Dynamics of Fluid Flow through Fracture Networks: A Numerical Approach to Simulate Fluid-Controlled Opening and Closing of Fracture Permeability
Enrique Gomez-Rivas and Paul D. Bons
Department of Geosciences, Eberhard Karls University of Tübingen, Germany
There is strong evidence for non-constant fluid flow in the Earth's crust. For example, huge veins and breccias that formed from fluids considerably hotter than their host rocks (Bons, 2001) or veins formed by the crack-seal mechanism (Ramsay, 1980) are the result of dynamic fluid circulation. Moreover, there is substantial evidence that fluids are overpressured in many sedimentary basins due to the presence of seals. As fluid pressure is one of the main parameters controlling rock failure, pressure differences can lead to the onset of new hydrofractures and/or reactivation of pre-existing ones. In all these systems fluid flow is not only localized in space, along fractures and high permeability beds, but also in time, in the form of fluid pulses.
The transport of fluids through a rock is typically described by the Darcian transport equation. The flux or discharge per unit area depends on a transport coefficient (permeability or hydraulic conductivity) and a driving force (hydraulic head). Most of the current conceptual and numerical fluid flow models are based on an assumed static system with predefined constant permeability and boundary conditions. In such models permeability remains static and it is essentially unaffected by flow. Since permeability is determined by the state of the system (porosity, fracture density, etc.), such models essentially assume that the system is constant and determines the flux as a dependent variable. In geological reality, however, the system (and hence permeability) reacts to flow, for example by sudden opening of hydrofractures or closure of fractures due to mineral precipitation. In the extreme case, it is the flux that determines the state of the system and not vice versa. The dynamic adaptation of the system's flow properties must be included in any model for geological fluid flow. When the reaction of the system to flow is incorporated into experiments or numerical simulations a self-organized critical behavior can emerge (e.g., Miller and Nur, 2000; Bons and van Milligen, 2001). Conceptually, cyclic successions of the following processes take place in a dynamic flow system: (1) build-up of fluid pressure, (2) onset or re-activation of hydrofractures due to fluid overpressure, (3) fracture propagation, (4) fluid flow, (5) drop of fluid pressure and, finally (6) closing of fractures due to the precipitation of minerals from fluids and/or to ductile flow of host rocks.
With the aim of systematically studying crustal-scale dynamic fluid flow, we have developed a new numerical workflow to incorporate the dynamics of self-organized systems. We use the numerical platform Elle as a framework to simulate such systems by looping through three processes: (a) stochastic release of fluid batches at the bottom of the model, (b) dynamic update of the existing fracture permeability and activation of new hydrofractures depending on fluid pressure distribution and (c) Darcian fluid flow through fractures.
The first process is based on the assumption that certain volumes of fluid are produced below the model and are driven up to the base of the model in the form of fluid batches. The frequency, mass of fluid and location of fluid batches are calculated according to a stochastic function. When a new batch of fluid is inserted, fluid pressure is increased at the selected nodes.
For the second process (update fracture permeability) we determine whether each fracture should open or close depending on a driving stress (Ds). This driving stress is defined as the difference between two forces acting at fracture boundaries: (1) fluid pressure and (2) remote normal stress acting perpendicular to the fracture. The remote normal stress includes the lithostatic overburden pressure as well as a normal stress applied by an external far stress field. If, according to this balance of forces, a fracture should open we compute its new aperture using the linear elastic fracture mechanics theory (e.g. Pollard and Segall, 1987). We assume that each fracture segment is a mode I fracture (i.e. crack) in a linear elastic homogeneous and isotropic medium, and we thus calculate the new aperture depending on fracture length, host rock elastic properties (i.e. Yong's modulus) and the driving stress. If, on the contrary, a fracture should close we calculate the new aperture using a time-dependent closure function that incorporates the ductile flow of the host rock and other parameterized processes, like mineral precipitation. It is important to notice that fracture opening is instantaneous in our model, while fracture closing is a time-dependent process.
The third module calculates fluid flow through the fracture network according to the fluid pressure distribution and hydraulic conductivity calculated from fracture apertures. A simple explicit finite difference method is used to compute Darcian flow through fractures and new fluid pressure distribution, which will be used to determine new fracture apertures in the subsequent time step.
With this numerical scheme we have developed series of simulations to understand the principles that operate in dynamic fluid flow systems. The results indicate that fluid flow at the crustal scale can operate as a self-organized system, in which fluid overpressure causes quick fracture propagation and fast release of fluid batches that are rapidly transported upwards to regain equilibrium. The differences in closure rates, which depend on host rock ductile flow rates and fracture closing rates due to mineral precipitation, define a transition from systems that reach a stable permeability, and hence a steady-state fluid flow, to systems in which fracture permeability strongly fluctuates over time. In the first case fractures do not close quickly and the system evolves towards a steady-state. This is the preferred scenario for extensive alterations in which fluids have enough time to invade host rocks from faults. On the contrary, if fractures can close quickly a self-organized pulsating regime can emerge. In such systems fluid flows in avalanches through mobile hydrofractures. These cases can account for localized alterations, like crack-seal veins or hydrothermal mineral deposits along fault zones.
This research work was carried out within the framework of DGMK (German Society for Petroleum and Coal Science and Technology) project 718.
Bons P.D. (2001). The formation of large quartz veins by rapid ascent of fluids in mobile hydrofractures. Tectonophysics 336, 1-17.
Bons P.D., van Milligen B.P. (2001). A new experiment to model self-organized critical transport and accumulation of melt and hydrocarbons from their source rocks. Geology 29, 919-922.
Miller S.A., Nur A. (2000). Permeability as a toggle switch in fluid-controlled crustal processes. Earth and Planetary Science Letters 183, 133-146.
Pollard D.D., Segall P. (1987). Theoretical displacement and stresses near fractures in rock: With applications to faults, joints, veins, dikes and solution surfaces. In: Atkinson, B.K. (ed.), Fracture mechanics of rock. Academic, San Diego, California, pp. 277-350.
Ramsay J.G. 1980. The crack-seal mechanism of rock deformation. Nature 284, 135-9.
AAPG Search and Discovery Article #120034©2012 AAPG Hedberg Conference Fundamental Controls on Flow in Carbonates, Saint-Cyr Sur Mer, Provence, France, July 8-13, 2012