This document summarizes a paper that quantifies uncertainties in petrophysical properties derived from well logs. It shows that the interpretation model used can be a major source of uncertainty, and that Monte Carlo modeling provides a way to quantify this. Different log analysis models are compared for water, oil, and gas bearing sands. For gas sands, density and sonic porosity estimates without hydrocarbon corrections exceed the actual porosity range. Core data provides the best uncertainty estimates by validating logs, and Monte Carlo can match these when using the proper interpretation model.
Uncertainty in Petrophysics From Bayes To Monte CarloSimon Stromberg
Increasingly, reduced petrophysical data sets are being used to make critical decisions about the location of deepwater exploration wells. In addition, while drilling deepwater wells, reduced data sets are being used to make well design and completion decisions that may impact the safe operation of the well. However, despite numerous examples in the literature of how data is used to make decisions, very little attention has been given to reliability of the data and its impact on uncertainty, diagnosis, and risk. This presentation will act as a catalyst for starting a discussion on the impact of data reliability on risk assessment. The talk will cover the fundamental principles of uncertainty risk and the impact of data reliability on decision making. Two examples will be used to illustrate the issues. The first will look at risking of exploration wells using AVO response that has low/marginal reliability. The second example will be the risk analysis of a published paper: ‘Detecting Shallow Drilling Hazard in Large Boreholes Using LWD Acoustics’. This paper avoided the issue of data reliability. The potential impact of not considering data reliability will be explored and discussed with the group.
Căn hộ HOT nhất quận 8- chỉ 956 triệu căn- thiết kế đẹp- tiện ích xung quanhnguyennguyenanh
Chủ đầu tư : Công ty CP TM-DV-XD-Kinh doanh nhà Vạn Thái.
Dự án Topaz City tọa lạc vị trí đẹp, ở góc đường Tạ Quang Bửu và Cao Lỗ, Phường 4, Q.8. Tuyến đường kết nối với các đường lớn đi về trung tâm Quận 1, Q5, Đại Lộ Nguyễn Văn Linh đi Q7 và Bình Chánh, đại lộ Võ Văn Kiệt đi Quận 6 …Từ chung cư Topaz city bạn chỉ tốn 10 phút để đi đến Quận 1, và Q5 qua cầu Nguyễn Tri Phương và Cầu chữ Y. TOPAZ CITY-Đô thị đẳng cấp bên sông liền kề quận 1,4,5 và Phú Mỹ Hưng giá 956tr/căn 2pn.
Tuyến đường đẹp, là chốn an cư lý tưởng cho sự lựa chọn về nhà ở - là nơi sinh lợi cho đầu tư
Topaz City với thiết kế: 69,63-69,90-70,14-72,96-95,57(m2)
Tiện ích:
- Trường học, khu vui chơi dành riêng cho thiếu nhi,..
- Hồ bơi nội, ngoại khu, quảng trường ngọc trai,...
- Trung tâm thương mại, mua sắm, spa, gym ngay tầng trệt khu chung cư và khuôn viên hệ thống cây xanh rộng lớn thoáng mát.
Không những bạn được tận hưởng những tiện ích trong tương lai ngoài ra bạn còn được sở hữu ngay những tiện tích hiện hữu ngay xung quanh căn hộ như: Bệnh viện quận 8, hồ bơi Hòa Bình, Đại học FTU, Rmit,...
Thanh toán trước 20% và 80% còn lại sẽ thanh toán theo tiến độ của dự án.
Ngân hàng hỗ trợ vay 70% trả trong vòng 15 năm lãi suất ưu đãi.
Pháp lý hợp lệ.
Liên hệ tư vấn mua nhà: Ms Anh 0914144303
Uncertainty in Petrophysics From Bayes To Monte CarloSimon Stromberg
Increasingly, reduced petrophysical data sets are being used to make critical decisions about the location of deepwater exploration wells. In addition, while drilling deepwater wells, reduced data sets are being used to make well design and completion decisions that may impact the safe operation of the well. However, despite numerous examples in the literature of how data is used to make decisions, very little attention has been given to reliability of the data and its impact on uncertainty, diagnosis, and risk. This presentation will act as a catalyst for starting a discussion on the impact of data reliability on risk assessment. The talk will cover the fundamental principles of uncertainty risk and the impact of data reliability on decision making. Two examples will be used to illustrate the issues. The first will look at risking of exploration wells using AVO response that has low/marginal reliability. The second example will be the risk analysis of a published paper: ‘Detecting Shallow Drilling Hazard in Large Boreholes Using LWD Acoustics’. This paper avoided the issue of data reliability. The potential impact of not considering data reliability will be explored and discussed with the group.
Căn hộ HOT nhất quận 8- chỉ 956 triệu căn- thiết kế đẹp- tiện ích xung quanhnguyennguyenanh
Chủ đầu tư : Công ty CP TM-DV-XD-Kinh doanh nhà Vạn Thái.
Dự án Topaz City tọa lạc vị trí đẹp, ở góc đường Tạ Quang Bửu và Cao Lỗ, Phường 4, Q.8. Tuyến đường kết nối với các đường lớn đi về trung tâm Quận 1, Q5, Đại Lộ Nguyễn Văn Linh đi Q7 và Bình Chánh, đại lộ Võ Văn Kiệt đi Quận 6 …Từ chung cư Topaz city bạn chỉ tốn 10 phút để đi đến Quận 1, và Q5 qua cầu Nguyễn Tri Phương và Cầu chữ Y. TOPAZ CITY-Đô thị đẳng cấp bên sông liền kề quận 1,4,5 và Phú Mỹ Hưng giá 956tr/căn 2pn.
Tuyến đường đẹp, là chốn an cư lý tưởng cho sự lựa chọn về nhà ở - là nơi sinh lợi cho đầu tư
Topaz City với thiết kế: 69,63-69,90-70,14-72,96-95,57(m2)
Tiện ích:
- Trường học, khu vui chơi dành riêng cho thiếu nhi,..
- Hồ bơi nội, ngoại khu, quảng trường ngọc trai,...
- Trung tâm thương mại, mua sắm, spa, gym ngay tầng trệt khu chung cư và khuôn viên hệ thống cây xanh rộng lớn thoáng mát.
Không những bạn được tận hưởng những tiện ích trong tương lai ngoài ra bạn còn được sở hữu ngay những tiện tích hiện hữu ngay xung quanh căn hộ như: Bệnh viện quận 8, hồ bơi Hòa Bình, Đại học FTU, Rmit,...
Thanh toán trước 20% và 80% còn lại sẽ thanh toán theo tiến độ của dự án.
Ngân hàng hỗ trợ vay 70% trả trong vòng 15 năm lãi suất ưu đãi.
Pháp lý hợp lệ.
Liên hệ tư vấn mua nhà: Ms Anh 0914144303
The Executive Briefing Service from New Haven Technologies provides MSPs using ConnectWise with executive-level reporting capabilities, dashboards and SmartPhone reports.
Number of iterations needed in Monte Carlo Simulation using reliability analy...IJERA Editor
There are many methods in geotechnical engineering which could take advantage of Monte Carlo Simulation to
establish probability of failure, since closed form solutions are almost impossible to use in most cases. The
problem that arises with using Monte Carlo Simulation is the number of iterations needed for a particular
simulation.This article will show why it’s important to calculate number of iterations needed for Monte Carlo
Simulation used in reliability analysis for tunnel supports using convergence – confinement method. Number if
iterations needed will be calculated with two methods. In the first method, the analyst has to accept a distribution
function for the performance function. The other method suggested by this article is to calculate number of
iterations based on the convergence of the factor the analyst is interested in the calculation.
Reliability analysis will be performed for the diversion tunnel in Rrëshen, Albania, by using both methods
mentioned and results will be confronted
Distillation Column Process Fault Detection in the Chemical IndustriesISA Interchange
Chemical plants are complex large-scale systems which need designing robust fault detection schemes to ensure high product quality, reliability and safety under different operating conditions. The present paper is concerned with a feasibility study of the application of the black-box modeling method and Kullback Leibler divergence (KLD) to the fault detection in a distillation column process. A Nonlinear Auto-Regressive Moving Average with eXogenous input (NARMAX) polynomial model is firstly developed to estimate the nonlinear behavior of the plant. Furthermore, the KLD is applied to detect abnormal modes. The proposed FD method is implemented and validated experimentally using realistic faults of a distillation plant of laboratory scale. The experimental results clearly demonstrate the fact that proposed method is effective and gives early alarm to operators.
Fault Detection in the Distillation Column ProcessISA Interchange
Chemical plants are complex large-scale systems which need designing robust fault detection schemes to ensure high product quality, reliability and safety under different operating conditions. The present paper is concerned with a feasibility study of the application of the black-box modeling method and Kullback Leibler divergence (KLD) to the fault detection in a distillation column process. A Nonlinear Auto-Regressive Moving Average with eXogenous input (NARMAX) polynomial model is firstly developed to estimate the nonlinear behavior of the plant. Furthermore, the KLD is applied to detect abnormal modes. The proposed FD method is implemented and validated experimentally using realistic faults of a distillation plant of laboratory scale. The experimental results clearly demonstrate the fact that proposed method is effective and gives early alarm to operators.
NONLINEAR EXTENSION OF ASYMMETRIC GARCH MODEL WITHIN NEURAL NETWORK FRAMEWORKcscpconf
The importance of volatility for all market participants has led to the development and
application of various econometric models. The most popular models in modelling volatility are
GARCH type models because they can account excess kurtosis and asymmetric effects of
financial time series. Since standard GARCH(1,1) model usually indicate high persistence in the
conditional variance, the empirical researches turned to GJR-GARCH model and reveal its
superiority in fitting the asymmetric heteroscedasticity in the data. In order to capture both
asymmetry and nonlinearity in data, the goal of this paper is to develop a parsimonious NN
model as an extension to GJR-GARCH model and to determine if GJR-GARCH-NN outperforms
the GJR-GARCH model.
Nonlinear Extension of Asymmetric Garch Model within Neural Network Framework csandit
The importance of volatility for all market partici
pants has led to the development and
application of various econometric models. The most
popular models in modelling volatility are
GARCH type models because they can account excess k
urtosis and asymmetric effects of
financial time series. Since standard GARCH(1,1) mo
del usually indicate high persistence in the
conditional variance, the empirical researches turn
ed to GJR-GARCH model and reveal its
superiority in fitting the asymmetric heteroscedast
icity in the data. In order to capture both
asymmetry and nonlinearity in data, the goal of thi
s paper is to develop a parsimonious NN
model as an extension to GJR-GARCH model and to det
ermine if GJR-GARCH-NN outperforms
the GJR-GARCH model.
Fault Modeling for Verilog Register Transfer Levelidescitation
As the complexity of Very Large Scale Integration
(VLSI) increases, testing becomes tedious. Currently fault
models are used to test digital circuits at gate level or at levels
lower than gate. Modeling faults at these levels, leads to
increase in the design cycle time period. Hence, there is a
need to explore new approaches for modeling faults at higher
levels. This paper proposes fault modeling at the Register
Transfer Level (RTL) for digital circuits. Using this level of
modeling, results are obtained for fault coverage, area and
test patterns. A software prototype, FEVER, has been developed
in C which reads a RTL description and generates two output
files: one a modified RTL with test features and two a file
consisting of set of test patterns. These modified RTL and test
patterns are further used for fault simulation and fault
coverage analysis. Comparison is performed between the RTL
and Gate level modeling for ISCAS benchmarks and the
results of the same are presented. Results are obtained using
Synopsys, TetraMax and it is shown that it is possible to achieve
100% fault coverage with no area overhead at the RTL level
The Executive Briefing Service from New Haven Technologies provides MSPs using ConnectWise with executive-level reporting capabilities, dashboards and SmartPhone reports.
Number of iterations needed in Monte Carlo Simulation using reliability analy...IJERA Editor
There are many methods in geotechnical engineering which could take advantage of Monte Carlo Simulation to
establish probability of failure, since closed form solutions are almost impossible to use in most cases. The
problem that arises with using Monte Carlo Simulation is the number of iterations needed for a particular
simulation.This article will show why it’s important to calculate number of iterations needed for Monte Carlo
Simulation used in reliability analysis for tunnel supports using convergence – confinement method. Number if
iterations needed will be calculated with two methods. In the first method, the analyst has to accept a distribution
function for the performance function. The other method suggested by this article is to calculate number of
iterations based on the convergence of the factor the analyst is interested in the calculation.
Reliability analysis will be performed for the diversion tunnel in Rrëshen, Albania, by using both methods
mentioned and results will be confronted
Distillation Column Process Fault Detection in the Chemical IndustriesISA Interchange
Chemical plants are complex large-scale systems which need designing robust fault detection schemes to ensure high product quality, reliability and safety under different operating conditions. The present paper is concerned with a feasibility study of the application of the black-box modeling method and Kullback Leibler divergence (KLD) to the fault detection in a distillation column process. A Nonlinear Auto-Regressive Moving Average with eXogenous input (NARMAX) polynomial model is firstly developed to estimate the nonlinear behavior of the plant. Furthermore, the KLD is applied to detect abnormal modes. The proposed FD method is implemented and validated experimentally using realistic faults of a distillation plant of laboratory scale. The experimental results clearly demonstrate the fact that proposed method is effective and gives early alarm to operators.
Fault Detection in the Distillation Column ProcessISA Interchange
Chemical plants are complex large-scale systems which need designing robust fault detection schemes to ensure high product quality, reliability and safety under different operating conditions. The present paper is concerned with a feasibility study of the application of the black-box modeling method and Kullback Leibler divergence (KLD) to the fault detection in a distillation column process. A Nonlinear Auto-Regressive Moving Average with eXogenous input (NARMAX) polynomial model is firstly developed to estimate the nonlinear behavior of the plant. Furthermore, the KLD is applied to detect abnormal modes. The proposed FD method is implemented and validated experimentally using realistic faults of a distillation plant of laboratory scale. The experimental results clearly demonstrate the fact that proposed method is effective and gives early alarm to operators.
NONLINEAR EXTENSION OF ASYMMETRIC GARCH MODEL WITHIN NEURAL NETWORK FRAMEWORKcscpconf
The importance of volatility for all market participants has led to the development and
application of various econometric models. The most popular models in modelling volatility are
GARCH type models because they can account excess kurtosis and asymmetric effects of
financial time series. Since standard GARCH(1,1) model usually indicate high persistence in the
conditional variance, the empirical researches turned to GJR-GARCH model and reveal its
superiority in fitting the asymmetric heteroscedasticity in the data. In order to capture both
asymmetry and nonlinearity in data, the goal of this paper is to develop a parsimonious NN
model as an extension to GJR-GARCH model and to determine if GJR-GARCH-NN outperforms
the GJR-GARCH model.
Nonlinear Extension of Asymmetric Garch Model within Neural Network Framework csandit
The importance of volatility for all market partici
pants has led to the development and
application of various econometric models. The most
popular models in modelling volatility are
GARCH type models because they can account excess k
urtosis and asymmetric effects of
financial time series. Since standard GARCH(1,1) mo
del usually indicate high persistence in the
conditional variance, the empirical researches turn
ed to GJR-GARCH model and reveal its
superiority in fitting the asymmetric heteroscedast
icity in the data. In order to capture both
asymmetry and nonlinearity in data, the goal of thi
s paper is to develop a parsimonious NN
model as an extension to GJR-GARCH model and to det
ermine if GJR-GARCH-NN outperforms
the GJR-GARCH model.
Fault Modeling for Verilog Register Transfer Levelidescitation
As the complexity of Very Large Scale Integration
(VLSI) increases, testing becomes tedious. Currently fault
models are used to test digital circuits at gate level or at levels
lower than gate. Modeling faults at these levels, leads to
increase in the design cycle time period. Hence, there is a
need to explore new approaches for modeling faults at higher
levels. This paper proposes fault modeling at the Register
Transfer Level (RTL) for digital circuits. Using this level of
modeling, results are obtained for fault coverage, area and
test patterns. A software prototype, FEVER, has been developed
in C which reads a RTL description and generates two output
files: one a modified RTL with test features and two a file
consisting of set of test patterns. These modified RTL and test
patterns are further used for fault simulation and fault
coverage analysis. Comparison is performed between the RTL
and Gate level modeling for ISCAS benchmarks and the
results of the same are presented. Results are obtained using
Synopsys, TetraMax and it is shown that it is possible to achieve
100% fault coverage with no area overhead at the RTL level
2008 IFAC World Congress: Oil and gas production optimization - lost potentia...Steinar Elgsæter
The information content in measurements of offshore oil and gas production is often low, and when a production model is fitted to such data, uncertainty may result. If production is optimized with an uncertain model, some potential production profit may be lost. The costs and risks of introducing additional excitation are typically large and cannot be justified unless the potential increase in profits are quantified. In previous work it is discussed how bootstrapping can be used to estimate uncertainty resulting from fitting production models to data with low information content. In this paper we propose how lost potential resulting from estimated uncertainty can be estimated using Monte-Carlo analysis. Based on a conservative formulation of the production optimization problem, a potential for production optimization in excess of 2% and lost potential due to the form of uncertainty considered in excess of 0.5% was identified using field data from a North Sea field.
Democratizing Fuzzing at Scale by Abhishek Aryaabh.arya
Presented at NUS: Fuzzing and Software Security Summer School 2024
This keynote talks about the democratization of fuzzing at scale, highlighting the collaboration between open source communities, academia, and industry to advance the field of fuzzing. It delves into the history of fuzzing, the development of scalable fuzzing platforms, and the empowerment of community-driven research. The talk will further discuss recent advancements leveraging AI/ML and offer insights into the future evolution of the fuzzing landscape.
Water scarcity is the lack of fresh water resources to meet the standard water demand. There are two type of water scarcity. One is physical. The other is economic water scarcity.
Sachpazis:Terzaghi Bearing Capacity Estimation in simple terms with Calculati...Dr.Costas Sachpazis
Terzaghi's soil bearing capacity theory, developed by Karl Terzaghi, is a fundamental principle in geotechnical engineering used to determine the bearing capacity of shallow foundations. This theory provides a method to calculate the ultimate bearing capacity of soil, which is the maximum load per unit area that the soil can support without undergoing shear failure. The Calculation HTML Code included.
Cosmetic shop management system project report.pdfKamal Acharya
Buying new cosmetic products is difficult. It can even be scary for those who have sensitive skin and are prone to skin trouble. The information needed to alleviate this problem is on the back of each product, but it's thought to interpret those ingredient lists unless you have a background in chemistry.
Instead of buying and hoping for the best, we can use data science to help us predict which products may be good fits for us. It includes various function programs to do the above mentioned tasks.
Data file handling has been effectively used in the program.
The automated cosmetic shop management system should deal with the automation of general workflow and administration process of the shop. The main processes of the system focus on customer's request where the system is able to search the most appropriate products and deliver it to the customers. It should help the employees to quickly identify the list of cosmetic product that have reached the minimum quantity and also keep a track of expired date for each cosmetic product. It should help the employees to find the rack number in which the product is placed.It is also Faster and more efficient way.
Overview of the fundamental roles in Hydropower generation and the components involved in wider Electrical Engineering.
This paper presents the design and construction of hydroelectric dams from the hydrologist’s survey of the valley before construction, all aspects and involved disciplines, fluid dynamics, structural engineering, generation and mains frequency regulation to the very transmission of power through the network in the United Kingdom.
Author: Robbie Edward Sayers
Collaborators and co editors: Charlie Sims and Connor Healey.
(C) 2024 Robbie E. Sayers
Student information management system project report ii.pdfKamal Acharya
Our project explains about the student management. This project mainly explains the various actions related to student details. This project shows some ease in adding, editing and deleting the student details. It also provides a less time consuming process for viewing, adding, editing and deleting the marks of the students.
Explore the innovative world of trenchless pipe repair with our comprehensive guide, "The Benefits and Techniques of Trenchless Pipe Repair." This document delves into the modern methods of repairing underground pipes without the need for extensive excavation, highlighting the numerous advantages and the latest techniques used in the industry.
Learn about the cost savings, reduced environmental impact, and minimal disruption associated with trenchless technology. Discover detailed explanations of popular techniques such as pipe bursting, cured-in-place pipe (CIPP) lining, and directional drilling. Understand how these methods can be applied to various types of infrastructure, from residential plumbing to large-scale municipal systems.
Ideal for homeowners, contractors, engineers, and anyone interested in modern plumbing solutions, this guide provides valuable insights into why trenchless pipe repair is becoming the preferred choice for pipe rehabilitation. Stay informed about the latest advancements and best practices in the field.
Automobile Management System Project Report.pdfKamal Acharya
The proposed project is developed to manage the automobile in the automobile dealer company. The main module in this project is login, automobile management, customer management, sales, complaints and reports. The first module is the login. The automobile showroom owner should login to the project for usage. The username and password are verified and if it is correct, next form opens. If the username and password are not correct, it shows the error message.
When a customer search for a automobile, if the automobile is available, they will be taken to a page that shows the details of the automobile including automobile name, automobile ID, quantity, price etc. “Automobile Management System” is useful for maintaining automobiles, customers effectively and hence helps for establishing good relation between customer and automobile organization. It contains various customized modules for effectively maintaining automobiles and stock information accurately and safely.
When the automobile is sold to the customer, stock will be reduced automatically. When a new purchase is made, stock will be increased automatically. While selecting automobiles for sale, the proposed software will automatically check for total number of available stock of that particular item, if the total stock of that particular item is less than 5, software will notify the user to purchase the particular item.
Also when the user tries to sale items which are not in stock, the system will prompt the user that the stock is not enough. Customers of this system can search for a automobile; can purchase a automobile easily by selecting fast. On the other hand the stock of automobiles can be maintained perfectly by the automobile shop manager overcoming the drawbacks of existing system.
Vaccine management system project report documentation..pdfKamal Acharya
The Division of Vaccine and Immunization is facing increasing difficulty monitoring vaccines and other commodities distribution once they have been distributed from the national stores. With the introduction of new vaccines, more challenges have been anticipated with this additions posing serious threat to the already over strained vaccine supply chain system in Kenya.
Saudi Arabia stands as a titan in the global energy landscape, renowned for its abundant oil and gas resources. It's the largest exporter of petroleum and holds some of the world's most significant reserves. Let's delve into the top 10 oil and gas projects shaping Saudi Arabia's energy future in 2024.
1. Copyright 2005, Society of Petroleum Engineers Inc.
This paper was prepared for presentation at the 2005 Asia Pacific Oil & Gas Conference and
Exhibition held in Jakarta, Indonesia, 5 – 7 April 2005.
This paper was selected for presentation by an SPE Program Committee following review of
information contained in a proposal submitted by the author(s). Contents of the paper, as
presented, have not been reviewed by the Society of Petroleum Engineers and are subject to
correction by the author(s). The material, as presented, does not necessarily reflect any
position of the Society of Petroleum Engineers, its officers, or members. Papers presented at
SPE meetings are subject to publication review by Editorial Committees of the Society of
Petroleum Engineers. Electronic reproduction, distribution, or storage of any part of this paper
for commercial purposes without the written consent of the Society of Petroleum Engineers is
prohibited. Permission to reproduce in print is restricted to a proposal of not more than 300
words; illustrations may not be copied. The proposal must contain conspicuous
acknowledgment of where and by whom the paper was presented. Write Librarian, SPE, P.O.
Box 833836, Richardson, TX 75083-3836, U.S.A., fax 01-972-952-9435.
Abstract
Typical petrophysical deliverables for volumetric and
modeling purposes are net reservoir, porosity, permeability,
water saturation and contact locations. These data are usually
provided without quantitative determination of their
uncertainties.
Current computing power renders it now feasible to use
Monte-Carlo simulation to determine the uncertainty in
petrophysical deliverables. Unfortunately, quantitative
uncertainty definition is more than just using Monte-Carlo
simulation to vary the inputs in your interpretation model. The
largest source of uncertainty may be the interpretation model
itself.
This paper will use a variety of porosity interpretation
models to illustrate how the impact of each input on the
uncertainty varies with the combination of input values used in
any given model. It will show that use of the incorrect model
through oil and gas zones may give porosity estimates with
Monte-Carlo derived uncertainty ranges that exclude the
actual porosity.
Core data provides the best means of quantifying actual
uncertainty in the petrophysical deliverables. Methodologies
for deriving uncertainties quantitatively by comparison with
core data will be presented. In the absence of core data,
interpretation models should have been tested against core
data through the same or similar formations nearby. Monte-
Carlo simulation can then be used as an effective means of
quantifying petrophysical uncertainty. Comparisons between
the core comparison and Monte-Carlo techniques will be
made, showing that similar results are achieved with the
appropriate interpretation models.
The methodologies described in this paper are
straightforward to implement and enable petrophysical
deliverables to be treated appropriately in volumetric and
modeling studies. In addition, quantification of petrophysical
uncertainty assists in operational decision-making by letting
users know how reliable the numbers produced actually are,
and what range of properties is physically realistic. Such work
also allows the key contributions to uncertainty to be defined
and targeted if overall volumetric uncertainty must be reduced.
Introduction
Petrophysical evaluations are carried out for a number of
different purposes, including operational decision-making,
volume in place estimation and reservoir modeling. In all
cases, the uncertainty in the deliverables of net reservoir,
porosity, permeability, water saturation and contact locations
are critical. However, these data are usually provided without
quantitative determination of their uncertainties.
This paper will highlight the ease with which uncertainties
can be derived using Monte-Carlo simulation. It will also
illustrate how flexible this technique is when it comes to
working with different interpretation models, which is not
commonly done. The largest source of uncertainty in
petrophysical interpretation may be the interpretation model
itself.
Given the large number of possible interpretation models
for all the different petrophysical deliverables, this paper will
only use the most basic petrophysical deliverable, being
porosity, to illustrate the relationship between uncertainty and
the log interpretation model selected.
It will also be shown that verification of log porosity using
an independent measure such as core porosity can also provide
quantitative uncertainties allowing comparison with the log
derived uncertainties.
The State of Uncertainty in Petrophysics
The requirement for quantification of petrophysical
uncertainty is not a recent development. Many papers are in
the literature describing functions for uncertainty definition
and how to use Monte-Carlo modeling for the same purposes.
Although work such as that of Amaefule & Keelan (1989),
Chen & Fang (1986) and Hook (1983) provides an excellent
foundation on which to calculate uncertainties, the
methodologies are both time consuming to program and
inflexible with regard to interpretation model.
With the computing power available on desktop machines
today, engineers no longer have to use these analytical
techniques to derive uncertainty. Monte-Carlo models are
straightforward to build and no longer time consuming to run.
The literature contains a number of examples of Monte-Carlo
simulation being used to characterize petrophysical
uncertainty, such as the work of Spalburg (2004).
SPE 93125
Quantifying Petrophysical Uncertainties
S.J. Adams, WellEval.com Ltd.
2. 2 SPE 93125
However, none of these examples highlight the uncertainty
owing to the interpretation models being used.
Monte-Carlo Modeling & Assumptions
In order to understand the problems associated with Monte-
Carlo simulation and how best to overcome them, a simple
explanation of the technique is warranted.
Monte Carlo methods use random numbers and probability
descriptors for the input variables to investigate problems
expressed as mathematical formulae. As an example, if a
simple density porosity calculation is considered, as shown in
the equation below:
φd = (ρma – ρ)/( ρma – ρfl)
where ρma is the matrix density, ρ is the density log
measurement and ρfl is the density of the fluid in the pore
space of the zone investigated by the density tool and φd is the
log-derived density porosity.
The input values (ρma, ρ, ρfl) all have uncertainties
associated with them, so the resulting output (φd) will also
have an uncertainty. With Monte-Carlo simulation, the
uncertainty in the output is determined by randomly selecting
input values from their uncertainty distributions and
calculating the output value. The output value is stored then
the input selection and calculation processes are repeated a
large number of times. Finally all the output values are
examined statistically to determine the uncertainty in the
output value.
Monte-Carlo modeling is very flexible, allowing different
interpretation models to be built and the uncertainties tested
quickly. Dependencies between input variables may also be
accounted for in the input value determination.
The downside to Monte-Carlo simulation is that a large
number of cycles (>500) are typically required for meaningful
statistics to be developed. This point is illustrated below where
the equation for density porosity above has been modeled
through a water-bearing sand. In Figure 1 the distribution of
porosities does not begin to approach a reasonable (“normal”)
shape until 500 scenarios or more are run.
0.00
0.05
0.10
0.15
0.20
0.25
0.16 0.17 0.18 0.19 0.2 0.21 0.22 0.23 0.24 0.25 0.26
density porosity (v/v)
normalisedfrequency
50
100
500
10000
30000
Figure 1 – Histogram of the density porosities derived using
Monte-Carlo simulation through a water-bearing sand. Only
the number of scenarios (from 50 to 30000) changes between
each curve.
0.16
0.17
0.18
0.19
0.20
0.21
0.22
0.23
0.24
10 100 1000 10000 100000
number of scenarios
porosityvalues(v/v)
P90
P50
P10
Figure 2 – The P90, P50 and P10 statistics derived from the
Monte-Carlo density porosity distributions vary with the
number of scenarios modeled.
Figure 2 shows how the statistics derived from the
porosity distributions do not approach the correct values until
at least 500 scenarios have been run.
Note that the required number of scenarios for statistical
accuracy will increase with the number of input variables used
in any particular model.
Porosity Uncertainty Using Monte-Carlo in
Theoretical Cases
To illustrate the significance of the assumptions and models
used for uncertainty quantification, the basic petrophysical
deliverable of total porosity is used.
Monte-Carlo models have been built for density porosity,
sonic porosity and density-neutron porosities. The
uncertainties in these three different methods are compared
through water, oil and gas bearing sand models.
Figure 3 compares the porosities calculated for the same
density log measurement in known water, oil and gas systems.
This Figure serves to illustrate that not correcting for the
presence of hydrocarbons will result in significant errors in
density porosity estimates. Indeed, failure to correct for
hydrocarbons in a gas-bearing zone will result in most likely
porosity estimates that do not include the actual porosity value
in the P90 to P10 uncertainty range.
0
0.1
0.2
0.3
0.4
0.5
0.1 0.15 0.2 0.25 0.3
density porosity (v/v)
normalisedfrequency
water
oil
gas
Figure 3 – Histogram of the density porosities derived using
Monte-Carlo simulation through water, oil and gas-bearing
sands. Note that these porosity estimates are corrected for the
presence of hydrocarbons.
3. SPE 93125 3
Figure 4 compares the porosities calculated from the
density-neutron log combination using the same scenarios as
modeled for the density porosity. In this case, the reduced
neutron response through the gas-bearing sand results in some
correction for the hydrocarbons. However, this “correction”
would not be so apparent were the sands shaley. The porosities
estimated through the oil sands show little correction for the
presence of hydrocarbons.
0
0.1
0.2
0.3
0.4
0.5
0.1 0.15 0.2 0.25 0.3
density-neutron porosity (v/v)
normalisedfrequency
water
oil
gas
Figure 4 – Histogram of the density-neutron porosities
derived using Monte-Carlo simulation through water, oil and
gas-bearing sands. Note that no assumptions have been made
about the presence of hydrocarbons.
Figure 5 compares the porosities calculated from the sonic
log using the same scenarios as modeled for the density
porosity. Again, the porosity estimated for the water-bearing
sands is a match with the density log-based estimate.
However, the porosities for the oil and gas-bearing sands are a
little too high unless corrections for the presence of
hydrocarbons are made. Of course, in the case of this
theoretical model, such corrections are possible using the work
of Batzle and Wang (1992), but in real cases, the porosities
through the hydrocarbon-bearing intervals must be derived
from another source before quantitative corrections for
hydrocarbons can be made.
0
0.1
0.2
0.3
0.4
0.1 0.15 0.2 0.25 0.3
sonic porosity (v/v)
normalisedfrequency
water
oil
gas
Figure 5 – Histogram of the sonic porosities derived using
Monte-Carlo simulation through water, oil and gas-bearing
sands. Note that no assumptions have been made about the
presence of hydrocarbons.
To better illustrate that the various porosity models do
actually give different results and different uncertainty
distributions Figures 6, 7 and 8 compare the water, oil and
gas-bearing sand porosities for the three porosity interpretation
techniques.
In the water-bearing sands (Figure 6), all three techniques
give similar porosity values, but the uncertainty distributions
are slightly different, as should be expected. In the oil-bearing
sands (Figure 7), the best estimate of the porosities differs
significantly between the different interpretation techniques,
yet the range of the uncertainties for each technique remains
similar to that observed for the water-bearing case. And in the
case of gas-bearing sands (Figure 8), the differences in the
best estimate of porosity increase even more between the
interpretation techniques, while the uncertainty ranges remain
virtually unchanged from the water-bearing case.
It is clear from the foregoing that even porosity estimation
from wireline log data can give different answers depending
on the method used i.e. on the logs used and whether or not
hydrocarbon corrections are carried out. Accordingly the
uncertainty estimates also differ depending on the models
used.
0
0.1
0.2
0.3
0.4
0.5
0.1 0.15 0.2 0.25 0.3
porosity (v/v)
normalisedfrequency
density
density-neutron
sonic
Figure 6 – Histogram of the porosities derived using Monte-
Carlo simulation through water-bearing sands.
0
0.1
0.2
0.3
0.4
0.5
0.1 0.15 0.2 0.25 0.3
porosity (v/v)
normalisedfrequency
density
density-neutron
sonic
Figure 7 – Histogram of the porosities derived using Monte-
Carlo simulation through oil-bearing sands.
4. 4 SPE 93125
0
0.1
0.2
0.3
0.4
0.5
0.1 0.15 0.2 0.25 0.3
porosity (v/v)
normalisedfrequency
density
density-neutron
sonic
Figure 8 – Histogram of the porosities derived using Monte-
Carlo simulation through gas-bearing sands.
Porosity Uncertainty Using Monte-Carlo in Real
Cases
To allow the conclusions drawn from the theoretical models
presented in the previous section to be verified, real data has
been selected from cored wells through water, oil and gas
columns. Figures 9, 10 and 11 show the data. Note that only
the “density HC corr” data has been hydrocarbon corrected
(using invaded zone resistivity logs).
In the water-bearing sands (Figure 9), the log-derived
density and sonic porosities have similar average values, close
to those from the core data. While the density-neutron
combination actually overestimates porosities in these sands.
The data also confirm that the uncertainty ranges are different
for each measurement type. Note too that the log-derived
porosities have not been calibrated to the core data.
What is particularly interesting about Figure 9 is that the
actual average porosity value confirmed by both the core and
hydrocarbon corrected density porosity is less than the P90
estimate from the density-neutron combination.
In the oil-bearing sands (Figure 10), the porosity estimates
are much closer together, with all the uncertainty ranges (P90
to P10) including the actual best estimate porosity from the
core data. What is significant here is that the density porosities
should be corrected for the density difference due to even oil
being lighter than water i.e. the non-hydrocarbon corrected
density porosities are already 0.5 p.u. too high. The density-
neutron porosities are also on average 1.0 p.u. too high.
The largest differences are observed in the gas-bearing
sands (Figure 11), with the sonic and non-hydrocarbon
corrected density porosities being more than 2.0 p.u. too high.
Indeed the P90 to P10 uncertainty ranges for these porosity
models do not include the actual best estimate porosity from
the core data. Even the density-neutron combination
overestimates porosity by 0.5 p.u.
0
0.1
0.2
0.3
0.4
0.5
0.1 0.15 0.2 0.25 0.3
porosity (v/v)
normalisedfrequency
density
density HC corr.
density-neutron
sonic
core
Figure 9 - The log-derived porosity statistics for water-
bearing sands in a medium porosity shaley sand reservoir.
0
0.1
0.2
0.3
0.4
0.5
0.1 0.15 0.2 0.25 0.3
porosity (v/v)
normalisedfrequency
density
density HC corr.
density-neutron
sonic
core
Figure 10 - shows the log-derived porosity statistics for oil-
bearing sands in a similar medium porosity shaley sand
reservoir.
0
0.1
0.2
0.3
0.4
0.1 0.15 0.2 0.25 0.3
porosity (v/v)
normalisedfrequency
density
density HC corr.
density-neutron
sonic
core
Figure 11 - The log-derived porosity statistics for gas-bearing
sands in a similar medium porosity shaley sand reservoir.
A second set of examples from a different region are
presented as Figures 12, 13 and 14.
In the water-bearing reservoir (Figure 12), the log-derived
density and sonic porosities have similar average values, close
to those from the core data. While the density-neutron
combination again overestimates porosities in these sands.
In the oil-bearing reservoir here (Figure 13), the porosity
estimates still show divergent most likely values. In fact the
density-neutron based porosity estimate again does not
encompass the actual best porosity estimate from core within
5. SPE 93125 5
the P90 to P10 range. In this example too, the value of
correcting the density porosities for even oil is apparent.
The largest differences are again observed in the gas-
bearing reservoir (Figure 14), with the sonic and non-
hydrocarbon corrected density porosities being more than 5.0
p.u. too high. Here too, the P90 to P10 uncertainty ranges for
these porosity models do not include the actual best estimate
porosity from the core data. Even the density-neutron
combination does a poor job, underestimating porosity by 2.3
p.u.
0
0.1
0.2
0.3
0.4
0.1 0.15 0.2 0.25 0.3
porosity (v/v)
normalisedfrequency
density
density HC corr.
density-neutron
sonic
core
Figure 12 - The log-derived porosity statistics for water-
bearing sands in a medium porosity limestone reservoir.
0
0.1
0.2
0.3
0.4
0.15 0.2 0.25 0.3 0.35
porosity (v/v)
normalisedfrequency
density
density HC corr.
density-neutron
sonic
core
Figure 13 - The log-derived porosity statistics for oil-bearing
limestone in the same unit as Figure 12.
0
0.1
0.2
0.3
0.4
0.15 0.2 0.25 0.3 0.35
porosity (v/v)
normalisedfrequency
density
density HC corr.
density-neutron
sonic
core
Figure 14 - The log-derived porosity statistics for gas-bearing
limestone in the same unit as Figures 12 and 13.
Porosity Uncertainty By Core Comparison
Since the real cases presented in the previous section also had
core data acquired over the same logged intervals, it is
possible to compare the log-derived total porosities with those
measured on the equivalent piece of core.
When making such a comparison, there are two factors to
bear in mind. Firstly, the depth match between log and core
data must be excellent so that the same intervals are in fact
being compared. Secondly, the porosity resolution at the log
scale is not the same as that derived from the core plug scale.
If the core porosity data is not “filtered” back to a similar
resolution to the log-derived data, then the variability (or
uncertainty) implied by the comparison will be larger than it
should be.
Figures 9, 10, 11, 12, 13 and 14 all show very similar most
likely porosity estimates and uncertainty distributions for the
hydrocarbon-corrected density and the core porosities. This
observation implies that the best match to the core porosities is
using these hydrocarbon-corrected density porosities.
Although the other porosity estimation techniques can provide
reliable porosities in some circumstances, provided the
hydrocarbon influence on the log measurements being used
are taken into account.
Overall Porosity Uncertainty Interpretation
From the foregoing, it is apparent that the uncertain ranges
estimated using Monte-Carlo simulation are interpretation
model dependent. It is still possible for calculated uncertainty
ranges not to include the actual reservoir porosities, if an
inappropriate porosity interpretation model is used.
The best way to ensure that the appropriate interpretation
model is selected is by comparison with core data. If no core
data is available, then the work presented herein suggests that
hydrocarbon-corrected density porosities should be used. If it
is not possible to carry out these calculations, then whatever
model is selected should either include hydrocarbon correction
or model the likely range of hydrocarbon densities in the
uncertainty analyses.
Uncertainty in Other Petrophysical Deliverables
Of course the techniques discussed and conclusions drawn
from the work presented in this paper are equally valid for
other petrophysical properties such as water saturation,
permeability, net reservoir and contact locations.
Although not detailed in this paper, since the impact of the
porosity uncertainties illustrated is sufficient to illustrate the
value of model uncertainty quantification, it is good practice to
derive uncertainties in all petrophysical deliverables so that
users are aware of any limitations in the data presented.
Conclusions
Monte-Carlo simulation is well suited to uncertainty
quantification in the current petrophysical environment.
However, simply calculating uncertainty is insufficient unless
it can be shown that the interpretation model applied is
appropriate. This conclusion is true for all petrophysical
deliverables, not just porosity as presented in this paper. Good
quality core data provides an excellent basis on which to
determine the appropriate interpretation model.
6. 6 SPE 93125
With Monte-Carlo modeling, care should also be taken to
ensure that sufficient scenarios are run to determine valid
statistics on the output values. Generally a few tens of
scenarios are insufficient. Typically greater than 500 runs are
required.
Petrophysical evaluation should attempt to determine
uncertainties in at least the critical items of porosity and water
saturation. Knowledge of the possible range of values enables
Operators to make better data gathering and completion
decisions. Reservoir modeling studies are also more likely to
include scenarios approaching the real reservoir.
Acknowledgements
The author would like to acknowledge the feedback received
from many clients over the years that have seen the value of
uncertainty quantification in their petrophysical deliverables
once the data was made available to them.
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