Vasily Demyanov

Uncertainty quantification for porous media flows

Uncertainty quantification is an increasingly important aspect of many areas of computational science, where the challenge is to make reliable predictions about the performance of complex physical systems in the absence of complete or reliable data. Predicting flows of oil and water through oil reservoirs is an example of a complex system where accuracy in prediction is needed primarily for financial reasons. Simulation of fluid flow in oil reservoirs is usually carried out using large commercially written finite difference simulators solving conservation equations describing the multi-phase flow through the porous reservoir rocks. This paper examines a Bayesian Framework for uncertainty quantification in porous media flows that uses a stochastic sampling algorithm to generate models that match observed data. Machine learning algorithms are used to speed up the identification of regions in parameter space where good matches to observed data can be found.

History matching and uncertainty quantification: multiobjective particle swarm optimisation approach

Quantifying uncertainty in hydrocarbon production forecasts is critical in the petroleum industry because of the dominant role uncertainty quantification plays in reservoir management decisions. An efficient application of global optimisation methods to history matching and uncertainty quantification of real complex reservoirs has been an extensively an active area of research. The goals of these methods are to navigate the parameter space for multiple good fitting models quickly and identify as many different optima as possible. Obtaining multiple optima can result in an ensemble of history matches that has divergent prediction profiles for more accurate and reliable predictive uncertainty estimates. The present study extends the application of particle swarm optimisation to handle multi-objective optimisation in reservoir history matching context. Previous research studies in assisted history matching primarily focused on optimising a single objective function in which all the production data coming from the wells are aggregated into a single misfit value. The single misfit value is constructed by summing the weighted squared differences between historical and simulated production data. In the multiobjective optimisation scheme, multiple objectives can be defined representing each or some of the weighted squared difference of a production type. By constructing multiple objectives that measure the contribution of each objective in the multi-objective optimisation scheme, it can be possible to find a set of solutions which optimally balances the different objectives simultaneously while maintaining solution diversity. The advantage of this construction is that the tradeoffs between the objectives can be explored and explicitly exploited in the course of optimisation to find all possible combination of good fitting model solutions that have similar match quality. In history matching, it is desirable to have various solutions that map to relatively similar low misfit values that can represent all the possible geological scenarios. The new multi-objective particle swarm optimisation uses a crowding distance mechanism jointly with a mutation operator to preserve the diversity of solutions. In this paper, the multi-objective particle swarm optimisation scheme has been investigated on history matching a well-known synthetic reservoir simulation model and the results were compared with a single objective methodology. Analyses of history matching quality and predictive uncertainty estimation based on the resulted models have been conducted to obtain the uncertainty predictions envelopes for both strategies. The comparative results suggest that, for the reservoir under consideration, the multiobjective particle swarm approach obtains better history matches and has achieved over twofold faster convergence speed than the single objective approach. The benefits of using multi-objective scheme by comparison with the single objective scheme to obtain a diverse set of history matches while reducing the number of simulations required for achieving a similar matching performance have led to more reliable predictions. Introduction Research studies in assisted history matching techniques, such as genetic algorithms (Romero et al., 2000), neighbourhood algorithm (Christie et al., 2006; Nicotra et al., 2005), chaotic approach (Mantica et al., 2002), evolutionary strategies (SchulzeRiegert et al., 2001), and particle swam optimisation (Mohamed et al., 2010b), primarily focused on a specific optimisation method

Hierarchical benchmark case study for history matching, uncertainty quantification and reservoir characterisation

Benchmark problems have been generated to test a number of issues related to predicting reservoir behaviour (e.g. Floris et al., 2001, Christie and Blunt, 2001, Peters et al., 2010). However, such cases are usually focused on a particular aspect of the reservoir model (e.g. upscaling, property distribution, history matching, uncertainty prediction, etc.) and the other decisions in constructing the model are fixed by log values that are related to the distribution of cell properties away from the wells, fixed grids and structural features and fixed fluid properties. This is because all these features require an element of interpretation, from indirect measurements of the reservoir, noisy and incomplete data and judgments based on domain knowledge. Therefore, there is a need for a case study that would consider interpretational uncertainty integrated throughout the reservoir modelling workflow. In this benchmark study we require the modeller to make interpretational choices as well as to select the techniques applied to the case study, namely the geomodelling approach, history matching algorithm and/or uncertainty quantification technique. The interpretational choices will be around the following areas: (1)Top structure interpretation from seismic and well picks. (2)Fault location, dimensions and the connectivity of the network uncertainty. (3)Facies modelling approach. (4)Facies interpretations from well logs cutoffs. (5)Petrophysical property prediction from the available well data. (6)Grid resolution-choice between number of iterations and model resolution to capture the reservoir features adequately. A semi-synthetic study is based on real field data provided: production data, seismic sections to interpret the faults and top structures, wireline logs to identify facies correlations and saturation profile and porosity and permeability data and a host of other data. To make this problem useable in a manageable time period multiple hierarchically related gridded models were produced for a range of different interpretational choices.

Geological feature selection in reservoir modelling and history matching with Multiple Kernel Learning

There is a continuous challenge in identifying and propagating geologically realistic features into reservoir models. Many of the contemporary geostatistical algorithms are limited by various modelling assumptions, like stationarity or Gaussianity. Another related challenge is to ensure the realistic geological features introduced into a geomodel are preserved during the model update in history matching studies, when the model properties are tuned to fit the flow response to production data. The above challenges motivate exploration and application of other statistical approaches to build and calibrate reservoir models, in particular, methods based on statistical learning.The paper proposes a novel data driven approach - Multiple Kernel Learning (MKL) - for modelling porous property distributions in sub-surface reservoirs. Multiple Kernel Learning aims to extract relevant spatial features from spatial patterns and to combine them in a non-linear way. This ability allows to handle multiple geological scenarios, which represent different spatial scales and a range of modelling concepts/assumptions. Multiple Kernel Learning is not restricted by deterministic or statistical modelling assumptions and, therefore, is more flexible for modelling heterogeneity at different scales and integrating data and knowledge.We demonstrate an MKL application to a problem of history matching based on a diverse prior information embedded into a range of possible geological scenarios. MKL was able to select the most influential prior geological scenarios and fuse the selected spatial features into a multi-scale property model. The MKL was applied to Brugge history matching benchmark example by calibrating the parameters of the MKL reservoir model parameters to production data. The history matching results were compared to the ones obtained from other contemporary approaches - EnKF and kernel PCA with stochastic optimisation.

Optimisation of decision making under uncertainty throughout field lifetime

Assessing the change in uncertainty in reservoir production forecasts over field lifetime is rarely undertaken because of the complexity of joining together the individual workflows. This becomes particularly important in complex fields such as naturally fractured reservoirs. The impact of this problem has been identified in previous and many solutions have been proposed but never implemented on complex reservoir problems due to the computational cost of quantifying uncertainty and optimising the reservoir development, specifically knowing how many and what kind of simulations to run.This paper demonstrates a workflow that propagates uncertainty throughout field lifetime, and into the decision making process by a combination of a metric-based approach, multi-objective optimisation and Bayesian estimation of uncertainty. The workflow propagates uncertainty estimates from appraisal into initial development optimisation, then updates uncertainty through history matching and finally propagates it into late-life optimisation. The combination of techniques applied, namely the metric approach and multi-objective optimisation, help evaluate development options under uncertainty. This was achieved with a significantly reduced number of flow simulations, such that the combined workflow is computationally feasible to run for a real-field problem.This workflow is applied to two synthetic naturally fractured reservoir (NFR) case studies in appraisal, field development, history matching and mid-life EOR stages. The first is a simple sector model, while the second is a more complex full field example based on a real life analogue. This study infers geological uncertainty from an ensemble of models that are based on the carbonate Brazilian outcrop which are propagated through the field lifetime, before and after the start of production, with the inclusion of production data significantly collapsing the spread of P10-P90 in reservoir forecasts. The workflow links uncertainty estimation with the appropriate optimisation at appraisal, development and reservoir management stages to maximise oil recovery under uncertainty. Workflow for effective propagation of uncertainty throughout field lifetime.Workflow aims to achieve results of MCMC approaches but with fewer simulations.Model classification using MDS to try and reduce number of realisation.Optimisation under uncertainty using multi-objective PSO (MOPSO) and Bayesian inference.MO history matching and Bayesian inference reduces compute time in post-production phase.MOO under uncertainty finds optimal across chosen ensemble of models.Clustering reduces workload but removes possible scenarios which impacts on results.Applied to 2 case studies, 1 a sector model, 2 a full field example.

Comparison of Evolutionary and Swarm Intelligence Methods for History Matching and Uncertainty Quantification in Petroleum Reservoir Models

Petroleum reservoir models are vital tools to help engineers in making field development decisions. Uncertainty of reservoir models in predicting future performance of a field needs to be quantified for risk management practices. Rigorous optimisation and uncertainty quantification of the reservoir simulation models are the two important steps in any reservoir engineering study. These steps facilitate decision making and have a direct impact on technical and financial performance of oil and gas companies.

Optimized History Matching with Direct Sequential Image Transforming for Non-Stationary Reservoirs

History matching techniques are usually applied for conditioning static modeling to reservoir production data. One common problem in applying these techniques is the highly non-linear relationship between the distribution of the fluid dynamic production data and the petrophysical parameters, which frequently have a non-stationary character. This paper proposes a multi-scale optimization approach for geostatistical history matching that aims at tackling the problem inherent to the convergence of static models with complex spatial patterns toward the reservoir production observations. The proposed methodology couples adaptive stochastic optimization and direct sequential simulation with local anisotropy correction as the core of image transforming in a twofold procedure: a global optimization stage and a refining optimization stage. The former consists of optimizing the trend model of anisotropy defined over the space of geological parameters. The latter achieves the local refining optimization based on best individual well production matches. Overall, large-scale trend model parameters are tuned with adaptive stochastic optimization followed by the local refining optimization across multiple realizations using a regional image perturbation algorithm. A deltaic reservoir example illustrates the application of the proposed methodology. The deltaic channel pattern is fairly well reproduced and the optimization procedures allow the match of static models’ dynamic responses to historical production observations.

Impact of reservoir uncertainty on selection of advanced completion type

Well performance prediction is a key Petroleum Engineering task. However, large discrepancies between Petroleum Engineering models and reality still frequently occur; despite the continuous increase in the complexity and predictive quality of reservoir models. To-day’s field development decisions are still made with a high level of uncertainty in the underlying data and its economic impact.

Microbial carbonates: a sampling and measurement challenge for petrophysics addressed by capturing the bioarchitectural components

Abstract Ancient and modern stromatolites are potentially a challenge for petrophysicists when characterizing biosediments of microbial origin. Because of the heterogeneity, sometimes very cemented and lacking porosity, sometimes highly porous, these widely differing states can be used to develop techniques that can have wider application to addressing the representative elementary volume (REV – single or multiple REVs) challenge in microbial carbonates. Effective media properties – like porosity – need to be defined on REV scales and the challenge is that this scale is often close to or significantly larger than the traditional core plugs on which properties are traditionally measured. A combination of outcrop images, image analysis techniques, micro-computed tomography (CT) and modelling have been used to capture the porosity (or in some cases, precursor porosity) architecture and provide a framework for estimating petrophysical property sensitivities in a range of situations that can be subjected to further calibration by measurements in relevant microbial reservoir rocks. This work will help guide the sampling approach along with the interpretation and use of petrophysical measurements from microbial carbonates. The bioarchitectural component, when controlling porosity in microbial carbonates, presents a significant challenge as the REV scale is often much larger than core plugs, requiring careful screening of existing data and measurement and additional geostatistical model-based approaches (with further calibration).

Optimized History Matching with Stochastic Image Transforming of a Deltaic Reservoir

The focus of this paper is to demonstrate an integrated characterization approach for a complex deltaic reservoir by using petrophysical properties and dynamic production data. Accurately characterizing deltaic reservoirs requires a non-stationary approach to the reservoir description. By linking the non-stationary characterization step with the dynamic flow modeling, the probability of success in locating infill wells increases. In this work, is presented a hybrid method which integrates the optimization firstly in the space of the anisotropy model parameters and secondly refines it in the space of the static models with a regional perturbation technique. It is an iterative methodology for optimized history matching, using adaptive stochastic sampling in the multiparameter space, and direct sequential simulation as the engine for the image transformation of the porosity and permeability models of the reservoir. The results show coherence when compared with the true case model. The approach provides the simultaneous simulation of the morphology and the property value.