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### NARROW

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P.L. Essley

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Journal Articles

Journal:
Journal of Petroleum Technology

Publisher: Society of Petroleum Engineers (SPE)

*Journal of Petroleum Technology*17 (08): 911–918.

Paper Number: SPE-1140-PA

Published: 01 August 1965

Abstract

Several different types of interest tables are commonly used by petroleumengineers. Conventional (or year-end) and midyear tables are based on aneffective interest rate i, while continuous interest tables are expressed as afunction of a nominal rate j. To avoid confusion, a rate of return i calculatedusing midyear or year-end tables should be called an effective rate of return, while a rate of return j calculated using continuous interest tables should becalled a nominal rate of return. When either type of rate is known, the othercan he determined readily from a simple equation. Conversion factory to adjustreceiving income other than at the end of a period are derived and their usediscussed. Introduction The use of interest tables seems to be quite simple. However, there are anumber of different types of commonly used interest tables that give differentresults. For instance, for a single problem one engineer using conventionalinterest tables might calculate a rate of return of 41 per cent. another usingmidyear tables might calculate a rate of return of 55 per cent, while stillanother using continuous interest tables might calculate a rate of return of 44per cent. This occasionally can result in considerable confusion when twonegotiating companies use different types of interest tables, or when differentdepartments of a company use different types of tables. The purpose of thispaper is to point out the relationship between the various types of interesttables, to show how results compare, and to show how answers obtained using onetype of table can be converted to equivalent answers from other types oftables. Nomenclature and Symbols In addition to the different types of tables in common use, there are anumber of ways to express compound interest to account for different patternsof income or to simplify the solution of different types of interest problems. A set of interest tables. of any type, may include a compound interest table. apresent worth table, several annuity tables, a sinking fund table, a partialpayment table, an equivalent nominal rate table. auxiliary tables, or othertables. Such interest tables are related through simple mathematicalexpressions. Unfortunately, there is no uniformity in what we call thesefactors, or tables. Identical tables, obtained from different sources, may havecompletely different, apparently unrelated, names (i.e., present value vsprincipal, which will amount to a given sum). On the other hand, similarnomenclature is often used with the different types of tables. Thus, a set ofconventional interest tables and set of continuously compounded interest tablesmight both include a table labeled "present worth", which will containdifferent factors within the tables. A similar lack of standardization existswith regard to the mathematical symbols used in interest equations. Such lackof standardization might cause a casual user of interest tables to becomeconfused. The nomenclature and symbols used in this paper are similar to thoseused by the Financial Publishing Co. Conventional Compound-Interest Equations and Tables Conventional interest tables are based on the premise that interest iscompounded periodically and that income, or payments, is received at the end ofeach period. The following are the common ways that compound interest can beexpressed. Amount of $1 at Compound Interest The amount of compound interest is often called the amount of 1", the"single payment compound amount". or the "amount". It shows how $1 at compoundinterest will grow. Expressed as an equation, it is (Amount of 1) = s = (1 + i) . . . (1) where i = the uniform rate of interest, fraction n = the number of periodsof interest conversions, and I indicates conventional interest equations, whereincome is received and compounded at the end of each period. The amount at theend of each period is obtained by multiplying the amount at the beginning ofthe period by the ratio of increase (1 + i). A compound interest table can beconstructed for any rate by successive multiplication by the ratio ofincrease. JPT P. 911ˆ

Journal Articles

Journal:
Journal of Petroleum Technology

Publisher: Society of Petroleum Engineers (SPE)

*Journal of Petroleum Technology*17 (01): 19–25.

Paper Number: SPE-920-PA

Published: 01 January 1965

Abstract

Reservoir engineering involves more than applied reservoir mechanics. The objective of engineering is optimization. To obtain optimum profit from a field the engineer or the engineering team must identify and define all individual reservoirs and their physical properties, deduce each reservoir's performance, prevent drilling of unnecessary wells, initiate operating controls at the proper time, and consider all important economic factors, including income taxes. Early and accurate identification and definition of the reservoir system is essential to effective engineering. Conventional geologic techniques seldom provide sufficient data to identify and define each individual reservoir; the engineer must supplement the geologic study with engineering data and tests to provide the necessary information. Reservoir engineering is difficult. The most successful practitioner is usually the engineer who, through extensive efforts to understand the reservoir, manages to acquire a few more facts and thus needs fewer assumptions. Introduction Reservoir engineering has advanced rapidly during the last decade. The industry is drilling wells on wider spacing, unitizing earlier, and recovering a greater percentage of the oil in place. Techniques are better, tools are better, and background knowledge of reservoir conditions has been greatly improved. In spite of these general advances, many reservoirs are being developed in an inefficient manner, vital engineering considerations often are neglected or ignored, and individual engineering efforts often are inferior to those of a decade ago. Reservoir engineers often disagree in their interpretation of a reservoir's performance. It is not uncommon for two engineers to take exactly opposite positions before a state commission. Such disagreements understandably confuse and bewilder management, lawyers, state commission members and laymen. Can they be blamed if they question the technical competence of a professional group whose members cannot agree among themselves?There is considerable difference between the reservoir engineering practiced by different companies. The differences between good engineering and ineffective engineering generally involve only minor variations in fundamental knowledge but involve major differences in emphasis of what is important. Some companies or groups emphasize calculation procedures and reservoir mechanics, but pay little attention to reservoir geology. Others emphasize geology and make extensive efforts to identify individual reservoirs and deduce their performance during the development period or during the early operating period. They use reservoir engineering equations and calculation procedures primarily as tools to provide additional insight of a reservoir's performance. Those utilizing the latter approach generally are the most successful. The differences in practice observed indicate that many individuals, including managers, field personnel, educators, scientists and reservoir engineers do not understand the full scope of reservoir engineering or bow the reservoir engineer can be used most effectively. A better understanding of the basic purpose of reservoir engineering and how it can be utilized most effectively should result in improved engineering. Reservoir Engineering - A Group Effort The Purpose of EngineeringThe goal of engineering is optimization. The purpose of reservoir engineering is to provide the facts, information and knowledge necessary to control operations to obtain the maximum possible recovery from a reservoir at the least possible cost. Since a maximum recovery generally is not obtained by a minimum expenditure, the engineer must seek some optimum combination of recovery, cost, and other pertinent factors. How one defines "optimum" will depend upon the policies of the various operators and is immaterial to the views presented in this paper. From an operator's point of view any procedure or course of action that results in an optimum profit to the company is effective engineering, and any that doesn't is not. There are two reasons why a company may not receive effective engineering. Its engineers may be poorly trained and fail to perform property. However, a company can employ competent engineers and receive good engineering work from them, but as a company, still do an ineffective job of engineering. For instance, an engineer might do an excellent job of water flooding a reservoir. However, if even greater profit could have been received by water flooding five years earlier, then obviously the reservoir was not effectively engineered by the operator. JPT P. 19ˆ