Lab Assignment Coversheet This sheet must be included with your work submission Required Academic Integrity Statement Texas A M University Policy Statement Academic Integrity Statement All syllabi shall contain a section that states the Aggie Honor Code and refers the student to the Honor Council Rules and Procedures 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 preprinted and 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 received unauthorized 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 Points Adherence to the SPE Style Guide Petroleum Engineering Handbook 10 Grammar Professionalism 5 Completeness of Literature Review 15 Completeness of Introduction 10 Completeness of Methodology 15 Completeness of Discussion 15 Completeness of Conclusions 10 Completeness of References 10 Completeness of Nomenclature 10 Final Grade 100 Literature Review The concepts that were used during this lab is the utilization of Newton Raphson Method with the Jacobian Matrix for multivariable functions A Jacobian matrix is a matrix comprised of first order partial derivatives of a multivariable function Figure 1 shows an example of this particular type of matrix Newton Raphson Method which was used in the execution of Jacobian matrix is a mathematical technique predicated on using the derivative of the function to estimate its intercept with the axis or axes of independent variable s Fig 1 Jacobian Matrix of First Order Partial Derivatives of Multivariable Functions Introduction A major goal of this lab was to find the accurate values of x y and z to make u x y z v x y z and w x y z zero by programming imperative functions in Visual Basis for Application in Excel and by using an integrated Excel tool called a solver Not only that the Euclidean norm can be minimized by changing the values of x y and z Before beginning the experiment here were the equations were kept into mind Initial values of x y and z that were used to start the experiment was 5 5 and 5 u x y z xz 2 y 2 z 3 zy 15 Eq 1 1 v x y z x2 y y 3 z 2 zx 20 Eq 2 2 w x y z 2 xy z 2 3 y 2 x zy 5 Eq 3 Methodology Option Explicit Function u x As Double y As Double z As Double As Double u x z 2 y 2 z 3 z y 15 End Function Function dudx x As Double y As Double z As Double As Double dudx z End Function Function dudy x As Double y As Double z As Double As Double dudy 4 y z 3 z End Function Function dudz x As Double y As Double z As Double As Double dudz x 2 y 2 3 y End Function Function v x As Double y As Double z As Double As Double v x 2 y 0 5 y 3 z 2 z x 20 End Function Function dvdx x As Double y As Double z As Double As Double dvdx 2 x y 2 z End Function Function dvdy x As Double y As Double z As Double As Double dvdy x 2 1 5 y 2 z End Function Function dvdz x As Double y As Double z As Double As Double dvdz 0 5 y 3 2 x End Function Function w x As Double y As Double z As Double As Double w 2 x y z 2 3 y 2 x z y 5 End Function Function dwdx x As Double y As Double z As Double As Double dwdx 2 y z 2 3 y 2 End Function Function dwdy x As Double y As Double z As Double As Double dwdy 2 x z 2 6 y x z End Function Function dwdz x As Double y As Double z As Double As Double dwdz 4 x y z y End Function According to the code from the Visual Basics for Application for Excel u v and w functions were concocted and the firstorder partial derivatives of each respective multivariable function with respect to x y and z separately were created as well Then a solver was utilized to solve for the x y and z values that make the u v and w functions zero Later iterations method was used to obtain the same values of x y and z During the iterations method partial derivatives of each function within the Jacobian Matrix were computed Next the function values of u v and were outputted With that the change in x y and z respectively were computed by multiplying the inverse of the Jacobian Matrix by the u v and w three by one matrix With the sufficient given information the new x y and z values were calculated and compared to x y and z values obtained from the solver method All of these steps were done during each iteration Discussion From the solver method the x y and z values that caused the u v and w functions to be zero were 3271050 …
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