We describe a numerical investigation of seismicity induced by injection into a single isolated fracture. Injection into a single isolated fracture is a simple analog for shear stimulation in enhanced geothermal systems (EGS) during which water is injected into fractured, low permeability rock, triggering slip on preexisting large scale fracture zones. A model was developed and used that couples (1) fluid flow, (2) rate and state friction, and (3) mechanical stress interaction between fracture elements. Based on the results of this model, we propose a mechanism to describe the process by which the stimulated region grows during shear stimulation, which we refer to as the sequential stimulation (SS) mechanism. If the SS mechanism is realistic, it would undermine assumptions that are made for the estimation of the minimum principal stress and unstimulated hydraulic diffusivity. We investigated the effect of injection pressure on induced seismicity. For injection at constant pressure, there was not a significant dependence of maximum event magnitude on injection pressure, but there were more relatively large events for higher injection pressure. Decreasing injection pressure over time significantly reduced the maximum event magnitude. Significant seismicity occurred after shut-in, which was consistent with observations from EGS stimulations. Production of fluid from the well immediately after injection inhibited shut-in seismic events. The results of the model in this study were found to be broadly consistent with results from prior work using a simpler treatment of friction that we refer to as static/dynamic. We investigated the effect of shear-induced pore volume dilation and the rate and state characteristic length scale, [Formula: see text]. Shear-induced pore dilation resulted in a larger number of lower magnitude events. A larger value of [Formula: see text] caused slip to occur aseismically.

No abstract

Spontaneous water imbibition into gas-saturated rocks is an important physical process during water injection into highly fractured petroleum and geothermal reservoirs. Few methods, however, are available for characterizing the process of spontaneous water imbibition into gas-saturated rocks. To this end, a method has been developed. Water relative permeability and capillary pressure can be calculated separately from water imbibition data using this method. A linear relationship between imbibition rate and the reciprocal of the gas recovery by spontaneous water imbibition was found and confirmed both theoretically and experimentally, even at different initial water saturations. The effect of initial water saturation on imbibition rate, residual gas saturation, and the gas recovery has been investigated. There was almost no effect of initial water saturation on residual gas saturation by spontaneous water imbibition. The higher the initial water saturation, the lower the water imbibition rate and the ultimate gas recovery. It was found that the capillary pressure did not vary with initial water saturation in a certain range. The capillary pressure calculated using the new method was approximately equal to the values measured using an X-ray CT technique in a glass-bead pack. The computed water relative permeability was consistent with published experimental results. The method developed in this paper is also of importance for scaling-up experimental data.

A method was developed to scale the experimental data of spontaneous water imbibition (cocurrent) for gas/water/rock systems. In this method, a dimensionless time was defined with the effects of relative permeability, wettability, and gravity included. The definition was not empirical but based on a theoretical derivation. Using this dimensionless time, experimental data from spontaneous water imbibition in different rocks with different size, porosity, permeability, initial water saturation, interfacial tension, and wettability might be scaled. The scaling model proposed in this study for gas/water/rock systems was verified experimentally for different rocks (Berea, chalk, and graywacke from The Geysers) with significantly different properties; it was also verified experimentally at different initial water saturations in the same rock. The scaling results from this study demonstrated that the cocurrent spontaneous water imbibition in gas/water/rock systems could be scaled and predicted.

[1] Two-phase flow through fractured media is important in geothermal, nuclear, and petroleum applications. In this research an experimental apparatus was built to capture the unstable nature of the two-phase flow in a smooth-walled fracture and display the flow structures under different flow configurations in real time. The air-water relative permeability was obtained from experiment and showed deviation from the X curve behavior suggested by earlier studies. Through this work the relationship between the phase channel morphology and relative permeability in fractures was determined. A physical tortuous channel approach was proposed to quantify the effects of the flow structure. This approach could replicate the experimental results with a good accuracy. Other relative permeability models (viscous coupling model, X curve model, and Corey curve model) were also compared. Except for the viscous coupling model, these models did not interpret the experimental relative permeabilities as well as the proposed tortuous channel model. Hence we concluded that the two-phase relative permeability in fractures depends not only on liquid type and fracture geometry but also on the structure of the two-phase flow.

Scaling the experimental data of spontaneous imbibition without serious limitations has been difficult. To this end, a general approach was developed to scale the experimental data of spontaneous imbibition for most systems (gas/liquid/rock and oil/water/ rock systems) in both cocurrent and countercurrent cases. We defined a dimensionless time with almost all the parameters considered. These include porosity, permeability, size, shape, boundary conditions, wetting-and nonwetting-phase relative permeabilities, interfacial tension (IFT), wettability, and gravity. The definition of the dimensionless time was not empirical; instead, it was based on theoretical analysis of the fluid-flow mechanisms that govern spontaneous imbibition. The general scaling method was confirmed against the experimental data from spontaneous water imbibition conducted at different IFTs in oil-saturated rocks with different sizes and permeabilities. A general analytical solution to the relationship between recovery and imbibition time for linear spontaneous imbibition was derived. The analytical solution predicts a linear correlation between the imbibition rate and the reciprocal of the recovery by spontaneous imbibition in most fluid/ fluid/rock systems. IntroductionAn important fluid-flow phenomenon during water injection or aquifer invasion into reservoirs is spontaneous water imbibition. Scaling the experimental data of spontaneous water imbibition in different fluid/fluid/rock systems is of essential importance in designing the water-injection projects and predicting the reservoir production performances. Ignoring the effects of relative permeability, capillary pressure, and gravity in the dimensionless time might be the reason that the existing scaling methods do not always function successfully. It is known that these parameters influence the spontaneous imbibition in porous media significantly. For that reason, these parameters should be honored properly in the scaling.Many papers have been published to characterize and scale spontaneous water imbibition in both oil/water/rock systems (Li et al.

The stability of natural convective flow in a porous medium heated both uniformly and non-uniformly from below is studied in order to determine the possibility of oscillatory and other unsteady flows, and to explore the conditions under which they may occur. The results of the numerical work are directly comparable with experiments using a Hele Shaw cell and also, in the uniformly heated case, with the results of Combarnous & Le Fur (1969) and Caltagirone, Cloupeau & Combarnous (1971). It is shown that for the uniformly heated problem there exist, in certain cases, two distinct possible modes of flow, one of which is fluctuating, the other being steady. However in the non-uniformly heated case the boundary conditions force the solution into a unique mode of flow which is regularly oscillatory when there is considerable non-uniformity in the heat input at the lower boundary, provided that the Rayleigh number is sufficiently high.

[1] The Brooks and Corey relative permeability model has been accepted widely as a way to calculate relative permeability using capillary pressure data. However, the Purcell model was found to be the best fit to the experimental data of the wetting-phase relative permeability in the cases studied here, as long as the measured capillary pressure curve had the same residual saturation as the relative permeability curve. The differences between the experimental data of relative permeability and the data calculated using the Purcell relative permeability model for the wetting phase were almost negligible. A physical model was developed to explain the insignificance of the effect of tortuosity on the calculation of the wetting-phase relative permeability. For the nonwetting-phase, the relative permeabilities calculated using the models were very close to the experimental values in drainage except for the Purcell model. However, in the case of imbibition, the relative permeabilities calculated using the models were different from the experimental data. This study showed that relative permeability could be calculated satisfactorily by choosing a suitable model, especially in drainage processes. In the reverse procedure, capillary pressure could also be computed once relative permeability data are available.