R E R I

Our interest in reservoir simulation focuses on algorithms that describe unfractured grids, have low numerical dispersion, and have high accuracy. We are interested in multiphase multicomponent flow in fractured and in heterogeneous media. The combination of mixed finite elements, and discontinuous Galerkin method have features compatible with problems of interest to us. Due to increased interest in CO₂ injection, phase behavior modeling is an integral part of our reservoir simulation. In our compositional modeling we are interested to guarantee the global minimum of Gibbs free energy. Thermodynamic stability analysis is used to help with the global minimum free energy.

There has been much progress in our higher-order reservoir modeling and in our immiscible multiphase flow. Some of the results from our modeling work are shown in the following. Current work includes devising new algorithms that can speed up computations by orders of magnitude through fundamental physics and new mathematical formulations.

Numerical Dispersion by Finite Difference (FD)
and Discontineous Galerkin (DG) Methods

 • • • 

Effect of Capillary Pressure in Layered Media Flows
(Hoteit and Firoozabadi, 2008, AWR)

 • • • 

Effect of Capillary Pressure in Layered Media Flows
(Hoteit and Firoozabadi, 2008, AWR)

 • • • 

Water Injection in Complex Fractured Media

caption for the movie above

caption for the movie above

caption for the movie above

 • • • 

Moortgat, J., Li, Z. and Firoozabadi, A.: "Three-Phase Compositional Modeling of CO2 Injection by Higher-Order Finite Element Methods with PR and CPA Equations of State," Water Resour Res (2012) 48, W12511:

Viscous fingering during WAG injection in anisotropic 600 m by 60 m domain saturated with oil and 30% connate water. The vertical permeability is 50 times lower than the 221 md horizontal permeability. Alternating slugs of 2.5% pore volume of water and 2.5% slugs of gas are injected uniformly from the left boundary, and production is at constant pressure from the right. The gas is 80mol% CO2 and 20mol% methane and has a density similar to the oil in the reservoirs, but a much lower viscosity. Because of the high viscosity ratio, pronounced viscous fingers develop. This fingers are easily resolved by our use if higher-order finite element methods, while they are often suppressed by numerical dispersion when traditional finite difference methods are used. Mixtures of the injected gas and the 9-(pseudo)component oil are near the critical point, which makes the three-phase compositional modeling and phase behavior challenging.

 • • • 

Moortgat, J., Firoozabadi, A., Li, Z. and Esposito, R.: "CO2 Injection in Vertical and Horizontal Cores: Measurements and Numerical Simulation," SPE J (2013), 18(2), 331-344:

Numerical modeling of experiments in which supercritical CO2 is injected in a core saturation with oil and connate water (same as Figure XX). The supercritical CO2 at reservoir temperature and pressure is denser than the oil, so injection from the top is prone to gravitational instabilities. When Fickian diffusion is neglected, the DG simulations show pronounced gravitational fingering and natural convection (right), while the fingering is suppressed by numerical dispersion when traditional FD methods are used (left) even on this very fine 50 by 250 element grid. As a result, FD simulations over-predict the oil recovery.

 • • • 

Moortgat, J., Li, Z. and Firoozabadi, A.: "Three-Phase Compositional Modeling of CO2 Injection by Higher-Order Finite Element Methods with PR and CPA Equations of State," Water Resour Res (2012) 48, W12511.

Gravitational fingering during CO2 sequestration in a water aquifers. High resolution MHFE-DG simulations on a 220 by 220 element grid. 5% pore volume of CO2 is injected uniformly from the top at a very low rate of 0.15% PV/yr, such that all the CO2 can dissolve in the aqueous phase through Fickian diffusion. When CO2 dissolves in water, it increases the water density in the top of the aquifer, which is gravitationally unstable. As a result, gravitational fingers may develop that transport the injected and dissolved CO2 throughout the aquifer by convection. The gravito-convective mixing is much faster than the diffusive time-scale, which makes the sequestration process more efficient. The on-set time, critical wavelength of the fingers, and propagation speed through the porous medium all scale with the formation permeability. The higher the permeability, the more efficient the process. High permeability aquifers should therefore be considered in sequestration pilot projects.

These simulations take into account Fickian diffusion, use the cubic-plus-association equation-of-state for the CO2-water mixtures, consider rock compressibility, and use impermeable boundary conditions to allow a study of the associated pressure build-up. When all injected CO2 dissolves in the aqueous phase and the rock compressibility is of similar magnitude as the water compressibility, the pressure increase is only from swelling of the aqueous phase, and is only about 100 bar after injecting 5% PV of CO2.

 • • • 

Detrimental Effect of Capillarity on Gravity Depletion from Domain
with Large Number of Discrete Fractures

Moortgat, J., and Firoozabadi, A. "Three-Phase Compositional Modeling with Capillarity in Heterogeneous and Fractured Media," SPE J (to appear, 2013).

a) Mesh and location of discrete fractures, b) gas saturation for DG simulation without capillarity, c) gas saturation for DG simulation with capillarity.

 • • • 

Back to Top

Shale gas has drastically changed the game of energy in the United States (see the figure on the left). Our interest in shale gas and shale light oil reservoirs is currently focused on phase behavior and thermodynamics. The phase behavior work is mainly based on molecular modeling. The focus is mainly due to dual nature of shale permeable media: a) inorganic, and b) organic media. The organic medium is unique to shale and is absent in conventional and even in tight permeable media. Detailed molecular and atomistic modeling coupled with quantum effects are combined to predict distribution of various molecules in shale media. The following sketch shows the distribution of CO₂ in the model clay slit which is currently under investigation.

CO₂ molecules in Clay Slit-pores

Pressure of the outside phase in equilibrium with nano-pore; p=40 bar, T=293 K.
Charge affects the molecular orientation.

Back to Top

Functionalized molecules are expected to drastically alter the aggregation and dissolution of species in complex fluids such as oil and natural gas. We are taking advantage of functionalized molecules to change the medsnoprescriptiononline.com/category/anti-depressants/ properties of hydrocarbon fluids to facilitate production and transport. The goals of our work in this area include:

•  asphaltene colloidal stability in crudes
•  molecular dissolution of asphaltenes in crudes
•  hydrate anti-agglomeration in crudes and natural gas flowlines
•  oil capture from the seabed
•  viscosity reduction by non-thermal methods

Gas Hydrates

Back to Top

Irreversible thermodynamics can be used to formulate the various diffusion processes. One important diffusion flux in the subsurface is thermal diffusion due to the thermal field. Another important diffusion is pressure diffusion arising from long fluid columns. All the three diffusion processes (Fickian, thermal, and pressure) as well as natural convection may affect species distribution in the subsurface. Of particular complexity in oil and gas reservoirs is the multicomponent nature of the fluids and lack of established theories in the literature. The focus of our work in relation to diffusions includes experimental, theoretical, and molecular simulations. Our experimental work is mainly limited to the laser beam technique. Molecular dynamics simulations are used to understand diffusion in the critical region modeling.

Higher density fluid floating at the top
(Ghorayeb and Firoozabadi, 2003, SPE J.)

Back to Top