David Randell

Locating and quantifying gas emission sources using remotely obtained concentration data

We describe a method for detecting, locating and quantifying sources of gas emissions to the atmosphere using remotely obtained gas concentration data; the method is applicable to gases of environmental concern. We demonstrate its performance using methane data collected from aircraft. Atmospheric point concentration measurements are modelled as the sum of a spatially and temporally smooth atmospheric background concentration, augmented by concentrations due to local sources. We model source emission rates with a Gaussian mixture model and use a Markov random eld to represent the atmospheric background concentration component of the measurements. A Gaussian plume atmospheric eddy dispersion model represents gas dispersion between sources and measurement locations. Initial point estimates of background concentrations and source emission rates are obtained using mixed‘2-‘1 optimisation over a discretised grid of potential source locations. Subsequent reversible jump Markov chain Monte Carlo inference provides estimated values and uncertainties for the number, emission rates and locations of sources unconstrained by a grid. Source area, atmospheric background concentrations and other model parameters, including plume model spreading and Lagrangian turbulence time scale, are also estimated. We investigate the performance of the approach rst using a synthetic problem, then apply the method to real airborne data from a 1600km 2 area containing two landlls,

Estimation of Storm Peak and Intrastorm Directional–Seasonal Design Conditions in the North Sea

Specification of realistic environmental design conditions for marine structures is of fundamental importance to their reliability over time. Design conditions for extreme waves and storm severities are typically estimated by extreme value analysis of time series of measured or hindcast significant wave height, HS. This analysis is complicated by two effects. Firstly, HS exhibits temporal dependence. Secondly, the characteristics of H sp S are non-stationary with respect to multiple covariates, particularly wave direction and season. We develop directional-seasonal design values for storm peak significant wave height (H sp S ) by estimation of, and simulation under a non-stationary extreme value model for H sp S . Design values for significant wave height (HS) are estimated by simulating storm trajectories of HS consistent with the simulated storm peak events. Design distributions for individual maximum wave height (Hmax) are estimated by marginalisation using the known conditional distribution for Hmax given HS. Particular attention is paid to the assessment of model bias and quantification of model parameter and design value uncertainty using bootstrap resampling. We also outline existing work on extension to estimation of maximum crest elevation and total extreme water level.

Fibre Optic Sensing For Improved Wellbore Production Surveillance

Since our previous publication1 significant progress has been made to further mature the application of Fiber-Optic (FO) based Distributed Acoustic Sensing (DAS) for production and injection profiling. A considerable number of new field surveys were conducted to further improve the evaluation algorithms or workflows which convert the DAS noise recordings into flowrates from individual zones. For gas producing wells, a new graphical user-interface has been developed that allows the user to visualize and QC the data in real time. Additional flow and visualization software have been developed for single phase gas producers to enable the user to select and evaluate the data in a user-friendly manner using the most up-to-date evaluation algorithms. There are still improvements to be made in enabling Distributed Sensing infrastructure, such as handling and evaluation of very large data volumes, seamless FO data transfer, the robustness & cost of the FO system installation, and the overall integration of FO surveillance into traditional workflows. It will take some time before all these issues are addressed but we believe that FO based applications will play a key role in future well and reservoir surveillance. In this paper we present two recent examples of single-phase flow profiling using DAS. The first example is from a single-phase gas producer in one of the Unconventional plays in North America and the second example is from a long horizontal, smart polymer injector operated by Petroleum Development Oman (PDO).

Modelling Covariate Effects in Extremes of Storm Severity on the Australian North West Shelf

Careful modelling of covariate effects is critical to reliable specification of design criteria. We present a spline based methodology to incorporate spatial, directional, temporal and other covariate effects in extreme value models for environmental variables such as storm severity. For storm peak significant wave height events, the approach uses quantile regression to estimate a suitable extremal threshold, a Poisson process model for the rate of occurrence of threshold exceedances, and a generalised Pareto model for size of threshold . Multidimensional covariate effects are incorporated at each stage using penalised tensor products of B-splines to give smooth model parameter variation as a function of multiple covariates. Optimal smoothing penalties are selected using cross-validation, and model uncertainty is quantified using a bootstrap resampling procedure. The method is applied to estimate return values for a large spatial neighbourhood of locations off the North West Shelf of Australia, incorporating spatial and directional effects.

Fast computation of large scale marginal extremes with multi-dimensional covariates

Safe and reliable design and operation of fixed and floating marine structures often located in remote and hostile environments is challenging. Rigorous extreme value analysis of meteorological and oceanographic data can greatly aid the design of such structures. Extreme value analysis is typically undertaken for single spatial locations or for small neighbourhoods; moreover, non-stationary effects of covariates on extreme values are typically accommodated in an ad-hoc manner. The objective of the work summarised here is to improve design practice by estimating environmental design conditions (such as return values for extreme waves, winds and currents) for a whole ocean basin, including additional covariate effects (such as storm direction) as necessary, in a consistent manner. Whole-basin non-stationary extreme value modelling is computationally complex, requiring inter-alia the estimation of tail functions, the parameters of which vary with respect to multi-dimensional covariates characterised by us using tensor products of penalised B-splines. We outline two technical contributions which make whole-basin non-stationary analysis feasible. Firstly, we adopt generalised linear array methods to reduce the computational burden of matrix manipulations. Secondly, using high-performance computing, we develop a parallel implementation of maximum likelihood estimation for the generalised Pareto distribution. Together, these innovations allow estimation of rigorous whole-basin extreme value models in reasonable time. We evaluate the new approach in application to marginal extreme value modelling of storm peak significant wave heights in two ocean basins, accommodating spatial and directional covariate effects.

NON-STATIONARY ESTIMATION OF JOINT DESIGN CRITERIA WITH A MULTIVARIATE CONDITIONAL EXTREMES APPROACH

Understanding the interaction of ocean environments with fixed and floating structures is critical to the design of offshore and coastal facilities. Structural response to environmental loading is typically the combined effect of multiple environmental parameters over a period of time. Knowledge of the tails of marginal and joint distributions of these parameters (e.g. storm peak significant wave height and associated current) as a function of covariates (e.g. dominant wave and current directions) is central to the estimation of extreme structural response, and hence of structural reliability and safety. In this paper, we present a framework for the joint estimation of multivariate extremal dependencies with multi-dimensional covariates. We demonstrate proof of principle with a synthetic bi-variate example with two covariates quantified by rigorous uncertainty analysis. We further substantiate it using two practical applications (associated current given significant wave height for northern North Sea and joint current profile for offshore Brazil locations). Further applications include the estimation of associated criteria for response-based design (e.g., TP given HS), extreme current profiles with depth for mooring and riser loading, weathervaning systems with non-stationary effects for the design of FLNG/FPSO installations, etc. Copyright

Consistent Design Criteria for South China Sea With a Large-Scale Extreme Value Model

Existing metocean design criteria for offshore facilities in the South China Sea have been estimated using different data and procedures, some of which are at least partly ad hoc. As a result, it is probable that existing criteria are inconsistent, in the sense that assets designed to the same design codes have different realised levels of integrity. To address this concern in this paper, we apply a large-scale extreme value model adapted to parallel computing environment, applied to the recent high-resolution SEAFINE hindcast database. This not only ensures design criteria that are statistically and spatially consistent but is also faster by avoiding the need for repetitive site-specific analysis. We have to overcome several challenges before we can apply a large-scale extreme model on the SEAFINE database. These include identifying a spatially consistent set of storm peaks and validating the hindcast data with real measurements. We then estimate marginal return values for significant wave height for locations within a large spatial neighbourhood, accounting for spatial and storm directional variability of peaks over threshold. A quantile regression identifies the extreme value threshold, the rate of exceedance of which is described using a Poisson process. The size of threshold exceedances is described by a generalised Pareto model. The characteristics of the threshold, rate and size models are all non-stationary with respect to directional and spatial covariates, parameterised in terms of (multidimensional) penalised B-splines. Parameter estimation is computationally challenging, but a combination of efficient generalised linear array algorithms executed within a parallel computing environment enable maximum likelihood estimation of all models. Bootstrap resampling is used to estimate uncertainties of model parameters and return values. We thus estimate consistent marginal return values for significant wave height and their uncertainties, at all locations in the spatial neighbourhood. In addition, we quantify directional variability of return values across different return periods. We rigorously validate the proposed spatiodirectional model with that of a direction-only model by deriving model diagnostics for the same site and demonstrating equivalent goodness of fits. To our knowledge this is the first of a kind of application of large-scale estimation for the South China Sea. With this approach, design criteria for large spatial domains, non-stationary with respect to the appropriate environmental covariates, can be estimated efficiently, consistently and with quantified uncertainty.

Threshold Modeling of Nonstationary Extremes

It is common for extremes of a variable to be nonstationary, varying systemati cally with covariate values. We consider the incorporation of covariate effects into threshold-based extreme value models, using parametric and nonparametric regres sion functions. We use quantile regression to set a covariate-dependent threshold. As an example we model storm peak significant wave heights as a function of storm direction, season, and a climate index.

Estimation of Storm Peak and Intra-Storm Directional-Seasonal Design Conditions in the North Sea

Specification of realistic environmental design conditions for marine structures is of fundamental importance to their reliability over time. Design conditions for extreme waves and storm severities are typically estimated by extreme value analysis of time series of measured or hindcast significant wave height, HS. This analysis is complicated by two effects. Firstly, HS exhibits temporal dependence. Secondly, the characteristics of Display FormulaHSsp are non-stationary with respect to multiple covariates, particularly wave direction and season.We develop directional-seasonal design values for storm peak significant wave height (Display FormulaHSsp) by estimation of, and simulation under a non-stationary extreme value model for Display FormulaHSsp. Design values for significant wave height (HS) are estimated by simulating storm trajectories of HS consistent with the simulated storm peak events. Design distributions for individual maximum wave height (Hmax) are estimated by marginalisation using the known conditional distribution for Hmax given HS. Particular attention is paid to the assessment of model bias and quantification of model parameter and design value uncertainty using bootstrap resampling. We also outline existing work on extension to estimation of maximum crest elevation and total extreme water level.Copyright

Omnidirectional return values for storm severity from directional extreme value models: the effect of physical environment and sample size

Ewans and Jonathan [2008] shows that characteristics of extreme storm severity in the northern North Sea vary with storm direction. Jonathan et al. [2008] demonstrates, when directional effects are present, that omnidirectional return values should be estimated using a directional extreme value model. Omnidirectional return values so calculated are different in general to those estimated using a model which incorrectly assumes stationarity (or inhomogeneity) with respect to direction. The extent of directional variability of extreme storm severity depends on a number of physical factors, including fetch variability. Our ability to assess directional variability of extreme value parameters and return values also improves with increasing sample size in general. In this work, we estimate directional extreme value models for samples of hindcast storm peak significant wave height from locations in ocean basins worldwide, for a range of physical environments, sample sizes and periods of observation. At each location, we compare distributions of omnidirectional 100-year return values estimated using a directional model, to those (incorrectly) estimated assuming stationarity. The directional model for peaks over threshold of storm peak significant wave height is estimated using a non-homogeneous point process model as outlined in Randell et al. [2013]. Directional models for extreme value threshold (using quantile regression), rate of occurrence of threshold exceedances (using a Poisson model), and size of exceedances (using a generalised Pareto model) are estimated. Model parameters are described as smooth functions of direction using periodic B-splines. Parameter estimation is performed using maximum likelihood estimation penalised for parameter roughness. A bootstrap re-sampling procedure, encompassing all inference steps, quantifies uncertainties in, and dependence structure of, parameter estimates and omnidirectional return values. Physical environment has a large effect on estimated distributions of 100-year return values; the most severe environments of those considered are the Gulf of Mexico and northern North Sea. However, when return value distributions are normalised relative to their median values, the (normalised) return value distributions for all locations considered are remarkably similar. Moreover, once the effect of sample size is accounted for, the widths of return value distributions (quantified in terms of the inter-quartile range) are also remarkably consistent. The effect on estimated return value distributions of neglecting the influence of nonstationarity at different stages of the extreme value modelling procedure is unpredictable; a fully non-stationary model is recommended. In general, accommodating non-stationarity in extreme value threshold and rate of occurrence of threshold exceedance appears most critical.