Research

Induced seismicity and ground deformation

Seismicity and ground deformation (fissures, subsidence, and uplift) induced by fluid injection and withdrawal is an area of study in geophysics and hydrogeology. They are also matters of public concern due to the risks posed by such deformation to human life and property. We use geological, geophysical, and well data of oilfields and aquifers to model various physical processes in the subsurface for assessment and mitigation of such risks. The challenge here is the numerical modeling of a multiphysics and multiscale problem. Underground injection and production of fluids leads to stress accumulation around faults, reservoir boundaries, and wells, and a part of the accumulated stress is released seismically/aseismically during induced earthquakes or other slow slip events. Solving the equations of fluid flow, geomechanics, and fault slip in a monolithic solver is computationally challenging and expensive. Sequential solution schemes provide the desired computational speed in such multiphysics problems. In case of long-term fluid withdrawal from relatively soft rocks, large strain (>3%) and plastic deformation in the rock make the problem even more challenging to solve. Here is a model problem schematic:

Long-term production-induced seismicity in plastic rocks

We proposed a finite strain formulation for solving this problem in Zhao and Jha, A new coupled multiphase flow–finite strain deformation–fault slip framework for induced seismicity, JCP, 2021. See below videos of stress evolution. See the paper for details.

Computational mechanics

We develop new computational frameworks to model coupled multiphase (oil, water, and gas) 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 of the equations, design of numerically stable and fast algorithms to solve the discretized problem, and computer implementations of the algorithms to enable parallel computing required for real-world simulations.

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

Reservoir characterization

Reservoir characterization refers to the task of estimating spatial distributions of rock properties in the reservoir, such as porosity, permeability, and compressibility. We use ensemble-based methods to assimilate multiple sources of data (well flow rates and pressures, surface deformation measurements from InSAR, GPS and ground leveling stations, and geophone data from seismic events) with coupled flow and geomechanical simulation predictions to estimate these properties. More precisely, we use the measured data to reduce the uncertainty in the rock properties by reducing the variance in prior probability distributions as it learns from the data following the rules of coupled flow and geomechanics.

An example of results from our coupled flow-geomechanical simulation is shown below (Jha et al., IJNAMG, 2015). East-west (Ux) and up-down (Uz) motions of the reservoir surface resulting from seasonal gas injection and production operation in an underground gas storage field is shown in the two videos. During summer months, gas is injected in the field causing the reservoir to expand upward (red Uz values) and sideways (red Ux for eastward motion, blue Ux for westward motion). During winter, gas is produced to meet the demand for heating gas, and this causes the reservoir to shrink (blue color). The seasonal nature of ground motion appears like a beating heart in the videos.

The challenge here is to develop a consistent and robust theory of poromechanical inversion based on realistic datasets that can be available in a field. We used well rate and pressure data, which informs primarily permeability and compressibility, and the InSAR data (calibrated with the GPS station data), which informs primarily Young’s modulus and compressibility, for joint estimation of both hydraulic (permeability) and mechanical (modulus and compressibility) properties. We used the ensemble smoother method, which is faster than the ensemble Kalman filter method, for data assimilation and inversion.

Above: Comparison of the line-of-sight displacement between one member of the posterior ensemble (left columns) and the interferometric synthetic aperture radar (InSAR) data (right columns) at successive timesteps shown between the columns as month/year. See Jha et al., IJNAMG, 2015 for details.

Transport in fractured rock

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.

Above: 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.

During push-pull tests in fractured deformable aquifers, the shape and size of the solute concentration contours are controlled by the connectivity of the well to the fractures and by the advective-dispersive transport processes.

Above: Tracer concentrations in fractures (black straight lines) and in the rock matrix at three time steps. The push-pull well is denoted by the blue horizontal line. Solute concentration in the rock matrix is shown via dash contour lines drawn at an increment of 0.1.

See videos below to understand how the injected solute mixes with the ambient water in a deformable stress-sensitive aquifer.

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.

Above: 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 (Jha et al, PRL, 2011)

R3_5_Pe10000_PRL2011

We developed a two-equation model (like the k-epsilon model in turbulence) 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.

Above: Snapshots of the concentration field at two time steps. A set of more viscous blobs (dark color) is displaced through a less viscous fluid (light color) under left-to-right flow and periodic boundary conditions. Fingers of the less viscous fluid initiate at the unstable interface, grow inside the more viscous blobs, split into multiple fingers, coalesce together, and connect across the blobs as the two fluids mix.

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.

Above: Snapshots of the concentration field in a Stokes flow channel at two time steps. Red, blue, and green represent three different fluids with the ratio of their viscosities as follows: blue/red = 55, green/blue = 5. The more mobile red fluid stretches to become a finger while squeezing the less mobile blue fluid in a thin region between red and yellow fluids.

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.

Above: 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: a mild viscosity contrast between the two fluids leads to poor mixing at outlet, Middle: too strong viscosity contrast leads to channeling of the less viscous fluid inside the domain and poor mixing at outlet, Bottom: an intermediate or optimum value of the viscosity contrast leads to the highest degree of 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 such flows.

Above: 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.

Above: Concentration fields during transport of two tracer blobs (shown in blue and red colors) within a heterogeneous aquifer saturated with groundwater shown in green color. The tracers are miscible with the water. The flow direction is from left to right and advection-dominated conditions exist. The blobs get stretched with the flow field as they mix with the ambient water. This gives birth to regions of anomalous mixing, which controls the amount of reaction product that will form as a result of chemical reaction between the two tracers.
Above: Displacement of a groundwater contaminant (fluid 2) by the ambient water (fluid 1). Initial condition is shown in the left figure. Middle: contaminant viscosity higher than water. Right: contaminant viscosity lower than water. The contaminant 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.