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 Print your name 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 One key numerical methods concept that is utilize during lab is the 4th Order Runge Ketta Method It is an approach used to integrate a differential equation It also achieves the accuracy of a Taylor series approach without requiring strenuous calculations of higher derivatives The equation for the classical fourth order RK method is 1 y i 1 yi k 1 2 k 2 2 k 3 k 4 h Eq 1 6 where k 1 f x i y i Eq 2 1 1 k 2 f x i h k 1 h Eq 3 2 2 12 h 12 k h k 3 f x i 2 Eq 4 k 4 f x i h y i k 3 h Eq 5 Values of k1 k2 k3 and k4 are calculated to determine multiple estimates of slopes The multiple estimates of slopes are calculated for the sake of coming up with an improved average slope for the interval The classical fourth order RK method symbolizes a weight average of the estimated slopes that can be used to obtain a more accurate value for the integration of a differential equation Introduction The purpose of this lab is to apply the classical 4th Order Runge Ketta Method to calculate the bottom hole pressure for the gas at a depth of 10 500 feet with the given surface conditions and data Equation 6 is the differential equation that is used for the sake of applying the 4th Order Runge Ketta Method g dp g Eq 6 dy 144 g c Where p pressure psi y depth ft g gas density lbm ft3 g gravitational acceleration 32 174 ft s2 144 in2 per ft2 gc conversion constant 32 174 ft lbm lbf s2 The given surface conditions and data are Static Surface Pressure pts 500 psia Depth to Mid Perforation 10 500 feet TVD Gas Gravity of 72 Wellhead Temperature Tts 90 degrees Fahrenheit Bottomhole Temperature Tws 240 degrees Fahrenheit Universal Gas Constant R 10 732 ft3 lbf 0R lb mol Other equations that are needed to apply the 4th Order Runge Ketta Method to the differential equation are Equations 7 8 and 9 g p Ma Eq 7 zRT M a 28 97 g Eq 8 T Rankine T Fahrenheit 459 67 Eq 9 Lastly a VBA function is needed to calculate the z factor of natural gas Function zfact ptab As Double T As Double grav As Double As Double Where zfact fraction real gas deviation factor ptab pressure psia T temperature 0R Grav gas gravity Methodology Here is the code that is concocted and utilized to successfully apply the 4th Order Kunge Retta Method to the pressuregradient differential equation Option Explicit Function dp dy y As Double p As Double As Double returns the static pressure gradient of natural gas Dim T R As Double Dim z factor As Double Dim gas density As Double Const Const Const Const gas grav As Double 0 72 M air As Double 28 97 R gas As Double 10 732 Gradient Conversion Factor As Double 144 T R T func y z factor zfact p T R gas grav gas density p gas grav M air z factor R gas T R dp dy gas density Gradient Conversion Factor End Function Function T func y As Double As Double Dim T1 As Double T2 As Double T ts As Double T ws As Double Depth As Double With ThisWorkbook Worksheets Lab 7 Depth Cells 2 5 T ts Cells 3 5 T ws Cells 4 5 T1 T ts 459 67 unit conversion from F to R T2 T ws 459 67 unit conversion from F to R T func T1 y Depth T2 T1 End With End Function ZFACT Calculates gas compressibility z factor for the tables Function zfact ptab As Double T As Double grav As Double As Double Dim pc As Double tc As Double tr As Double pr As Double a1 As Double a2 As Double a3 As Double a4 As Double Dim a5 As Double a6 As Double a7 As Double a8 As Double a9 As Double a10 As Double a11 As Double Dim c1 As Double c2 As Double c3 As Double c4 As Double zz As Double dr As Double dc4dr As Double Dim fun As Double dfun As Double del As …
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