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Donald L. Turcotte

Publications and source records attributed to Donald L. Turcotte.

10 recordsLinked to original sources
arXiv2015

A damage model for fracking

Injections of large volumes of water into tight shale reservoirs allows the extraction of oil and gas not previously accessible. This large volume "super" fracking induces damage that allows the oil and/or gas to flow to an extraction well. The purpose of this paper is to provide a model for understanding super fracking. We assume that water is injected from a small spherical cavity into a homogeneous elastic medium. The high pressure of the injected water generates hoop stresses that reactivate natural fractures in the tight shales. These fractures migrate outward as water is added creating a spherical shell of damaged rock. The porosity associated with these fractures is equal to the water volume injected. We obtain an analytic expression for this volume. We apply our model to a typical tight shale reservoir and show that the predicted water volumes are in good agreement with the volumes used in super fracking.

physics.geo-ph↗
arXiv2014

Anisotropy in Fracking: A Percolation Model for Observed Microseismicity

Hydraulic fracturing (fracking) using high pressures and a low viscosity fluid allow the extraction of large quantiles of oil and gas from very low permeability shale formations. The initial production of oil and gas at depth leads to high pressures and an extensive distribution of natural fractures which reduce the pressures. With time these fractures heal, sealing the remaining oil and gas in place. High volume fracking opens the healed fractures allowing the oil and gas to flow the horizontal productions wells. We model the injection process using invasion percolation. We utilize a 2D square lattice of bonds to model the sealed natural fractures. The bonds are assigned random strengths and the fluid, injected at a point, opens the weakest bond adjacent to the growing cluster of opened bonds. Our model exhibits burst dynamics in which the clusters extends rapidly into regions with weak bonds. We associate these bursts with the microseismic activity generated by fracking injections. A principal object of this paper is to study the role of anisotropic stress distributions. Bonds in the $y$-direction are assigned higher random strengths than bonds in the $x$-direction. We illustrate the spatial distribution of clusters and the spatial distribution of bursts (small earthquakes) for several degrees of anisotropy. The results are compared with observed distributions of microseismicity in a fracking injection. Both our bursts and the observed microseismicity satisfy Gutenberg-Richter frequency-size statistics.

physics.geo-ph↗
arXiv2014

Loopless non-trapping invasion percolation model for fracking

Recent developments in hydraulic fracturing (fracking) have enabled the recovery of large quantities of natural gas and oil from old, low permeability shales. These developments include a change from low-volume, high-viscosity fluid injection to high-volume, low-viscosity injection. The injected fluid introduces distributed damage that provides fracture permeability for the extraction of the gas and oil. In order to model this process, we utilize a loopless non-trapping invasion percolation previously introduced to model optimal polymers in a strongly disordered medium, and for determining minimum energy spanning trees on a lattice. We performed numerical simulations on a 2D square lattice and find significant differences from other percolation models. Additionally, we find that the growing fracture network satisfies both Horton-Strahler and Tokunaga network statistics. As with other invasion percolation models, our model displays burst dynamics, in which the cluster extends rapidly into a connected region. We introduce an alternative definition of bursts to be a consecutive series of opened bonds whose strengths are all below a specified value. Using this definition of bursts, we find good agreement with a power-law frequency-area distribution. These results are generally consistent with the observed distribution of microseismicity observed during a high-volume frack.

physics.geo-ph↗
arXiv2010

A damage model based on failure threshold weakening

A variety of studies have modeled the physics of material deformation and damage as examples of generalized phase transitions, involving either critical phenomena or spinodal nucleation. Here we study a model for frictional sliding with long range interactions and recurrent damage that is parameterized by a process of damage and partial healing during sliding. We introduce a failure threshold weakening parameter into the cellular-automaton slider-block model which allows blocks to fail at a reduced failure threshold for all subsequent failures during an event. We show that a critical point is reached beyond which the probability of a system-wide event scales with this weakening parameter. We provide a mapping to the percolation transition, and show that the values of the scaling exponents approach the values for mean-field percolation (spinodal nucleation) as lattice size $L$ is increased for fixed $R$. We also examine the effect of the weakening parameter on the frequency-magnitude scaling relationship and the ergodic behavior of the model.

physics.geo-ph↗
arXiv2006

Space-Time Clustering and Correlations of Major Earthquakes

Earthquake occurrence in nature is thought to result from correlated elastic stresses, leading to clustering in space and time. We show that occurrence of major earthquakes in California correlates with time intervals when fluctuations in small earthquakes are suppressed relative to the long term average. We estimate a probability of less than 1% that this coincidence is due to random clustering.

physics.data-an↗
arXiv2005

A RELM earthquake forecast based on pattern informatics

We present a RELM forecast of future earthquakes in California that is primarily based on the pattern informatics (PI) method. This method identifies regions that have systematic fluctuations in seismicity, and it has been demonstrated to be successful. A PI forecast map originally published on 19 February 2002 for southern California successfully forecast the locations of sixteen of eighteen M>5 earthquakes during the past three years. The method has also been successfully applied to Japan and on a worldwide basis. An alternative approach to earthquake forecasting is the relative intensity (RI) method. The RI forecast map is based on recent levels of seismic activity of small earthquakes. Recent advances in the PI method show considerable improvement, particularly when compared with the RI method using relative operating characteristic (ROC) diagrams for binary forecasts. The RELM application requires a probability for each location for a number of magnitude bins over a five year period. We have therefore constructed a hybrid forecast in which we combine the PI method with the RI method to compute a map of probabilities for events occurring at any location, rather than just the most probable locations. These probabilities are further converted, using Gutenberg-Richter scaling laws, to anticipated rates of future earthquakes that can be evaluated using the RELM test.

physics.geo-ph↗
arXiv2005

Earthquake forecasting and its verification

No proven method is currently available for the reliable short time prediction of earthquakes (minutes to months). However, it is possible to make probabilistic hazard assessments for earthquake risk. These are primarily based on the association of small earthquakes with future large earthquakes. In this paper we discuss a new approach to earthquake forecasting. This approach is based on a pattern informatics (PI) method which quantifies temporal variations in seismicity. The output is a map of areas in a seismogenic region (``hotspots'') where earthquakes are forecast to occur in a future 10-year time span. This approach has been successfully applied to California, to Japan, and on a worldwide basis. These forecasts are binary--an earthquake is forecast either to occur or to not occur. The standard approach to the evaluation of a binary forecast is the use of the relative operating characteristic (ROC) diagram, which is a more restrictive test and less subject to bias than maximum likelihood tests. To test our PI method, we made two types of retrospective forecasts for California. The first is the PI method and the second is a relative intensity (RI) forecast based on the hypothesis that future earthquakes will occur where earthquakes have occurred in the recent past. While both retrospective forecasts are for the ten year period 1 January 2000 to 31 December 2009, we performed an interim analysis 5 years into the forecast. The PI method out performs the RI method under most circumstances.

cond-mat.stat-mech↗
arXiv2005

A model for the distribution of aftershock waiting times

In this work the distribution of inter-occurrence times between earthquakes in aftershock sequences is analyzed and a model based on a non-homogeneous Poisson (NHP) process is proposed to quantify the observed scaling. In this model the generalized Omori's law for the decay of aftershocks is used as a time-dependent rate in the NHP process. The analytically derived distribution of inter-occurrence times is applied to several major aftershock sequences in California to confirm the validity of the proposed hypothesis.

physics.geo-ph↗
arXiv2005

Inter-arrival time distribution for the non-homogeneous Poisson process

We derive an analytical expression of the inter-arrival time distribution for a non-homogeneous Poisson process (NHPP). This expression is exact and is applicable to any time interval, finite or infinite. As an illustration, we present simulation results for three different intensity functions.

cond-mat.stat-mech↗