Benjamin Loret

Deformable Porous Media Saturated by Three Immiscible Fluids: Constitutive Modelling and Simulations of Injection and Imbibition Tests

A number of environmental and petroleum engineering applications involve the coexistence of three non-miscible fluids. In this work, basic constitutive relations and computational schemes are developed in order to simulate fluid injection and imbibition processes in a deformable rock through the finite element method. For this purpose, the following ingredients are worked out: (i) simple, but general formulas for the effective saturations; (ii) constitutive expressions for the relative permeabilities of water, oil and gas in terms of effective saturations; and (iii) constitutive capillary pressure relationships. These ingredients are introduced in a domestic finite element code where the primary variables are the solid displacement vector and the three fluid pressures. Given the abundance of experimental data in the petroleum engineering field, the whole framework is firstly tested by simulating gas injection into a rock core sample initially saturated by water and oil. Sensitivity analyses are performed upon varying key constitutive, loading and numerical parameters, to assess the physical and computational outputs of the proposed framework. Particular attention is given to the influence on the model predictions of several expressions defining relative permeabilities. Simulations of water-alternated-gas injection and of counter-current water imbibition tests are also performed, to establish the reliability of the proposed constitutive and computational framework.

Stabilization of Forced Heat Convection: Applications to Enhanced Geothermal Systems (EGS)

The natural permeability of geothermal reservoirs is low and needs to be enhanced to ensure an efficient use and economic viability. Next to chemical enhancement, the main technique used for that purpose is hydraulic fracturing. Here, hydraulic fracturing is introduced in a thermo-poroelastic framework. The main addition to this framework is a fracturing model, phrased in terms of Terzaghi’s effective stress that governs the evolution of size and aperture of the fractures in all directions of space. At any geometrical point, a fracture-induced anisotropic permeability tensor is calculated: Next to the injection pressure and thermal shrinking, the directional properties of this tensor are strongly influenced by geological stresses. The fully integrated framework is henceforth used in simulating thermal recovery from enhanced geothermal reservoirs. Evidently, the credibility of the numerical simulations cannot be sufficiently trusted with large spurious wiggles in the temperature field and consequently in those of the effective stresses. This paper provides several approaches to stabilize convection of heat due to extreme injection conditions at early stages, sudden increase in permeability due to hydraulic fracturing, and near the production wells at late injection stages. Emphasis is paid to the subgrid scale/gradient subgrid scale method where the transient problem is placed into a stabilized advection–diffusion–reaction problem.

Energy Production Landscape and Fluid Injections in Energy-Related Activities

The energy landscape is changing in these decades due to several factors, namely the realization that fossil resources are finite, the environmental concerns induced by pollution due these fossil resources, the unclear future in terms of potential and reliable alternative energies, and the increasing world competition due to the economic emergence, today of China, tomorrow of India, and next of Africa. Each of these factors is thought to contribute to increase the cost of energy both at the country and individual levels. Recent and current energy productions worldwide are overviewed, including quantified amounts and trends. Data are listed per country, per capita, or per energy type, highlighting conventional and unconventional resources. Emphasis is laid on the environmental and geomechanical issues associated with fluid injections and withdrawals, subsidence, uplift, and microseismicity. Carbon dioxide sequestration is paid a particular attention. A short account of the technical details of the geological landscape and injection operations of the three main pilot sites that have been tested so far is provided to help discovering the many issues that are posed by carbon sequestration.

Units, Physical Constants, Acronyms

The definitions of the basic, standard and non standard units and of the acronyms used in the book are listed in this chapter.

Carbon Dioxide Sequestration and Enhanced Recovery Techniques

Selection of sites appropriate to sequester carbon dioxide should identify the source (production) sites, the transport vehicles, and the fate of the injected CO(_{2}). The ensuing alterations of the mechanical properties of the reservoir, the magnitude of the subsidence/heave, and the induced microseismicity are key issues to be scrutinized for both safety considerations and public acceptance. This chapter is devoted to modeling aspects of carbon dioxide sequestration. It capitalizes on the overview of the current deployment of pilot tests of Chap. 1 and on the analysis of the thermophysical properties of water and carbon dioxide reported in Chap. 4. Emphasis is laid on the solubility properties of carbon dioxide in water and aqueous solutions, on mutual solubilities in the absence and presence of methane and on the ensuing chemo-mechanical couplings with the rock formation in actual reservoirs. Crack closing and reopening due to salt crystallization (a small scale issue) and the sealing capacity of the caprock (a macroscopic issue) are relevant subjects for the storage in deep sedimentary basins. Wettability, capillary pressures, relative permeabilities, and stability of gas sequestration in saline aquifers and coal seams are addressed. Gas replacement techniques aimed at sequestration of carbon dioxide while enhancing the recovery of oil or gas are overviewed.

Deformable Porous Medium Saturated by Three Immiscible Fluids

A number of processes in civil, environmental, and hydrocarbon engineering involve the co-existence of three non-miscible fluids, typically water, a nonaqueous phase liquid (NAPL), e.g. a chlorinated solvent, oil, supercritical CO(_2), and a gas, e.g. air, methane, CO(_2) in gaseous phase. Immiscibility is accompanied by the presence of a meniscus and endows each fluid with its own pressure. The relative wettability characteristics of the three fluids are complex and depend on the physical properties and chemical content of the fluids and on the mineralogy of the rock. In water wet rocks, water is more wetting than oil which is more wetting than gas, because the water–oil contact angle is smaller than 90(^{circ }); thus, water keeps preferentially in contact with the rock matrix and oil tends to spread spontaneously. As a consequence, small pores are mostly filled by water, oil may invade intermediate pores, and gas tends to occupy the middle of large pores only. The presence of three immiscible fluid phases implies the formulation of the capillary pressures and relative permeabilities to be significantly distinct from the two-fluid phase context. Moreover, specific issues, like the regime of the equations of mass conservation, deserve attention.

Fully coupled hydro–mechanical controls on non-diffusive seismicity triggering front driven by hydraulic fracturing

The spatio–temporal evolution of fluid-injection-induced seismicity is often bounded by a triggering front that expands away from the injection point in space and time. For some injection scenarios, the triggering front is thought to be directly linked to pore pressure diffusion, but in the case of hydraulic fracturing, the stress interaction of the growing tensile fracture with natural joints may be more significant. In order to explore the concept of a triggering front in this context, we use a fully coupled hydro–mechanical finite-discrete element (FDEM) approach to simulate microseismicity induced by hydraulic fracture growth. The medium contains a network of randomly oriented pre-existing fractures that are activated based on the Mohr–Coulomb failure criterion. As expected, the primary triggering front is defined by the envelope of microseismicity that tracks the hydraulic fracture, although more distal events are triggered by mechanical stress changes beyond the bounds of the triggering front. However, these distal events are approximately synchronous with initiation of the hydraulic fracture and are attributed to far-field elastic perturbations associated with the stress wave spread in the medium. A field example indicates that patterns of seismicity that emerge from our simulations have characteristics similar to observed microseismicity during hydraulic fracturing.

A Numerical Model of Internal Erosion for Multiphase Geomaterials

Internal erosion is the detachment of fine soil particles due to seepage flow, with ensuing increasing porosity, and transport of these particles out of the soil mass. In the present study, firstly we have formulated the constitutive equations of the internal erosion, that is, the erosion criteria and the rate equation of the mass transfer. The driving force for erosion is assumed to be given by the interaction term, i.e. relative velocity between two phases in the equation of motions for the two-phase mixture. Then, field equations to simulate hydro-mechanical behavior due to the internal erosion were derived in the framework of multiphase mixture theory. In addition, laboratory erosion tests using gap-graded sandy soil are simulated by the proposed model and the validity are discussed with respect to the rate of eroded soil mass and the particle size distribution after the erosion test.