We quantify the capillary pressure effect on the phase equilibrium of the CO2-water system. Our interest is in the capillarypressure range between 0 and 100 bars for temperatures between 293 and 372 K and bulk (wetting-phase) pressures between 25 and 255 bars. For this purpose, we have implemented the capillary pressure effect in the PRSV equation of state. Inclusion of capillary pressure in the phase equilibrium of the CO2-water system makes it possible to determine the capillary-pressure effect on the CO2 storage capacity and heat-energy recovery for CO2-water injection into geothermal reservoirs. We illustrate the process using a 2D model of the geothermal reservoir in the Delft Sandstone Member, below the city of Delft (The Netherlands). The process involves phase transitions between single-phase and two-phase regions. To deal with phase appearance and disappearance, we have applied a new and effective solution approach, the so-called "nonisothermal negative saturation?? (NegSat) solution approach.
The results show that the capillary pressure promotes evaporation. In the pressure and temperature range of our interest, capillary pressure reduces the CO2 solubility in water and the aqueous-phase density up to 64% and 1.3%, respectively, whereas it increases the water solubility in the CO2-rich phase and the CO2-rich-phase density up to 3,945% (40.5 times) and 1,544%, respectively. Capillary pressure shifts the CO2 liquid-vapor transition and consequently the upper critical point of the CO2-water system to a lower pressure. The intensity of the shift depends on the value of the capillary pressure and the bulk (wetting-phase) pressure. For instance, the CO2 liquid-vapor transition at T = 293 K occurs approximately at 60 bars for Pc = 0 bars, whereas it occurs at 15 bars for Pc = 45 bars.
For mixed CO2-water injection into the geothermal reservoir (200 bars < P < 260 bars, 290 K < T < 360 K), inclusion of the capillary pressure effect in the phase-equilibrium behavior does not significantly alter the capillary CO2-trapping mechanism. In other words, CO2 banks are mainly formed in the highly permeable zones that are surrounded by less permeable zones. However, for injected CO2 concentrations close to the bubble point, the effect of capillary pressure on the
phase equilibrium reduces the heat recovery by 37% and the CO2-storage capacity also by 37%. For overall injected CO2 mole fractions between 4% and 13%, the reduction in the heat recovery and CO2-storage capacity is 10%. Based on simulations, we construct a plot of the recuperated heat energy versus the maximally stored CO2 for a variety of conditions; we compare the results including and excluding the effect of capillary pressure in the phase-equilibrium calculations.
In a transition period from a fossil fuel based society to a sustainable energy society it is expected that CO2 capture and subsequent sequestration (CCS) in geological formations will play a major role in reducing greenhouse gas emissions. Possibilities of sequestration include storage in aquifers and depleted gas reservoir. The storage capacity of gas reservoirs for CO2 depends also on the sorption in the omnipresent minerals and shales. It is important to investigate whether adsorption on shales gives an important contribution to the storage capacity. It is also important to relate the adsorption to the carbon content in the shale. Only a few measurements have been reported in the literature for high-pressure gas sorption on shales, and interest is largely focused on shales occurring outside Europe. We present results using a high pressure manometric set-up on a dried black shale sample from Belgium. It consists of more than 57% of clay minerals and 6.58% organic matter. The excess sorption isotherm shows an initial increase to a maximum value of 0.19 mmol/gram and then starts to decrease until it becomes zero at 82 bar and subsequently the excess sorption becomes negative. Similar behavior was also observed for other shales and coal reported in the literature.
We derive the equation for excess sorption in the manometric set-up allowing for a changing void volume. This equation is based on the finite density of the adsorbed phase. However, this is not the only mechanism causing a maximum in the sorption curve. Other reasons for void volume change are swelling of the shale and volume changes due to chemical reactions excluding sorption. Further research is necessary to investigate reasons for void volume changes in shales.
Cold mixed CO2/water injection into hot-water reservoirs can be used for simultaneous geothermal-energy (heat) production and subsurface CO2 storage. This paper studies this process in a 2D geothermal homogeneous reservoir, a layered reservoir, and a heterogeneous reservoir represented by a stochastic-random field. We give a set of simulations for a variety of CO2/water-injection ratios. In this process, often regions of two-phase flow are connected to regions of single-phase flow. Different systems of equations apply for single-phase and two-phase regions. We develop a solution approach, called the nonisothermal-negative-saturation (NegSat) solution approach, to solve efficiently nonisothermal compositional flow problems (e.g., CO2/water injection into geothermal reservoirs) that involve phase appearance, phase disappearance, and phase transitions. The advantage of this solution approach is that it circumvents using different equations for single-phase and two-phase regions and the ensuing unstable switching procedure. In the NegSat approach, a single-phase multicomponent fluid is replaced by an equivalent fictitious two-phase fluid with specific properties. The equivalent properties are such that the extended saturation of a fictitious gas is negative in the single-phase aqueous region.
Solvent injection has been considered as an efficient method for enhancing oil recovery from fractured reservoirs. If the mass transfer would be solely based on diffusion, oil recovery would be unacceptably slow. The success of this method therefore depends on the degree of enhancement of the mass exchange rate between the solvent residing in the fracture and the oil residing in the matrix.
A series of soak experiments have been conducted to investigate the mass transfer rate between the fracture and the matrix. In a soak experiment, a porous medium containing oil is immersed in an open space containing the solvent to simulate the matrix and the fracture respectively. We use a CT scanner to visualize the process. The experimental data are compared with a simulation model that takes diffusive and gravitational forces into account.
We find that the initial stage of all experiments can be described by a diffusion-based model with an enhanced "effective diffusion coefficient??. In the second stage enhancement of the transfer rate occurs due to the natural convection of solvent in the fracture. The experiments are quantitatively modeled by numerical simulations. We find that transfer rates depend on the properties of the rock permeability, the viscosity and the density of solvent and oil. The gravity enhanced transfer is quantified by comparison of experimental and simulated results.
Gas oil gravity drainage is an effective oil recovery process, which has been proven in the field. Under favorable conditions the displacement is stable and for the right surface tension combinations the residual oil saturation is low. In the absence of gas dissolution, the recovery after gas injection is usually low as a large amount of oil remains capillary trapped in the matrix blocks. However, when the main gas constitutes is soluble in the oil, the dissolution leads to mixing and interfacial tension (IFT) reduction, which cause gravity enhanced transfer between matrix and fracture. Therefore, a study of the mechanisms that control the interactions between fracture and matrix (e.g. capillarity, gravity, phase behavior and flow behavior) can help to optimize recovery. This paper concerns an experimental study to investigate whether gravity drainage is also an effective recovery process in fractured reservoirs. In this study, we describe six gas injection experiments conducted at different miscibility conditions, i.e., immiscible, developed miscible and first contact miscible (FCM), using CO2, nitrogen and flue gas.
In addition, the impact of switching from an immiscible (Nitrogen, Flue gas) injection gas to non-equilibrium and fully miscible CO2 injection is investigated. In one of the experiments, we study the effect of a permeability barrier on the recovery efficiency from the matrix block when CO2 is injected in the fracture at immiscible and miscible conditions. Accurate modeling for the transfer between fracture and matrix is also essential for accurate recovery predictions. In this study, a numerical model is developed to perform compositional simulations of gas injection for different miscibility scenarios. Results revealed that ultimate oil recovery increases considerably once miscibility is reached. Miscibility can usually be achieved at high pressures only. High pressure gas injection has two disadvantages, viz., (1) one may need a larger mass of gas to fill the pore space from where the oil is recovered and (2) the density of injected gas increases significantly, which reduces the density difference between the gas and oil. This leads to less effective gravity mediated recovery. Even if the impermeable layer
impairs the performance of the gas oil gravity drainage (GOGD) process for immiscible gas injection, it improves the recoveries for first contact miscible gas injection.
This paper gives an analysis of the Thomas and Windle model (Thomas and Windle 1982) to determine its usefulness for describing anomalous diffusion of CO2 in coal and its relation to matrix swelling. In addition, a finite-element description for this model is derived. For reasons of easy reference, a shortened derivation of the Thomas and Windle model is presented, which was originally derived to describe diffusion in polymers. proposed by Hui et al. (1987a, 1987b). Because the cumulative sorption showed t a behavior with a > 0.5, the behavior was described as enhanced diffusion or even superdiffusion. Analysis of the model equation shows no evidence for superdiffusion even if non-Fickian behavior is observed [i.e., there is (1) an initial phase in which the coal surface gets saturated with a slope > 0.5 in a log-log plot of cumulative sorption vs. time, (2) an intermediate phase that shows the typical square-root-of-time behavior of an ordinary diffusion process, and (3) a final phase with a slope < 0.5 toward equilibrium]. The cumulative mass is for all times less than what would have been obtained for pure diffusion in a particle characterized by a rubber diffusion coefficient. The slow saturation at the surface masks a process where fast stress-induced diffusion dominates, which indeed can be faster than Fickian. The cumulative sorption rates give behavior similar to the Rückenstein model (Rückenstein et al. 1971), but the advantage of the Thomas and Windle model is that it can also calculate the resulting coal-swelling effects.
There is a renewed interest in using combustion to recover medium- or high-viscosity oil. Despite numerous experimental, numerical, and analytical studies, the mechanisms for incomplete fuel combustion or oxygen consumption are not fully understood. Incomplete oxygen consumption may lead to low-temperature oxidation reactions downstream. This paper shows that these features emerge in a relatively simple 1D model, where air is injected in a porous medium filled with inert gas, water, and an oil mixture consisting of precoke, medium oil, and light oil. Precoke is a component that is dissolved in the oil but has essentially the same composition as coke. At high temperatures, precoke is converted to coke, which participates in high-temperature oxidation. At high temperatures, medium-oil components are cracked, releasing gaseous oil. Light-oil components and water are vaporized. The model possesses an analytical solution, which was obtained by a concept introduced by Zeldovich et al. (1985). This concept, which underlies most analytical approaches such as the reaction-sheet approximation and large-activation-energy asymptotics, entails that reaction can occur only in a very small temperature range because of the highly nonlinear nature of the Arrhenius factor. For a temperature below this range, the reaction rate is too slow, and for temperatures above this range, the reaction rate is so fast that either the fuel or oxygen concentrations become zero. The model results, in the absence of external heat losses, show that there are two combustion regimes in which coke or oxygen is partially consumed. In one regime, the reaction zone moves in front of the heat wave; whereas, in the other regime, the order of the waves is reversed. There are also two combustion regimes in which the coke and oxygen are completely consumed. Also, here the reaction zone can move in front of or at the back of the heat wave. Each combustion regime is described by a sequence of waves; we derive formulas for parameters in these waves. We analyze our formulas for typical in-situ-combustion data and compare the results with numerical simulation. The main conclusion is that mainly two key parameters (i.e., the injected oxygen mole fraction and the fuel concentration) determine the combustion-front structure and when either incomplete oxygen consumption or incomplete fuel consumption occurs in the high-temperature oxidation zone.
We use upscaling through homogenization to predict oil recovery from fractured reservoirs consisting of matrix columns, also called vertically fractured reservoirs (VFRs), for a variety of conditions. The upscaled VFR model overcomes limitations of the dual-porosity model, including the use of a shape factor. The purpose of this paper is to investigate three main physical aspects of multiphase flow in fractured reservoirs: reservoir wettability, viscosity ratio, and heterogeneity in rock/fluid properties. The main characteristic that determines reservoir behavior is the Péclet number that expresses the ratio of the average imbibition time divided by the residence time of the fluids in the fractures. The second characteristic dimensionless number is the gravity number.
Upscaled VFR simulations, aimed at studying the mentioned features, add new insights. First, we discuss the results at low Péclet numbers. For only small gravity numbers, the effect of contact angle, delay time for the nonequilibrium capillary effect, the heterogeneity of the matrix-column size, and the matrix permeability can be ignored without appreciable loss of accuracy. The ultimate oil recovery for mixed-wet VFRs is approximately equal to the Amott index, and the oil production does not depend on the absolute value of the phase viscosity but on viscosity ratio. However, large gravity numbers enhance underriding, aggravated by large contact angles, longer delay times, and higher viscosity ratios. Layering can lead to an improvement or deterioration, depending on the fracture aperture and permeability distribution. At low Péclet numbers, the fractured reservoir behaves very similarly to a conventional reservoir and depends largely on the viscosity ratio and the gravity number. At high Péclet numbers, after water breakthrough, the oil recovery appears to be proportional to the cosine of the contact angle and inversely proportional to the sum of the oil and water viscosity. In addition, the mixed-wetting effect is more pronounced; there are significant influences of delay time (nonequilibrium effects), matrix permeability, matrix-column size, and the column-size distribution on oil recovery. At low gravity numbers and an effective length/thickness ratio larger than 10, the oil recovery is independent of the vertical-fracture-aperture distribution. For the same amount of injected water, the recovery at low Péclet numbers is larger than the recovery at high Péclet numbers.
Flow modeling in fractured reservoirs is largely confined to the so-called sugar-cube model. Here, we consider a situation where matrix blocks are connected to neighboring blocks so that part of the global flow occurs only in the matrix domain. We call this a partially fractured reservoir (PFR). As opposed to the sugar-cube model, global flow in the matrix blocks plays an important role in the PFR when the interconnections between the matrix blocks are sufficiently large. We apply homogenization to derive an upscaled model for PFRs that combines dual-porosity and dual-permeability concepts simultaneously. We formulate a well-posed fully implicit 3D upscaled numerical model and investigate oil-recovery mechanisms for different dimensionless characteristic numbers. As we found previously for the sugar-cube model, the Péclet number, defined here as the ratio of the capillary diffusion time in the matrix to the residence time of the fluids in the fracture, plays a crucial role. The gravity number and specific fracture/matrix-interface area play a secondary role. For low Péclet numbers and high gravity numbers, the results are sensitive to gravity and water-injection rates, but relatively insensitive to the specific fracture/matrix-interface area, matrix-block size, and reservoir geometry (i.e., sugar cube vs. PFR). At low Péclet numbers and high gravity numbers, ECLIPSE simulations using the Barenblatt or Warren and Root (BWR) approach give poor predictions and overestimate the oil recovery, but, at short injection times, show good agreement with the solution of the PFR model at intermediate Péclet numbers. At high Péclet numbers, the results are relatively insensitive to gravity, but sensitive to the other conditions mentioned. In particular, when the specific fracture/matrix-interface area is large, it enhances the imbibition and, consequently, leads to a higher oil production. If this specific interface area is small, it leads to a considerable retardation of the imbibition process, which leads to an earlier water breakthrough and lower oil recovery. The BWR (commercial simulator) simulations and the sugar-cube model result in inaccurate predictions of the oil-production rate at high Péclet numbers. This can be inferred from the discrepancy with respect to the PFR model for which we assert that it accurately predicts the oil recovery. We conclude that, at low Péclet numbers and large gravity numbers, it is advantageous to increase the water-injection rate to improve the net present value. However, at high Péclet numbers, increasing the flow rate may lead to uneconomical water cuts.
Cold mixed CO2-water injection into hot-water reservoirs can be used for simultaneous geothermal-energy (heat) production and subsurface CO2 storage. This paper studies this process in a 2D geothermal reservoir for a homogeneous reservoir, a layered reservoir, and a heterogeneous reservoir represented by a stochastic-random field. We give a set of simulations for a variety of CO2-injection concentrations. In this process, often regions of two-phase flow are connected to regions of single-phase flow. Different systems of equations apply for single-phase and for two-phase regions. We develop a solution approach, called the non-isothermal negative saturation (NegSat) solution approach, to solve efficiently non-isothermal compositional flow problems (e.g., CO2-water injection into geothermal reservoirs) that involve phase disappearance, phase appearance, and phase transition. The advantage of the solution approach is that it circumvents using different equations for single-phase and two-phase regions and the ensuing unstable switching procedure. In the NegSat approach, a single-phase multi-component fluid is replaced by an equivalent fictitious two-phase fluid with specific properties. The equivalent properties are such that in the single-phase aqueous region, the extended saturation of a fictitious gas is negative.