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Abstract We study evaporation processes in fractured reservoirs under thermally enhanced conditions using pore-network models. The emphasis is on understanding evaporation phenomena and the combined effects of capillarity and viscous forces as are modified by the presence of thermal gradients and an applied heat flux. The temperature dependence of equilibrium vapor concentration and surface tension and macroscopic corner films are included. The phase distribution evolution, liquid saturation, film flow and recovery rates are obtained as functions of dimensionless parameters in the two cases of positive and negative temperature gradients. The results are obtained without the use of empirical or ad hoc coefficients and parameters. Strong evaporation effects under thermal conditions, associated with the variation of equilibrium concentrations, are clearly shown. The influence of surface tension variation induced by thermal gradients leads to destabilizing or stabilizing invasion percolation fronts, depending on the direction of the thermal gradient. The paper finds application to the recovery of volatile oils from fractured or heterogeneous reservoirs by thermal processes, such as steam injection. 1- Introduction Naturally fractured reservoirs contain a large portion of discovered hydrocarbon reserves worldwide. During primary production, the matrix-fracture pressure differential is the dominant driving force for matrix depletion [1, 2]. Waterflooding is a successful secondary process in water-wet fractured reservoirs, where water can imbibe into the matrix and oil counter flows to the fracture network [3, 4, 5]. However, for oil-wet reservoirs, injected water preferentially flows through the fracture network, resulting in low recovery efficiency [6]. For such reservoirs, improving the recovery efficiency can be obtained by implementing gas injection [7, 8]. The complexity of recovery phenomena in such cases emphasizes the need for sophisticated analysis tools, capable of modeling the intricate physical phenomena and sharply changing fluid interfaces. The development of the models for evaporation in porous media has been the subject of many studies at both macroscopic and microscopic scales. In the macroscopic approaches, the momentum, heat and mass balance equations are applied on continuum porous media, using volume averaging techniques [9, 10]. The weakness of the macroscopic models is the lack of understating of the phenomena at the pore and pore-network scales. More recently, the studies have been focused on microscopic modeling and comprehensive physics of the process (i.e. thermodynamics and transport events) are incorporated with the geometric descriptions of the void space of porous media. [11–15]. Immiscible displacement during drying of porous media was treated as a drainage process [16] and described by invasion percolation theory [17]. Sophisticated pore-network models have been developed for isothermal evaporation process in porous media that accounts for the viscous flow of the macroscopic films. It was demonstrated that film flow is a major transport mechanism in the drying of porous media [18–20].
Abstract Unlike other thermal recovery methods, air injection and in-situ combustion produces significant amounts of heat in the reservoir. However, the process is subject to acute external heat loss rates due to high temperature gradients in place. Consequently, reservoir temperatures may be reduced considerably, leading to a deteriorated combustion performance and debilitated field operations. Goal of this paper is to determine under which reservoir conditions the combustion temperatures could be maintained at sufficient levels. Previous investigators have partially addressed this issue using kinetic and combustion tube experiments. In the absence of heat losses, it has been repeatedly shown that water-soluble metallic additives improve the self-sustainability limit of combustion front in oil and sand mixtures. In general, this has been attributed to dual-role of the additives on the combustion performance:kinetics of heterogeneous oxidation reactions inside the combustion front are modified, namely the catalytic effect; specific surface area of the porous medium ahead of the combustion front is increased, namely the fuel deposition effect. It is currently a common belief that appropriate introduction of such materials in a reservoir environment could enhance the performance of combustion process and, hence, improve the recoveries. Determining their role on in-situ combustion performance requires that the mechanisms of combustion are well understood. Complex physical and chemical nature of the problem at the pore-scale has prevented detailed investigations using physical and numerical models, however. Here, we approach the problem analytically using a sequential reaction (HTO/LTO) combustion front propagation model, based on the large activation energy asymptotics, and introducing systematically the reaction kinetics and fuel deposition effects of the additives to the model. Coherent propagation of the reaction regions are then investigated in terms of their temperatures, propagation velocity and the oxygen consumption efficiency. It is found that an improved combustion performance can be observed only if both the kinetics and fuel deposition effects develop under the reservoir conditions. 1. Introduction Thermal recovery is the principal approach to reduce viscosity of heavy crude oil by applying heat into a subsurface oil reservoir. The necessary thermal energy can be generated at the surface and introduced into the reservoir by means of injecting steam, hot water or gas. It may also be generated in-situ (in-place) by injecting air and oxidizing heavy components of the crude oil in place. The latter approach for heavy oil recovery has long been recognized as the air injection and in-situ combustion (Prats, 1982). Air injection and in-situ combustion processes have several advantages when compared with the other thermal heavy oil recovery techniques. Among them, the most important one is related to instant availability and low-cost of the injection fluid regardless of the reservoir location. Furthermore, and perhaps even more distinctively, air injection processes bypass a necessity to minimize the wellbore-related heat losses and the accompanying injector insulation costs realized during the other thermal recovery operations. During air injection, unlike the high-temperature injection fluids, no heat losses take place until the injected air reaches the reservoir and confronts the deposited hydrocarbons, i.e., fuel.
Abstract Gas expansion near the wellbore during production causes the evaporation of connate water. When the reservoir permeability is low, capillarity is controlling, causing liquid movement to the near-wellbore region where drying rates are higher. In tight gas sands or in shale gas formations, where capillarity is high, the gas production itself can cause depletion of the water saturation below residual values, due to such evaporation. In this work we present a study of the fundamental processes involved during the flow of a gas in a liquid- saturated porous medium. We have modeled evaporation by accounting for the capillary driven film flow or ‘wicking’ of saline liquid to the wellbore or the near-fracture region and the effect of gas expansion. It is shown that, for gas reservoirs with connate water saturation, large pressure drawdowns lead to a drying front that develops at the formation face and propagates into the reservoir. When pressure drops are lower, water rapidly redistributes due to capillarity-induced movement of liquid from high-to low-saturation regions. This phase redistribution causes higher drying rates near the wellbore. The results show, for the first time, the effect of both capillarity- induced film flow and gas compressibility on the rate of drying in gas wells. The model can be used to help maximize gas production under conditions such as waterblocking by optimizing the operating conditions. Additionally it can be used to obtain a better understanding of the impact of capillarity on evaporation and consequent processes, such as salt precipitation. Introduction Problems involving gas flow past trapped liquids in porous media are encountered in a variety of contexts, such as waterblock removal in gas wells, evaporation of volatile oils, and recovery of residual oil. In the case of a binary system, such as gas and water, the thermodynamic phase equilibrium can be represented by a simple linear law and gas injection reduces to a drying problem where the remaining liquid is evaporated by the flowing gas. Drying of wetting liquids in porous media has been studied by several authors. These studies mainly focused on pass-over drying where gas is passed over a porous medium saturated with the wetting liquid. This form of drying is controlled by the gas flow rate. However when the liquid recedes into the porous medium, drying is controlled by the rate of diffusion of the components in the liquid phase in the pore spaces. Early in 1949, Allerton et al.1 studied through-drying of packed beds of crushed quartz and other porous materials by convection of dry gas. The study however did not consider the effect of gas compressibility or capillarity. Whitaker2 developed a diffusion theory of drying using volume averaging methods with constant pressure in the gas phase. This eliminated the effect of compressibility of gas on the drying rates and hence is useful only in a pass-over drying context. Experimental and simulation studies of gas injection3,4,5 showed that trapped water is first removed by a viscous displacement followed by a long period of evaporation. These studies showed that higher pressure drop, permeability and temperatures caused greater rates of evaporation and faster progression of saturation drying fronts in both fractured and unfractured wells.
- North America > United States > Texas (0.28)
- North America > United States > Colorado (0.28)
Abstract Lean gas injection has been considered as a process to improve the recovery of bypassed volatile oils from the matrix of fractured reservoirs. The characterization of flow and mass transfer in fractured reservoirs is a challenging task, due to the complexity of the pore space, the heterogeneity in the permeability of the rock, as well as the complex interplay between capillary, viscous and buoyancy forces. In the present paper we study the effect of heterogeneity. We develop a three-dimensional pore-network simulator that accounts for evaporation and diffusion of the volatile liquid trapped in heterogeneous pore networks. A series of numerical simulations are performed in common types of natural porous media. We investigate the effect of permeability gradients on the saturation profile, the recovery rates of the trapped liquid clusters, the evaporation patterns and the stability of the receding evaporation front. The case of a negative permeability gradient (high permeability close to the fracture, low permeability far away) leads to a stable evaporation front. Conversely, the effect of positive permeability gradients (low permeability close to the fracture, higher permeability far away) leads to a fingered pattern, that results in lower recovery times due to higher liquid saturation at the product surface.The paper finds application to problems of evaporation or drying of volatile liquids or other liquids from porous media. These arise in enhanced oil recovery in fractured systems, as well as in the remediation of contaminated soils. Introduction The injection of an unsaturated lean gas has been proposed as a means to aid the recovery of volatile liquids that remain inside the matrix blocks, after the primary recovery of light oil from fractured reservoirs (Le Gallo et al.[1]). During primary recovery in a fractured system, oil is produced mainly from the fractures, leaving the porous matrix highly saturated. A schematic of this process is shown in Fig. 1. Lean gas flows in the fractures of the porous medium. Volatile components contained in the matrix evaporate and diffuse to the matrix-fracture interface, from where they are convected in the fractures towards the production wells. The process can be approximated as that of the drying of a single-component liquid occupying a porous medium. The more realistic case involves a multicomponent liquid, the light ends of which are volatile. Evaporation of volatile oils from a fractured medium has attracted recently some attention in the petroleum literature. Le Romancer et al.[2], investigated experimentally the effect of gas diffusion during gas injection for the cases of methane, nitrogen, and carbon dioxide. The effect of gas diffusion on mass transfer, was also examined by Da Silva and Belery[3], Morel et al.[4], Espie et al.[5], Burger and Mohanty[6]. Le Gallo et al.[1], conducted core experiments and numerical simulations to identify the different mechanisms involved in mass transfer between matrix blocks and fractures during gas injection. Lenormand et al.[7], presented a simplified model to calculate the transfer of a component by diffusion as a function of fracture geometry, fluid velocity in fracture and composition in the matrix/fracture system. Tsimpanogiannis et al.[8] showed numerically that in the case of gas diffusion in the liquid phase, during lean gas injection, the evaporation process slows down, however, not significantly. Stubos and Poulou[9] provided simple expressions for the calculation of the front position and fluid production rates. A simplified description of the liquid-gas patterns within an idealized matrix block is shown in Fig. 2. The process is driven by the injection of a purge gas at one side (the open end) of the medium, all other boundaries of which can be taken as no-flow boundaries. The liquid evaporates and is transferred by diffusion and convection towards the open end, where it is purged. The movement of the liquid-gas interfaces is controlled by the complex interplay of capillary, viscous and buoyancy forces.
Abstract We derive an effective continuum model to describe the nucleation and subsequent growth of a gas phase from a supersaturated, slightly compressible binary liquid in a porous medium, driven by solute diffusion. The evolution of the gas results either from the reduction of the system pressure at a constant rate. The model addresses two stages before the onset of bulk gas flow, nucleation and gas phase growth. We assume negligible gradients due to gravity or viscous forces, thus the critical gas saturation, which signals the onset of bulk gas flow, is only a function of the nucleation fraction. We show that the important quantities characterizing the process, such as the fraction of pores that host activated sites, the deviation from thermodynamic equilibrium, the maximum supersaturation in the system and the critical gas saturation depend crucially on the nucleation characteristics of the medium. We use heterogeneous nucleation models primarily in the form of pre-existing gas, trapped in hydrophobic cavities, but also in terms of a rate-dependent nucleation, to investigate in detail the nucleation behavior. Using scaling analysis and a simpler analytical model we show that the relevant quantities during nucleation can be expressed in terms of a simple combination of dimensionless parameters, which include rate effects, for either type of nucleation model. The theory predicts that the maximum supersaturation in the system is a weakly increasing function of rate, which in the region of typical experimental parameters, can be approximated as a power law with a small exponent. This function depends sensitively on the probbaility density function of the nucleation cavity sizes. It also predicts that the final nucleation fraction, thus the critical gas saturation, is a power law of the decline rate. The theoretical exponents are shown to be in good agreement with experimental data. The subsequent evolution of the gas phase and the approach to the critical gas saturation is also described.
- North America > United States > California (0.28)
- North America > United States > Texas (0.28)
- Reservoir Description and Dynamics > Reservoir Fluid Dynamics > Flow in porous media (1.00)
- Reservoir Description and Dynamics > Improved and Enhanced Recovery (1.00)
- Reservoir Description and Dynamics > Formation Evaluation & Management (1.00)
- Production and Well Operations > Well & Reservoir Surveillance and Monitoring (1.00)
Abstract In a recent study it was shown that the ratio of the flow rates of the produced fluids in an immiscible displacement can be used to identify geometrical and petrophysical characteristics of a reservoir. In this paper we develop an extended version of this approach and apply it to displacements in 1–D laboratory cores. Because of the possible importance of capillary effects, we pay attention to the capillary end effect at the outlet and to late times. It is shown that the exponent in the power-law dependence of the relative permeability to saturation, near its residual value, can be determined from a segment of the curve of the outlet fractional flow sometime after breakthrough. The asymptotic predictions are verified by obtaining an analytical solution to the full problem, including end-effects, for a model case corresponding to Burgers' equation. Experimental results for the high-rate displacement of some gas-liquids pairs are reported. In agreement with the theoretical predictions, a power-law segment in the outlet fractional flow curve can be identified, before capillary effects set in. The exponents obtained are discussed in terms of pore-scale models for gas-liquid displacement. Introduction Relative permeabilities are important functions for the modeling and prediction of the recovery of fluids from porous media. They express integrated information on the pore structure topology and geometry and on the pore occupancy by the corresponding fluids. Of particular interest is their dependence near the end-point saturations (corresponding to residual or trapped fluids), where a power-law behavior is expected. Sensitivity studies using numerical simulation have shown that this behavior has the most important effect on recovery rates. Reflecting the same fact, most of the empirical models used (e.g. Corey, see Bear) contain a power law in the residual saturation region. From theoretical considerations, this power-law dependence reflects two different mechanisms, the trapping of a disconnected non-wetting phase, where film flow is absent, in the case of imbibition, and the continuous drainage of a wetting phase, through film flow, in the case of drainage. In the latter case, the residual saturation is theoretically zero. The experimental determination of the relative permeability functions, including their behavior near the trapped saturation, is usually done using steady- or unsteady-state displacements. The well-known JBN technique provides information on the relative permeabilities in the saturation region after breakthrough of the injected fluid. It is based on an analysis of fluid rate production data and of the pressure drop across the sample, using the classical Buckley-Leverett equation in which capillarity is neglected. In general, the method is most accurate away from trapped saturations, where relative permeabilities are not too small. An alternative for determining the exponent of the power law dependence near residual saturations is to consider the behavior at late times. In a recent study, we showed that for displacements in porous media and various injection patterns, the variation of the ratio of the produced flow rates as a function of time can be used to identify certain geometrical and petrophysical characteristics of the medium. In particular, for a 1–D displacement this ratio can be used to estimate the relative permeability exponents. The objective of this paper is to evaluate the potential of such a method as a diagnostic tool for displacements in laboratory cores. For this purpose we will assess the conditions for which the approach of Ref. [1] is applicable, provide a suitable extension and subsequently apply to experimental data in gas-liquid displacements.
Abstract In many applications involving the injection of a fluid in a porous medium to displace another, a main objective is the maximization of the displacement efficiency. For a fixed arrangement of injection and production wells, such optimization is possible by controlling the injection rate policy. This paper is an abbreviated version of Ref. [1], where we described a fundamental approach based on optimal control theory, for the simplified case when the fluids are miscible, of equal viscosity and in the absence of dispersion and gravity effects. Both homogeneous and heterogeneous porous media are considered. The optimal injection policy that maximizes the displacement efficiency at the time of arrival of the injected fluid, is of the "bang-bang" type, namely where the rates take their extreme values in the range allowed. This result applies to both homogeneous and heterogeneous media. Examples in simple geometries and for various constraints are shown. In the heterogeneous case, the effect of the permeability heterogeneity, particularly its spatial correlation structure, on diverting the flow paths, is analysed. "Bang-bang" injection remains the optimal approach, compared to constant rate, if they were both designed under the assumption that the medium was homogeneous. Introduction The injection of a fluid in a porous medium to displace another is common to oil recovery applications. The displacement occurs by injection from various injection wells and by production from a number of production wells. A variety of patterns have been analyzed in classical works (e.g. Muskat), several decades ago. A typical example of relevance to our work, is shown in Figure 1 and involves two injection wells and a production well in a bounded reservoir. In practice, the location of injection and production wells is generally determined based on a variety of geologic, economic, and practical considerations. In many applications, the main objective is the maximization of the displacement efficiency. Aspects of the optimization of displacement processes in porous media have been studied before, notably by Ramirez and his co-workers, in the context of maximizing the profitability over a fixed time interval of various Enhanced Oil Recovery (EOR) processes. In these, the important variable is the volume of a (costly) component (e.g. surfactant, polymer) injected along with the fluid, which improves the microscopic (pore-level) displacement efficiency. However, in problems where the injected fluid composition is fixed and it is not a control parameter (for example in water displacing oil), the only available control of the displacement is the allocation of the injected fluid to the injection wells (and of the produced fluid to the production wells). In general, this can be accomplished by varying the injection rates and/or the injection (or production) intervals in individual wells. In the 2-D geometry of interest here, the wells can be considered as point sources and sinks, thus the maximization of the displacement efficiency should be sought by optimizing well injection rates. This fundamental problem has not been systematically addressed before (although some attempts have been made, e.g. see Asheim and Virnovsky. The conventional approach has been to design symmetric well patterns, and allocate injection rates equally to all wells. This practice relies on the premise that the permeability field is homogeneous, an assumption which is rarely true. Indeed, in heterogeneous porous media, the flow streamlines do not necessarily have the symmetry of the well pattern, even at constant injection rates. Injection at constant and equally partitioned rates, which is a common practice, has not been shown to be the optimal policy, certainly not in the absence of well symmetry, even for a homogeneous porous medium.
Abstract In a recent publication we proposed a direct method for the inversion of the permeability field of an isotropic porous medium based on the analysis of the displacement of a passive tracer. By monitoring the displacement front at successive time intervals (for example, using a tomographic method), the permeability can be directly obtained from the solution of a non-linear boundary-value problem. In this paper we extend this approach to the case when the porous medium is anisotropic. When the principal axes of anisotropy are known and fixed, a procedure is proposed, in which the tracer is injected two (or three) consecutive times along the two (or three) principal directions (for the case of a 2-D (or 3-D) problem, respectively). It is shown that the diagonal components can be obtained from the solution of two (or three) coupled boundary-value problems involving the experimentally obtainedfields of arrival times. Numerical examples show that the method works well when the permeability variation is not very sharp (for example, for correlated distributions). When thepermeability tensor is full and the principal axes vary in space, we propose a procedure involving the injection in three different directions (for the case of a 2-D problem). In principle, the components of the permeability tensor canbe determined from the solution of three coupled boundary-value problems. However, the inversion method encounters significant numerical problems. For the case of small off-diagonal components, a practical procedure is proposed to decouple the problems in the inversion method for both 2-D and 3-D. Introduction Permeability heterogeneity is an important feature of natural porous media, as it affects significantly flow and fluid displacement properties. Two main approaches exist for its identification, one based on pressure transients and another on production data. The first approach makes use of the diffusion equation, which governs transient single-phase flow, the second requires the solution of convective flow equations. The classical approach for identifying permeability is based on the inversion of pressure data from well tests. Typically, this approach gives information on the average permeability value around the testing well. Spatial heterogeneity can be roughly estimated through interpolation among estimated permeabilities at various wells and the application of geostatistics. Promising methods for the estimation of key statistical properties, for the case of small fluctuations of the logarithm of the permeability, were suggested by Oliver. Under the assumption of a stationary field, Yortsos and Al-Afaleg proposed a multiple-well pressure transient method that leads to the estimation of the correlation function (semi-variogram) of the heterogeneity.
Abstract The sustained propagation of combustion fronts in porous media is a necessary condition for the success of an in-situ combustion project for oil recovery. Compared to other recovery methods, in-situ combustion involves the added complexity of exothermic chemical reactions and temperature-dependent chemical kinetics. This gives rise to reaction zones of a spatially narrow width, within which heat release rates, temperatures and species concentrations vary significantly. This sharp variation makes difficult the simulation of combustion processes using coarse grids and the implementation of upscaling methods. In this paper, we propose a method for solving this problem by treating the reaction region as a place of discontinuities in the appropriate variables, which include, for example, fluxes of heat and mass. Using a rigorous perturbation approach, similar to that used in the propagation of flames [3], and smoldering combustion [7], we derive appropriate jump conditions that relate the change in these variables across the front. These conditions account for the kinetics of the reaction between the oxidant and the fuel, the changes in the morphology of the pore space and the heat and mass transfer in the reaction zone. Then, the modeling of the problem reduces to the modeling of the dynamics of a combustion front, on the regions of either side of which transport of momentum (fluids), heat and mass, but not chemical reactions, must be considered. Properties of the two regions are coupled using the derived jump conditions. This methodology allows to explicitly incorporate permeability heterogeneity effects in the process description, without the undue complexity of the coupled chemical reactions. Introduction The propagation of combustion fronts in porous media is a subject of interest to a variety of applications, ranging from the in-situ combustion for the recovery of oil [1], to filtration combustion [5] and to smoldering combustion [5]. While these problems may differ in application and context, they share a common characteristic, namely that the main combustion reaction involves the burning of a stationary solid fuel, which in the first two applications is part of the initial state of the system, while in the second it is created by a preceding Low-Temperature-Oxidation (LTO) process. In-situ combustion for oil recovery has been studied quite extensively since the mid 1950s. The two texts by Prats [1] and Boberg [2] summarize the relevant literature on the subject until the late 1980s. A large number of experimental, analytical and numerical studies have been reported on a variety of in-situ combustion topics. Of interest to this paper is a particular but important issue of in-situ combustion, specifically the dynamics of combustion fronts. They are influenced by a number of factors, including fluid flow of injection and produced gases, mass transfer of the injected oxidant, heat transfer in the porous medium and the surroundings, the rate of reaction(s), the heterogeneity of the medium and possibly the evolution of the pore morphology due to the combustion reaction.
Abstract Despite the significant progress made in recent years, a fundamental understanding of immiscible displacements at the macroscale is lacking. In this paper we use a version of percolation theory, based on Invasion Percolation in a Gradient, to connect drainage processes at the pore-network scale with the displacement at the macroscale. When the mobility ratio M is sufficiently small, the displacement is stabilized and can be described by Invasion Percolation in a Stabilizing Gradient. In the opposite case, the displacement has common features with Invasion Percolation in a Destabilizing Gradient. A phase diagram of fully developed drainage is then developed. The transition between stabilized displacement and fingering is controlled by the change of the sign of the gradient of the percolation probability, and the transition boundary is described by a scaling law involving the capillary number and the viscosity ratio. The theory is subsequently extended to correlated pore networks and a phase diagram involving the correlation length A is constructed. As the regimes of stabilized displacement are also those for which conventional theories (such as the Buckley-Leverett equation) apply, the phase diagram helps to delineate their validity. P. 877