Flow Regime Analysis of the Pressure Build-Up during CO2 Injection in Saturated Porous Rock Formations

In this work, we are concerned with the theoretical and numerical analysis of the pressure build-up on the cap of an aquifer during CO2 injection in saturated porous rock formations in all flow regimes of the problem. The latter are specific regions of the parameter space of the plume flow, defined by the CO2-to-brine relative mobility and the buoyancy parameter (injection pressure to buoyancy pressure scale ratio). In addition to the known asymptotic self-similar solutions for low buoyancy, we introduce two novel ones for the high buoyancy regimes via power series solutions of asymptotic self-similarity equations. The explicit results for the peak value of pressure on the cap, which arises in the vicinity of the well, are derived and discussed for all flow regimes. The analytical results derived in this work are applied for the purpose of cap integrity considerations in six test cases of CO2 geological storage from the PCOR partnership, most of which correspond to high buoyancy conditions. The validity of the self-similar solutions (late time asymptotics) is verified with CFD numerical simulations performed with the software Ansys-Fluent. The result is that the self-similar solutions and the associated pressure estimations are valid in typical injection durations of interest, even for early times

A New Analytical Method for Calculating Subsidence Resulting by Fluid Withdrawal from Disk-Shaped Confined Aquifers

This work presents the derivation of analytical solutions concerning the radial subsidence distribution ensuing from fluid extraction from a disk-shaped confined aquifer in homogeneous formations. The study draws upon methodologies developed in petroleum geomechanics of deep reservoirs to estimate surface uplift due to CO2 injection using Hankel-transformed thin plate theory. These methods yield simplified expressions as compared to previous results derived using the superposition principle on surface uplift from a uniform pressure field. Hence, closed-form formulas for the subsidence at the well location are re-derived, while the formulas for the subsidence field are deducted by both methods and the mathematical relation between the two methodologies is discussed. Additionally, innovative closed-form asymptotic solutions for radial subsidence distribution are deduced for scenarios involving deep aquifers. These solutions demonstrate exceptional accuracy when aquifer depth exceeds aquifer diameter, exhibiting independence from formation permeability and fluid viscosity. The study explores the influence of physical parameters on the subsidence field

Finite element modeling of nanoindentation on C-S-H: Effect of pile-up and contact friction

In this paper we computationally study the indentation response of a rigid axisymmetric indenter on a semi-infinite elasto-plastic material of the Mohr-Coulomb type. The finite element method is used to quantify the effect of material properties (E, c,) and contact friction (μ) on the indentation response of C-S-H phases. The high E/c-ratio for both C-S-H phases, together with their cohesive-frictional behavior, leads to pile-up phenomena around the penetrated probe. The influence of all these parameters on the actual area of contact and its subsequent effect on commonly extracted quantities of the indentation test, namely indentation modulus (M) and indentation hardness (H), is investigated. It is shown that contact friction affects the contact area between the indenter and indented material and as a consequence interferes, to a certain extent, with the procedure for estimating elastic and plastic material properties. The effect is more pronounced for the hardness measurements

Flow regime analysis of the pressure build-up during CO2 injection in saturated porous rock formations

In this work, we are concerned with the theoretical and numerical analysis of the pressure build-up on the cap of an aquifer during CO2 injection in saturated porous rock formations in all flow regimes of the problem. The latter are specific regions of the parameter space of the plume flow, defined by the CO2-to-brine relative mobility and the buoyancy parameter (injection pressure to buoyancy pressure scale ratio). In addition to the known asymptotic self-similar solutions for low buoyancy, we introduce two novel ones for the high buoyancy regimes via power series solutions of asymptotic self-similarity equations. The explicit results for the peak value of pressure on the cap, which arises in the vicinity of the well, are derived and discussed for all flow regimes. The analytical results derived in this work are applied for the purpose of cap integrity considerations in six test cases of CO2 geological storage from the PCOR partnership, most of which correspond to high buoyancy conditions. The validity of the self-similar solutions (late time asymptotics) is verified with CFD numerical simulations performed with the software Ansys-Fluent. The result is that the self-similar solutions and the associated pressure estimations are valid in typical injection durations of interest, even for early times

A New Analytical Method for Calculating Subsidence Resulting by Fluid Withdrawal from Disk-Shaped Confined Aquifers

This work presents the derivation of analytical solutions concerning the radial subsidence distribution ensuing from fluid extraction from a disk-shaped confined aquifer in homogeneous formations. The study draws upon methodologies developed in petroleum geomechanics of deep reservoirs to estimate surface uplift due to CO2 injection using Hankel-transformed thin plate theory. These methods yield simplified expressions as compared to previous results derived using the superposition principle on surface uplift from a uniform pressure field. Hence, closed-form formulas for the subsidence at the well location are re-derived, while the formulas for the subsidence field are deducted by both methods and the mathematical relation between the two methodologies is discussed. Additionally, innovative closed-form asymptotic solutions for radial subsidence distribution are deduced for scenarios involving deep aquifers. These solutions demonstrate exceptional accuracy when aquifer depth exceeds aquifer diameter, exhibiting independence from formation permeability and fluid viscosity. The study explores the influence of physical parameters on the subsidence field

The influence of diffusion in the fracture resistance method for wellbore strengthening: A rock mechanics approach

AIP Conference Proceedings, Volume 2040, 30 November 2018, Article number 150001© 2018 Author(s). A coupled finite element model was constructed to investigate the influence of diffusion in the fracture resistance method for wellbore strengthening. We simulate the unwanted fluid-driven fracture that is created from a narrow drilling mud window with the cohesive zone approach in a poroelastic formation. The fluid flow within the fracture is modelled by the lubrication theory assuming incompressible Newtonian viscous fluid while the fluid movement in the formation follows the Darcy law. The deformation of the porous continuum is considered to obey the Biot effective stress principal. Plugging is simulated by shutting-in the flow rate at the well and constraining the fracture aperture at a 1m distance from the well so as to allow the fluid to bleed in the formation. From the poroelastic analysis, we obtain the fracture dimensions, fluid pressures, in-situ stress field change and the principal stresses during injection and plugging the fracture. From the principal stresses, we apply a normalized Griffith criterion suitable for predicting fracture onset. It was found that during plugging, the fracture tip effectively resists propagation, however, a new fracture is predicted to onset at the plug location owing to the diffusion of drilling fluids from the fracture towards the formation causing severe stress concentration compared to elastic models which fail to predict such physical mechanisms

A working model for estimating CO2-induced uplift of cap rocks under different flow regimes in CO2 sequestration

In this work we study the deflections of an impermeable caprock in the various flow regimes of the plume evolution in the CO2 sequestration problem. The pressure distributions causing the deflections are determined by three different ways: via CFD simulations, known analytical solutions and a novel model based on mass conservation (plug flow model). We find that the different approaches for calculating the deflections are in very good agreement exhibiting minor deviations near the well; the overall deviations also grow slowly with time. We also find that the magnitude of deflections is inversely proportional to the gravity number, that is, large deflections correspond to the low buoyancy regime. These findings suggest that the deflections are mainly driven by the injected volume of CO2, a fact which is naturally built in the proposed model, dictating a piecewise logarithmic pressure profile which greatly facilitates analytical treatment of the deflection field calculations. This methodology can be used for predicting deflections with relative ease that are useful for caprock uplift and integrity considerations

On the stress dependency of sand production coefficient in hydro-dynamical sanding criteria

Solids production is a complex physical process which is controlled by several factors including mechanical failure from in-situ stresses and hydrodynamic erosion from fluid flow. Hydrodynamic models for the prediction of sand production involve sanding criteria based on filtration theories. Such models contain a constitutive model parameter, the coefficient λ, with dimensions of inverse length which is calibrated by sand erosion tests, but its nature and its dependencies have not been clarified to date. The aim of this work is an attempt to refine the hydrodynamic models by investigating the dependence of the sand production coefficient λ on the external stress conditions and on the plastic zone Λ that is developed on hollow cylinders tests and propose an expression describing its importance in the sand production prediction modelling. The aim of the work is obtained through simulations with finite elements by utilizing the well-established Arbitrary Lagrangian-Eulerian (ALE) analysis considering the poro-mechanical coupling of the fluid-solid system for simulating hollow cylinder tests. Best fitting experimental data estimated values for the sand production coefficient for various values of external stress are obtained through back analysis. The dependence of λ on the external stress turns out to be fairly smooth and a three-parameter model is proposed to describe that dependence: a scale parameter, an exponent, and a stress parameter defining the magnitude of stress at which erosion onset is predicted. It turns out that the stress parameter is associated with the minimum stress required for plastic yielding to occur, which was also estimated theoretically. This finding is in agreement with the physical assumption underlying the simulations that erosion onsets and progresses after the material reaches a critical plastic strain as a consequence of material plastic yielding. A power law model describing the dependence of λ on the plastic zone depth is also proposed and discussed

A hydrodynamic model for analyzing the closure stresses in the wellbore strengthening problem

The problem of creating unwanted fractures while drilling ultradeep wells is mitigated with the application of wellbore strengthening techniques. Despite the numerous applications, an open question remains about the efficiency of the loss of circulation materials (LCM) and its implications on the closure stress distribution change during plugging. This work investigates the effects on the stress field before and after plugging along the fracture extension axis by introducing a hydrodynamic plug. With the hydrodynamic plug, fluid flow is constrained by pressure conditions at specific locations in the fracture simulating the LCM. Three different scenarios were considered. First, the efficiency of the bridge is simulated by varying the pressure drop. Second, the location of the bridge inside the fracture and finally a nearly packed fracture. The models are fully coupled and were solved with the finite element method in impermeable and permeable hard rocks. We find that for high-efficiency bridges, narrower fracture profiles are predicted, which causes the induced closure stresses to increase significantly. On the other hand, when the bridge is close and near the wellbore area, the fracture profiles are maintained wide and narrow when it is nearest to the tip. The predicted fracture geometry induces higher closure stresses when the plug is near the well and slightly reduces when it is near the tip. Finally, the pressure profile resulting from the packed fracture significantly affects the fracture dimensions, resulting in narrower fracture, however resulting in a smooth variation of induced closure stresses with high magnitude comparable to the stresses at the state of propagation. The diffusion occurring in the permeable case creates back-stresses that appear to have an additive contribution to the induced closure stresses. This underlines the significance of diffusion on the induced coupled closure stresses for large fractures while performing wellbore strengthening methodologies