Semianalytical Solution for \text{ CO}_{2} Plume Shape and Pressure Evolution During \text{ CO}_{2} Injection in Deep Saline Formations

The injection of supercritical carbon dioxide ( $\text{ CO}_{2})$ in deep saline aquifers leads to the formation of a $\text{ CO}_{2}$ rich phase plume that tends to float over the resident brine. As pressure builds up, $\text{ CO}_{2}$ density will increase because of its high compressibility. Current analytical solutions do not account for $\text{ CO}_{2}$ compressibility and consider a volumetric injection rate that is uniformly distributed along the whole thickness of the aquifer, which is unrealistic. Furthermore, the slope of the $\text{ CO}_{2}$ pressure with respect to the logarithm of distance obtained from these solutions differs from that of numerical solutions. We develop a semianalytical solution for the $\text{ CO}_{2}$ plume geometry and fluid pressure evolution, accounting for $\text{ CO}_{2}$ compressibility and buoyancy effects in the injection well, so $\text{ CO}_{2}$ is not uniformly injected along the aquifer thickness. We formulate the problem in terms of a $\text{ CO}_{2}$ potential that facilitates solution in horizontal layers, with which we discretize the aquifer. Capillary pressure is considered at the interface between the $\text{ CO}_{2}$ rich phase and the aqueous phase. When a prescribed $\text{ CO}_{2}$ mass flow rate is injected, $\text{ CO}_{2}$ advances initially through the top portion of the aquifer. As $\text{ CO}_{2}$ is being injected, the $\text{ CO}_{2}$ plume advances not only laterally, but also vertically downwards. However, the $\text{ CO}_{2}$ plume does not necessarily occupy the whole thickness of the aquifer. We found that even in the cases in which the $\text{ CO}_{2}$ plume reaches the bottom of the aquifer, most of the injected $\text{ CO}_{2}$ enters the aquifer through the layers at the top. Both $\text{ CO}_{2}$ plume position and fluid pressure compare well with numerical simulations. This solution permits quick evaluations of the $\text{ CO}_{2}$ plume position and fluid pressure distribution when injecting supercritical $\text{ CO}_{2}$ in a deep saline aquifer.     

Drying Kinetics of Porous Stones in the Presence of NaCl and \hbox {NaNO}_{3}: Experimental Assessment of the Factors Affecting Liquid and Vapour Transport

Salt decay is one of the most harmful and complex deterioration mechanisms of porous building materials in architectural heritage. Despite several decades of research, it is still insufficiently understood, which hampers the development of effective treatments and prediction models. One key aspect is the influence soluble salts have on the evaporative drying of porous materials. It is often observed, for example, that drying is slower for higher salt concentrations. However, there is still no consensus as to why it happens. In this article, we examine experimentally the drying kinetics of three natural stones impregnated with solutions of sodium chloride or sodium nitrate with different concentrations. The method consisted of the following sequence of determinations: capillary absorption, drying kinetics, vapour pressure and vapour conductivity. It also included a morphological analysis of the efflorescence formed during drying. We have concluded that the slower drying rate was mainly due to the reduced sorptivity that arises at higher salt concentrations. In the cases where compact salt crusts formed on the surface of the stone, there was an additional reduction in the drying rate because these crusts obstructed vapour transport. However, in most cases, efflorescence was porous and had negligible obstructive effects. Efflorescence morphology is conditioned by well-determined causal factors, such as porosity, pore size and mineralogical structure of the stone, or the type of salt and its concentration. Here, it also revealed that it incorporated a component of unpredictability. This suggests that it may be necessary to move beyond purely deterministic approaches to salt decay.     

Visual Investigation of Improvement in Extra-Heavy Oil Recovery by Borate-Assisted $$\hbox {CO}_{2}$$-Foam Injection

The significant reduction in heavy oil viscosity when mixed with \(\hbox {CO}_{2}\) is well documented. However, for \(\hbox {CO}_{2}\) injection to be an efficient method for improving heavy oil recovery, other mechanisms are required to improve the mobility ratio between the \(\hbox {CO}_{2}\) front and the resident heavy oil. In situ generation of \(\hbox {CO}_{2}\)-foam can improve \(\hbox {CO}_{2}\) injection performance by (a) increasing the effective viscosity of \(\hbox {CO}_{2}\) in the reservoir and (b) increasing the contact area between the heavy oil and injected \(\hbox {CO}_{2}\) and hence improving \(\hbox {CO}_{2}\) dissolution rate. However, in situ generation of stable \(\hbox {CO}_{2}\)-foam capable of travelling from the injection well to the production well is hard to achieve. We have previously published the results of a series of foam stability experiments using alkali and in the presence of heavy crude oil (Farzaneh and Sohrabi 2015). The results showed that stability of \(\hbox {CO}_{2}\)-foam decreased by addition of NaOH, while it increased by addition of \(\hbox {Na}_{2}\hbox {CO}_{3}\). However, the highest increase in \(\hbox {CO}_{2}\)-foam stability was achieved by adding borate to the surfactant solution. Borate is a mild alkaline with an excellent pH buffering ability. The previous study was performed in a foam column in the absence of a porous medium. In this paper, we present the results of a new series of experiments carried out in a high-pressure glass micromodel to visually investigate the performance of borate–surfactant \(\hbox {CO}_{2}\)-foam injection in an extra-heavy crude oil in a transparent porous medium. In the first part of the paper, the pore-scale interactions of \(\hbox {CO}_{2}\)-foam and extra-heavy oil and the mechanisms of oil displacement and hence oil recovery are presented through image analysis of micromodel images. The results show that very high oil recovery was achieved by co-injection of the borate–surfactant solution with \(\hbox {CO}_{2}\), due to in-situ formation of stable foam. Dissolution of \(\hbox {CO}_{2}\) in heavy oil resulted in significant reduction in its viscosity. \(\hbox {CO}_{2}\)-foam significantly increased the contact area between the oil and \(\hbox {CO}_{2}\) significantly and thus the efficiency of the process. The synergy effect between the borate and surfactant resulted in (1) alteration of the wettability of the porous medium towards water wet and (2) significant reduction of the oil–water IFT. As a result, a bank of oil-in-water (O/W) emulsion was formed in the porous medium and moved ahead of the \(\hbox {CO}_{2}\)-foam front. The in-situ generated O/W emulsion has a much lower viscosity than the original oil and plays a major role in the observed additional oil recovery in the range of performed experiments. Borate also made \(\hbox {CO}_{2}\)-foam more stable by changing the system to non-spreading oil and reducing coalescence of the foam bubbles. The results of these visual experiments suggest that borate can be a useful additive for improving heavy oil recovery in the range of the performed tests, by increasing \(\hbox {CO}_{2}\)-foam stability and producing O/W emulsions.     

Transport of Ca+2 and $${{\rm SO}_{4}^{-2}}$$ Ions in Porous Media of Clay Product and Its Association with the Efflorescence Phenomenon

This study investigates the displacement of SO₄^-2{{\rm SO}_{4}^{-2}} and Ca⁺² ions in a red-clay ceramic, simulating the process of efflorescence. Ceramic bodies were molded (70 × 27 × 9mm³) by vacuum extrusion formulated with different contents of CaSO₄· 2H₂O (0, 2, 4, 8, and 16% in weight) and burnt at different temperatures (800, 850, 900, and 950°C) for 12 h. Ceramic bodies were characterized in terms of water absorption, apparent porosity and pore size distribution. Efflorescence was evaluated according to the norms of ASTM C67/2003 and by testing the solubilization of SO₄^-2{{\rm SO}_{4}^{-2}} and Ca⁺² ions after 1 h with the ceramic bodies immersed in hot water as well as after 7, 14, and 28 consecutive days with the ceramic bodies immersed in cold water. In the quantification of efflorescence, a new image analysis methodology was developed by using the graphic software Image Tools 3.0. The results allowed in establishing a relationship between the efflorescence of the investigated ions, physical properties (water absorption and apparent porosity), pore size distribution, and solubilization.     

Transport of Ca+2 and $${{\rm SO}_{4}^{-2}}$$ ions in Porous Media of Clay Product and its Association with the Efflorescence Phenomenon

This study investigates the displacement of SO₄^-2{{\rm SO}_{4}^{-2}} and Ca⁺² ions in a red-clay ceramic, simulating the process of efflorescence. Ceramic bodies were molded (70 × 27 × 9 mm³) by vacuum extrusion formulated with different contents of CaSO₄ · 2H₂O (0, 2, 4, 8, and 16% in weight) and burnt at different temperatures (800, 850, 900, and 950°C) for 12 h. Ceramic bodies were characterized in terms of water absorption, apparent porosity, and pore size distribution. Efflorescence was evaluated according to the norms of ASTM C67/2003 and by testing the solubilization of SO₄^-2{{\rm SO}_{4}^{-2}} and Ca⁺² ions after 1 h with the ceramic bodies immersed in hot water as well as after 7, 14, and 28 consecutive days with the ceramic bodies immersed in cold water. In the quantification of efflorescence, a new image analysis methodology was developed by using the graphic software Image Tools 3.0. The results allowed in establishing a relationship between the efflorescence of the investigated ions, physical properties (water absorption and apparent porosity), pore size distribution, and solubilization.     

Residual Trapping Beneath Impermeable Barriers During Buoyant Migration of \mathrm{CO}_2

The presence of impermeable barriers in a reservoir can significantly impede the buoyant migration of $\mathrm{CO}_2$ injected deep into a heterogeneous geological formation. An important consequence of the presence of these impermeable barriers in terms of the long-term storage of $\mathrm{CO}_2$ is the residual trapping that takes place beneath the barriers, which acts to both increase the storage potential of the reservoir and improve the storage security of the $\mathrm{CO}_2$ . Analytical results for the total amount of $\mathrm{CO}_2$ trapped in a reservoir with an uncorrelated random distribution of impermeable barriers are obtained for both two and three-dimensional cases. In two dimensions, it is shown that the total amount of $\mathrm{CO}_2$ contained in this fashion scales as $n^{5/4}$ , where $n$ is the number of barriers in the vertical direction. In three dimensions, the trapped amount scales as $n^c$ , where $5/4 \le c \le 2$ depending on the aspect ratio of the barriers. The analytical two-dimensional results are compared with results of detailed numerical simulations, and good agreement is observed.     

On the Validation of a Compositional Model for the Simulation of $$\text {CO}_2$$ Injection into Saline Aquifers

In this work we apply a recently proposed Bayesian Markov chain Monte Carlo framework (Akbarabadi et al. in Comput Geosci 19(6):1231–1250, 2015) to quantify uncertainty in the three-dimensional permeability field of a rock core. This process establishes the credibility of a compositional two-phase flow model to describe the displacement of brine by \(\text {CO}_2\) and \(\text {CO}_2\) storage in saline aquifers. We investigate the predictive capabilities of the compositional model in the context of an unsteady-state \(\text {CO}_2\)-brine drainage experiment at the laboratory scale, performed at field-scale aquifer conditions. We employ forward models consisting of a system of discretized partial differential equations along with relative permeability curves obtained by a curve fitting of experimental measurements. We consider a forward model to be validated when: (1) numerical simulations reveal that the Bayesian framework has accurately characterized the core’s permeability and (2) Monte Carlo predictions show excellent agreement between measured and simulated data. A large set of numerical studies with an accurate compositional simulator shows that forward models have been successfully validated. For such models, our numerical results show that we are able to capture all the dominant features and general trends of the \(\text {CO}_2\) saturation fields observed in the core. Our study is consistent with the design and findings of real experiments. Fluid properties, relative permeability data, measured porosity field, physical dimensions, and thermodynamic conditions are the same as those reported in Akbarabadi and Piri (Adv Water Resour 52:190–206, 2013). However, the measured saturation data are from flow experiments different from those reported in Akbarabadi and Piri (2013), and will be presented here.     

Flow Dynamics of \hbox {CO}_{2}/brine at the Interface Between the Storage Formation and Sealing Units in a Multi-layered Model

Pressure distribution and \(\hbox {CO}_{2}\) plume migration are two major interests in \(\hbox {CO}_{2}\) geologic storage as they determine the injectivity and storage capacity. In this study, we adopted a three-layer model comprising a storage formation and the over- and underlying seals and determined three distinct flow regions based on the vertical flux exchange of \(\hbox {CO}_{2}\) and native brine. Regions 1 and 2 showed \(\hbox {CO}_{2}\) flowing from the storage formation to adjacent seals with counter-flowing brine. The characteristics of these fluxes in Region 1 were governed by permeability change due to salt precipitation whereas buoyancy force controlled the flux pattern in Region 2. Region 3 showed brine flowing from storage formation toward the over- and underlying seals, which enabled the displaced brine to escape from the storage formation and make room for \(\hbox {CO}_{2}\) to store as well as reduce the pressure build-up. In the multi-layered model, the counter-flowing brine in flow Region 1 resulted in localized salt precipitation at the upper and lower boundary of storage formation. We assessed the bottom-hole pressure and \(\hbox {CO}_{2}\) mass in caprock with respect to reservoir size. While the formation thickness influenced the bottom-hole pressure in the early stage of injection, the horizontal extension of the reservoir was more influential to pressure build-up during the injection period, and to the stabilized pressure during the post-injection period. The \(\hbox {CO}_{2}\) mass in caprock gently increased during the injection period as well as during the post-injection period and reached about 4–5 % of injected \(\hbox {CO}_{2}\) . The percentage of escaped brine from the storage formation ranged from 80–100 % of the \(\hbox {CO}_{2}\) mass stored in the storage formation depending on the reservoir scale.     

Numerical Modeling of Salt Transport and Precipitation in Non-Isothermal Partially Saturated Porous Media Considering Kinetics of Salt Phase Changes

Water and salts strongly influence the durability of porous materials. One of the most adverse phenomena which is related to the salt and moisture presence in the pore system of building materials is salt crystallization. The process is associated with the supersaturation ratio. The salt phase change kinetics is taken into account during the modeling of coupled moisture, salt, and heat transport. To solve the set of governing, differential equations the finite element and the finite difference methods are used. Three different rate laws are assumed in modeling the salt phase change. The drying, cooling, and warming of the cement mortar sample, during which the salt phase change occurs, have been simulated using the developed software. The changes of salt concentration in the pore solution and the amount of precipitated salt due to variation of boundary conditions are presented and discussed. The results obtained in the numerical simulation assuming the first, second, and fourth order rate low indicate that the higher order of the rate law the longer time delay between the change of boundary conditions and the salt precipitation. Such an analysis might be very useful during the determination of the material parameters by solving the inverse problem.     

Application of an Inverse Simulator of Single-Phase Flow Analysis for Leakage Pathway Estimation in a Multiphase System for Geologic $$\hbox {CO}_{2}$$ Storage

When \(\hbox {CO}_{2}\) is injected in a brine reservoir, brine or \(\hbox {CO}_{2}\) can be discharged into a permeable formation saturated with brine above the storage reservoir along a leakage pathway, if present. In most situations, the overlying formation can act as a single-phase aquifer with only brine leakage before \(\hbox {CO}_{2}\) leaks. This study examines the applicability of a developed inverse code for single-phase fluids to detect leakage pathway locations in view of the overlying formation using pressure anomalies induced by leaks. Before applying inverse analysis, forward modeling is performed using the TOUGH2 model to determine brine and \(\hbox {CO}_{2}\) leakage in a homogeneous conceptual model, and the simulated pressure profiles at monitoring wells are used as measurements in the inverse model. In the inverse code, an important consideration is that the vertical hydraulic conductivity and cross-sectional area of a leakage pathway that are inherent to a leakage term in the mass balance equation are integrated as a single parameter to estimate the leakage pathway locations. This method eliminates the impact of the uncertainty of the leakage pathway size on the accuracy of leakage pathway estimation. The inverse model examines the effect of the number of monitoring wells, monitoring periods and \(\hbox {CO}_{2}\) leakage into the overlying formation on the accuracy of leakage pathway estimation according to eleven application examples. The comparison between the results of the single-phase inverse code and iTOUGH2 code illustrates that the single-phase inverse model can be applicable to the leakage pathway estimation in a multiphase flow system.     

An Analysis of the Movement of Wetting and Nonwetting Fluids in Homogeneous Porous Media

The movement of wetting and nonwetting fluid flow in columns packed with glass beads is used to understand the more complicated flows in homogeneous porous media. The motion of two immiscible liquids (oil and water) is observed with different surfactants. Through dimensional analyses, fluid velocity is well correlated with interfacial tension and less dependent on particle size. In water–oil (W/O) experiments, finger pattern flows are observed if water is the displacing fluid that flows in an oil-filled porous media, whereas oil ganglia tend to form if oil is the displacing fluid in the water-wetted porous media. The results are well described by a simple model based on an earlier theory of flow in a tube.     

A Numerical Model of Tracer Transport in a Non-isothermal Two-Phase Flow System for {\text{ CO}}_2 Geological Storage Characterization

For the purpose of characterizing geologically stored $\text{ CO}_{2}Air sparging is an in situ soil/groundwater remediation technology, which involves the injection of pressurized air through air sparging well below the zone of contamination. To investigate the rate-dependent flow properties during multistep air sparging, a rule-based dynamic two-phase flow model was developed and applied to a 3D pore network which is employed to characterize the void structure of porous media. The simulated dynamic two-phase flow at the pore scale or microscale was translated into functional relationships at the continuum-scale of capillary pressure?Csaturation (P ^c?CS) and relative permeability??saturation (K _r?CS) relationships. A significant contribution from the air injection pressure step and duration time of each air injection pressure on both of the above relationships was observed during the multistep air sparging tests. It is observed from the simulation that at a given matric potential, larger amount of water is retained during transient flow than that during steady flow. Shorter the duration of each air injection pressure step, there is higher fraction of retained water. The relative air/water permeability values are also greatly affected by the pressure step. With large air injection pressure step, the air/water relative permeability is much higher than that with a smaller air injection pressure step at the same water saturation level. However, the impact of pressure step on relative permeability is not consistent for flows with different capillary numbers (N _ca). When compared with relative air permeability, relative water permeability has a higher scatter. It was further observed that the dynamic effects on the relative permeability curve are more apparent for networks with larger pore sizes than that with smaller pore sizes. In addition, the effect of pore size on relative water permeability is higher than that on relative air permeability.     

A Novel Analysis of the Electrical Transport Mechanisms in Porous Media

Effects of water saturation and wettability on the dielectric constant are investigated experimentally using four-electrode impedance measurements, and theoretically using models that account for the electrical double layer polarization. Complex impedance measurements, performed on Berea sandstone and on Ottawa-sand packs in the frequency range 10Hz to 1MHz, appear to indicate that the dielectric constant varies linearly with water saturations above 50%. The rate of change of dielectric constant with saturation is found to be a function of frequency. As the frequency increases this rate of change decreases. The decrease in the slope of the dielectric constant-water saturation profile with frequency is not intuitively obvious, but has been proven theoretically in this work. The dielectric constant of water-wet samples is found higher than that of the oil-wet samples at all water saturations. The difference is more pronounced at high water saturations near unity. The wettability changes have been simulated using a generalized Maxwell–Wagner model by varying the amount of ionic surface charge of rocks. In general oil-wetting agents react with the formation matrix by connecting their positively charged tails to the negatively charged silica surfaces, lowering the surface charge density. Simulations show that the effect of wettability changes on the dielectric constant is very significant. These conclusions are consistent with the experimental results presented in this study.     

Network Model of Flow,Transport and Biofilm Effects in Porous Media

In this paper, we develop a network model to determine porosity and permeability changes in a porous medium as a result of changes in the amount of biomass. The biomass is in the form of biofilms. Biofilms form when certain types of bacteria reproduce, bond to surfaces, and produce extracellular polymer (EPS) filaments that link together the bacteria. The pore spaces are modeled as a system of interconnected pipes in two and three dimensions. The radii of the pipes are given by a lognormal probability distribution. Volumetric flow rates through each of the pipes, and through the medium, are determined by solving a linear system of equations, with a symmetric and positive definite matrix. Transport through the medium is modeled by upwind, explicit finite difference approximations in the individual pipes. Methods for handling the boundary conditions between pipes and for visualizing the results of numerical simulations are developed. Increases in biomass, as a result of transport and reaction, decrease the pipe radii, which decreases the permeability of the medium. Relationships between biomass accumulation and permeability and porosity reduction are presented.