesion yield stress

\(\Upphi\) :

Frictional angle or slope

\(\bar{\Upphi }\) :

Mobilised friction angle

\(\Upphi_{\text{L}}\) :

Limit friction angle

\(\Upphi_{\text{cv}}\) :

Friction angle of constant volume

\(\theta\) :

Deviator polar angle

\(\varphi\) :

Dilation angle

\(\bar{\varphi }\) :

Mobilised dilation angle

\(\sigma\) :

Normal stress

\(\sigma_{1}\) :

Major principal stress

\(\sigma_{2}\) :

Intermediate principal stress

\(\sigma_{3}\) :

Minor principal stress

\(\sigma_{\text{m}}\) :

Mean principal stress

\(\sigma_{\theta }\) :

Tangential stress

\(\tau_{ \max }\) :

Maximum shear stress

q :

Equivalent or von Mises stress

\(\hat{\sigma }\) :

Mean stress or equivalent pressure stress (\(\hat{\sigma } \approx \sigma_{\text{m}}\))

\(I_{1}\) :

First stress invariant of the stress tensor

\(J_{2}\) :

Second invariant of the deviatoric stress tensor

\(J_{3}\) :

Third invariant of the deviatoric stress tensor

g :

An invariant related to the third deviatoric stress invariant \(J_{3}\)

\(S_{ij} S_{jk} S_{ki}\) :

Components of the deviatoric stress tensor

\(\delta_{ij}\) :

Kronecker delta

\(e^{ - p}\) :

Effective strain (hardening parameter)

\(e_{e}^{f}\) :

Effective strain at the limit friction angle

\(e_{e}^{c}\) :

Effective strain at zero cohesion

\(\check{e}_{\text{m}}\) :

Meridional eccentricity

\(H_{n}\) :

Parameter that is a function of \(e_{m}\) and \(\theta\)

\(e_{\text{d}}\) :

Deviatoric eccentricity

K :

Ratio of yield stress in triaxial tension to yield stress in triaxial compression

\(\sigma_{\text{c}}\) :

Uniaxial compressive yield stress

\(\dot{m}\) :

Rate of solid mass eroded

\(\rho_{\text{s}}\) :

Solids or particle density

\(\rho_{\text{d}}\) :

Dry density

λ:

Sand production coefficient

\(\vartheta\) :

Porosity

c :

Concentration of fluidised solids transported

\(q_{i}\) :

Fluid flux

\(v_{\text{e}}\) :

Erosion velocity

\(v_{w}\) :

Pore fluid velocity

\(\gamma^{\text{p}}\) :

Plastic shear strain

\(\dot{\gamma }^{\text{p}}\) :

Plastic shear strain rate

\(\gamma_{\text{peak}}^{\text{p}}\) :

Cut-off value of plastic shear strain

\(\bar{\epsilon}^{p}\) :

Equivalent plastic strain

\(\dot{\bar{\epsilon}}^{p}\) :

Equivalent plastic strain rate

\(\epsilon\) :

Void ratio

k :

Ratio of average horizontal stress to the vertical stress

\(\upsilon\) :

Poisson’s ratio

\(z\) :

Subsurface depth

\(E_{h}\) :

Average deformation modulus

T :

Tensile strength

G :

Flow potential

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  1. School of Civil Engineering, University of Leeds, Leeds, UK

    Kenneth Eshiet & Yong Sheng

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  1. Kenneth Eshiet
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  2. Yong Sheng
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Correspondence to Yong Sheng.

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Eshiet, K., Sheng, Y. Influence of rock failure behaviour on predictions in sand production problems. Environ Earth Sci 70, 1339–1365 (2013). https://doi.org/10.1007/s12665-013-2219-0

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