Using data management approaches to improve decision analysis in petroleum field development under uncertainty : Gerenciamento de dados para melhorar as decisoes de desenvolvimento de um campo petrolifero, sob incertezas

SEYED KOUROSH MAHJOUR

USING DATA MANAGEMENT APPROACHES TO

IMPROVE DECISION ANALYSIS IN PETROLEUM

FIELD DEVELOPMENT UNDER UNCERTAINTY

GERENCIAMENTO DE DADOS PARA MELHORAR AS

DECISÕES DE DESENVOLVIMENTO DE UM CAMPO

PETROLÍFERO, SOB INCERTEZAS

CAMPINAS

2020

UNIVERSIDADE ESTADUAL DE CAMPINAS

FACULDADE DE ENGENHARIA MECÂNICA

Seyed Kourosh Mahjour

USING DATA MANAGEMENT APPROACHES TO

IMPROVE DECISION ANALYSIS IN PETROLEUM

FIELD DEVELOPMENT UNDER UNCERTAINTY

GERENCIAMENTO DE DADOS PARA MELHORAR AS

DECISÕES DE DESENVOLVIMENTO DE UM CAMPO

PETROLÍFERO, SOB INCERTEZAS

Thesis presented to the Mechanical Engineering

Faculty and Geosciences Institute of the

University of Campinas in partial fulfillment of

the requirements for the degree of Doctor of

Philosophy

in

Petroleum

Sciences

and

Engineering in the area of Reservoirs and

Management.

Tese de Doutorado apresentada à Faculdade de

Engenharia Mecânica e Instituto de Geociências

da Universidade Estadual de Campinas como

parte dos requisitos exigidos para a obtenção do

título de Doutor em Ciências e Engenharia de

Petróleo na área de Reservatórios e Gestão.

Orientador: Prof. Dr. Denis José Schiozer

Este exemplar corresponde à versão

final da tese defendida pelo aluno

Seyed Kourosh Mahjour e orientada

pelo Prof. Dr. Denis José Schiozer.

______________________________

Prof. Dr. Denis José Schiozer

CAMPINAS

2020

Ficha catalográfica

Universidade Estadual de Campinas Biblioteca da Área de Engenharia e Arquitetura

Luciana Pietrosanto Milla - CRB 8/8129

Mahjour, Seyed Kourosh,

M279u MahUsing data management approaches to improve decision analysis in petroleum field development under uncertainty / Seyed Kourosh Mahjour. – Campinas, SP : [s.n.], 2020.

MahOrientador: Denis José Schiozer.

MahTese (doutorado) – Universidade Estadual de Campinas, Faculdade de Engenharia Mecânica.

Mah1. Engenharia do petróleo. 2. Reservatórios (Simulação). 3. Avaliação de riscos. 4. Incerteza. I. Schiozer, Denis José, 1963-. II. Universidade Estadual de Campinas. Faculdade de Engenharia Mecânica. III. Título.

Informações para Biblioteca Digital

Título em outro idioma: Gerenciamento de dados para melhorar as decisoes de

desenvolvimento de um camp petrolifero, sob incertezas

Palavras-chave em inglês:

Petroleum engineering Reservoirs (Simulation) Risk assesment

Uncertainty

Área de concentração: Reservatórios e Gestão

Titulação: Doutor em Ciências e Engenharia de Petróleo Banca examinadora:

Denis José Schiozer [Orientador] Guilherme Palermo Coelho Luis Augusto Angelotti Meira Ana Paula de Araujo Costa Marcia Ida de Oliveira Silva

Data de defesa: 27-04-2020

Programa de Pós-Graduação: Ciências e Engenharia de Petróleo Identificação e informações acadêmicas do(a) aluno(a)

- ORCID do autor: https://orcid.org/0000-0001-7825-9707 - Currículo Lattes do autor: http://lattes.cnpq.br/1494134917066698

UNIVERSIDADE ESTADUAL DE CAMPINAS FACULDADE

DE ENGENHARIA MECÂNICA E INSTITUTO DE

GEOCIÊNCIAS

PHD THESIS

USING DATA MANAGEMENT APPROACHES TO

IMPROVE DECISION ANALYSIS IN PETROLEUM

FIELD DEVELOPMENT UNDER UNCERTAINTY

Autor: Seyed Kourosh Mahjour

Orientador: Prof. Dr. Denis José Schiozer

A Banca Examinadora composta pelos membros abaixo aprovou esta tese: Prof. Dr. Denis José Schiozer, presidente

DEP / FEM / UNICAMP

Prof. Dr. Guilherme Palermo Coelho FT/UNICAMP

Prof. Dr. Luis Augusto Angelotti Meira FT/UNICAMP

Dr. Ana Paula de Araújo Costa PETROBRAS

Dr. Márcia Ida de Oliveira Silva PETROBRAS

A ata da defesa com as respectivas assinaturas dos membros encontra-se no

processo de vida acadêmica do aluno.

DEDICATION

ACKNOWLEDGMENTS

Firstly, I would like to express my sincere gratitude to my supervisor Prof. Dr. Denis José Schiozer. His guidance and immense knowledge were invaluable for this thesis. He consistently allowed this research to be my own work, but steered me in the right direction whenever he thought I needed it. I could not have imagined having a better advisor and mentor. I would also like to express my sincere gratitude to my friend Antonio Alberto de Souza dos Santos. He has given me continuous support since I first arrived to Brazil, and has always been present whenever I had a question about my research or writing. I would also like to show my sincere gratitude to my friend Manuel Gomes Correia. He has guided me to start learning something new in my work with a friendly behavior. My sincere thanks to all my fellow students, colleagues, researchers, and staff at UNISIM, at CEPETRO, and at the Division of Petroleum Engineering, that directly or indirectly helped me in this period. My sincere gratitude goes to Energi Simulation and to PETROBRAS for the financial support of this work, and to CMG, and Petrel for software licenses and technical support.

Finally, I must express my very profound gratitude to my mother, father and brothers, and to my friends, for providing me with unfailing support and continuous encouragement throughout my years of study. This accomplishment would not have been possible without them. Thank you.

RESUMO

O gerenciamento de dados durante a análise de decisão no desenvolvimento de campos de petróleo tem um papel significativo na melhoria da interpretação das características do reservatório. Portanto, nos últimos anos, diferentes análises têm sido amplamente aplicadas em diferentes etapas, desde a caracterização, simulação, redução de incertezas e otimização de reservatórios até a análise de decisão. Além disso, a definição de uma estratégia de produção eficiente e confiável requer a consideração de diferentes incertezas do reservatório, econômicas e operacionais. Embora seja ideal gerar realizações com todas as combinações possíveis de incertezas, isto pode resultar em centenas ou milhares de realizações independentes, o que exigiria um tempo extremamente elevado para analisar dos resultados. Portanto, a seleção de um subconjunto de modelos, modelos representativos (RMs), do conjunto completo, considerando o espaço de incertezas de todo o conjunto, geralmente é essencial para reduzir o esforço computacional e acelerar a análise. Neste trabalho, inicialmente foi desenvolvido um fluxo de trabalho, incluindo Hierarchical Cluster Analysis (HCA), modelagem geoestatística e quantificação de incertezas para identificar unidades de fluxo e gerar modelos de reservatório para fins de simulação. A seguir, apresentamos uma solução, com base em uma abordagem estatística integrada e incertezas geológicas, para selecionar RMs do conjunto total de modelos 3D baseado em unidades de fluxo (FUs). O método proposto incluiu uma combinação de escala multidimensional e análise de cluster (IMC). Posteriormente, geramos um novo fluxo de trabalho para selecionar um subconjunto de modelos de reservatório combinando clusterização à distância e assimilação de dados sob todos os tipos de incertezas voltadas para o desenvolvimento e gerenciamento de campo. Finalmente, buscamos comparar duas técnicas de redução de cenários com foco no desenvolvimento do campo: (1) técnica de clusterização baseada na distância entre propriedades com coeficiente de correspondência simples (DCSMC) como um método de redução de cenários com foco nas propriedades estáticas; e (2) técnica RMFinder como método de redução de cenários com foco nas propriedades dinâmicas. Finalmente, foi gerada uma nova estrutura robusta de posicionamento de poço usando os RMs obtidos a partir da integração do método DCMC e da ferramenta RMFinder. As metodologias e fluxos de trabalho aplicados para identificar a unidade de fluxo, caracterizar o reservatório, quantificar a incerteza, e selecionar modelos representativos e foram testadas e avaliadas no caso benchmark UNISIM-II-D, considerando diferentes tipos de incertezas e heterogeneidades do reservatório.

Palavras Chave: gerenciamento de dados; processo de tomada de decisão; caracterização

de reservatórios; simulação numérica de reservatório e otimização de estratégia de produção; desenvolvimento do campo, quantificação de incertezas; seleção de modelos representativos.

ABSTRACT

Data management is critical in decision analysis for the development of petroleum fields and has significant roles in improving the interpretive ability of reservoir features. Hence, in recent years, it has been widely applied in different phases of reservoir characterization, simulation and management, where a fundamental part is to include subsurface uncertainties. Although it is ideal to generate realizations with all the possible combinations of uncertainties, this can result in hundreds or thousands of independent realizations, which would be extremely time-consuming to analyze the results. Therefore, selecting a subset of models, representative models (RMs), from the full-set showing the uncertainty space of the full ensemble is often essential to reduce the CPU effort and accelerate the analysis. In this work, we first developed a workflow including Hierarchical Cluster Analysis (HCA), geostatistical modeling and uncertainty quantification to identify flow units (FUs) and to generate models for simulation purposes. We also presented a solution, based on an integrated statistical approach and geological uncertainties, to select RMs from the 3D FU models. The proposed method including the integration of multi-dimensional scaling and cluster analysis (IMC). Subsequently, we generated a new workflow to select a subset of reservoir models combining distance-based clustering and data assimilation under all types of uncertainties aimed at the field development and management. Next, two scenario reduction techniques were compared focusing on field development purposes: (1) Distance-based Clustering with Simple Matching Coefficient (DCSMC) as a method of scenario reduction using static features; and (2) RMFinder method as a method of scenario reduction using dynamic features. Finally, we generated a novel robust well placement framework using the obtained RMs from the integration of the DCMC method and RMFinder method. The applied methodologies and workflows to identify flow unit, characterize reservoir, quantify uncertainty, and select representative models were tested and evaluated in a synthetic benchmark case named UNISIM-II-D considering different uncertainty types and reservoir heterogeneity.

Keywords: data management; decision-making process; reservoir characterization;

numerical simulation and optimization; uncertainty quantification; representative model selection

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NOMENCLATURE

BHP Bottom-Hole Pressure

CDF Cumulative Distribution Function

Cpor Rock compressibility

Cv Variation coefficient

FU Flow Unit

DA Data Assimilation

DCSMC Distance-based Clustering with Simple Matching Coefficient

DFN Discrete Fracture Network

DLHG Discretized Latin Hypercube with Geostatistical

FZI Flow Zone Index

HCA Hierarchical Clustering Analysis

ICV Inflow Control Valve

IMC Integration of Multi-dimensional scaling and Cluster analysis

Krw Water relative permeability

LH Latin Hypercube

MDS Multi-Dimensional Scaling

MPS Module for Parallel Simulations

Np Cumulative oil production

NPV Net Present Value

NTG Net-to-Gross

NQDS Normalized Quadratic Deviation with Signal

ORF Oil Recovery Factor

Qg Gas rate

Qo Oil rate

Qw Water rate

Qwi Water injection rate

POD Proper Orthogonal Decomposition

PVM Parallel Virtual Machine

PVT Pressure–Volume Temperature

RM Representative Model

ROM Reduced-Order Model

RQI Reservoir Quality Index

SFU Storage Flow Units

SGS Sequential Gaussian Simulation

SIS Sequential Indicator Simulation

SMLP Stratigraphic Modified Lorenz Plot

SZU Speed Zone Units

TFU Trans-missive Flow Units

Vdp Dykstra and parsons coefficient

Wi Cumulative water injection

TABLE OF CONTENTS

1 INTRODUCTION ... 11

1.1 Motivation ... 14

1.2 Objective ... 15

1.3 Case study ... 15

1.4 Outline and Structure ... 16

1.4.1 Article 1: Flow Units Characterization Methods in a Synthetic Carbonate Reservoir Model ... 16

1.4.2 Article 2: Developing a Workflow to Represent Fractured Carbonate Reservoirs for Simulation Models under Uncertainties Based on Flow Unit Concept 17 1.4.3 Article 3: Using an Integrated Multidimensional Scaling and Clustering Method to Reduce the Number of Scenarios Based on Flow Unit Models under Geological Uncertainties ... 18

1.4.4 Article 4: Developing a Workflow to Select Representative Reservoir Models Combining Distance Based Clustering and Data Assimilation for Decision Making Process 18 1.4.5 Article 5: Scenario Reduction Methodologies under Uncertainties for Reservoir Development Purposes: Distance-based Clustering with Simple Matching Coefficient Method and Metaheuristic Algorithm ... 19

2 ARTICLE 1: FLOW UNITS CHARACTERIZATION METHODS IN A SYNTHETIC CARBONATE RESERVOIR MODEL ... 21

3 ARTICLE 2: DEVELOPING A WORKFLOW TO REPRESENT FRACTURED CARBONATE RESERVOIRS FOR SIMULATION MODELS UNDER UNCERTAINTIES BASED ON FLOW UNIT CONCEPT ... 32

4 ARTICLE 3: USING INTEGRATED MULTIDIMENSIONAL SCALING AND CLUSTERING METHOD TO REDUCE THE NUMBER OF SCENARIOS BASED ON FLOW UNIT MODELS UNDER GEOLOGICAL UNCERTAINTIES ... 62

5 ARTICLE 4: DEVELOPING A WORKFLOW TO SELECT REPRESENTATIVE RESERVOIR MODELS COMBINING DISTANCE BASED CLUSTERING AND DATA ASSIMILATION FOR DECISION MAKING PROCESS ... 88

6 ARTICLE5: SCENARIO REDUCTION METHODOLOGIES UNDER UNCERTAINTIES FOR RESERVOIR DEVELOPMENT PURPOSES: DISTANCE-BASED CLUSTERING WITH SIMPLE MATCHING COEFFICIENT METHOD AND METAHEURISTIC ALGORITHM ... 125

7 CONCLUSIONS... 155

8 RECOMMENDATIONS FOR FUTURE WORKS ... 158

REFERENCES ... 159

APPENDIX A - ADDITIONAL EXPLANATIONS AND CORRECTIONS OF THE ARTICLES ... 164

APPENDIX B – LICENSE AGREEMENTS FROMPUBLISHERS GRANTING PERMISSION TO REPRODUCE PUBLISHED ARTICLES IN THIS THESIS ... 165

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1 INTRODUCTION

In the recent decade, there has been tremendous data growth in all fields of study. Quality and quantity of data are becoming the basis of competitiveness, productivity, growth, and innovation in many petroleum companies. The volume of data puts us in a special space in which data management becomes an essential part. Data management approaches extremely increase the accuracy of results interpretation and accelerate the outcome assessments (Cong et al., 2007). They can help the user to acquire, store, protect, and process required data to ensure the availability, validity, and timeliness of the data (Smith et al., 2020). There has been a vast variety of data management techniques such as data analysis, data mining, data visualization, data assimilation, etc. (Miles, 2016). They can be applied in different steps of the decision-making process in the development of petroleum fields including reservoir characterization, simulation, and uncertainties reduction.

Modeling and simulation of fluid flow in the naturally fractured reservoir have been a significant topic in the petroleum industry. The huge potential of hydrocarbon reserves in the fractured reservoirs has been a major motivation to develop this field of study. Bourbiaux (2010) described the specificities of some well-known naturally fractured reservoirs. Hence, many efforts had been taken to represent and address some of the challenges to build geological fractured models and integrate them into the numerical simulation (Lemonnier et al., 2010a, Lemonnier et al., 2010b, Delorme et al., 2014, and Noetinger et al., 2016). A robust 3D model of a fractured reservoir is necessary for the simulation of flow behavior and prediction of production performance. In most cases, the geological zonation methods cannot provide a suitable image of heterogeneous trends of carbonate reservoirs. Thus, given the fluid production conditions, a suitable zonation is essential for a better reservoir characterization.

The flow unit conception has widely been performed in the reservoir representation and modeling. Flow units are defined as some regions in a reservoir that are horizontally continuous and homogeneous in terms of petrophysical features (Hearn et al., 1984; Abbaszadeh et al., 1996; Lopez and Aguilera, 2015; Enayati-Bidgoli and Rahimpour-Bonab, 2016). Different methods have been applied to identify flow units based on different geological conditions, data limitation, and study objectives. Most researchers have applied flow zone index (FZI) using petrophysical data and then classified the obtained FZI into the different groups, such as flow units (Aminian et al., 2003; Al-Ajmi and Holditch, 2000; Soto et al., 2001; Svirsky et al., 2004). Aminian et al. (2003)

delivered a neural network technique to determine flow unit types and predict the

petrophysical parameters in the reservoir. Mahjour et al. (2016) made a comparison of different methods to identify flow units in the Tabnaak gas field in southern Iran. They

concluded thathierarchical cluster analysis is more efficient than the other methods used

for the general assessment of flow units in field scale. Their integrated model is in accordance with the well log analyses and core data results.

Flow units are also applied to divide a reservoir into different zones which are suitable for the simulation process, field development (Shan et al., 2018) and production strategies definition (Enayati-Bidgoli et al., 2014). A 3D flow unit modeling is generally utilized in the field exploration and development planning, ultimate oil recovery

prediction, well placement optimization, and production strategies definition (Enayati-Bidgoli et al., 2014).

In recent years, the quantification and understanding of geological uncertainty types in the fractured carbonates have also become increasingly important for flow unit modeling and integration with reservoir simulation. Petrophysical models are created by well-log and core data within a short interval. Lateral flow unit changes are expected among the wells, given these long inter-well distances, which presents a challenge for the modeling process. Since, in petrophysical modeling, the main parameter that controls the petrophysical distributions is flow unit, these properties are expected to change along with flow units over short distances. The distribution of petrophysical parameters depends on flow units; therefore, the uncertainty of flow unit distribution will introduce additional uncertainty to these parameters. Furthermore, other types of uncertainties should be considered during fracture modeling (e.g. fracture spacing, length, and aperture), fluid flow modeling (e.g. relative permeability curves, rock compressibility, and PVT data), operational uncertainties associated with production system accessibility, and economic uncertainties linked to the oil price, investments and operational costs to provide a broad set of reservoir simulation models.

Given the high number of uncertainties and their complexity which can have a severe effect on the financial outcomes and high investments (Santos et al., 2018), the most modern workflows in the field development are directed toward probabilistic approaches wherein hundreds to thousands of reservoir models are generated to evaluate reservoirs under uncertainties. Ideally, the engineers should consider all possible models to perform a reliable production strategy. However, the evaluation of such a large ensemble of simulation models in decision analysis technically requires computing the flow responses of all models which can be very time-consuming and complicated (Suzuki and Caers, 2008). Since the computational cost is a challenging subject for a suitable assessment in the decision-making process, it is mandatory to find solutions for accelerating the analysis of the results, especially for larger and complex reservoirs. It is imperative to introduce a flexible and user-friendly methodology that can be performed in a wide range of reservoir models. Three main approaches to accelerate the process are presented: 1- parallel computing, 2- reduced-order model (ROM), and 3- representative models (RMs).

By developing faster processors, parallel computing is the fastest and most attractive approach to run large-scale reservoir simulations for companies that are well-funded. Schiozer (1999) presented a parallel virtual machine (PVM) for accelerating the processes. The author used a program named Module for Parallel Simulations (MPS), which conducts PVM to distribute the runs effectively by taking into account the speed and dynamic characteristics of each machine. Zhang et al. (2001) presented a program for reducing memory requirement and improving computational proficiency for the simulation of largescale multi-component and multi-phase fluid flow where the role of computer memory and CPU are significant. Al-Shaalan et al. (2017) applied a parallel computing for complex well modeling in a large-scale simulation. In their work, a distributed memory approach based on message-passing interface (MPI) is performed to parallelize, in which each processor is responsible for the computation of one or several

13

complex wells. Despite showing many benefits, the improvement of software for parallel calculating has its own complexity.

Reduced-Order Model (ROM) is used to build a simpler model that can reflect exactly the original model in terms of the output of a simulator. One of the approaches of ROM is upscaling or multiscale methods (Rios et al., 2019; Correia et al. 2016; Correia et al. 2014; Maschio et al. 2003). It is performed based on rebuilding a fine grid numerical model into a coarser grid model. The upscaling procedure presents two main challenges: 1- loose the finer grid resolution and, 2- the extra computation efforts to apply upscaling before the simulation process. Another method of ROM is to create basic functions using the snapshots of time-variant problems to obtain a reduced model. In this approach, the Proper Orthogonal Decomposition (POD) techniques are used to compute these basis functions for alleviating the computational costs with a minimal loss of resolution (Awais et al., 2007; Heyouni et al., 2006; Lall et al., 2003). The central idea behind the POD method is to convert the high-dimensional models into reliable representations of reduced dimensionality. POD has been carried out for the reduction of models in many application areas (Wang et al., 2018; Cao et al., 2016; Winton et al., 2011; Aquino et al., 2007; Bui-Thanh et al., 2004; Cao et al., 2006; Fic et al., 2005). However, the changes in many parameters during history matching strongly reduce the accelerating of POD when used in the reservoir simulation. Insuasty et al. (2015) presented tensor-based techniques, which are useful to find the representations of high-dimensional data structures. They compared the method with POD for production optimization under uncertainty and showed that the obtained results in tensor models have more accuracy in proportion to the classical POD models, although the computational gain is low.

Meanwhile, there is another method named the RMs selection to accelerate the assessment of outcomes. RMs are a few models that statistically reflect the same dynamic and static properties of the full set of models. In this term, Steagall et al. (2001) explained a method wherein three categories of the models are defined based on Net Present Value (NPV): pessimistic, probable and optimistic. Due to such categories, some RMs which are close to P90, P50 and P10 (cumulative probabilities 90%, 50%, and 10%, respectively) are selected. The main assumption of this approach is that these percentiles are the main inputs for decision analysis, and models selected in this manner are consistent for application in the field development. Schiozer et al. (2004) proposed selecting the RMs close to P10, P50 and P90 based not only on NPV but also other field objective functions such as cumulative oil production (Np), cumulative water production (Wp) and oil recovery factor (ORF). Although their method is used in several works, selecting the most suitable models close to P10, P50 and P90 is still complicated and based on subjective criteria. Sarma et al. (2013) introduced an algorithm called minimax to select the RMs for uncertainty quantifications. The method can select a small subset from a large ensemble of reservoir model while preserving the uncertainty range of some field objective functions. The authors also claimed that the minimax solution is better than clustering approach in terms of the fast computation of magnitude orders. However, they did not address the usefulness of the selected RMs in decision analysis workflows. Meira et al. (2019) introduced an optimization-based method for RMs selection given the NPV value and simulation results. They presented the RMFinder technique to automatically select the RMs based on the cross-plot and risk curve of the main output

objectives and the probability distribution of the uncertain variables with levels of the problem. In all mentioned methods for selecting the RMs, defining a production strategy is obligatory, which in itself provides imprecise results since each production strategy can render different effects on the well and field objective functions. Hence, there are some data mining applications to select the RMs based on clustering methods while defining a production strategy is not required. Data mining is applied to analyze large data in order to identify meaningful patterns and rules. Although clustering methods are widely used in the petroleum industry (Pinheiro et al., 2018; Fei et al., 2016; Haghighat Sefat et al., 2016; Schedit and Caers 2009), in most cases, they merely focus on geological uncertainties and other dynamic uncertainties are not considered. These techniques are essentially based on the similarity (or dissimilarity) between the geostatistical models using some defined distance between them such as Hausdorff distance (Suzuki and Caers, 2008) and the EnKF metric (Caers and Park, 2008). The fundamental assumption in using similarity distance is that similar geostatistical models have similar flow behaviour, and it is not necessary to run all models. Instead, selecting one model from the similar models can be considered as a RM. Scheidt and Caers introduced the reduction scenarios method based on kernel-based clustering algorithms to apply uncertainty analysis for reservoir management (Caers and Park, 2008). Armstrong et al. (2013) proposed multistage coding with respect to the recourse procedure for defining the distance function and selecting the RMs in a mineral deposit problem. In the context of well placement and well control optimization, various approaches have also been applied to select the RMs using distance-based clustering (Shirangi et al., 2012; Wang et al., 2012; Torrado et al., 2015).

It is worth noting that the suitable methods for selecting the RMs can be different according to the different objectives. For example, the applied methods to select a production strategy under uncertainty focused on well placement optimization may not be the most appropriate methods to be used with well control optimization (Shirangi and Durlofsky, 2016). Furthermore, two important issues should be jointly taken into account for selecting a suitable way to reduce the number of scenarios. First, the number of models should be large enough in order to preserve the uncertainty space. Second, the number of models should be kept limited in order to decrease the computation time for simulation purposes (Shirangi and Durlofsky, 2016). The computational complexity imposed by the number of realizations remains an exciting topic (Heitsch and Römisch, 2003) and therefore, adds important challenges in order to study suitable scenario reduction methods.

1.1 Motivation

Brazilian pre-salt reservoirs from Santos Basin, Brazil, are a great recent oil discovery and they represent a good opportunity for research development. One of the main challenges of the pre-salt of Santos Basin is how to make reliable decisions during field development and management given the complexity of (1) geological and fluid properties that control the reservoir performance, and (2) different types of uncertainties that should be considered for relieving the risks. These challenges make the difficulty of interpretation and a large number of scenarios. Hence, develop and test the new methodologies to address this challenge is inevitable.

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Since data management approaches enhance the interpretive capability of reservoir features for engineers, as a motivation of this study, we decided to generate practical methodologies and workflows during the decision-making process focusing data management applications to increase the accuracy of the results and accelerate the analysis.

1.2 Objective

The main objective of this work is to apply data management approaches in reservoir characterization and simulation to obtain more reliable and accurate outcomes and accelerate the processes of decision-making during oil field development and management.

The following specific objectives focusing data management approaches are defined:

1. Identification of flow unit using data mining approaches to apply in reservoir modelling;

2. Representation of a fractured reservoir model, based on flow unit concept and integration with the numerical simulation to generate an ensemble of reservoir models under different types of uncertainties in an initial field management phase;

3. Selection of few geological RMs using a combined data management method including the Integration of Multi-dimensional scaling and Cluster analysis (IMC) to form an ensemble full set of reservoir models. This ensemble full set should guarantee the representation of uncertainty space.. The goal of the proposed method is to avoid numerical flow simulation of all models that have a close response and to highlight the models that cover the geological uncertainties and variety of flow responses; 4. Development of a new workflow to select RMs considering different uncertainty

types and reservoir heterogeneities using the integration of distance based clustering and data assimilation. This can provide an applicable solution to select appropriate RMs for the field development and management process;

5. Comparison between two scenario reduction techniques focusing on field development purposes: (1) Distance-based Clustering with Simple Matching Coefficient (DCSMC) as a method of scenario reduction using static features; and (2) RMFinder technique as a method of scenario reduction using dynamic features. 6. Comparison between two empirical data distributions considering the size of

distributions using the Kolmogorov-Smirnov (K-S).

1.3 Case study

To confirm the proposed workflows and methodologies, a synthetic fracture benchmark named UNISIM-II-D is used. The model was built by Correia et al. (2015). The required data set and related papers about the model are accessible at UNISIM’s benchmarks webpage. Before representing UNISIM-II-D at a coarse scale, it is essential to describe the reference model, UNISIM-II-R.

Reference Model: UNISIM-II-R is a reference model and was built to be used as

the real reservoir with known production data. Brazilian pre-salt reservoir data combined with synthetic information has been used to build this model. The high level of details

and his fine grid resolution make this model a reliable and practical model for different reservoir-management applications. Correia et al. (2015) described UNISIM-II-R in more detail.

UNISIM-II-D:To build the geological and fracture data obtained from UNISIM-II-R model such as well log and seismic data for three wells. UNISIM-II-D was built for studies related to the initial stage of the field-development plan, including the history production period of 516 days with available information of one vertical production well (wildcat well). The operational conditions were considered as follows: a minimum

bottom-hole pressure of 250 Kgf/cm2 and a maximum surface gas production of 50000

Kgf/cm2.

The resolution of the fine grid cell (UNISIM-II-R) is 25m × 25m × 1m and an

upscaling procedure was applied to the model to decrease the computational efforts for simulation objectives. The average coarse model grid cell size of 100m x 100m x 8m is considered suitable for representing the heterogeneity. So, roughly 95000 grid cells (41000 active cells) with acceptable estimates of petrophysical properties were generated. Figure 1.1 illustrates a coarse grid 3D permeability model reached from an example model of uncertainty approach.

Figure 1.1. Base case permeability I distribution after the upscaling procedure.

1.4 Outline and Structure

This work is divided into five scientific articles, detailed in the following subsections. Emphasis is given to the specific goals addressed in each article, and their contributions to the structure of this work.

1.4.1 Article 1:

Flow Units Characterization Methods in a

Synthetic Carbonate Reservoir Model

Seyed Kourosh Mahjour, Manuel Gomes Correia, Antonio Alberto de Souza dos Santos, Denis José Schiozer

17

9º CONGRESSO BRASILEIRO DE PESQUISA E DESENVOLVIMENTO EM PETRÓLEO E GÁS, 9-11 november (2017), Maceio, Brasil.

The main purpose of this article is to describe flow units characterization to identify barriers, baffles, and speed zone units (SZU) or Super_K layers using stratigraphic modified Lorenz plot (SMLP) method and recognize trans-missive flow units (TFU) and storage flow units (SFU) based on flow zone indicators (FZI). To reach this goal, synthetic porosity and permeability data are used from three wells (Exploration Well 1, Exploration Well 2 and Wildcat Well) of a carbonate benchmark model named UNISIM-II in a Pre-salt carbonate reservoir in Santos Basin, Brazil. Nine flow units are obtained using FZI method for each well, whereas 7, 8, 10 flow units are gained from Exploration Well 1, Exploration Well 2 and Wildcat Well, respectively based on SMLP method. Furthermore, for the better evaluation of flow units, R35 values (synthetic pore throat radius measured at 35% mercury saturation) by Winland’s equation and Dykstra-Parsons coefficient are applied to categorize pore-throats sizes and quantify reservoir heterogeneity, respectively. Finally, we analysed each flow unit according to pore size and facies. Three types of pore-throats sizes are obtained including nonporous, mega-porous and macromega-porous. The value of Dykstra-Parsons permeability coefficient was 0.76, which indicates that the reservoir is vertically heterogeneous. According to the main goal, the classified permeability and porosity model recognize reservoir barriers and productive zones. Furthermore, the presence of nanoporous zones reduced reservoir quality. Data analyses showed that high-quality flow units mainly consist of Super_K and Megaporous, which are associated with geological facies.

1.4.2 Article 2: Developing a Workflow to Represent Fractured

Carbonate Reservoirs for Simulation Models under

Uncertainties Based on Flow Unit Concept

Seyed Kourosh Mahjour, Manuel Gomes Correia, Antonio Alberto de Souza dos Santos, Denis José Schiozer

Oil & Gas Science and Technology - Rev. IFP Energies nouvelles 74, 15 (2019). https://doi.org/10.2516/ogst/2018096.

The main contribution of this article is to build an integrated workflow for a fractured reservoir model to generate an ensemble of simulation models based on flow unit concept which can span the uncertainty space. The workflow includes applying Hierarchical Clustering Analysis (HCA) to identify flow units, geostatistical methods to extend the flow units and petrophysical properties within the inter-well area, and uncertainty analysis to integrate dynamic and static uncertainties for generating ensemble reservoir simulation models.

The output of the HCA method is six flow units and one non-reservoir zone (totally seven units). The obtained flow units are evaluated by the cophenetic coefficient, correlation coefficient, and variation coefficient. Geostatistical techniques are then applied to extend the flow units, petrophysical properties and fractures into the inter-well area. Given the number of grids in the fine grid models and long simulation time for each model, upscaling process is applied to decrease in computational time and process. For generating an ensemble of 200 simulation models, dynamic and static uncertainties which

are defined in uncertainty analysis process are combined using Discretized Latin Hypercube with Geostatistical (DLHG) method.

The results represent the importance of robust reservoir characterization and integration with reservoir simulation, especially in an initial stage of a field management plan where a small amount of data is available. As a validation of the methodology, a base production strategy is defined to check the reliability of the created models with a reference model working with a real reservoir with known results. The models based on the workflow reveal sufficient consistency with the reference model under operational conditions and these are useful for the subsequent stages of field development.

1.4.3 Article 3: Using an Integrated Multidimensional Scaling

and Clustering Method to Reduce the Number of

Scenarios Based on Flow Unit Models under Geological

Uncertainties

Seyed Kourosh Mahjour, Manuel Gomes Correia, Antonio Alberto de Souza dos Santos, Denis José Schiozer

Journal of Energy Resources Technology 142(6), 063005 (2020).

https://doi.org/10.1115/1.4045736.

In this article, we present a possible solution, based on statistical approach, to select the representative models (RMs) using the similarity measure between 3D FU models. The proposed method includes the integration of multi-dimensional scaling and cluster analysis (IMC).

The IMC begins with smoothing and converting 3D FU models into 1D arrays. A matrix is then built from all present models so that each column shows a single model, and each row shows a single grid cell. Next, based on the definition of similarity distance and using multidimensional scaling method, the reservoir models are mapped into a low-dimensional space in which there are different clustering techniques for dividing the models into a few clusters. The centroid-based sampling method is subsequently applied to each cluster to select a single RM and generate a subset of the models. Eventually, a numerical simulation and then uncertainty analysis are carried out on the RMs and full set to validate and check the consistency of the methodology.

This method proves to offer a good performance in reducing the number of models so that only 9% of the geostatistical models in the ensemble (18 selected models from 200 models) can be sufficient for the uncertainty quantification if an appropriate clustering method and similarity measures are used.

1.4.4 Article

4:

Developing

a

Workflow

to

Select

Representative Reservoir Models Combining Distance

Based Clustering and Data Assimilation for Decision

Making Process

Seyed Kourosh Mahjour, Manuel Gomes Correia, Antonio Alberto de Souza dos Santos, Denis José Schiozer

19

Journal of Petroleum Science and Engineering Volume 190, 107078 (2020). https://doi.org/10.1016/j.petrol.2020.107078

In this article, we develop a new workflow to select RMs based on the integration of distance based clustering and data assimilation aimed at the field development and management.

The workflow begins with the generation of geostatistical models using a statistical sampling and then reducing them through distance based clustering. Next, discrete Latin hypercube with geostatistical realizations (DLHG) method is performed to combine other types of uncertainty with the reduced geostatistical models and build the simulation models. Eventually, data assimilation (DA) is applied to select the subset of models that match the past reservoir performance and production data. In addition, the uncertainty range are evaluated for the defined well and field objective functions using the cumulative distribution function (CDF) and non-parametric Kolmogorov-Smirnov (K-S) test.

The results show that the workflow can effectively and suitably identify the RMs considering different uncertainty types, reservoir heterogeneity and many field and well objective functions. The selected RMs are used for making production forecasts and development planning support.

1.4.5 Article 5: Scenario Reduction Methodologies under

Uncertainties for Reservoir Development Purposes:

Distance-based Clustering with Simple Matching

Coefficient Method and Metaheuristic Algorithm

Seyed Kourosh Mahjour, Antonio Alberto de Souza dos Santos, Manuel Gomes Correia, Denis José Schiozer

Arabian Journal for Science and Engineering, submitted (2020)

In this article, we attempt to compare two scenario reduction techniques focusing on field development purposes: (1) Distance-based Clustering with Simple Matching Coefficient (DCSMC) as a method of scenario reduction using static features; and (2) RMFinder technique as a method of scenario reduction using dynamic features.

To this end, we apply a set of statistical experiments to compare and evaluate the outcomes of different scenario reduction methods resulted from various production strategies. We compared the methodologies, looking at the (1) precision of the results, (2) computational time, and (3) restrictions of the methods. The comparative work is applied to a synthetic benchmark case named UNISIM-II-D considering the flow unit modeling.

The outcomes show that both scenario reduction methods are reliable to select representative models (RMs) from a specific production strategy. However, the obtained RM set from a defined strategy using the DCSMC method can be applied to other different strategies and maintain the representativeness of the models for those while the RM set selected using RMfinder tool is strongly dependent on the strategy type, so that each strategy has its own RM set.

Due to the field development workflow in which the RMFinder method is used, the number of required flow simulation models and the computational time are greater than

the workflow in which the DCSMC method is applied. In the end, the obtained RMs from the DCSMC method can be more reliable during the field development process when there is no enough information about a suitable strategy for oil production.

21

2 ARTICLE 1: FLOW UNITS CHARACTERIZATION

METHODS

IN

A

SYNTHETIC

CARBONATE

RESERVOIR MODEL

Seyed Kourosh Mahjour, Manuel Gomes Correia, Antonio Alberto de Souza dos Santos, Denis José Schiozer

9º CONGRESSO BRASILEIRO DE PESQUISA E DESENVOLVIMENTO EM PETRÓLEO E GÁS.

Abstract

Geologists and petroleum engineers have complex challenges to determine the regions that have analogous features and properties for a proper characterization, porosity– permeability modelling and dynamic reservoir simulation in heterogeneous carbonate reservoirs. Hence, the investigation of reservoir rock properties such as porosity, permeability and pore throat assists engineers to identify accurate flow units, rock typing, barrier and productive zones performance, and select well placement during field development. Two common rock-typing methods of flow unit identification are considered in this study. Flow units are determined firstly using flow zone indicators (FZI) and secondly using a stratigraphic modified Lorenz plot (SMLP). The main purpose of this research is to describe flow units characterization to identify barriers, baffles, and speed zone units (SZU) or Super_K layers using stratigraphic modified Lorenz plot (SMLP) method and recognize transmissive flow units (TFU) and storage flow units (SFU) based on flow zone indicators (FZI). To reach this goal, synthetic porosity and permeability data are used from three wells (Exploration Well 1, Exploration Well 2 and Wildcat Well) of a carbonate benchmark model named UNISIM-II in a Pre-salt carbonate reservoir in Santos Basin, Brazil. Nine flow units are obtained using FZI method for each well, whereas 7, 8, 10 flow units are gained from Exploration Well 1, Exploration Well 2 and Wildcat Well, respectively based on SMLP method. Furthermore, for the better evaluation of flow units, R35 values (synthetic pore throat radius measured at 35% mercury saturation) by Winland’s equation and Dykstra-Parsons coefficient are applied to categorize pore-throats sizes and quantify reservoir heterogeneity, respectively. Finally, we analyzed each flow unit according to pore size and facies. Three types of pore-throats sizes are obtained including nonporous, mega-porous and macroporous. The value of Dykstra-Parsons permeability coefficient was 0.76, which indicates that the reservoir is vertically heterogeneous. According to the main goal, the classified permeability and porosity model recognize reservoir barriers and productive zones. Furthermore, the presence of nanoporous zones reduced reservoir quality. Data analyses showed that high-quality flow units mainly consist of Super_K and Megaporous, which are associated with geological facies.

Keywords: flow units, pore types, reservoir characterization, porosity, permeability

Introduction

Geologists and petroleum engineers encounter intricate challenges to determine the regions that have analogous features and properties for a better characterization,

modelling and reservoir simulation in heterogeneous carbonate reservoirs. Therefore, since the last few decades, extensive studies have been carried out to advance the reservoir characterization and effective management strategies.

Pre-salt carbonate reservoirs from Santos Basin in Brazil indicate a good opportunity to study and improve reservoir characterization as an important recent oil discovery. One of the main challenges in these reservoirs is a description of rock heterogeneities, facies and flow units distribution, and the existence of high permeability layers (speed zones). Speed zones have a strong effect on the reservoir behavior, especially for the management of early water breakthrough, which may affect the location of fluid injection or production wells and the assessment of possible drilling of complex wells with accurate completions. Identification of flow units is one of the presented methods that assist to recognize permeable reservoir zones and porosity and permeability relationship even in heterogeneous carbonate reservoirs (Mahjour et al., 2015).

Flow unit is a key and basic unit concerning the fine description of future reservoir (Amaefule, 1993). Reservoir flow units represent lateral and vertical continuity and bedding characteristics, and it can be feasible for a reservoir classification to distinctive zones with similar flow regime. In each flow unit the homogeneity of data is preserved and this homogeneity fades in the borders (Mahjour et al., 2016). Several techniques were applied by several authors to identify flow units in a formation such as flow zone indicators (FZI) and stratigraphic modified Lorenz plot (SMLP) (Amaefule, 1993). Improvement of such flow unit techniques for reservoir zonation leads to the division of reservoir into different zones based on the parameters affecting fluid flow, which is a significant factor in comparison of different zones in terms of reservoir behavior. Although the porosity-permeability plot exhibits a large scatter in heterogeneous carbonate reservoirs, using data classification based on flow units, a meaningful relation between porosity and permeability can be obtained (Mahjour et al., 2015).

The main purpose of this research is to describe flow unit characterization to identify barrier (seals), baffle (zones control fluid flow) and speed zones (Super_K) using stratigraphic modified Lorenz plot (SMLP) method and recognize transmissive flow units (TFU) and storage flow units (SFU) based on flow zone indicators (FZI). To achieve this goal porosity and permeability data are used from three wells (Exploration Well 1, Exploration Well 2, and Wildcat Well) of a carbonate benchmark model named UNISIM-II in a Pre-salt carbonate reservoir in Santos Basin, Brazil. The benchmark model is based on a combination of Pre-salt characteristics and Ghawar field information according to its diagenetic events and flow features similar to Pre-salt (Correia et al., 2015). This study also quantifies reservoir heterogeneity using Dykstra-Parsons permeability coefficient, porosity-permeability regression, and pore-throats sizes based on R35 values (pore throat radius measured at 35% mercury saturation) using Winland’s equation (Pittman, 1992).

Methodology

The data acquired for this study is based on synthetic porosity and permeability data for three wells (Exploration well 1, Exploration well 2 and Wildcat well) from a benchmark case (UNISIM-II) that includes a simulation model with geological trends and rock/fluid data with dynamic characteristics from Brazilian Pre-salt reservoirs (Correia et

23

al., 2015). Due to the lack of geologic information, the reservoir model involves a combination of Pre-salt reservoirs and Ghawar field data in Brazil and Saudi Arabia, respectively. Synthetic porosity and permeability data are examined for heterogeneity measures using Dykstra Parson Coefficient, flow units identification via two statistical methodologies including flow zone indicator values (FZI), and stratigraphic modified Lorenz plot (SMLP) methods and calculation of pore size using Winland’s equation. These methods are detailed below.

Quantification of Heterogeneity Level Using Dykstra-Parsons

Coefficient (V

dp

)

Comparing to sandstone reservoirs, carbonates exploration are commonly more challenging because of inherent heterogeneities. Heterogeneity in carbonates can be related to different lithology, mineralogy, pore types, pore connectivity, and sedimentary facies. Permeability and porosity heterogeneity are quantified using Dykstra and Parsons

Coefficient (Vdp). In this method, the calculation of Vdp, data should be ranked in order

of decreasing magnitude and indicated on a chart of log probability scale.

Dykstra- Parsons coefficient (Vdp), is obtained as follows:

V_dp = (k₅₀− k_84.1)/k₅₀ (1) where K50 is median reservoir permeability and K84.1 is permeability at 84.1 percentile

Jensen et al. (1997) proposed that lower values of Vdp (0 – 0.5) represent small

heterogeneities (zero being homogeneous), while larger values (0.7–1) show large to

extremely large heterogeneities. Most reservoirs have Vdp values between 0.5 and 0.9 for

permeability data.

Hydraulic Flow Unit Determination Using Flow Zone Indicator (FZI)

Rock typing based on reservoir quality index (RQI) and flow zone indicator (FZI) was applied using Kozeny-Carman equation for the determination and classification of hydraulic flow units (HFU) (Nooruddin et al., 2011). Each of HFU has a unique FZI value (Al-Ajmi and Holditch, 2000). From dividing sides of Kozeny-Carman formula by porosity and taking the square root of both sides, Equation (2) will be obtained:

K ∅= 1 SVgrKT ( ∅e 1−∅e) (2)

where (k) is the permeability in µm2_{, (Ø) is the total porosity in fraction, (K}

T) is Kozeny

constant and usually has values of between 5 and 100 in most reservoir rocks, (SVgr) is

the surface area per unit grain volume in µm-1 and (Øe) is the effective porosity in fraction.

If permeability and porosity are respectively represented in millidarcy (mD) and fraction, then:

RQI = 0.0314 _∅k

e (3)

where the constant 0.0314 is the permeability conversion factor from μm2 _{to mD and RQI}

is rock quality index (µm).

Input data for this equation include effective core porosity (Øe) (Tiab and

Donaldson, 2004). Furthermore, porosity must be converted to normalize one as shown below:

∅Z =

∅e

1−∅e (4)

where ØZ (normalized porosity) represents ratio the of pore space volume to the grain

volume.

A flow zone indicator (FZI) value is a function of mineralogy and texture; FZI value is defined by the following equation:

FZI = RQI/∅_z (5)

Each hydraulic flow unit must be indicated by one FZI (Abbaszadeh et al., 1996).

The points with analogous FZI are placed in the same flow unit. There are several practical methods to identify hydraulic flow units using FZI, including histogram analysis, normal probability diagram, and analytic classification algorithm. In this paper, we used normal probability plot. The method is explained below. A normal distribution makes a distinct straight line on a probability plot. Therefore, the number of straight lines in the probability plot of the logarithm of FZI is used to indicate the number of hydraulic flow units in the reservoir (Mahjour et al., 2016).

Flow Unit Determination Using a Stratigraphic Modified Lorenz Plot

(SMLP)

Gunter et al. (1997) applied the stratigraphic modified Lorenz plot (SMLP) to evaluate the minimum number of flow units in a reservoir based on cumulative storage capacity (cumulative %KØ) versus cumulative flow capacity (cumulative %Kh). To construct the SMLP, continuous (ft-by-ft) core porosity and permeability data and the respective K/Ø ratios are ordered in the stratigraphic sequence of the reservoir (Gomes et al., 2008). The equation for calculating a single value of cumulative flow capacity is as follows:

(Kh)_cum = K h₁− h₀ + K h2− h1 + ⋯ Ki hi− hi−1 (6)

where K is permeability (mD), and h is the thickness of the sample interval.

A similar equation can be used to determine a single value of cumulative storage capacity:

(Øh)_cum = Ø₁ h1− h0 + Ø2 h2− h1 + ⋯ Øi hi− hi−1 (7)

25

The slope of the segments on this plot demonstrates the main flow units in their correct stratigraphic position. Flow units (speed zones, baffle zones and barrier zones) are determined by selecting changes in slope or inflection points. Steeper slopes have a greater percentage of flow capacity compare to storage capacity, and by the definition, have a high reservoir process speed. They are known “speed zones” (Gomes et al., 2008) or sometimes as “hydraulic units”. Segments with lower gradients have storage capacity but little flow capacity and are typically reservoir baffles. Segments with neither flow nor storage capacity are seals or barriers, if laterally extensive. The shape of the curve can be classified into three sections: 1- Speed Zone Unit (SZU), with high Øh % and Kh% values, 2- Baffles with high Øh % but low Kh% values, and 3- Barriers with low Øh % and Kh% values.

Winland Pore Throat Prediction Method

Winland et al., (1976) used mercury injection capillary pressure curves and multiple regression analysis to develop an empirical equation using porosity, air permeability, and the pore aperture corresponding to a mercury saturation of 35% from over 300 sandstone and limestone samples. The Winland equation was used and published by Kolodzie (1980). The Winland equation is:

Log R35 = 0.732 + 0.588 log K − 0.846 log ∅ (8)

where R35 is the pore aperture radius (in microns) at 35% mercury saturation in a mercury porosimetry test, K is core permeability (in milliDarcy), and Ø is the core porosity (in percent). Pore systems may be classified into “pore types” using pore throat radius or pore size (Pittman, 1992). Table 1 illustrates the five petrophysical pore types with distinctive reservoir performances.

Table 1. Pore types (Pitman, 1992)

Pore type Size range (µm) Megaporous >10 Macroporous 2-10 Mesoporous 0.5-2 Microporous 0.1-0.5 Nanoporous <0.1

Results

Level of Heterogeneity

Permeability and porosity heterogeneity are quantified via Dykstra-Parsons coefficient and the results showed that permeability and porosity data for three wells are heterogeneous. The heterogeneity value of permeability data for Exploitation Well 1, Exploration Well 2 and Wildcat Well are 0.70, 074 and 0.85 respectively, whereas for porosity data are 0.48, 0.53 and 0.70. Due to space restriction, we have just shown the

figures for Wildcat Well in this article. Figure 1 shows the chart of log normal probability scale to obtain Dykstra-Parsons coefficient for Wildcat Well.

Flow Zone Indicator (FZI)

Probability plot of logFZI for each well represented nine hydraulic flow units by visual inspection and a straight line drawn through it. Figure 2 indicates probability plot of logFZI for Wildcat Well.

Figure 1. Lognormal permeability and porosity distribution (Wildcat Well)

Identification of hydraulic flow units, which have an important role in flow transmissibility and storage, can be used in secondary recovery and additional production of the reservoir. According to the obtained hydraulic flow units from probability plots, transmissive flow units (TFU) and storage flow units (SFU) are defined using Lorenz plot for porosity and permeability data (Corbett et al., 2001). TFU and SFU are distinguished in the intersection of tangent and unit slope to Lorenz plot if data of each flow unit is marked on Lorenz plot.

The HFU-coded Lorenz plot indicated that around 40% of the total flow in Exploration well 1 is corresponding to HFU1. Around 72% and 78% of the total flow in Exploration Well 2 and Wildcat Well respectively, are related to HFU 1 as well. On the other hand, the contribution of HFU 1 for storing the fluid in Exploration Well 1, Exploration Well 2 and Wildcat Well is 0.2 %, 6%, and 8%, respectively. Figure 3 shows Lorenz plot for Wildcat Well.

27

Figure 2. Probability plot of logFZI for Wildcat Well

Stratigraphic Modified Lorenz Plot (SMLP)

Flow units 7, 8, and 10 flow units are obtained from Exploration Well 1, Exploration Well 2 and Wildcat Well, respectively using SMLP method. Determining baffles, barriers, and speed zone units (SZU) or Super_K using SMLP method showed that baffle zones are dominant in three wells. Figure 4 shows that Wildcat Well includes 10 flow units. In this well, flow units 1, 2, 4, 6, 8, and 10 are baffles and flow units 3, 5, 7, and 9 are speed zones. Baffles, barriers, and speed zone units for other wells are illustrated in Table 2.

Figure 3. Lorenz Plot for Wildcat Well

Figure 4. Stratigraphic modified Lorenz plot for Wildcat Well

Table 2. Identification of baffles, barriers and speed zone units (SZU) for Exploration Well 1 and 2 using SMLP plot

Well FU1 FU2 FU3 FU4 FU5 FU6 FU7 FU8

Exploration Well 1

Baffle Baffle Barrier Baffle Speed

zone

Baffle Baffle Speed

29

Exploration

Well 2

Baffle Baffle Speed

zone Baffle Speed zone Baffle Speed zone Baffle

Winland Pore Throat

Determining pore throat size (R35) from porosity and permeability data for the reservoir units provided the best basis for defining reservoir flow units. In this study, three types of pore throat sizes are obtained: macroporous, megaporous, and nanoporous. Macroporous was dominant for three wells (around 77%).

Matching of Flow Units

Through Petrel software, well sections of three wells are generated (Figure 5 for Wildcat Well). The facies log data is used to compare with flow units and pore types. Note that there is a good boundary matching among FZI method, pore size and facies in high and low permeable zones whereas this agreement was faded for SMLP method. The presence of nanoporous zones reduced reservoir quality. Data analyses showed that high quality flow units mainly consist of Super_K and megaporous, which are associated with geological facies. Furthermore, the value of logFZI and R35 are greater in high permeable flow units.

Figure 5. Well section for Wildcat Well

Conclusions

Flow zone indicator (FZI), stratigraphic modified Lorenz plot (SMLP), and Winland R35 method are applied in this research. The following conclusions are drawn from the current study.

 FZI analysis showed that there are nine flow units for each well, whereas flow units 7, 8 and 10 flow units are obtained from Exploration Well 1, Exploration Well 2 and Wildcat Well, respectively using SMLP method.

 Among hydraulic flow units; HFU 1 is one of the most important reservoir subunits in the flow transmissibility. On the other hand, baffles, barriers, and speed zone units (SZU) are achieved using SMLP method for each well.

 The concept of flow unit is integrated with the pore size data to investigate the rock physical characteristics, providing a good basis for simulation purposes.

 In this study, three types of pore throat sizes are obtained: megaporous, macroporous, and nanoporous. Macroporous was dominant in three wells.

 In general, there is a good boundary agreement between good quality HFU and pore types with reservoir facies and vice versa.

Acknowledgment

The authors are grateful to the Centre of Petroleum Studies (Cepetro-Unicamp/Brazil), UNISIM, Foundation Computer Modeling Group (FCMG) and the Petroleum Engineering Division (DEP-FEM Unicamp/Brazil) for their support of this work, and Schlumberger for the software license Petrel.

References

 Abbaszadeh, M., Fujii, H., Fujimoto, F., “Permeability Prediction by Hydraulic Flow Units- Theory and Applications ” , paper SPE 30158 prepared for presentation at the SPE Petrovietnam Conference held in Hochiminh, Vietnam, 1-3 March, 1996.  AL-Ajmi, F.A. and Holditch, S.A., “Permeability estimation using hydraulic flow

units in a central Arabia reservoir”, paper SPE 63254, 2000.

 Amaefule, J.O., Altunbay, M., Tiab, D., Kersey, D.G., Kedan, D.K., “Enhanced reservoir description: Using core and log data to identify hydraulic (flow) units and predict permeability in uncored intervals/wells” ,paper, SPE 26436 prepared for presentation at 68th Ann. Tech. Conf, and Exhibit, Houston, TX,1993.

 Corbett, P.W.M., Ellabad, Y., Mohammed ,K., “The Recognition, Modeling and Validation of Hydraulic Units in Reservoir Rock”, prepared for presentation at 3rd Institute of Mathematics and its Applications Conference on Modelling Permeable Rocks, 27–29 March, Cambridge, 2001.

 Correia, M.G. Hohendorff, A. T. F. S. Gaspar, and D. Schiozer, “UNISIM-II-D: Benchmark Case Proposal Based on a Carbonate Reservoir”, SPE Latin American and Caribbean Petroleum Engineering Conference in Quito, Ecuador, 18–20 November 2015.

 Gomes, J.S., Riberto, M.T., Strohmenger, C.J., Negahban, S. and Kalam, M.Z., “Carbonate reservoir rock typing the link between geology and SCAL”,paper SPE 118284, 2008.

 Gunter, G.W., Finneran, J.M., Hartmann, D.J., Miller, J.D., “Early Determination of Reservoir Flow Units Using an Integrated Petrophysical Method “, paper SPE 38679 prepared for presentation at the 1997 SPE Annual Technical Conference and Exhibition held in San Antonio, Texas, 5-8 October, 1997.

31

 Kolodzie, S.J., “Analysis of pore throat size and use of the Waxman-Smits equation

to determine OOIP in spindle field, Colorado”, prepared for presentation at the 55th Annual Technical Conference and Exhibition, Sept. 21-24, Dallas, Texas, 1980.  Mahjour, S.K., Al-Askari, M.K.G. & Masihi, M., “Flow-units verification, using

statistical zonation and application of Stratigraphic Modified Lorenz Plot in Tabnak gas field”, Egyptian Journal of Petroleum, 2015.05.018.

 Mahjour, S.K., Al-Askari, M.K.G. & Masihi, M., “Identification of flow units using methods of Testerman statistical zonation, flow zone index, and cluster analysis in Tabnaak gas field”, J Petrol Explor Prod Technol, 2016, 6: 577.

 Nooruddin. H, Hossain. M, “Modified Kozeny-Carmen correlation for enhanced hydraulic flow unit characterization”, J. Pet. Sci. Eng., 80, pp. 107-115, 2011.  Pittman, E.D., “Estimating pore throat size in sandstones from routine core-analysis

data”, AAPG Bull., 76: 191-198, 1992.

 Tiab D, Donaldson EC., “Petrophysics: Theory and Practice of Measuring reservoir Rock and Fluid Transport Properties. s.l”, Gulf Professional Publishing, 2004.

3 ARTICLE 2: DEVELOPING A WORKFLOW TO

REPRESENT

FRACTURED

CARBONATE

RESERVOIRS FOR SIMULATION MODELS UNDER

UNCERTAINTIES BASED ON FLOW UNIT CONCEPT

Seyed Kourosh Mahjour, Manuel Gomes Correia, Antonio Alberto de Souza dos Santos, Denis José Schiozer

Oil & Gas Science and Technology - Rev. IFP Energies nouvelles 74, 15 (2019). https://doi.org/10.2516/ogst/2018096.

Abstract

Description of fractured reservoir rock under uncertainties in a 3D model and integration with reservoir simulation is still a challenging topic. In particular, mapping the potential zones with a reservoir quality can be very useful for making decisions and support development planning. This mapping can be done through the concept of flow units. In this paper, an integrated approach including a hierarchical cluster analysis (HCA), geostatistical modeling and uncertainty analysis is developed and applied to a fractured carbonate in order to integrate on numerical simulation. The workflow begins with different HCA methods, performed to well-logs in three wells, to identify flow units and rock types. Geostatistical techniques are then applied to extend the flow units, petrophysical properties and fractures into the inter-well area. Finally, uncertainty analysis is applied to combine different types of uncertainties for generating ensemble reservoir simulation models. The obtained clusters from different HCA methods are evaluated by the cophenetic coefficient, correlation coefficient, and variation coefficient, and the most appropriate clustering method is used to identify flow units for geostatistical modelling. We subsequently define uncertainties for static and dynamic properties such as permeability, porosity, net-to-gross, fracture, water-relative permeability, fluid properties, and rock compressibility. Discretized Latin hypercube with geostatistical (DLHG) method is applied to combine the defined uncertainties and create an ensemble of 200 simulation models which can span the uncertainty space. Eventually, a base production strategy is defined under operational conditions to check the consistency and reliability of the models created with UNISIM-II-R (reference model) as a real reservoir with known results. Results represent the compatibility of the methodology to characterize fractured reservoirs since those models are consistent with the reference model (used to generate the simulation models). The proposed workflow provides an efficient and useful means of supporting development planning under uncertainty. Keywords: reservoir characterization, reservoir simulation, hierarchical cluster analysis, geostatistical methods, uncertainty analysis

1- Introduction

Modeling and simulation of fluid flow in the naturally fractured reservoir have been a significant topic in the petroleum industry. The huge potential hydrocarbon reserve in the fractured reservoirs has been a major motivation to develop this field of study.