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Hydraulic fracturing

Hydraulic fracture and natural fracture interact mechanically and hydraulically. This interaction can be modeled and upscaled in order to map hydraulic fractures in a naturally fractured rock.

The natural fracture experiences tensile and shear stresses as a result of the opening of the hydraulic fracture. Above is a time-lapse evolution of shear strain induced by hydraulic fracturing.


Induced seismicity

Seismicity induced by fluid injection and withdrawal is a matter of public concern. We use geological, geophysical, and engineering data of real fields to model various physical processes in the subsurface for assessment and mitigation of the risks of induced seismicity. The challenge here is the multi-physics and multi-scale nature of the physical problem. Fluid injection and production occurs over years and decades while a triggered event may last for seconds during rupture of the seismogenic fault. 

Above snapshots are from a simulation of seismicity induced by CO2 injection in an aquifer intersected by a sealing fault. The profile of the aquifer projected on the fault is visible in the top two figures. The blue-colored rupture front in the bottom right figure shows that the rupture propagates downdip which is consistent with the normal faulting boundary conditions in the simulation.


Vertical cross-section view of the vertical displacement field in a faulted geologic basin. Red color indicates upward displacement, blue indicates downward displacement. Aquifer is overpressurized due to carbon dioxide injection, which leads to volumetric expansion of the aquifer that builds up shear traction and reduces compression on the fault. The bottom intersection point of aquifer with the fault (hypocenter) reaches the failure envelope first thereby nucleating rupture and the subsequent earthquake.


Production of oil and gas from faulted reservoirs requires assessment of the risk of inducing slip on critically-stressed faults in the reservoir. Changes in the Coulomb Failure Function (CFF) calculated on the fault surface quantifies this risk. Above: Production and injection-induced changes in CFF (bars) on a fault that sourced a Mw = 6 earthquake in Italy in year 2012 after decades of production from a nearby oilfield.


Computational mechanics

We develop new computational frameworks to model coupled multiphase flow and geomechanics of faulted and fractured reservoirs.  The challenges here are related to the mathematical formulation of the coupled problem, space discretization and time integration, design of numerically stable and computationally efficient algorithms to solve the discretized problem, and computer implementation for parallel computing.

Our work featured on the Computational Infrastructure for Geodynamics (CIG) webpage and in their August 2014 Newsletter.


Reservoir characterization

Reservoir characterization refers to the estimation of spatial distributions of rock and fluid properties in the reservoir, such as porosity, permeability, and pore compressibility. We use ensemble-based methods to assimilate multiple sources of data such as well flow rates and pressures, surface deformation measurements from InSAR and GPS satellites, and seismic measurements from geophones, into a forward prediction model based on coupled flow and geomechanics. The challenge here is to develop a consistent and robust theory of poromechanical inversion.

Joint inversion of flow and surface deformation data is used for statistical estimation of rock properties in a gas storage reservoir shown above. The Ensemble Smoother method is used for data assimilation and inversion.


Fluid mixing in porous media

Mixing of fluids is an important phenomenon that controls many natural and industrial processes from gravity current flows to DNA testing. Mixing in porous media and low Reynolds number flows is especially difficult because of the absence of turbulence. Development and control of mixing in such flows is an active area of research.

Mixing from viscous fingering

In enhanced oil recovery techniques such as miscible gas flooding where CO2 is injected to mix with and mobilize crude oil, recovery efficiency can be increased by developing miscibility between the two fluids. We show that viscous fingering, a type of hydrodynamic instability, can be used to induce disorder in the flow and thereby enhance mixing. Tip-splitting and channeling during viscous fingering are two different mechanisms for creation of interfacial area and subsequent mixing across the interface. 

Snapshot of the mixture concentration field from a numerical simulation of  displacement of a more viscous fluid (dark color) by a less viscous fluid (light color) in a porous medium.

We develop a two-equation model for the concentration variance and mean scalar dissipation rate to quantify the evolution of the degree of mixing in a viscously unstable displacement. Fastest mixing is achieved by optimizing the interplay between tip-splitting and channeling mechanisms.

Snapshot of the concentration field during flow of the less viscous fluid, initially distributed as blobs, through a more viscous ambient fluid in a periodic domain. Flow is from left to right.

Stokes flow in a Hele-Shaw cell serves as a simple analog for porous media flows. We study spreading and mixing of slugs of different viscosities flowing in the gap between two parallel rigid plates.

Concentration fields of slugs of three miscible fluids--red, blue, and green. Ratio of viscosities: blue/red = 55, green/blue = 5. Initial placement of slugs is shown in the top figure. More mobile red fluid flows through the less mobile blue fluid.


Mixing during slug injection

Mixing at low Reynolds number can be enhanced by alternating injection of slugs of the two fluids of different viscosities, for example by solvent-alternating-gas injection during enhanced oil recovery. This is also relevant for achieving fast mixing in microfluidic flows. We show that the synergetic action of alternating injection and viscous fingering leads to a dramatic increase in the mixing efficiency at optimum viscosity contrasts.

Alternating injection of slugs of the yellow fluid (less viscous) and the black fluid (more viscous) in a porous medium. The goal is to control mixing at the outlet (right edge) by varying fluid properties and injection rate. Top: mild viscosity contrast leads to poor mixing at outlet, Middle: strong viscosity contrast leads to channeling inside the domain and poor mixing at outlet, Bottom: optimum viscosity contrast leads to highest mixing at the outlet.


Mixing and dilution in heterogeneous formations

Heterogeneity of the porous medium is another source of disorder in the flow that causes spreading and dilution of tracers in groundwater flows. We develop reduced-order models to describe and predict mixing during simulation of such flows.

Concentration fields of a contaminant (yellow color) in a vertical section through an aquifer with groundwater (black color) flow from left to right. Flow through the heterogeneous medium stretches the contaminant-water interface significantly thereby enhancing its dilution in some areas while trapping it at high concentrations in other areas. Top: mildly heterogeneous medium, Bottom: strongly heterogeneous medium.


Concentration field during transport of two passive and miscible tracers (blue and red colors) with the groundwater (green) flow. The flow direction is from left to right. Mixing of the two tracers in an advection-dominated flow is non-trivial. It creates regions of anomalously high and low degree of mixing which directly influences the amount of product formed as a result of chemical reaction between the two tracers.


Displacement of a groundwater contaminant (fluid 2) by the ambient water (fluid 1) for two scenarios: contaminant viscosity higher (middle) or lower (right) than water. The plume structure depends strongly on the interplay between viscous fingering and permeability-based heterogeneity. Mixing between the two fluids and contaminant breakthrough characteristics at the outflow well are determined by this interplay.