FORMATION EVALUATION
Lecture 7
Lithologies
1
Importance of Lithology
Without a good Lithology Interpretation we
cannot calculate
the correct porosity
OR the correct hydrocarbon
saturation
2
Importance
Lecture 6
Formation density and neutron
logs
Formation Density Log
Formation density logs
These are active gamma logs, i.e., there is a source of
gamma rays on the tool as well as 2 detectors
The dens
Relative Permeability
Diagrams:
A model reservoir
Paul Glover
1
Darcys Law: flow rate (laminar)
Q = kaA(DP/L)/m
Absolute permeability (ka) in ideal case, a property
of the rock only, not the fluid.
2
0N1 Mathematics Lecture 8 Predicate Logic
48
Lecture 8
Predicate Logic
Many mathematical sentences involve unknowns or variables.
Examples.
(i) x > 2 (where x stands for an unknown real number).
(ii)
0N1 Mathematics Lecture 14 By contradiction
72
Lecture 14
Proof by contradiction
*
Recommended reading: Richard
Hammack, Book of Proof, Chapter 6.
Suppose we want to prove some statement q. Assume
tha
0N1 Mathematics Lecture 12 Methods of Proof 64
Lecture 12
Methods of proof, continued
II Statements of the form (8x)(p(x) ! q(x)
An example is
For all x, if x > 2 then x2 > 4.
In practice such a sente
0N1 Mathematics Lecture 10 Predicate Logic Logical equivalences 57
Lecture 10
Logical equivalences
Statements can be formed from predicates by means of a mixture of connectives and quantiers.
Examples
78
0N1 Mathematics Lecture 16 Polynomials
Lecture 16
Polynomials, continued
Division with remainder
If f (x) is a polynomial and ax + b is a linear polynomial we
can investigate whether ax + b is a fa
0N1 Mathematics Lecture 1
7
Lecture Notes
Lecture 1
Sets
A set is any collection of objects, for example, set of numbers.
The objects of a set are called the elements of the set.
A set may be specied
0N1 Mathematics Arrangements for the Course
2
Arrangements for the Course
Aims of 0N1
A basic course in pure mathematical topics for members
of the foundation year.
Key ingredient: language of Mathe
14
0N1 Mathematics Lecture 3
Lecture 3
Operations on Sets
A
A[B
A\B
B
Figure 2: Sets A and B and their intersection A \ B and union
A [ B.
Suppose A and B are sets. Then A \ B denotes the set of
all e
23
0N1 Mathematics Lecture 4 Set Theory
Lecture 4
Set theory
The identities in (1)-(7) of the previous lecture are called the
laws of Boolean algebra. Several of them are obvious because * obvious = e
0N1 Mathematics Lecture 18 Roots and Coefficients 87
Lecture 18
Relations between the roots and
the coe cients of a polynomial
Consider
ax2 + bx + c = a(x
The right hand side (RHS) is
a(x2
x
)(x
)
*
T
0N1 Mathematics Lecture 6 Propositional Logic 38
Lecture 6
Propositional Logic, Continued
Notice that p ! q and q ! p are dierent; q ! p is called
the converse of p ! q.
Example. Let p = x > 2 and q =
ON1 Test 5 Friday 9 November 2012
This test counts 6% of assessment for the course.
Time allocated: 11:3511:50
Name:
Student Number:
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Marking scheme: 2 marks for a complete correct answ
0N1 Mathematics Exercises 5 Predicate Logic
1
Exercises 5
1. In each of the following nd values of x and y which make p(x, y) true
and nd values which make p(x, y) false. (Only one example of each is
ON1 Test 4 Friday 26 October 2011
This test counts 4% of assessment for the course.
Time allocated: 11:4011:50
PLEASE FILL IN CLEARLY, IN BLOCK CAPITALS:
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Marking
ON1 Test 3 Friday 19 October 2012
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Time allowed: 10 minutes
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ON1 Test 2 Friday 12 October 2012
This test counts 4% of assessment for the course.
Time allowed: 5 minutes
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ON1 Test 1 Friday 5 October 2012
This test counts 4% of assessment for the course.
Time allowed: 5 minutes
PLEASE FILL IN CLEARLY, IN BLOCK CAPITALS:
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0N1 Mathematics Exercises 7
1
1. Which of the following statements are true?
(i) 105 is divisible by 15.
(ii) 13 | 2971.
(iii) 99 is a divisor of 3960.
(iv) 75 and 192 have no common factors.
2. Find
0N1 Mathematics Exercises 10
1
1. Prove, by induction on n, that n < 2n for every positive integer n.
2. Prove, by induction on n, that
1 + 3 + 5 + + (2n 1) = n2
for every positive integer n.
3. A seq
0N1 Mathematics Exercises 9
1
1. Find the remainder when
(i) x4 5x3 + 6x2 7 is divided by (x 1)(x 3).
(ii) x4 + x2 7 is divided by x2 4.
2. Find the constants a and b such that, when x4 ax2 + b is div
0N1 Mathematics
Assignment 2
1.
(i) If A B is it necessarily true that B A?
(ii) If A B and A C is it necessarily true that B = C?
(iii) If A B and B C is it necessarily true that A C?
(iv) If A B is
0N1 Mathematics Exercises 6
1
1. Find whether the following statements are true or false where the universal
set is
Z = cfw_. . . , 3, 2, 1, 0, 1, 2, 3, . . ..
(i)
(ii)
(iii)
(iv)
(v)
(vi)
(x)(y)(z)z
0N1 Mathematics Assignment 4
1. Determine the truth value of each of the compound statements (a), (b)
and (c) given the following information:
(i)
(ii)
(iii)
(iv)
The statement Mr Black is taller than
0N1 Mathematics Exercises 3
1. Using the laws of Boolean algebra simplify the following expressions.
(i)
(ii)
(iii)
(iv)
( )
( )
( )
( )
2. Let = cfw_ : 1 > 2 and < 4 and let = cfw_ : 5 2
20. Prov