Uncertainty Quantification Of Unconventional Reservoirs Using Assisted History Matching Methods

A hallmark of unconventional reservoirs is characterization uncertainty. Assisted History Matching (AHM) methods provide attractive means for uncertainty quantification (UQ), because they yield an ensemble of qualifying models instead of a single candidate. Here we integrate embedded discrete fracture model (EDFM), one of fractured-reservoirs modeling techniques, with a commercial AHM and optimization tool. We develop a new parameterization scheme that allows for altering individual properties of multiple wells or fracture groups. The reservoir is divided into three types of regions: formation matrix; EDFM fracture groups; and stimulated rock volume (SRV) around fracture groups. The method is developed in a sleek, stand-alone form and is composed of four main steps: (1) reading parameters exported by tool; (2) generating an EDFM instance; (3) running the instance on a simulator; and (4) calculating a pre-defined objective function. We present two applications. First, we test the method on a hypothetical case with synthetic production data from two wells. Using 20 history-matching parameters, we compare the performance of five AHM algorithms. Two of which are based on Bayesian approach, two are stochastic particle-swarm optimization (PSO), and one is commercial DECE algorithm. Performance is measured with metrics, such as solutions sample size, total simulation runs, marginal parameter posterior distributions, and distributions of estimated ultimate recovery (EUR). In the second application, we assess the effect of natural fractures on UQ of a single horizontal well in the middle Bakken. This is achieved by comparing four AHM scenarios with increasingly varying natural-fracture intensity. Results of the first study show that, based on pre-set acceptance criteria, DECE fails to generate any satisfying solutions. Bayesian methods are noticeably superior to PSO, although PSO is capable to generate large number of solutions. PSO tends to be focused on narrow regions of the posteriors and seems to significantly underestimate uncertainty. Bayesian Algorithm I, a method with a proxy-based acceptance/rejection sampler, ranks first in efficiency but evidently underperforms in accuracy. Results from the second study reveal that, even though varying intensity of natural fractures cam significantly alter other model parameters, that appears not to have influence on UQ (or long-term production)

As unconventional reservoir activity grows in demand, reservoir engineers relying on history matching are challenged with this time-consuming task in order to characterize hydraulic fracture and reservoir properties, which are expensive and difficult to obtain. Assisted History Matching for Unconventional Reservoirs delivers a critical tool for today’s engineers proposing an Assisted History Matching (AHM) workflow. The AHM workflow has benefits of quantifying uncertainty without bias or being trapped in any local minima and this reference helps the engineer integrate an efficient and non-intrusive model for fractures that work with any commercial simulator. Additional benefits include various applications of field case studies such as the Marcellus shale play and visuals on the advantages and disadvantages of alternative models. Rounding out with additional references for deeper learning, Assisted History Matching for Unconventional Reservoirs gives reservoir engineers a holistic view on how to model today’s fractures and unconventional reservoirs. Provides understanding on simulations for hydraulic fractures, natural fractures, and shale reservoirs using embedded discrete fracture model (EDFM) Reviews automatic and assisted history matching algorithms including visuals on advantages and limitations of each model Captures data on uncertainties of fractures and reservoir properties for better probabilistic production forecasting and well placement

The information of fractures geometry and reservoir properties can be retrieved from the production data, which is always available at no additional cost. However, in unconventional reservoirs, it is insufficient to obtain only one realization because the non-uniqueness of history matching and subsurface uncertainties cannot be captured. Therefore, the objective of this study is to obtain multiple realizations in shale reservoirs by adopting Assisted History Matching (AHM). We used multiple proxy-based Markov Chain Monte Carlo (MCMC) algorithm and Embedded Discrete Fracture Model (EDFM) to perform AHM. The reason is that MCMC has benefits of quantifying uncertainty without bias or being trapped in any local minima. Also, using MCMC with proxy model unlocks the limitation of an infeasible number of simulations required by a traditional MCMC algorithm. For fractures modeling, EDFM can mimic fractures flow behavior with a higher computational efficiency than a traditional local grid refinement (LGR) method and more accuracy than the continuum approach. We applied the AHM workflow to actual shale gas wells. We found that the algorithm can find multiple history matching solutions and quantify the fractures and reservoir properties posterior distributions. Then, we predicted the production probabilistically. Moreover, we investigated the performance of neural network (NN) and k-nearest neighbors (KNN) as a proxy model in the proxy-based MCMC algorithm. We found that NN performed better in term of accuracy than KNN but NN required twice running time of KNN. Lastly, we studied the effect of enhanced permeability area (EPA) and natural fractures existence on the history matching solutions and production forecast. We concluded that we would over-predict fracture geometries and properties and estimated ultimate recovery (EUR) if we assumed no EPA or no natural fractures even though they actually existed. The degree of over-prediction depends on fractures and reservoir properties, EPA and natural fractures properties, which can only be quantified after performing AHM. The benefits from this study are that we can characterize fractures geometry, reservoir properties, and natural fractures in a probabilistic manner. These multiple realizations can be further used for a probabilistic production forecast, future fracturing design improvement, and infill well placement decision

Uncertainty associated with reservoir simulation studies should be thoroughly captured during history matching process and adequately explained during production forecasts. Lacking information and limited accuracy of measurements typically cause uncertain reservoir properties in the reservoir simulation models. Unconventional tight reservoirs, for instances, often deal with complex dynamic flow behavior and inexact dimensions of hydraulic fractures that directly affect production estimation. Non-unique history matching solutions on the basis of probabilistic logic are recognized in order to avoid underestimating prediction results. Assisted history matching techniques have been widely proposed in many literature to quantify the uncertainty. However, few applications were done in unconventional reservoirs where some distinct uncertain factors could significantly influence well performance. In this thesis, a probabilistic workflow was developed using proxy-modeling approach to encompass uncertain parameters of unconventional reservoirs and obtain reliable prediction. Proxy-models were constructed by Design of Experiments (DoE) and Response Surface Methodology (RSM). As preliminary screening tools, significant parameters were identified, thus removing those that were insignificant for the reduced dimensions. Furthermore, proxy-models were systematically built to approximate the actual simulation, then sampling algorithms, e.g. Markov Chain Monte Carlo (MCMC) method, successfully estimated probabilistic history matching solutions. An iterative procedure was also introduced to gradually improve the accuracy of proxy-models at the interested region with low history matching errors. The workflow was applied to case studies in Middle Bakken reservoir and Marcellus Shale formation. In addition to estimating misfit function for the errors, proxy-models are also regressed on the simulated quantity of the measurements at various points in time, which is shown to be very useful. This alternative method was utilized in a synthetic tight reservoir model, which analyzed the impact of complex fracture network relative to instantaneous well performance at different stages. The results in this thesis show that the proxy-based approach reasonably provides simplified approximation of actual simulation. Besides, they are very flexible and practical for demonstrating the non-unique history matching solutions and analyzing the probability distributions of complicated reservoir and fracture properties. Ultimately, the developed workflow delivers probabilistic production forecasts with efficient computational requirement.

Shale Gas and Tight Oil Reservoir Simulation delivers the latest research and applications used to better manage and interpret simulating production from shale gas and tight oil reservoirs. Starting with basic fundamentals, the book then includes real field data that will not only generate reliable reserve estimation, but also predict the effective range of reservoir and fracture properties through multiple history matching solutions. Also included are new insights into the numerical modelling of CO2 injection for enhanced oil recovery in tight oil reservoirs. This information is critical for a better understanding of the impacts of key reservoir properties and complex fractures. Models the well performance of shale gas and tight oil reservoirs with complex fracture geometries Teaches how to perform sensitivity studies, history matching, production forecasts, and economic optimization for shale-gas and tight-oil reservoirs Helps readers investigate data mining techniques, including the introduction of nonparametric smoothing models

Various uncertainty quantication methodologies are presented using a combination of several deterministic decline curve analysis models and two bootstrapping algorithms. The bootstrapping algorithms are the conventional bootstrapping method (CBM) and the modied bootstrapping method (MBM). The combined deterministic-stochastic combination models are applied to 126 sample wells from the Permian basin. Results are presented for 12 to 72 months of production hindcast given an average well production history of 120 months. Previous researchers used the Arps model and both conventional and modied bootstrapping with block re-sampling techniques to reliably quantify uncertainty in production forecasts. In this work, we applied both stochastic techniques to other decline curve analysis models|namely, the Duong and the Stretched Exponential Production Decline (SEPD) models. The algorithms were applied to sample wells spread across the three main sub-basins of the Permian. A description of how both the deterministic and stochastic methods can be combined is provided. Also, pseudo-codes that describes the methodologies applied in this work is provided to permit readers to replicate results if necessary. Based on the average forecast error plot in the Permian Basin for 126 active wells, we can also conclude that the MBM-Arps, CBM-Arps, and MBM-SEPD combinations produce P50 forecasts that match cumulative production best regardless of the sub-basin and amount of production hindcast used. Regardless of concerns about the coverage rate, the CBM-Arps, MBM-Arps, CBM-SEPD, and MBMSEPD algorithm combinations produce cumulative P50 predictions within 20% of the true cumulative production value using only a 24-month hindcast. With a 12 month-hindcast, the MBM-Arps combined model produced cumulative P50 predictions with a forecast error of approximately 20%. Also, the CBM-SEPD and MBM-SEPD models were within 30% of the true cumulative production using a 12- month hindcast. Another important result is that all the deterministic-stochastic method combinations studied under-predicted the true cumulative production to varying degrees. However, the CBM-Duong combination was found to severely under-predict cumulative production, especially for the 12-month hindcast. It is not a suitable model combination based on forecast error, especially when hindcast fractions on the low end of the spectrum are used. Accordingly, the CBM- Duong combination is not recommended, especially if production history of no more than 24 months is available for hindcasting. As expected, the coverage rate increased, and the forecast error decreased for all the algorithm combinations with increasing hindcast duration. The novelty of this work lies in its extension of the bootstrapping technique to other decline curve analysis models. The software developed can also be used to analyze many wells quickly on a standard engineering computer. This research is also important because realistic estimates of reserves can be estimated in plays like the Permian basin when uncertainty is correctly quantied.

Given the dynamic production data of a reservoir, numerical optimization tools such as history matching can minimize the global error and find an optimal reservoir model that can approximate the fracture geometry and petrophysical parameters in the subsurface. For unconventional reservoirs, the idea behind the automatic history matching is well developed and the workflow is also applied to statistically generate an ensemble of solutions that quantitatively characterizes associated uncertainties. However, more uncertainties regarding fracture and reservoir properties could be further reduced by using available information. Therefore, the objective of this study is to minimize uncertainty when make realizations of shale reservoirs, by integration of data from geology and geomechanics. We utilized the developed automatic history matching (AHM) code and modified the proxy engine, by substituting the neural network (NN) model with XGBoost (XGBOOST) model. The XGBOOST is found to perform more efficiently and accurately than NN, when the size of the available dataset for training is small. Furthermore, the AHM workflow is capable of modelling non-uniform half-length of hydraulic fractures in the corner point gridding system and complex, realistic natural fracture distributions using the fractal theory. Both of these functionalities partially fulfill some degrees of reality, by mimicking the irregular half-length outputted from fracture modelling software and naturally occurring patterns often found at cores. We applied this innovative approach to actual shale gas and shale oil wells. We then found that by coupling additional data into the AHM process, the fracture geometries and petrophysical properties can be more accurately depicted. The obtained results are also highly assimilating with the field experience from the engineers. In addition, by studying natural fractures in the model, we found out that the connectivity between natural fractures and wellbore/hydraulic fractures plays an important role in determining the well’s EUR potential. This study is beneficial because more reliable and robust results based on geological/geomechanical information, along with non-deterministic realizations of reservoir and fractures, can provide invaluable guidance towards well spacing planning, EUR estimation and economic appraisal, and fracture design optimizations

Reservoir characterization and history matching are essential steps in various subsurface applications, such as petroleum exploration and production and geological carbon sequestration, aiming to estimate the rock and fluid properties of the subsurface from geophysical measurements and borehole data. Mathematically, both tasks can be formulated as inverse problems, which attempt to find optimal earth models that are consistent with the true measurements. The objective of this dissertation is to develop a stochastic inversion method to improve the accuracy of predicted reservoir properties as well as quantification of the associated uncertainty by assimilating both the surface geophysical observations and the production data from borehole using Ensemble Smoother with Multiple Data Assimilation. To avoid the common phenomenon of ensemble collapse in which the model uncertainty would be underestimated, we propose to re-parameterize the high-dimensional geophysics data with data order reduction methods, for example, singular value decomposition and deep convolutional autoencoder, and then perform the models updating efficiently in the low-dimensional data space. We first apply the method to seismic and rock physics inversion for the joint estimation of elastic and petrophysical properties from the pre-stack seismic data. In the production or monitoring stage, we extend the proposed method to seismic history matching for the prediction of porosity and permeability models by integrating both the time-lapse seismic and production data. The proposed method is tested on synthetic examples and successfully applied in petroleum exploration and production and carbon dioxide sequestration.

This book explores methods for managing uncertainty in reservoir characterization and optimization. It covers the fundamentals, challenges, and solutions to tackle the challenges made by geological uncertainty. The first chapter discusses types and sources of uncertainty and the challenges in different phases of reservoir management, along with general methods to manage it. The second chapter focuses on geological uncertainty, explaining its impact on field development and methods to handle it using prior information, seismic and petrophysical data, and geological parametrization. The third chapter deals with reducing geological uncertainty through history matching and the various methods used, including closed-loop management, ensemble assimilation, and stochastic optimization. The fourth chapter presents dimensionality reduction methods to tackle high-dimensional geological realizations. The fifth chapter covers field development optimization using robust optimization, including solutions for its challenges such as high computational cost and risk attitudes. The final chapter introduces different types of proxy models in history matching and robust optimization, discussing their pros and cons, and applications. The book will be of interest to researchers and professors, geologists and professionals in oil and gas production and exploration.

The development of naturally fractured reservoirs, especially shale gas and tight oil reservoirs, exploded in recent years due to advanced drilling and fracturing techniques. However, complex fracture geometries such as irregular fracture networks and non-planar fractures are often generated, especially in the presence of natural fractures. Accurate modelling of production from reservoirs with such geometries is challenging. Therefore, Embedded Discrete Fracture Modeling and Application in Reservoir Simulation demonstrates how production from reservoirs with complex fracture geometries can be modelled efficiently and effectively. This volume presents a conventional numerical model to handle simple and complex fractures using local grid refinement (LGR) and unstructured gridding. Moreover, it introduces an Embedded Discrete Fracture Model (EDFM) to efficiently deal with complex fractures by dividing the fractures into segments using matrix cell boundaries and creating non-neighboring connections (NNCs). A basic EDFM approach using Cartesian grids and advanced EDFM approach using Corner point and unstructured grids will be covered. Embedded Discrete Fracture Modeling and Application in Reservoir Simulation is an essential reference for anyone interested in performing reservoir simulation of conventional and unconventional fractured reservoirs. Highlights the current state-of-the-art in reservoir simulation of unconventional reservoirs Offers understanding of the impacts of key reservoir properties and complex fractures on well performance Provides case studies to show how to use the EDFM method for different needs