Generalized poroelasticity framework for micro‐inhomogeneous rocks

Müller, Tobias M.; Sahay, Pratap N.

doi:10.1111/1365-2478.12392

Cited by 23 publications

(25 citation statements)

References 29 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…In real rocks, stress concentrations at pore‐scale heterogeneities might lead to inhomogeneous deformation. Müller and Sahay (2016) captured this inhomogeneous deformation in a macroscopic theory, thereby extending the Biot constitutive equations to micro‐inhomogeneous rocks. Let us consider the volumetric deformation induced by confining

(p_{c})

and fluid

(p_{f})

pressures.…”

Section: Theorymentioning

confidence: 99%

“…With increasing dead volume, we expect to observe a continuous decrease of the bulk modulus. Since the increase of dead volume implies a decrease of the mechanical load, the pore fluid experiences the limit of non‐interacting fluid at a certain intermediate dead volume, that is, when the fluid takes the minimal load under undrained condition, the non‐interacting limit should be found (Müller and Sahay, 2016).…”

Section: Introductionmentioning

confidence: 99%

“…(2016). We provide a detailed derivation based on the poroelastic constitutive equations of Müller and Sahay (2016). This refined 1D model is a boundary condition that hydraulically connects the dead volume to the rock sample.…”

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

Drained‐to‐undrained transition of bulk modulus in fluid‐saturated porous rock induced by dead volume variation

Tan

Müller

et al. 2020

Geophysical Prospecting

Self Cite

View full text Add to dashboard Cite

We examine the effect of poroelastic boundary conditions when determining elastic properties of fluid‐saturated porous rocks from forced‐oscillation laboratory experiments. One undesired yet often unavoidable complication in the estimation of the undrained bulk modulus is due to the presence of the so‐called dead volume. It implies that some fluid mass can escape the rock sample under applying a confining pressure perturbation. Thus, the dead volume compromises the undrained state required to unambiguously determine the undrained bulk modulus. In this paper, we model data of recently performed low‐frequency (0.1 Hz) measurements. Therein, the dead volume has been systematically varied from 10% to 1000% of the pore volume. For the smallest dead volume, the inferred bulk modulus is close to the Biot–Gassmann undrained bulk modulus. With increasing dead volume, the experimentally inferred bulk modulus approaches the drained bulk modulus. We show that the transition from undrained to drained state as a function of dead volume can be modelled with a 1D poroelastic model for the rock sample‐dead volume system with a boundary condition that honours the continuity of the fluid volume flux. We discuss the limitations of the 1D model when applied to data recorded at higher frequencies (up to 100 Hz).

show abstract

(p_{c})

and fluid

(p_{f})

pressures.…”

Section: Theorymentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

Drained‐to‐undrained transition of bulk modulus in fluid‐saturated porous rock induced by dead volume variation

Tan

Müller

et al. 2020

Geophysical Prospecting

Self Cite

View full text Add to dashboard Cite

show abstract

“…Since the introduction of the poroelasticity theory by Biot (1941), the definition of an effective deformation moduli for the constitutive relations has been sought (Biot and Willis, 1957;Makhnenko and Labuz, 2016;and Cheng, 2016 for an overview). We use volume averaging of the pore-scale equations to define this parameter (Sahay et al, 2001;Sahay, 2013;Müller and Sahay, 2013;Müller and Sahay, 2016a), which describes the effects of pore-scale heterogeneities.…”

Section: Introductionmentioning

confidence: 99%

“…From the pore-scale simulations we infer the macroscopic deformation moduli by volume-averaging. We interpret these moduli in the framework of a generalized poroelasticity framework that accounts for micro-inhomogeneities in a generic way (Müller and Sahay, 2016a).…”

Section: Introductionmentioning

confidence: 99%

Drained pore modulus determination using digital rock technology

Ahmed

Müller

Madadi

et al. 2018

ASEG Extended Abstracts

View full text Add to dashboard Cite

SUMMARYGeomechanics helps us understand the life-cycle of a hydrocarbon reservoir and, in turn, impacts geophysical monitoring programs. A common geomechanical problem is to predict reservoir compaction or zones of abnormal pore pressure. These predictions mostly use simple empirical relations, but recently, the use of rock deformation models based on static poroelasticity are becoming the norm. These models require accurate values for the poroelastic parameters. We present a digital rock workflow to determine these poroelastic parameters which are difficult to extract from well-log or laboratory measurements. The drained pore modulus is determinant in the compaction problem. This modulus represents the ratio of pore volume change to confining pressure when the fluid pressure is constant. In laboratory experiments, bulk volume changes are accurately measured by sensors attached to the outer surface of the rock sample. In contrast, pore volume changes are notoriously difficult to measure because these changes need to quantify the pore boundary deformation. Hence, accurate measures of the drained pore modulus are challenging. We simulate static deformation experiments at the pore-scale utilizing digital rock images. We model an Ottawa F-42 sand pack obtained from X-ray micro-tomographic images. We stack two-dimensional micro-CT images to generate a three-dimensional F-42 sand pack sample. We extract a sub-volume from this sample for numerical simulation. We first segment the cropped sample consists of grains and pore spaces and then use the segmentation to generate a volumetric mesh. We compute the elastic, linear momentum balance in the structural domain (grains) and solve the system using the commercial software package ABAQUS. The network of grains (solid phase) is assumed elastic, isotropic, and homogeneous. We calculate the change in pore volume using a new post-processing algorithm, which allows us to compute the local changes in pore volume due to the applied load. This process yields an accurate drained pore modulus. We then use an alternative estimate of the drained pore modulus. We exploit its relation to the drained bulk modulus and the solid phase bulk modulus (i.e., Biot's coefficient) using the digital rock workflow. Finally, we compare the drained pore modulus values obtained from these two independent analyses and find reasonable agreement.

show abstract

A FEM for three‐field u–p–η poroelasticity with nonreciprocal interactions

Campos,

Gracie

2023

Num Anal Meth Geomechanics

View full text Add to dashboard Cite

The de la Cruz and Spanos (dCS) theory of poroelasticity is a pore‐scale volume averaged formulation and differs from the widely used Biot (BT) theory. A novel Finite Element Method (FEM) is developed for dCS theory to enable the study of nonreciprocal solid–fluid interactions, which are omitted from BT model. Solid deformations are quasi‐static and pore fluid flow is transient; dynamic effects are neglected. The form of the dCS theory chosen includes BT theory as a special case. The governing equations are written in terms of three fields: solid displacement u, fluid pressure p, and porosity η. Fully implicit time integration and a mixed‐element formulation are employed to ensure stability. The convergence rate of the FEM dCS model is shown to be optimal in a one‐dimensional consolidation problem. Examples of a footing and subsurface injection problems in two dimensions further attest the robustness of the implementation and are shown to reproduce BT model results as a special case. The effect of nonreciprocal solid–fluid interactions is studied in all examples and shows a wide range of importance depending on the properties of the porous media (e.g., permeability) and problem‐specific constraints. The developed FEM provides a tool to enable further comparisons between dCS and BT theories and validation in practical applications.

show abstract

Generalized poroelasticity framework for micro‐inhomogeneous rocks

Cited by 23 publications

References 29 publications

Drained‐to‐undrained transition of bulk modulus in fluid‐saturated porous rock induced by dead volume variation

Drained‐to‐undrained transition of bulk modulus in fluid‐saturated porous rock induced by dead volume variation

Drained pore modulus determination using digital rock technology

A FEM for three‐field u–p–η poroelasticity with nonreciprocal interactions

Contact Info

Product

Resources

About