D. W. Vasco

A Bayesian model for gas saturation estimation using marine seismic AVA and CSEM data

We develop a Bayesian model to jointly invert marine seismic amplitude versus angle (AVA) and controlled-source electromagnetic (CSEM) data for a layered reservoir model. We consider the porosity and fluid saturation of each layer in the reservoir, the bulk and shear moduli and density of each layer not in the reservoir, and the electrical conductivity of the overburden and bedrock as random variables. We also consider prestack seismic AVA data in a selected time window as well as real and quadrature components of the recorded electrical field as data. Using Markov chain Monte Carlo (MCMC) sampling methods, wedraw a large number of samples from the joint posterior distribution function. With these samples, we obtain not only the estimates of each unknown variable, but also various types of uncertainty information associated with the estimation. This method is applied to both synthetic and field data to investigate the combined use of seismic AVA and CSEM data for gas saturation estimation. Results show th...

The Northwest Geysers EGS Demonstration Project, California. Pre-stimulation Modeling and Interpretation of the Stimulation

The Northwest Geysers Enhanced Geothermal System (EGS) demonstration project aims to create an EGS by directly and systematically injecting cool water at relatively low pressure into a known High Temperature (280–400xa0°C) Zone (HTZ) located under the conventional (240xa0°C) geothermal steam reservoir at The Geysers geothermal field in California. In this paper, the results of coupled thermal, hydraulic, and mechanical (THM) analyses made using a model developed as part of the pre-stimulation phase of the EGS demonstration project is presented. The model simulations were conducted in order to investigate injection strategies and the resulting effects of cold-water injection upon the EGS system; in particular to predict the extent of the stimulation zone for a given injection schedule. The actual injection began on October 6, 2011, and in this paper a comparison of pre-stimulation model predictions with micro-earthquake (MEQ) monitoring data over the first few months of a one-year injection program is presented. The results show that, by using a calibrated THM model based on historic injection and MEQ data at a nearby well, the predicted extent of the stimulation zone (defined as a zone of high MEQ density around the injection well) compares well with observed seismicity. The modeling indicates that the MEQ events are related to shear reactivation of preexisting fractures, which is triggered by the combined effects of injection-induced cooling around the injection well and small changes in steam pressure as far as half a kilometer away from the injection well. Pressure-monitoring data at adjacent wells and satellite-based ground-surface deformation data were also used to validate and further calibrate reservoir-scale hydraulic and mechanical model properties. The pressure signature monitored from the start of the injection was particularly useful for a precise back-calculation of reservoir porosity. The first few months of reservoir pressure and surface deformation data were useful for estimating the reservoir-rock permeability and elastic modulus. Finally, although the extent of the calculated stimulation zone matches the field observations over the first few months of injection, the observed surface deformations and MEQ evolution showed more heterogeneous behavior as a result of more complex geology, including minor faults and fracture zones that are important for consideration in the analysis of energy production and the long-term evolution of the EGS system.

Inversion of airborne gravity gradient data, southwestern Oklahoma

The diagonal elements of the gravity gradient tensor, as recorded by the Bell airborne Gravity Gradient Survey System (GGSS), are used to determine the basement topography in southwestern Oklahoma. This determination is accomplished through a nonlinear inverse procedure based on the conjugate gradient algorithm. The resulting model contains a ridge of shallow basement material (< or =3.0 km deep) trending east-southeast. This ridge is bounded on the north and the south by basement troughs; the northern trough extends as deep as 10.0 km. The gradient field which results from this model fits most of the GGSS observations within their estimated errors of 12.0 E (1 Eotvos = 10 (super -6) mGal/cm). The model is in general agreement with a set of available oil well depths to the basement and with inferred faults in these igneous rocks. To assess the derived solution, the problem was linearized about the final model and the linear parameter resolution and parameter covariances were computed. Generally, the basement depths are well resolved and the resolution matrix is diagonally dominant. Furthermore, the parameter standard errors are small: 72 parameters out of 98 have errors less than 1.0 km.

Detailed characterization of a fractured limestone formation by use of stochastic inverse approaches

The authors discuss two inverse approaches to construction of fracture-flow models and their application in characterizing a fractured limestone formation. The first approach creates ``equivalent discontinuum`` models that conceptualize the fracture system as a partially filled lattice of conductors that are locally connected or disconnected to reproduce the observed hydrologic behavior. An alternative approach -- i.e., ``variable aperture lattice`` models -- represent the fracture system as a fully filled network composed of conductors of varying apertures or hydraulic conductivities. The fracture apertures are sampled from a specified distribution, usual log-normal, which is consistent with field data. The spatial arrangement of apertures is altered through inverse modeling to fit the available hydrologic data, such as transient pressure and/or tracer data. Unlike traditional discrete fracture-network approaches that rely on fracture geometry to reproduce flow and transport behavior, the inverse methods directly incorporate hydrologic data in deriving the fracture networks and thus naturally emphasize the underlying features that impact fluid flow and transport. However, hydrologic models derived by inversion are nonunique in general. The authors have addressed such nonuniqueness by examining an ensemble of models that satisfy the observation data within acceptable limits. They then determine properties that are shared by the ensemblemorexa0» of models and their associated uncertainties to create a conceptual model of the fracture system. They show the fracture-flow model to be consistent with geophysical imaging.«xa0less

On the Sensitivity and Spatial Resolution of Transient Pressure and Tracer Data For Heterogeneity Characterization

This paper examines the sensitivities of interwell tracer and transient pressure response to spatial distribution of permeability heterogeneity. Based on the sensitivities, we describe a formalism to quantify the spatial resolution and averaging (smearing) associated with estimates of permeabilities derived through inversion of tracer and/or pressure data. The spatial resolution is a measure of the effectiveness of the data in estimating local-scale (grid block) permeabilities. The averaging kernels quantify the inherent averaging associated with our estimates due to limited data or sampling. By examining the spatial resolution and averaging kernels as a function of various data types, we can quantitatively evaluate the relative importance of tracer versus pressure data for heterogeneity characterization and the improvement in estimates obtained by combining the data types. We illustrate the concepts by application to a quarter five-spot geometry and also to an experimental tracer response from a well-characterized slab of Antolini sandstone. Tracer data is found to yield much better resolution compared to transient pressure response. Also, both transient pressure data and tracer data appear to better resolve barriers to flow rather than channels to flow.

Joint inversion of seismic AVO and EM data for gas saturation estimation using a sampling- based stochastic model

Summary A stochastic model is developed to estimate gas saturation and porosity using seismic AVO and EM data. Markov chain Monte Carlo (MCMC) sampling methods are used to obtain posterior probability density functions of unknown parameters constrained by seismic AVO and EM data and prior information. Unlike conventional inverse methods, which search for an optimal solution giving the smallest misfit, MCMC methods estimate probability density functions of unknown gas saturation and porosity. This allows for evaluation of uncertainty as well as estimation of those parameters. A synthetic study, typical of gas exploration in the deep water of the Gulf of Mexico, is developed to demonstrate the benefits of joint inversion of seismic AVO and EM data. Results show that the inclusion of EM data reduces the uncertainty and ambiguity in gas saturation and porosity estimation.

Characterization of a fracture zone using seismic attributes at the In Salah CO2 storage project

AbstractThe In Salah carbon dioxide storage project in Algeria has injected more than 3 million tons of carbon dioxide into a water-filled tight-sand formation. During injection, interferometric synthetic aperture radar (InSAR) reveals a double-lobed pattern of up to a 20-mm surface uplift above the horizontal leg of an injection well. Interpretation of 3D seismic data reveals the presence of a subtle linear push-down feature located along the InSAR determined surface depression between the two lobes, which we interpreted to have to be caused by anomalously lower velocity from the fracture zone and the presence of CO2 displacing brine in this feature. To enhance the seismic interpretation, we calculated many poststack seismic attributes, including positive and negative curvatures as well as ant track, from the 3D seismic data. The maximum positive curvature attributes and ant track found the clearest linear features, with two parallel trends, which agreed well with the ant-track volume and the InSAR obser...

Changes in geophysical properties caused by fluid injection into porous rocks: analytical models

ABSTRACT Analytical models are provided that describe how the elastic compliance, electrical conductivity, and fluid‐flow permeability of rocks depend on stress and fluid pressure. In order to explain published laboratory data on how seismic velocities and electrical conductivity vary in sandstones and granites, the models require a population of cracks to be present in a possibly porous host phase. The central objective is to obtain a consistent mean‐field analytical model that shows how each modeled rock property depends on the nature of the crack population. The crack populations are described by a crack density, a probability distribution for the crack apertures and radii, and the averaged orientation of the cracks. The possibly anisotropic nature of the elasticity, conductivity, and permeability tensors is allowed for; however, only the isotropic limit is used when comparing to laboratory data. For the transport properties of conductivity and permeability, the percolation effect of the crack population linking up to form a connected path across a sample is modeled. However, this effect is important only in crystalline rock where the host phase has very small conductivity and permeability. In general, the importance of the crack population to the transport properties increases as the host phase becomes less conductive and less permeable.

On the propagation of a disturbance in a heterogeneous, deformable, porous medium saturated with two fluid phases

On the propagation of a disturbance in a heterogeneous, deformable, porous medium saturated with two fluid phases D. W. Vasco and Susan E. Minkoff There are several ways to approach the coupled model- ing of deformation and multi-phase fluid flow in a hetero- geneous porous medium, each with its own advantages and limitations. A numerical method is the most general, and there are several studies based upon numerical techniques (Noorishad et al. 1992, Rutqvist et al. 2002, Minkoff et al. 2003, Minkoff et al. 2004, Dean et al. 2006). Numerical methods can require significant computer resources, both CPU time and computer memory. Also, numerical meth- ods have difficulty modeling the wide range of behaviors in the coupled multiphase problem, which can include hy- perbolic elastic wave propagation as well as fluid diffusion, involving a broad range of time scales: from milli-seconds to hours or even days. Numerical methods tailored to seis- mic frequencies can improve the computational efficiency (Masson et al. 2006) but still face challenges in treat- ing multiple fluid phases and three-dimensional problems. Finally, numerical methods do not provide explicit expres- sions for observed quantities such as the arrival time of a propagating disturbance or its amplitude. Analytic meth- ods can be efficient and can provide explicit expressions for observed quantities. However, analytic methods are typically limited to relatively simple situations, such as a homogeneous half-space and a single fluid phase (Levy 1979, Simon et al. 1984, Gajo and Mongiovi 1995). As the medium is generalized, for example by including lay- ering, analytic methods become increasingly complicated and require significantly more computation time, facing the same limitations as numerical techniques (Wang and Kumpel 2003). Thus, analytic methods may not provide the generality required for solving commonly encountered inverse problems. For example, in many inverse problems one is interested in determining smoothly-varying hetero- geneous properties in a three-dimensional setting. In this paper we formulate and validate governing equa- tions for deformation in a porous medium containing two fluid phases and present an asymptotic, semi-analytic tech- nique for their solution. The equations, presented below, are generalizations of those for a medium containing a sin- ABSTRACT The coupled modeling of the flow of two immiscible fluid phases in a heterogeneous, elastic, porous mate- rial is formulated in a manner analogous to that for a single fluid phase. An asymptotic technique, valid when the heterogeneity is smoothly-varying, is used to derive equations for the phase velocities of the various modes of propagation. A cubic equation is associated with the phase velocities of the longitudinal modes. The coefficients of the cubic equation are expressed in terms of sums of the determinants of 3 ×3 matrices whose elements are the parameters found in the gov- erning equations. In addition to the three longitudinal modes, there is a transverse mode of propagation, a generalization of the elastic shear wave. Estimates of the phase velocities for a homogeneous medium, based upon the formulas in this paper, agree with previ- ous studies. Furthermore, predictions of longitudinal and transverse phase velocities, made for the Massilon sandstone containing varying amounts of air and water, are compatible with laboratory observations. INTRODUCTION Multiphase flow is an important physical process that underlies many critical activities such as waste disposal, geothermal production, oil and gas production, agricul- ture, and ground water management. Geophysical imag- ing methods are increasingly used to monitor the flow of fluids and gases in the subsurface (Calvert 2005, Rubin and Hubbard 2006). Therefore, it is important to have accurate and efficient techniques for modeling wave prop- agation in heterogeneous porous media saturated by one or more fluid phases. It is particularly helpful to have methods that provide insight into the the various physical factors controlling the propagation of a wave in a poroe- lastic medium.

Trajectory-based modeling of fluid transport in a medium with smoothly varying heterogeneity

© 2016. American Geophysical Union. All Rights Reserved. Using an asymptotic methodology, valid in the presence of smoothly varying heterogeneity and prescribed boundaries, we derive a trajectory-based solution for tracer transport. The analysis produces a Hamilton-Jacobi partial differential equation for the phase of the propagating tracer front. The trajectories follow from the characteristic equations that are equivalent to the Hamilton-Jacobi equation. The paths are determined by the fluid velocity field, the total porosity, and the dispersion tensor. Due to their dependence upon the local hydrodynamic dispersion, they differ from conventional streamlines. This difference is borne out in numerical calculations for both uniform and dipole flow fields. In an application to the computational X-ray imaging of a saline tracer test, we illustrate that the trajectories may serve as the basis for a form of tracer tomography. In particular, we use the onset time of a change in attenuation for each volume element of the X-ray image as a measure of the arrival time of the saline tracer. The arrival times are used to image the spatial variation of the effective hydraulic conductivity within the laboratory sample.