Department of Chemical and Petroleum Engineering Schulich School of Engineering University of Calgary 2500 University Drive N.W. Calgary, Alberta CANADA T2N 1N4
Room: EN B204m Telephone: (403) 210-6645 Fax: (403) 284-4852 E-mail: hhassanz@ucalgary.ca B.Sc. (Petroleum University of Technology, Ahwaz, Iran) 1994 M.Sc. (University of Tehran, Tehran, Iran) 1997 Ph.D. (University of Calgary) 2006
My research expertise is in analytical and numerical modeling of transport phenomena in porous media with application to geological storage of CO2 and acid-gases, upscaling of multi-scale reactive flow for simulation of oil recovery processes, double diffusive convection in aquifers and oil reservoirs, and modeling and upscaling of fluid flow and transport in fractured reservoirs. We have conducted research on geological storage of CO2 in deep saline aquifers, fluid flow in naturally fractured reservoirs, and upscaling of reactive flow, where we have used analytical and numerical modeling of the processes involved. Current research activities are as follows:
â– Buoyancy-driven induced dispersion in porous media with application to CO2 storage â– CO2 dissolution acceleration â– Upscaling of diffusive/dispersive processes in fractured porous media â– Block-to-block interaction in fractured porous media. â– Effect of nano-catalysts on the stability of reactive fronts in porous media
Abstract: The storage of carbon dioxide and acid gases in deep geological formations is considered
a promising option for mitigation of greenhouse gas emissions. Understanding of the
primary mechanisms, such as convective mixing and geochemistry that affect the longterm
geostorage process in deep saline aquifers is of prime importance. First, a linear
stability analysis of an unstable diffusive boundary layer in porous media is presented,
where the instability occurs due to a density difference between the carbon dioxide
saturated brine and the resident brine. The impact of geochemical reactions on the
stability of the boundary layer is examined. The equations are linearised, and the obtained
system of eigenvalue problems is solved numerically. The linear stability results have
revealed that geochemistry stabilises the boundary layer as reaction consumes the
dissolved carbon dioxide and makes the density profile, as the source of instability, more
uniform. A detailed physical discussion is also presented with an examination of vorticity
and concentration eigenfunctions and streamlines’ contours to reveal how the
geochemical reaction may affect the hydrodynamics of the process. We also investigate
the effects of the Rayleigh number and the diffusion time on the stability of a boundary
layer coupled with geochemical reactions. Nonlinear direct numerical simulations are
also presented, in which the evolution of density-driven instabilities for different reaction
rates are discussed. The development of instability is precisely studied for various
scenarios. The results indicate that the boundary layer will be more stable for systems
with a higher rate of reaction. However, our quantitative analyses show that more carbon
dioxide may be removed from the supercritical free phase as the measured flux at the
boundary is always higher for flow systems coupled with stronger geochemical reactions.
Notes: Buoyant boundary layers , Convection, Buoyancy-driven instability, Convection, Geophysical and Geological Flows, CO2 Storage, Convective Mixing, CO2 Sequestration
Abstract: A modified pressure decay method has been designed and tested for more reliable measurements of molecular diffusion coefficients of gases into liquids. Unlike the conventional pressure decay method, the experimental setup has been designed such that the interface pressure and consequently the dissolved gas concentration at the interface are kept constant. This is accomplished by continuously injecting the required amount of gas into the gas cap from a secondary supply cell to maintain the pressure constant at the gas−liquid interface. The pressure decay is measured in the supply cell. The advantage of the new technique is that, assuming the diffusion coefficient to be constant, a simple analysis allows determination of the equilibrium concentration and diffusion coefficient.
Abstract: The accurate numerical modelling of reactive flow is essential for the interpretation of experimental measurements and the design of field-scale processes. Sharp reaction fronts are difficult to capture using traditional numerical schemes, unless fine grid numerical simulations are used; however, fine grid simulations are computationally expensive. On the other hand, using coarse grid block simulations leads to excessive front dissipation and inaccurate results. In most practical cases, it is not feasible to choose small grid blocks; therefore, one needs to account for the small-scale gradients that cannot be captured by coarse grid blocks when using traditional methods. As a first step toward the development of upscaling techniques for reaction kinetics, an equivalent reaction constant for a simple steady-state convection-diffusion-reaction (CDR) was determined. This shows how an effective reaction constant can be obtained as a function of the Peclet number, Thiele modulus and size of the reaction zone, such that the coarse grid simulation agrees with the fine grid simulation.
Abstract: In situ catalytic upgrading of heavy oil and bitumen has been suggested and tested in the laboratory for utilization of heavy oil resources. Experimental observations have demonstrated potential, so this innovative recovery technique may have a role in the development of large resources of heavy oil and bitumen. Accurate analytical and numerical modelling is necessary in order to correctly interpret experimental measurements of the in situ upgrading, leading to a better understanding and design of field-scale processes. In this paper, we present modelling and parameter estimation for ultra-dispersed catalytic upgrading experiments conducted in a batch reactor. The Monte Carlo simulation technique was used to estimate the most appropriate reaction parameters. The combination of an analytical batch reactor model and the Monte Carlo simulation technique allows for the fast generation of a large number of upgrading experiment realizations. Comparisons of analytical modelling results with the experimental measurements of the upgrading experiments at different temperatures are in close agreement. Results reveal that ultra-dispersed catalytic upgrading in a batch reactor results in a fairly high residue conversion and can potentially increase the API gravity of the produced oil.
Abstract: Estimating the feasibility of acid gas geological disposal requires the knowledge of the water content of the gas phase at moderate pressures and temperatures (typically below 50 MPa, below 380 K) and up to 6 mol NaCl. In this paper, a non-iterative model is developed to predict the water content of sour and acid gases at equilibrium with pure water and brine. This model is based on equating the chemical potential of water and using the modified Redlich–Kwong equation of state to calculate the fugacity of the gas phase. The water content of pure CH4, CO2 and H2S are represented with average absolute deviations of less than 3.36, 7.04 and 8.4%, respectively. Experimental data of the water content of mixtures of the acid gases were reproduced with average absolute deviations of less than 6.32%.
Abstract: In this investigation available experimental data in the literature were used to propose a reaction mechanism for the destruction of methanol using non-thermal plasma technology. In a recent study [M. Derakhshesh, J. Abedi, M. Omidyeganeh, Modeling of hazardous air pollutant removal in the pulsed corona discharge, Phys. Lett. A 373 (2009) 1051–1057.] the reactor performance equation for destruction of pollutants was developed. The order of reaction for methanol decomposition is estimated using a recently developed performance model and the available experimental data. It is found that that methanol decomposition reaction follows order one. In addition, using the experimental data available in the literature the rate constant for methanol decomposition is obtained and the overall rate was compared with our previous study.
Abstract: One of the important parameters in existing commercial dual-porosity reservoir simulators is matrix–fracture shape factor, which is customarily obtained by assuming a constant pressure at the matrix–fracture boundary. In his work, Chang [1] and [2] addressed the impact of boundary conditions at the matrix–fracture interface and presented analytical solutions for the transient shape factor and showed that for a slab-shaped matrix block a constant pressure boundary condition leads to an asymptotic (long-time) shape factor of π2/L2, and that a constant volumetric flux leads to an asymptotic shape factor of 12/L2. In a recent paper [3], we reconfirmed Chang’s [1] and [2] results using a Laplace transform approach. In this study, we extend our previous analysis and use infinite-acting radial and linear dual-porosity models, where the boundary condition is chosen at the wellbore, as opposed to at the matrix boundary. The coupled equations for fracture and matrix are solved analytically, taking into account the transient exchange between matrix and fracture. The analytical solution that invokes the time dependency of fracture boundary condition under constant rate is then used to calculate the transient shape factors. It is shown that, for a well producing at constant rate from a naturally fractured reservoir, the appropriate value of stabilized shape factor is 12/L2. This contrasts with the commonly used shape factor for a slab-shaped matrix block that is subject to a constant pressure boundary condition, which is π2/L2. The errors in the matrix–fracture exchange term in a dual-porosity model associated with the use of a shape factor derived based on constant pressure boundary condition at the matrix boundary are then evaluated.
Abstract: Carbon dioxide injection into deep saline aquifers is an important option for managing CO2 emissions. Injected CO2 dissolves into formation brines from above, increasing brine density and creating an unstable hydrodynamic state favorable for natural convection. Long-term buoyancy-driven flow of high-density CO2-saturated brine leads to faster trapping through improved dissolution and can reduce the risk of CO2 leakage from storage sites. We investigate the role of natural flow of aquifers and associated dispersion on the onset of convection. A linear stability analysis of a transient concentration field in a laterally infinite, horizontal, and saturated porous layer with steady horizontal flow is presented. The layer is subjected to a sudden rise in CO2 concentration from the top and is closed from the bottom. Solution of the stability equations is obtained using a Galerkin technique and the resulting equations are integrated numerically. We found simple scaling relationships that follow tDc60(1 + PeT)Ra-2 for the onset time of convection and a0.05Ra/(1 + PeT) for the wavenumber of the initial instabilities. Results reveal that transverse dispersion increases the time to onset of convection for the entire range of Ra. Furthermore, transverse dispersion decreases the critical wavenumber of the instabilities. These results facilitate screening candidate sites for geological CO2 storage.
Abstract: Exothermic solid-solid reactions lead to sharp reaction fronts that cannot be captured by coarse spatial mesh size numerical simulations that are often required for large scale simulations. We present a coarse scale formulation with high accuracy by using a Taylor series expansion of the reaction term. Results show that such expansion could adequately maintain the accuracy of fine scale behaviour of a constant pattern reaction front while using a smaller number of numerical grid cells. Results for a one-dimensional solid-solid reacting system reveal reasonable computational time saving. The presented formulation improves our capabilities for conducting fast and accurate numerical simulations of industrial scale solid-solid reactions.
Abstract: One of the important challenges in geological storage of CO2 is predicting, monitoring, and managing the risk of leakage from natural and artificial pathways such as fractures, faults, and abandoned wells. The risk of leakage arises from the buoyancy of free-phase mobile CO2 (gas or supercritical fluid). When CO2 dissolves into formation brine, or is trapped as residual phase, buoyancy forces are negligible and the CO2 may be retained with minimal risk of leakage. Solubility trapping may therefore enable more secure storage in aquifer systems than is possible in dry systems (e.g., depleted gas fields) with comparable geological seals. A crucial question for an aquifer system is, what is the rate of dissolution? In this paper, we address that question by presenting a method for accelerating CO2 dissolution in saline aquifers by injecting brine on top of the injected CO2. We investigate the effects of different aquifer properties and determine the rate of solubility trapping in an idealized aquifer geometry. The acceleration of dissolution by brine injection increases the rate of solubility trapping in saline aquifers and therefore increases the security of storage. We show that, without brine injection, only a small fraction (less than 8%) of the injected CO2 would be trapped by dissolving in formation brine within 200 years. For the particular cases studied, however, more than 50% of the injected CO2 dissolves in the aquifer as induced by brine injection. Since the energy cost for brine injection can be small (<20%) compared to the energy required for CO2 compression for a five-fold increase in dissolution, such reservoir engineering techniques might be viable and practical for accelerating dissolution of CO2. The environmental benefit would be to decrease the risk of CO2 leakage at reasonably low cost.
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.
Abstract: 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 a simple CO2 storage case demonstrate that the black-oil simulation runs are at least four times faster than the compositional ones without loss of accuracy. The accuracy 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.
Abstract: CO2 storage in deep saline aquifers is considered a possible option for mitigation of greenhouse gas emissions from anthropogenic sources. Understanding of the underlying mechanisms, such as convective mixing, that affect the long-term fate of the injected CO2 in deep saline aquifers, is of prime importance. We present scaling analysis of the convective mixing of CO2 in saline aquifers based on direct numerical simulations. The convective mixing of CO2 in aquifers is studied, and three mixing periods are identified. It is found that, for Rayleigh numbers less than 600, mixing can be approximated by a scaling relationship for the Sherwood number, which is proportional to Ra1/2. Furthermore, it is shown that the onset of natural convection follows tDcRa-2 and the wavelengths of the initial convective instabilities are proportional to Ra. Such findings give insight into understanding the mixing mechanisms and long term fate of the injected CO2 for large scale geological sequestration in deep saline aquifers. In addition, a criterion is developed that provides the appropriate numerical mesh resolution required for accurate modeling of convective mixing of CO2 in deep saline aquifers.
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 et type functions or those with an oscillatory response, such as sine and wave functions.
Abstract: The matrix-fracture transfer shape factor is one of the important parameters in modeling naturally fractured reservoirs. Four decades after Warren and Root (1963, SPEJ, 245–255.) introduced the double porosity concept and suggested a relation for it, this parameter is still not completely understood. Even for a single-phase flow problem, investigators report different shape factors. This study shows that for a single-phase flow in a particular matrix block, the shape factor that Warren and Root defined is not unique and depends on the pressure in the fracture and how it changes with time. We use the Laplace domain analytical solutions of the diffusivity equation for different geometries and different boundary conditions to show that the shape factor depends on the fracture pressure change with time. In particular, by imposing a constant fracture pressure as it is typically done, one obtains the shape factor that Lim and Aziz (1995, J. Petroleum Sci. Eng. 13, 169.) calculated. However, other shape factors, similar to those reported in other studies are obtained, when other boundary conditions are chosen. Although, the time variability of the boundary conditions can be accounted for by the Duhamel’s theorem, in practice using large time-steps in numerical simulations can potentially introduce large errors in simulation results. However, numerical simulation models make use of a stepwise approximation of this theorem. It is shown in this paper that this approximation could lead to large errors in matrix-fracture transfer rate if large time-steps are chosen.
Abstract: Carbon dioxide injected into saline aquifers dissolves in the resident brines increasing their density, which might lead to convective mixing. Understanding the factors that drive convection in aquifers is important for assessing geological CO2 storage sites. A hydrodynamic stability analysis is performed for non-linear, transient concentration fields in a saturated, homogenous, porous medium under various boundary conditions. The onset of convection is predicted using linear stability analysis based on the amplification of the initial perturbations. The difficulty with such stability analysis is the choice of the initial conditions used to define the imposed perturbations. We use different noises to find the fastest growing noise as initial conditions for the stability analysis. The stability equations are solved using a Galerkin technique. The resulting coupled ordinary differential equations are integrated numerically using a fourth-order Runge–Kutta method. The upper and lower bounds of convection instabilities are obtained. We find that at high Rayleigh numbers, based on the fastest growing noise for all boundary conditions, both the instability time and the initial wavelength of the convective instabilities are independent of the porous layer thickness. The current analysis provides approximations that help in screening suitable candidates for homogenous geological CO2 sequestration sites.
Abstract: Accurate modelling of the fate of injected CO2 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.
Abstract: The reactive flows in porous media that involve the displacement of fluids
by di®erent physical properties may lead to a hydrodynamic instabil-
ity. The use of nano-particles as catalysts in porous media has recently
been increased and is generally relevant to applications that include
in-situ heavy oil upgrading and removal of reactive and non-reactive
pollutants in groundwater. The objective is to investigate the effects of
nano-catalysts and chemical reactions on this instability. In order to
understand the physics of this flow displacement, the basic equations
of conservation of mass and momentum are linearized and solved nu-
merically for a homogenous porous medium. The analysis reveals that
increasing the reaction rate enhances the instability around an interface
including nano-catalysts while increasing the nano-catalysts deposition
rate in porous media usually stabilizes the front. The effects of the inter-
face sharpness, nano-particle diffusion coeffcient, permeability of porous
media, and viscosity ratios of different phases will also be discussed.
Abstract: As concern about the adverse consequences of anthropogenic climate change has grown,
so too has research into methods to reduce the emissions of greenhouse gases that will
drive future climatic change. Carbon dioxide emissions arising from use of fossil-fuels
are likely to be the dominant drivers of climate change over the coming century. The use
of carbon dioxide and geologic storage (or sequestration) offers the possibility of
maintaining access to fossil energy while reducing emissions of carbon dioxide to the
atmosphere. One of the essential concerns in geologic storage is the risk of leakage of
CO2 from the injection sites. Carbon dioxide injected into saline aquifers, dissolves in the
resident brines, increasing their density potentially leading to convective mixing.
Convective mixing increases the rate of dissolution, and therefore decreases the timescale
over which leakage is possible. Understanding the factors that drive convective
mixing and accurate estimation of the rate of dissolution in saline aquifers is important
for assessing geological CO2 storage sites.
This dissertation has three components, which includes linear stability analysis,
prediction of CO2-brine PVT, and numerical modeling. A hydrodynamic stability
analysis is performed for non-linear, transient concentration fields in a saturated,
homogenous and isotropic porous medium under various initial and boundary conditions.
The role of the natural flow of aquifers and associated dispersion on the onset of
convection in the saline aquifers is also investigated. A fugacity and an activity models
are combined to develop an accurate thermodynamic module appropriate for geological
CO2 storage application. A three-dimensional, two-phase and two-component numerical
model for simulation of CO2 storage in saline aquifers is also developed. The numerical
model employs higher order and total-variation-diminishing schemes, capillary pressure,
relative permeability hysteresis, and full dispersion tensor formulation. The model also
takes into account an accurate representation of a CO2-brine mixture thermodynamic and
transport properties. The model is validated for a number of problems against one- and
two-dimensional standard analytical and numerical solutions.
v
The theoretical analysis and numerical model are used to investigate the role of
convective mixing on CO2 storage in homogenous and isotropic saline aquifers. Scaling
analysis of the convective mixing of CO2 in saline aquifers is presented. The convective
mixing of CO2 in aquifers is characterized, and three mixing periods are identified. It is
found that mixing achieved can be approximated by a scaling relationship for Sherwood
number as a measure of mixing. Furthermore, the onset of natural convection and the
wavelengths of the initial convective instabilities are determined. A criterion is also
developed that provides the appropriate numerical mesh resolution required for accurate
modeling of convective mixing of CO2 in deep saline aquifers. In addition, using the
model developed, a method to accelerate CO2 dissolution in brines is also suggested. The
acceleration of dissolution by brine pumping increases the rate of solubility trapping in
saline aquifers and therefore increases the security of storage. Results of this dissertation
give insight into appropriate implementation of large scale geological CO2 storage in
deep saline aquifers.
