Petroleum Engineering 620 — Fluid Flow in Petroleum Reservoirs Math Lecture 5 — The Laplace Transform

Tom BLASINGAME | t-blasingame@tamu.edu | Texas A&M U.

Objectives: (things you should know and/or be able to do)

Self-Study

Introduction to Laplace Transforms(Properties and Theorems)

Slide — 1

Petroleum Engineering 620 — Fluid Flow in Petroleum Reservoirs Math Lecture 5 — The Laplace Transform

Tom BLASINGAME | t-blasingame@tamu.edu | Texas A&M U.

Objectives: (things you should know and/or be able to do)

Slide — 2

Petroleum Engineering 620 — Fluid Flow in Petroleum Reservoirs Math Lecture 5 — The Laplace Transform

Tom BLASINGAME | t-blasingame@tamu.edu | Texas A&M U.

Objectives: (things you should know and/or be able to do)

Self-Study

Application of the Laplace Transform:Solution of Ordinary Differential Equations

Slide — 3

Petroleum Engineering 620 — Fluid Flow in Petroleum Reservoirs Math Lecture 5 — The Laplace Transform

Tom BLASINGAME | t-blasingame@tamu.edu | Texas A&M U.

Objectives: (things you should know and/or be able to do)

Slide — 4

Petroleum Engineering 620 — Fluid Flow in Petroleum Reservoirs Math Lecture 5 — The Laplace Transform

Tom BLASINGAME | t-blasingame@tamu.edu | Texas A&M U.

Objectives: (things you should know and/or be able to do)

Slide — 5

Petroleum Engineering 620 — Fluid Flow in Petroleum Reservoirs Math Lecture 5 — The Laplace Transform

Tom BLASINGAME | t-blasingame@tamu.edu | Texas A&M U. Slide — 6

Petroleum Engineering 620 — Fluid Flow in Petroleum Reservoirs Math Lecture 5 — The Laplace Transform

Tom BLASINGAME | t-blasingame@tamu.edu | Texas A&M U.

Properties of the Laplace Transform: Piecewise Step Data Function

Slide — 7

Petroleum Engineering 620 — Fluid Flow in Petroleum Reservoirs Math Lecture 5 — The Laplace Transform

Tom BLASINGAME | t-blasingame@tamu.edu | Texas A&M U.

Properties of the Laplace Transform: Piecewise Linear Data Function

Slide — 8

Petroleum Engineering 620 — Fluid Flow in Petroleum Reservoirs Math Lecture 5 — The Laplace Transform

Tom BLASINGAME | t-blasingame@tamu.edu | Texas A&M U.

Properties of the Laplace Transform: Piecewise Linear Data Function

Slide — 9

Petroleum Engineering 620 — Fluid Flow in Petroleum Reservoirs Math Lecture 5 — The Laplace Transform

Tom BLASINGAME | t-blasingame@tamu.edu | Texas A&M U.

Properties of the Laplace Transform: Piecewise Linear Data Function

Slide — 10

Petroleum Engineering 620 — Fluid Flow in Petroleum Reservoirs Math Lecture 5 — The Laplace Transform

Tom BLASINGAME | t-blasingame@tamu.edu | Texas A&M U.

Properties of the Laplace Transform: Piecewise Power-Law Data Function

Slide — 11

Petroleum Engineering 620 — Fluid Flow in Petroleum Reservoirs Math Lecture 5 — The Laplace Transform

Tom BLASINGAME | t-blasingame@tamu.edu | Texas A&M U.

Properties of the Laplace Transform: Piecewise Power-Law Data Function

Slide — 12

Petroleum Engineering 620 — Fluid Flow in Petroleum Reservoirs Math Lecture 5 — The Laplace Transform

Tom BLASINGAME | t-blasingame@tamu.edu | Texas A&M U. Slide — 13

Petroleum Engineering 620 — Fluid Flow in Petroleum Reservoirs Math Lecture 5 — The Laplace Transform

Tom BLASINGAME | t-blasingame@tamu.edu | Texas A&M U.

Numerical Laplace Transform and Inversion

Slide — 14

Petroleum Engineering 620 — Fluid Flow in Petroleum Reservoirs Math Lecture 5 — The Laplace Transform

Tom BLASINGAME | t-blasingame@tamu.edu | Texas A&M U.

Numerical Laplace Transform and Inversion

Slide — 15

Petroleum Engineering 620 — Fluid Flow in Petroleum Reservoirs Math Lecture 5 — The Laplace Transform

Tom BLASINGAME | t-blasingame@tamu.edu | Texas A&M U.

Numerical Laplace Transform and Inversion

Slide — 16

Petroleum Engineering 620 — Fluid Flow in Petroleum Reservoirs Math Lecture 5 — The Laplace Transform

Tom BLASINGAME | t-blasingame@tamu.edu | Texas A&M U.

Numerical Laplace Transform and Inversion

Slide — 17

Petroleum Engineering 620 — Fluid Flow in Petroleum Reservoirs Math Lecture 5 — The Laplace Transform

Tom BLASINGAME | t-blasingame@tamu.edu | Texas A&M U.

Numerical Laplace Transform and Inversion

Slide — 18