Uncertainty In Reservoir Models Research Articles

Integrating facies analysis and geostatistical methods in an onshore oil field using petrophysical groups

Reservoir facies studies are of great importance in different stages of exploration and development of hydrocarbon fields. We have aimed to generate a reservoir facies model for the Asmari Formation in an onshore oil field located in southwest Iran. Input data for electrofacies (EF) clustering algorithms are used, which include gamma-ray (GR), density (RHOB), porosity, and sonic logs from four wells. We obtain the petrophysical group (PG) and EF class using core drill data (mercury injection capillary pressure) and well-logs analysis. The integration of PGs and log EF significantly decreases the uncertainty in reservoir modeling, which alternatively enhances field development decisions. We compare the multiresolution graph-based clustering (MRGC) and k-means clustering methods. EF clustering results find nine EF classes. We delineate high-quality reservoirs based on lower GR, RHOB, and high-porosity logs. Next, we use the clustering results in the static reservoir modeling process, using the sequential index simulation and indicator kriging methods. The comparison between the facies obtained models and existing drilling core data finds that the absolute percentage error of the MRGC algorithm is less than that of the k-means algorithm. The results obtained by this study can provide useful information for the development of hydrocarbon exploration plans in the studied oil field.

Quantifying Uncertainty in Downscaling of Seismic Data to High-Resolution 3-D Lithological Models

Building high-resolution lithological models using seismic data can facilitate decision-makings for earth resources development, but they are subject to considerable uncertainties due to the limited seismic resolution. Traditionally, high-resolution lithological models are built deterministically or stochastic simulation is performed using seismic as “soft data” in geostatistical contexts. Many approaches have been developed to do the above, but in this work, we explicitly account for the uncertain relationship between seismic data and lithological models. We introduce a data-driven Bayesian approach to first quantify soft data uncertainty by generating multiple lithology proportions from seismic. The spatial lithology proportion uncertainty arises from the uncertain relationship between low-resolution seismic and lithology proportions. We quantify this proportion uncertainty by learning the statistical relationships with seismic using high-resolution borehole data. Once conditioning the statistical relationships to observed seismic, we can generate multiple realizations of spatial proportions. With the generated proportions as volume averages, a sequential indicator simulation (SISim) is then performed to build high-resolution lithofacies models. This approach is applied to a real channelized turbidite system with four lithofacies. We demonstrate that the generated high-resolution lithological models can preserve the global uncertainties captured by proportion trends while locally matching borehole observations. When compared with the conventional approaches that use deterministic soft data, our statistical learning approach avoids the problem of underestimating reservoir model uncertainty. More importantly, the lithofacies models from the proposed method are less likely to be falsified by observed data. Additionally, an open-source Python library for the uncertainty quantification is provided.

Hydraulic Flow Unit Classification and Prediction Using Machine Learning Techniques: A Case Study from the Nam Con Son Basin, Offshore Vietnam

The test study area is the Miocene reservoir of Nam Con Son Basin, offshore Vietnam. In the study we used unsupervised learning to automatically cluster hydraulic flow units (HU) based on flow zone indicators (FZI) in a core plug dataset. Then we applied supervised learning to predict HU by combining core and well log data. We tested several machine learning algorithms. In the first phase, we derived hydraulic flow unit clustering of porosity and permeability of core data using unsupervised machine learning methods such as Ward’s, K mean, Self-Organize Map (SOM) and Fuzzy C mean (FCM). Then we applied supervised machine learning methods including Artificial Neural Networks (ANN), Support Vector Machines (SVM), Boosted Tree (BT) and Random Forest (RF). We combined both core and log data to predict HU logs for the full well section of the wells without core data. We used four wells with six logs (GR, DT, NPHI, LLD, LSS and RHOB) and 578 cores from the Miocene reservoir to train, validate and test the data. Our goal was to show that the correct combination of cores and well logs data would provide reservoir engineers with a tool for HU classification and estimation of permeability in a continuous geological profile. Our research showed that machine learning effectively boosts the prediction of permeability, reduces uncertainty in reservoir modeling, and improves project economics.

Development and Identification of Petrophysical Rock Types for Effective Reservoir Characterization: Case Study of the Kristine Field, Offshore Sabah

Rock typing is an essential tool used to distribute rock and fluid properties in reservoir models. It provides estimates of oil reserves that are more accurate during field studies and prediction of reservoir performance. However, geomodelers are frequently faced with challenges of integrating geological facies with rock characteristics and fluid flow to predict petrophysical properties due to limited correlation between geological features and engineering concepts. Therefore, in this study, petrophysical rock types (PRTs) were defined using both core and log data, and the relationship between capillary properties, hydraulic flow units, permeability and porosity correlations was enhanced. The PRTs were determined through quantitative methods using mercury injection capillary pressure information and a probabilistic approach to distinguish convoluted pore systems. Subsequently, various pore structure characteristics were defined to detect petrophysical variation among pore systems to enhance petrophysical rank of rock types. Furthermore, for a reservoir, consistency in J-function curves for saturation height above free water level was determined. Finally, permeability generated from other empirical equations was compared with log-derived permeability to recommend a suitable approach for clastic formations in the Sabah Fields. By using capillary data to derive saturation height functions, the hydraulic units demonstrated consistent results of rock types, reduced the uncertainties in reservoir models and integrated geological description with engineering hydraulic features. The Winland R35 approach was found to be susceptible to pore throat radius, and traditional neutron–density rock typing approach was dependent on the shale cutoff used.

An innovative approach to permeability estimation of the fractured-vuggy carbonate reservoirs based on 2D images

Permeability analysis is an essential process in reservoir characterization, especially when evaluating those highly heterogeneous reservoirs such as fractures-vuggy carbonate reservoirs. Because of the biased sampling, no laboratory measurement can obtain the exact permeability values of the carbonate samples that contain fractures or large vugs. Besides this fact, the heterogeneity of the secondary pore distribution could cause unstable test results of permeability, which can bring out significant uncertainty in reservoir modeling if the problem is ignored. There are two widely used indirect methods for permeability estimation: one is based on the Kozeny-Carman equation, and the other one is based on the Navier-Stokes equations. Both two estimations need to evaluate the geometry properties of the rock pore-fracture system, which will introduce artificial uncertainty into the estimation results. This paper proposed an innovative approach to permeability estimation established through counting the pores, fractures, and vugs on 2D images. By considering the area distribution of those porous objects identified on the 2D images in a specified statistical interval, the absolute permeability values of the fractured-vuggy carbonate will be calculated directly without any artificial influence. The new approach is a general way to estimate permeability and does not consider rock facies and pore types. The estimation results show a more stable manner than core analysis data, which could help to select permeability values in reservoir modeling. On the other hand, by comparing the estimation results from different statistical intervals, the heterogeneity of the parameter is revealed.

Probabilistic risk-based Area of Review (AoR) determination for a deep-saline carbon storage site

Regulatory oversight of a geologic carbon sequestration (GCS) project relies on iterative estimations, throughout the project lifetime, of the area where increased risks to underground sources of drinking water (USDWs) may occur due to injection of CO2. This area, referred to as Area of Review (AoR), is typically delineated by predicting the migration of fluid between the reservoir and the lowermost USDW via an open wellbore using predictions from physics-based reservoir simulators. The inherent uncertainty in input parameters used in reservoir modeling therefore affects the accuracy of determining the AoR for a project. Furthermore, the standard analytical approaches for calculating a critical pressure to delineate the risk area yield an infinite AoR for cases where the injection reservoir is overpressured relative to the USDW. A methodology is presented here to better characterize the risk to USDWs while accounting for the uncertainty in reservoir modeling, with an application to a permitted GCS project with an overpressured injection formation, FutureGen 2.0. The methodology is demonstrated using the National Risk Assessment Partnership’s open-source integrated assessment model (NRAP-Open-IAM) to develop a probabilistic estimate of impact risk to USDW quality. CO2 and pressure predictions from the reservoir modeling conducted using the STOMP-CO2 simulator for the FutureGen 2.0 site are used in a NRAP-Open-IAM model with reservoir, wellbore, and aquifer components to: (1) assess the extent of potential leakage into the USDW for the predicted reservoir pressure conditions; (2) evaluate the extent of potential impact using “no-net-degradation” thresholds; and (3) account for uncertainty in reservoir permeabilities.

Application of Polynomial Chaos Expansion to Optimize Injection-Production Parameters under Uncertainty

The optimization of oil field development scheme considering the uncertainty of reservoir model is a challenging and difficult problem in reservoir engineering design. The most common method used in this regard is to generate multiple models based on statistical analysis of uncertain reservoir parameters and requires a large number of simulations to efficiently handle all uncertainties, thus requiring a huge amount of computational power. In order to reduce the computational burden, a method which combines reservoir simulation, an economic model, polynomial chaos expansion with response surface methodology, and Levy flight particle swarm optimization (LFPSO) algorithm is proposed to determine the optimal injection-production parameters with reservoir uncertainties at a reasonable computational cost. This approach is applied to a five-spot well pattern optimization design for obtaining the optimal parameters, including oil-water well distance, injection rate, and bottom hole pressure, while considering the uncertainties of porosity, permeability, and relative permeability. The results of the case study indicated that the integrated approach is practical and efficient for performing reservoir optimization with uncertain reservoir parameters.

Effect of Confinement on the Dynamic Contact Angle of Hydrocarbons

Unconventional hydrocarbon reservoirs and their characteristics have promoted an area of research exploring the effect of small pore size on the reservoir fluid and its associated properties. There is a general agreement that (i) the confined fluid flow and associated properties in shale are substantially different from its corresponding bulk properties and (ii) these differences have a significant impact on the prediction of well performance and ultimate recovery in shale reservoirs. However, experimental measurements of fluid flow and properties in shale rocks are currently very limited, which has led to a significant amount of uncertainty in reservoir modeling. In this study, a nonfluidic device is designed, fabricated, packaged, and tested, and an experimental investigation of the gas–liquid contact angle of hydrocarbons confined in nanosized channels within a nanofluidic platform is conducted. Reservoirs in the nanofluidic chip are filled with a hydrocarbon liquid and epi-fluorescence imaging is simu...

Integrated Work Flow of Preserving Facies Realism in History Matching: Application to the Brugge Field

Summary Data assimilation with ensemble-based inversion methods was successfully applied for parameter estimation in reservoir models. However, in certain complex-reservoir models, it remains challenging to estimate the model parameters and to preserve the geological realism simultaneously. In particular, when handling special-reservoir model parameters such as facies types concerning fluvial channels, one must realize that geological realism becomes one of the key concerns. The main objective of this work is to address these issues for a complex field with a newly extended version of a recently proposed facies-parameterization approach coupled with an ensemble-based data assimilation method. The proposed workflow combines the new facies parameterization and the adaptive gaussian mixture (AGM) filter into the data assimilation framework for channelized reservoirs. To handle discrete-facies parameters, we combine probability maps and truncated Gaussian fields to obtain a continuous parameterization of the facies fields. For the data assimilation, we use the AGM filter, which is an efficient history matching approach that incorporates a resampling routine that allows us to regenerate facies fields with information from the updated probability maps. This work flow is evaluated, for the first time, on a complex field case—the Brugge field. This reservoir model consists of layers with complex channelized structures and layers characterized by reservoir properties generated with variograms. With limited prior knowledge on the facies model, this work flow is shown to be able to preserve the channel continuity while reducing the reservoir model uncertainty with AGM. When applied to a complex reservoir, the proposed work flow provides a geologically consistent and realistic reservoir model that leads to improved capability of predicting subsurface flow behaviors.

Multi-objective optimization for rapid and robust optimal oilfield development under geological uncertainty

Optimal well placement is critical to oil and gas field development. Typical workflows involve procedures to place a new well or a group of new wells in a reservoir in order to maximize some pre-defined reservoir performance metric. However, there are two main drawbacks with these traditional optimization approaches: First, the impact of geological uncertainty is often neglected or there may be no framework to include geological uncertainty. Second, traditional optimization techniques normally cannot meet the requirement of optimizing two or more conflicting objectives simultaneously—this may be useful when maximizing oil recovery while also minimizing water production. Consequently, in recent years, multiple objective optimization to obtain robust solutions that minimize the decision risk under geological uncertainty becomes a topic of renewed interest. Therefore, in this work, we develop a new work flow for well placement optimization while considering geological uncertainty in reservoir models. In general, when considering geological uncertainty, the primary goal is to maximize the mean net present value (NPV) over all realizations. However, restricting the search to simply maximizing the mean NPV may be inappropriate or inadequate for decision-making. A more reasonable choice is to maximize the mean NPV while minimizing the spread of the optimal NPV’s obtained for each realization. Therefore, in this work, we apply multi-objective optimization techniques to maximize the mean and minimize the variance of NPV values over all geological realizations to provide robust well placement solutions for decision-makers to select according to their risk attitude towards field development plans.

Uncertainty in reservoir modeling

Uncertainty is due to incomplete and imprecise knowledge as a result of limited sampling of the subsurface heterogeneities. Well data and seismic data have incomplete coverage and finite resolution. The interpretations are uncertain. Reservoirs are heterogeneous and difficult to predict away from wells. Ignoring uncertainty and locking in important model parameters and choices amounts to an assumption of perfect knowledge and is generally an unacceptable approach. Uncertainty must be explicitly modeled. Understanding the (1) sources of uncertainty, (2) methods to represent uncertainty, (3) the formalisms of uncertainty, and (4) uncertainty modeling methods and workflows were essential for the integration of all reservoir information sources and providing good models for decision making in the presence of uncertainty.

Efficient Prediction of SAGD Productions Using Static Factor Clustering

Oil sands have great amount of reserves in the world with increasing commercial productions. Prediction of reservoir performances of oil sands is challenging mainly due to long simulation time for modeling heat and fluids flows in steam assisted gravity drainage (SAGD) operations. Because of accurate modeling difficulties and limited geophysical data, it requires many simulation cases of geostatistically generated fields to cover uncertainty in reservoir modeling. Therefore, it is imperative to develop a new technique to analyze production performances efficiently and economically. This paper presents a new ranking method using a static factor that can be used for efficient prediction of oil sands production. The features vector proposed can reflect shale barrier effects in terms of shale length and relative distance from the injection well. It preprocesses area that steam chamber bypasses, and then counts steam chamber expanding an area cumulatively. K-means clustering selects a few fields for full simulation run and they will cover cumulative probability distribution function (CDF) of all the fields examined. Accuracy of the prediction is high when cluster number is more than 10 based on cases of cluster number 5, 10, and 15. This technique is applied to fields with 3%, 5%, 10%, and 15% shale fraction and all the cases allow efficient and economical predictions of oil sands productions.

A method for reduction of uncertainties in reservoir model using observed data: application to a complex case

The aim of this paper is to show a methodology to reduce uncertainties in complex reservoir models using observed dynamic data. The basic idea is the use of the difference between observed and simulated data to constrain the probability redistribution of the uncertain attributes, reducing the spread of the posterior distribution and, as a consequence, reducing the dispersion of the reservoir response and mitigating risk. To capture the influence between attributes and reservoir responses, an influence matrix is proposed. The method deals with discrete and continuous attributes, which permits an adequate representation of the several types of uncertainties. The methodology was applied to a complex case and promising results are shown.

A new procedure to reduce uncertainties in reservoir models using statistical inference and observed data

Abstract A new procedure to reduce uncertainties in reservoir simulation models using statistical inference and observed data is presented in this paper. Observed data is used to guide the obtainment of posterior probability density functions ( pdf ). The process starts by sampling from prior pdf . Through an iterative procedure, posterior pdf is obtained in each iteration, which is used to sample new models for the next iteration, until a stop criterion is reached. A detailed relationship between all uncertain attributes defined in the analysis and well responses (water and oil rate, flow pressure etc.) is performed. Finally, final ensembles are sampled in order to assess the dispersion of the responses before and after the reduction of uncertainty. In order to assess the robustness of the proposed method, three reservoir models were studied. The first case is a simple reservoir with eight uncertain attributes and was used for validation purposes. The second case, is a more complex synthetic model with 16 uncertain attributes. Finally, the application to a real field is shown. The results showed that the proposed method has potential to deal with the problem of reservoir uncertainty management.

Carbonate rock characterization and modeling: Capillary pressure and permeability in multimodal rocks—A look beyond sample specific heterogeneity

Carbonate rocks are known for their heterogeneity and petrophysical complexity. This commonly leads to large uncertainties in reservoir models that are intended to predict fluid storage and fluid flow. In this article, focus is given to the characterization of pore systems at core-plug scale to provide improved models for permeability and saturation prediction. These methods fall under a wider rock-typing workflow. We examine the use of mercury-air capillary pressure data for rock-type definition and for predicting saturation and permeability. We present new methods for modeling saturation in rocks with multimodal pore-throat size distributions. The methods bear similarity to those previously published but with some key differences, mainly by relating the capillary pressure data to the pore systems representative for a rock type. We also present a new method for relating permeability to pore-throat sizes that is more versatile, in that it can be employed for all types of pore-throat size distributions—unimodal or multimodal. We demonstrate that a normalized pore-throat radius parameter forms a straight line relationship with permeability over six orders of magnitude. It appears to be a fundamental property for all pore systems so far examined. The wider implication of the workflows presented is that they offer better integration between the methods used for saturation prediction and the methods used for permeability prediction, something that is desirable for all subsurface studies.

Analysis of Uncertainty Introduced by Scaleup of Reservoir Attributes and Flow Response in Heterogeneous Reservoirs

SummaryReservoir heterogeneities occur over a wide range of length scales, and their interaction with various transport mechanisms controls the performance of subsurface flow and transport processes. Modeling these processes at large scales requires proper scaleup of petrophysical properties that are autocorrelated or heterogeneously distributed in space, and analyzing their interaction with underlying transport mechanisms.A method is proposed to investigate and quantify the uncertainty in reservoir models introduced by scaleup. It is demonstrated that when the volume support of the measurement is smaller than the representative elementary volume (REV) scale of the attribute to be modeled, there is uncertainty in the conditioning data because of scaleup and that uncertainty has to be propagated to spatial models for the attribute. This important consideration is demonstrated for mapping total porosity for a carbonate reservoir in the Gulf of Mexico. The results demonstrate that in most cases, the uncertainty distributions obtained by accounting for the scaleup procedure successfully characterize the variability in the actual core and log data observed along new wells. Conventional reservoir models considering the well data as "hard" conditioning data fail to predict the "true" values.Following this discussion on scaling of reservoir attributes, a conceptual understanding of the scaling characteristics of flow responses such as recovery factor (RF) is provided, in terms of the mean and variance of RF at different length scales. Finally, a new technique is presented to systematically quantify the scaling characteristics of transport processes by accounting for subscale heterogeneities and their interaction with various transport mechanisms based on the volume averaging approach. The objective is to provide a tool for understanding the scaling relationships for RF using detailed fine-scale compositional reservoir simulations over a subdomain of the reservoir.

Simultaneous inversion of PP and PS seismic data

Elastic parameters derived from seismic data are valuable input for reservoir characterization because they can be related to lithology and fluid content of the reservoir through empirical relationships. The relationship between physical properties of rocks and fluids and P-wave seismic data is nonunique. This leads to large uncertainties in reservoir models derived from P-wave seismic data. Because S- waves do not propagate through fluids, the combined use of P-and S-wave seismic data might increase our ability to derive fluid and lithology effects from seismic data, reducing the uncertainty in reservoir characterization and thereby improving 3D reservoir model-building. We present a joint inversion method for PP and PS seismic data by solving approximated linear expressions of PP and PS reflection coefficients simultaneously using a least-squares estimation algorithm. The resulting system of equations is solved by singular-value decomposition (SVD). By combining the two independent measurements (PP and PS seismic data), we stabilize the system of equations for PP and PS seismic data separately, leading to more robust parameter estimation. The method does not require any knowledge of PP and PS wavelets. We tested the stability of this joint inversion method on a 1D synthetic data set. We also applied the methodology to North Sea multicomponent field data to identify sand layers in a shallow formation. The identified sand layers from our inverted sections are consistent with observations from nearby well logs.

Markov Chain Monte Carlo for Modelling Permeability Variations in Reservoirs

Abstract Accurate representation of reservoir heterogeneity using stochastic modelling techniques requires careful synthesis of the multivariate probability distribution characterizing the spatial variations of petrophysical properties. A well designed scheme for sampling from that distribution is necessary in order to accurately portray the uncertainty in identifying reservoir properties arising from our imperfect knowledge of the reservoir under study. That uncertainty is data-dependent and most importantly, model-dependent. The paper presents a Markov Chain Monte Carlo (MCMC) methodology for sampling from the invariant or stationary probability distribution characterizing the reservoir permeability field. An initial random field is perturbed successively following a Gibbs sampling procedure. The updated values at the perturbed node are obtained by sampling from local probability distributions obtained by kriging. This iterative updating procedure is continued until a prescribed large number of iterations are performed. Hard data, histogram, and variogram models are honoured, as expected. The multiple point histogram (MPH) and entropy of MPH are used to assess the joint spatial uncertainty exhibited by the MCMC model. The paper also discusses and demonstrates a new approach for integrating secondary information within the MCMC framework. The reduction in joint spatial uncertainty subsequent to integrating the secondary information is demonstrated. Introduction The assessment of uncertainty is a crucial step for decisionmakers to reduce the financial risks during the development of a reservoir. The uncertainty in reservoir performance predictions is usually reflected by a number of parameters of interest, such as OIP, production profiles, ultimate recovery, and any forecast figure, etc. Reservoir complexity and the lack of data available are two main reasons that lead to uncertainty in reservoir modeling(1). Several papers(1–4) have addressed the issue of uncertainty assessment in detail. However, all efforts for quantifying uncertainty are model and data specific. The true reservoir permeability field is entirely characterized by a multivariate probability distribution describing the joint uncertainty in permeability at all locations in the reservoir. That multivariate distribution is usually unknown and hence the objective of stochastic simulation is to obtain the requisite multivariate distribution using the available data and the prior model for spatial continuity (or variability). Ultimately, this posterior probability distribution is sampled in order to obtain realizations of the permeability field. In this paper, a Markov Chain Monte Carlo (MCMC) procedure is used to update and sample from the posterior probability density function. The simulation commences from an initial kriged map. The local conditional probability distribution at each location is constructed using the values at neighbouring locations and subsequently, a value is sampled from that distribution. A Gibbs sampler is utilized implying that the sampled value is retained regardless of whether the mismatch against target statistics increases. The procedure is continued at all locations by following a random path. This iterative procedure is continued until a final realization is obtained that identifies target statistics, such as the prior variogram and/or the prior histogram of permeability values. The details of the MCMC algorithm are described next.

3D high-resolution digital models of outcrop analogue study sites to constrain reservoir model uncertainty: an example from Alport Castles, Derbyshire, UK

Advances in data capture and computer technology have made possible the collection of 3D high-resolution surface and subsurface digital geological data from outcrop analogues. This paper describes research to obtain the 3D distribution and internal sedimentary architecture of turbidite channels and associated sediments at a study site in the Peak District National Park, Derbyshire, UK. The 1D, 2D and 3D digital datasets included Total Station survey, terrestrial photogrammetry and remote sensing, sedimentary logs and a Ground Penetrating Radar (GPR) dataset. A grid of 2D GPR profiles was acquired behind a cliff outcrop; electromagnetic reflection events correlated with cliff face sedimentary horizons logged by Vertical Radar Profiling. All data were combined into a Digital Solid Model (DSM) dataset of the site within reservoir modelling software. The DSM was analysed to extract 3D architectural geometries for petroleum reservoir models. A deterministic base model was created using all information, along with a suite of heterogeneous turbidite reservoir models, using 1D, 2D or 3D information. The model suite shows significant variation from the deterministic model. Models built from 2D information underestimated connectivity and the continuity of geobodies, but overestimated channel sinuosity. Advantages of using 3D digital outcrop analogue data for 3D reservoir models are detailed.

Prediction under uncertainty in reservoir modeling

Reservoir simulation is routinely employed in the prediction of reservoir performance under different depletion and operating scenarios. Usually, a single history-matched model, conditioned to production data, is obtained. The model is then used to forecast future production profiles. Because the history match is non-unique, the forecast production profiles are therefore uncertain, although this uncertainty is not usually quantified. This paper presents a new approach for generating uncertain reservoir performance predictions and quantifying the uncertainty associated with forecasting future performance. Firstly, multiple reservoir realizations are generated using a new stochastic algorithm. This involves adaptively sampling the model parameter space using an algorithm, which biases the sampling towards regions of good fit. Using the complete ensemble of models generated, the posterior distribution is resampled in order to quantify the uncertainty associated with forecasting reservoir performance in a Bayesian framework. The strength of the method in performance prediction is demonstrated by using an upscaled model to history match fine scale data. The maximum likelihood model is then used in forecasting the fine grid performance, and the uncertainty associated with the predictions is quantified. It is demonstrated that the maximum likelihood model is highly accurate in reservoir performance prediction.