Hassan Hassanzadeh

Predicting PVT data for CO2-brine mixtures for black-oil simulation of CO2 geological storage

Accurate modeling of the storage or sequestration of CO2 injected into subsurface formations requires an accurate fluid model. This can be achieved using compositional reservoir simulations. However, sophisticated equations of state (EOS) approaches used in current compositional simulators are computationally expensive. It is advantageous and possible to use a simple, but accurate fluid model for the very specific case of geological CO2 storage. Using a black-oil simulation approach, the computational burden of flow simulation can be reduced significantly. In this work, an efficient and simple algorithm is developed for converting compositional data from EOS into black-oil PVT data. Our algorithm is capable of predicting CO2‐brine density, solubility, and formation volume factor, which are all necessary for black-oil flow simulations of CO2 storage in geological formations. Numerical simulations for asimple CO2storage case demonstrate that the black-oil simulationruns are atleast fourtimes fasterthan thecompositional oneswithout lossof accuracy. Theaccuracy in prediction of CO2‐brine black-oil PVT properties and higher computational efficiency of the black-oil approach promote application of black-oil simulation for large-scale geological storage of CO2 in saline aquifers.

Comparison of different numerical Laplace inversion methods for engineering applications

Abstract Laplace transform is a powerful method for enabling solving differential equation in engineering and science. Using the Laplace transform for solving differential equations, however, sometimes leads to solutions in the Laplace domain that are not readily invertible to the real domain by analytical means. Numerical inversion methods are then used to convert the obtained solution from the Laplace domain into the real domain. Four inversion methods are evaluated in this paper. Several test functions, which arise in engineering applications, are used to evaluate the inversion methods. We also show that each of the inversion methods is accurate for a particular case. This study shows that among all these methods, the Fourier transform inversion technique is the most powerful but also the most computationally expensive. Stehfest’s method, which is used in many engineering applications is easy to implement and leads to accurate results for many problems including diffusion-dominated ones and solutions that behave like e − t type functions. However, this method fails to predict e t type functions or those with an oscillatory response, such as sine and wave functions.

Modelling of Convective Mixing in CO Storage

Accurate modelling of the fate of injected CO 2 is necessary if geological storage is to be used at a large scale. In one form of geological storage, CO2 is injected into an aquifer that has a sealing caprock, forming a CO2 cap beneath the caprock. The diffusion of CO2 into underlying formation waters increases the density of water near the top of the aquifer, bringing the system to a hydro-dynamically unstable state. Instabilities can arise from the combination of an unstable density profile and inherent perturbations within the system, e.g., formation heterogeneity. If created, this instability causes convective mixing and greatly accelerates the dissolution of CO2 into the aquifer. Accurate estimation of the rate of dissolution is important for risk assessments because the timescale for dissolution is the timescale over which the CO2 has a chance to leak through the caprock or any imperfectly sealed wells. A new 2D numerical model which has been developed to study the diffusive and convective mixing in geological storage of CO2 is described. Effects of different formation parameters are investigated in this paper. Results reveal that there are two different timescales involved. The first timescale is the time to onset the instability and the second one is the time to achieve ultimate dissolution. Depending on system Rayleigh number and the formation heterogeneity, convective mixing can greatly accelerate the dissolution of CO2 in an aquifer. Two field scale problems were studied. In the first, based on the Nisku aquifer, more than 60% of the ultimate dissolution was achieved after 800 years, while the computed timescale for dissolution in the same aquifer in the absence of convection was orders of magnitude larger. In the case of the Glauconitic sandstone aquifer, there was no convective instability. Results suggest that the presence and strength of convective instability should play an important role in choosing aquifers for CO2 storage. risk of leakage of CO2 from a storage formation may need to analyze leakage mechanisms and their likelihood of occurrence during the full-time period over which mobile free-phase CO 2 is expected to remain in the reservoir. Once dissolved, risk assessments may well ignore the leakage pathways resulting from the very slow movement of CO2-saturated brines. An accurate assessment of the timescales for dissolution are therefore of the first order of importance. The CO2 injected into a saline reservoir is typically 40 – 60% less dense than the resident brines (4) . Driven by density contrasts, CO 2 will flow horizontally (in a horizontal aquifer) spreading under the caprock, and flow upwards, potentially leaking through any high permeability zones or artificial penetrations, such as abandoned wells. The free-phase CO2 (usually supercritical fluid) slowly dissolves in the brines. The resulting CO2-rich brines are slightly denser than undersaturated brines, making them negatively buoyant, and thus greatly reducing or eliminating the possibility of leakage. The rate of dissolution depends on the rate at which diffusion or convection brings undersaturated brine in contact with CO2. Convective mixing enhances the dissolution rate as compared to diffusion by distributing the CO2 into the aquifer (5) . Therefore, the role of convective mixing in CO2 sequestration and the timescales involved in the process are important. The dissolution time of the injected CO2 into brine is important because during this time the injected CO2 has a chance to leak into the atmosphere through the caprock and wellbores. Accurate modelling of the convective mixing in heterogeneous porous media plays a central role in predicting the fate of CO2 injected into aquifers. In this paper, geological CO2 storage is modelled by solving the convection-diffusion equation while considering the CO2-brine interface as a boundary condition. Geochemical reactions that can reduce the timescale of sequestration of CO2 are not included, since they generally occur on longer timescales (6) . The paper is organized as follows. First, the mathematical model for simulating density-driven flow through porous media is briefly presented. The model is validated with a benchmark problem for density-driven flow in porous media. Then, the geological CO2 sequestrations both in small and field scale are simulated using the model. Two important timescales, the effect of formation properties, as well as sensitivity to temporal and spatial discretisations, are discussed. Finally, the results are summarized and their relevance to geological storage of CO 2 in aquifers is discussed.

Advective–diffusive mass transfer in fractured porous media with variable rock matrix block size

Traditional dual porosity models do not take into account the effect of matrix block size distribution on the mass transfer between matrix and fracture. In this study, we introduce the matrix block size distributions into an advective-diffusive solute transport model of a divergent radial system to evaluate the mass transfer shape factor, which is considered as a first-order exchange coefficient between the fracture and matrix. The results obtained lead to a better understanding of the advective-diffusive mass transport in fractured porous media by identifying two early and late time periods of mass transfer. Results show that fractured rock matrix block size distribution has a great impact on mass transfer during early time period. In addition, two dimensionless shape factors are obtained for the late time, which depend on the injection flow rate and the distance of the rock matrix from the injection point.

Reservoir engineering to accelerate dissolution of stored CO2 in brines

Publisher Summary Deep aquifers are a particularly important class of geologic storage system because of their ubiquity and large capacity. Two important uncertainties in assessing CO2 storage in aquifers are storage efficiency and security, where efficiency denotes the fraction of total aquifer capacity that can be accessed for storage, and security refers to the possibility that stored CO2 will escape the aquifer system by migrating upwards through natural or artificial weaknesses in the capping formation. It is possible to engineer CO2 storage in aquifers by accelerating the dissolution of CO2 in brines to reduce the long term risk of leakage. Such reservoir engineering includes: optimizing the geometry of injection wells to maximize the rate at which buoyancy-driven flow of CO2 and brines drives dissolution; or use of wells and pumps to transport CO2 or brines within the reservoir to increase contact between CO2 and undersaturated brines accelerating the rate of dissolution and residual gas trapping.

Shear dispersion in a capillary tube with a porous wall.

An analytical expression is presented for the shear dispersion during solute transport in a coupled system comprised of a capillary tube and a porous medium. The dispersion coefficient is derived in a capillary tube with a porous wall by considering an accurate boundary condition, which is the continuity of concentration and mass flux, at the interface between the capillary tube and porous medium. A comparison of the obtained results with that in a non-coupled system identifies three regimes including: diffusion-dominated, transition, and advection-dominated. The results reveal that it is essential to include the exchange of solute between the capillary tube and porous medium in development of the shear dispersion coefficient for the last two regimes. The resulting equivalent transport equation revealed that due to mass transfer between the capillary tube and the porous medium, the dispersion coefficient is decreased while the effective velocity in the capillary tube increases. However, a larger effective advection term leads to faster breakthrough of a solute and enhances mass delivery to the porous medium as compared with the classical double-porosity model with a non-coupled dispersion coefficient. The obtained results also indicate that the finite porous medium gives faster breakthrough of a solute as compared with the infinite one. These results find applications in solute transport in porous capillaries and membranes.

Onset of dissolution-driven instabilities in fluids with nonmonotonic density profile.

Analog systems have recently been used in several experiments in the context of convective mixing of CO(2). We generalize the nonmonotonic density dependence of the growth of instabilities and provide a scaling relation for the onset of instability. The results of linear stability analysis and direct numerical simulations show that these fluids do not resemble the dynamics of CO(2)-water convective instabilities. A typical analog system, such as water-propylene glycol, is found to be less unstable than CO(2)-water. These results provide a basis for further research and proper selection of analog systems and are essential to the interpretation of experiments.

One-Dimensional Matrix-Fracture Transfer in Dual Porosity Systems with Variable Block Size Distribution

Most of the developed models for fractured reservoirs assume ideal matrix block size distribution. This assumption may not be valid in reality for naturally fractured reservoirs and possibly lead to errors in prediction of production from the naturally fractured reservoirs especially during a transient period or early time production from the matrix blocks. In this study, we investigate the effect of variable block size distribution on one- dimensional flow of compressible fluids in fractured reservoirs. The effect of different matrix block size distributions on the single phase matrix-fracture transfer is studied using a recently developed semi-analytical approach. The proposed model is able to simulate fluid exchange between matrix and fracture for continuous or discrete block size distributions using probability density functions or structural information of a fractured formation. The presented semi-analytical model demonstrates a good accuracy compared to the numerical results. There have been recent attempts to consider the effect of variable block size distribution in naturally fractured reservoir modeling for slightly compressible fluids with a constant viscosity and compressibility. The main objective of this study is to consider the effect of variable block size distribution on a one-dimensional matrix-fracture transfer function for single-phase flow of a compressible fluid in fractured porous media. In the proposed semi-analytical model, the pressure variability of viscosity and isothermal compressibility is considered by solving the nonlinear partial differential equation of compressible fluid flow in the fractured media. The closed form solution provided can be applied to flow of compressible fluids with variable matrix block size distribution in naturally fractured gas reservoirs.

Onset of Convection in CO Sequestration in Deep Inclined Saline Aquifers

CO2-sequestration in deep geological formations has been suggested as an option to reduce greenhouse gas emissions. Saline aquifers are one of the most promising options for carbon dioxide storage. It has been investigated that if the layer of aquifer is deep enough, at depths more than 800 meters, dissolution of CO2 into brine causes density of the mixture to increase. If the corresponding Rayleigh number of the porous medium is enough to initiate convection currents, the rate of dissolution will increase. Early time dissolution of CO2 in brine is mainly dominated by molecular diffusion while the late time dissolution is predominantly governed by convective mixing mechanism. In this paper, linear stability analysis of densitydriven miscible flow for carbon dioxide sequestration in deep inclined saline aquifers is presented. The effect of inclination and its influence on the pattern of convection cells has been investigated and the results are compared with the horizontal layer. The current analysis provides approximations for initial wavelength of the convective instabilities and onset of convection that help in selecting suitable candidates for geological CO2 sequestration sites.

A comparative study of flux-limiting methods for numerical simulation of gas–solid reactions with Arrhenius type reaction kinetics

Abstract Heterogeneous gas–solid reactions play an important role in a wide variety of engineering problems. Accurate numerical modeling is essential in order to correctly interpret experimental measurements, leading to developing a better understanding and design of industrial scale processes. The exothermic nature of gas–solid reactions results in large concentration and temperature gradients, leading to steep reaction fronts. Such sharp reaction fronts are difficult to capture using traditional numerical schemes unless by means of very fine grid numerical simulations. However, fine grid simulations of gas–solid reactions at large scale are computationally expensive. On the other hand, using coarse grid block simulations leads to excessive front dissipation/smearing and inaccurate results. In this study, we investigate the application of higher-order and flux-limiting methods for numerically modeling one-dimensional coupled heat and mass transfer accompanied with a gas–solid reaction. A comparative study of different numerical schemes is presented. Numerical simulations of gas–solid reactions show that at low grid resolution which is of practical importance Superbee, MC, and van Albada-2 flux limiters are superior as compared to other schemes. Results of this study will find application in numerical modeling of gas–solid reactions with Arrhenius type reaction kinetics involved in various industrial operations.