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TAMU PETE 301 - 301.505.Lab5_Situ_E

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(This sheet must be included with your work submission)Required Academic Integrity Statement: (Texas A&M University Policy Statement)Coursework Copyright Statement: (Texas A&M University Policy Statement)Lab Assignment Coversheet(This sheet must be included with your work submission)Required Academic Integrity Statement: (Texas A&M University Policy Statement)Academic Integrity StatementAll syllabi shall contain a section that states the Aggie Honor Code and refers the student to the Honor Council Rules andProcedures on the web.Aggie Honor Code"An Aggie does not lie, cheat, or steal or tolerate those who do."Upon accepting admission to Texas A&M University, a student immediately assumes a commitment to uphold the Honor Code, to accept responsibility for learning and to follow the philosophy and rules of the Honor System. Students will be required to state their commitment on examinations, research papers, and other academic work. Ignorance of the rules does not exclude any member of the Texas A&M University community from the requirements or the processes of the Honor System. For additional information please visit: www.tamu.edu/aggiehonor/On all course work, assignments, and examinations at Texas A&M University, the following Honor Pledge shall be preprintedand signed by the student:"On my honor, as an Aggie,I have neither given nor received unauthorized aid on this academic work."Aggie Code of Honor:An Aggie does not lie, cheat, or steal or tolerate those who do.Required Academic Integrity Statement:"On my honor, as an Aggie, I have neither given nor receivedunauthorized aid on this academic work." Evan Situ ____________(Print your name) Evan Situ _________(Your signature)Coursework Copyright Statement: (Texas A&M University Policy Statement)The handouts used in this course are copyrighted. By "handouts," this means all materials generated for this class, which include but are not limited to syllabi, quizzes, exams, lab problems, in-class materials, review sheets, and additional problem sets. Because these materials are copyrighted, you do not have the right to copy them, unless you are expressly granted permission.As commonly defined, plagiarism consists of passing off as one’s own the ideas, words, writings, etc., that belong to another. In accordance with this definition, you are committing plagiarism if you copy the work of another person and turn it in as your own, even if you should have the permission of that person. Plagiarism is one of the worst academic sins, for the plagiarist destroys the trust among colleagues without which research cannot be safely communicated.If you have any questions about plagiarism and/or copying, please consult the latest issue of the Texas A&M University Student Rules, under the section "Scholastic Dishonesty."Lab Assignment Grading Rubric(This sheet must be included with your work submission)Criteria PointsAdherence to the SPE Style Guide & Petroleum Engineering Handbook / 10Grammar/Professionalism / 5Completeness of Literature Review / 15Completeness of Introduction / 10Completeness of Methodology / 15Completeness of Discussion / 15Completeness of Conclusions / 10Completeness of References / 10Completeness of Nomenclature / 10Final Grade /100Literature ReviewNumerical methods concepts that were used during this particular lab were integration, trapezoidal rule approximation, relative error, and relative percentage error. First, integration is the process of finding an area of a curve of any function, f(x).Figure 1 displays this specific process. To find the area under the curve through integration from point a to point b, Eq. 1 wasused. Fig. 1 – Display of the Integration Process∫abf (x)dx=F(b)−F (a)…………………………………………………………………………………..Eq. 1Second, the trapezoidal rule approximation is the process of finding the area under the curve of any function, f(x), by summing up the areas of the trapezoids under the curve. Figure 2 shows how this particular Newton-Cotes Closed Integrationmethod works. To find the area under the curve through the utilization of the trapezoidal rule approximation, Eq. 2 was implemented. Fig. 2 – Display of Trapezoidal Rule Approximation ProcessI=(b−a)f(x0)+2∑i=1n−1f(xi)+f (xn)2 n…………………………………………………….………………………Eq.2Third, relative error is the difference between true value and the current value. Fourth, the relative percentage error is the relative error over the true value multiplied by 100. Eq. 3 and Eq. 4 were used to calculate both the relative error and the relative percentage error respectively.Relative Error= Current Value−True Value…………………………….……………………………Eq. 3Relative Percentage Error(%)=(Relative ErrorTrue Value)∗100……………………………………..………….Eq. 4IntroductionFor the lab, a VBA function must be constructed to evaluate the trapezoidal rule approximation of the definite given during lab. The goal of doing this was to calculate the accumulated oil production by analytical integration of the production rate equation and by trapezoidal rule approximation of the analytical integration of the production rate equation. Eq. 5, Eq. 6, andEq. 7 along with conditions were given to successfully conduct the experiment. The conditions were the initial production rate of 1,500 STB/day an initial nominal exponential decline of .0042 day-1, and times of zero and 950 days. ∫x1x2f(x)dx ≈∑i=1nAi……………………………………………………………………………………….Eq. 5f(x)=q(t)=qi1+t Di…………………………………………………………...…………………………….Eq. 6∫x1x2f(x)dx=∫t1t2q(t)dt=Np………………………………………….…………………………………..Eq. 7MethodologyOption ExplicitFunction my_trap(a As Double, b As Double, n As Long) As Double Dim delta_x As Double Dim i As Long delta_x = (b - a) / n my_trap = 0 For i = 1 To n - 1 my_trap = my_trap + my_f(a + i * delta_x) Next i my_trap = (b - a) * (my_f(a) + 2 * my_trap + my_f(b)) / (2 * n)End FunctionFunction my_f(t As Double) As Double Const qi As Double = 1500 Const Di As Double = 0.0042 my_f = qi / (1 + t * Di)End FunctionFunction my_trap_s(a As Single, b As Single, n As Long) As Single Dim


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TAMU PETE 301 - 301.505.Lab5_Situ_E

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