P3242~1
.PDF
School
University of Houston**We aren't endorsed by this school
Course
COMD 5341
Subject
Mathematics
Date
Dec 24, 2024
Pages
10
Uploaded by CountFieldKookabura39
You MUST hand-write all of your work on this page for this problem. Due Date: Thursday 27 April 2023 at 14:59:59 US CDTYou MUST show all work and clearly identify/label ALL features. Filename: P324_23A_Hwk_05_YOURLASTNAME.pdf Collaboration is expressly forbidden.(Submit in Class and to Canvas) (Page 1 of 10) Name: ___________________________ Signature: ___________________________ Petroleum Engineering 324/648 — Well Testing / Pressure Transient Testing Homework 5 — [PTA] History Matching of a Pressure Drawdown Test — Lee Text Example 3.1 Sunday 23 April 2023 — Due: Thursday 27 April 2023 (Turn in paper copy at the start of class, submit e-copy to Canvas) READ THIS PAGE CAREFULLY AND COMPLETELY BEFORE STARTING Assignment Submission: | Due date — Thursday 27 April 2023 at 14:19:59 US CDT (Submit in class and via Canvas)| ●Return EXACTLYyour completed assignment (exactly 10 pages). ●File name: P324_23A_Hwk_05_YOURLASTNAME.pdf ●Document: Single .pdf document ●Scan: >300 dpi COLOR scan from a printer/scanner ●Photos: DO NOT SUBMIT PHOTOS (photos will not be accepted) ●Submission: Paper copy in class and via Canvas. Assignment Requirements: (The assignment is open book/open notes) ●Print the assignment on a high-resolution color printer. ●Sign the Honor Code statement. ●Write your name and sign every page on the assignment. ●Collaboration is expressly forbidden. ●Collaboration/cheating = F course grade. Construction: ●Print the assignment on (high-quality) white paper — Single-sided printing ONLY — NO DOUBLE-SIDED PRINTING! ●HAND WRITE your work on the assignment. ●ONLY WRITE ON THE FRONT OF THE PAGE! ●COMPUTER-AIDED WORK IS ALLOWED (e.g., MS Excel, etc.) (work must be printed/cut/pasted as designated) Work Layout: You must show ALLwork — as appropriate, YOU MUST: — WORK: You must show all details in your calculations(no skipped steps). All portions of all analysis relations must be shown. — UNITS: You must show all units in all calculations.Work layout: (as appropriate for a given problem) — NEATNESS: You will be graded on the neatness of your work.■ Pencil: You must work in PENCIL, work in ink(i.e., use of pens) is unacceptable.■ Erasure: Erase any errors or work/comments not to be submitted. NO SCRATCH-OUTS! (penalties will apply). — LABELS: All work, trends, and features on every plot MUST be appropriately labeled — no exceptions.■ Work: All work must be fully labeled and documented — equations, relations, calculations, etc.■ Trends: This includes the slope, intercept, and the information used to construct a given trend.■ Features: Any description of features/points of interest on a given trend(times, pressures, etc.). — LINES: Use appropriate drafting care in construction of lines, trends, arrows, etc.— SKETCHING: Take great care in any sketches you create/use in your work.No-No's: ●NO ELECTRONIC/TYPING PERMITTED. (must be handwritten) ●NO COMMERCIAL OR RESEARCH SOFTWARE ALLOWED. ● NO INSERT OR EXTRA PAGES ARE ALLOWED! Last Words: ●Print your name and sign every page in the space provided (do this now). ●Neatness counts — more than you think. Keep your work complete and NEAT. ●Give your very best effort. ●You MUST show all work and clearly identify/label ALL features — NO EXCEPTIONS! ●Scholastic dishonesty — don't even think about it! Aggie Code of Honor: An Aggie does not lie, cheat, or steal or tolerate those who do.Required Academic Integrity Statement: (Texas A&M University Policy on Academic Integrity) "On my honor, as an Aggie, I have neither given nor received unauthorized aid on this academic work." ___________________________________ (your printed name) ___________________________________ (your signature) ← One staple here.
Petroleum Engineering 324/648 — Well Testing / Pressure Transient Testing Homework 5 — [PTA] History Matching of a Pressure Drawdown Test — Lee Text Example 3.1 Sunday 23 April 2023 — Due: Thursday 27 April 2023 (Turn in paper copy at the start of class, submit e-copy to Canvas) You MUST hand-write all of your work on this page for this problem. Due Date: Thursday 27 April 2023 at 14:59:59 US CDTYou MUST show all work and clearly identify/label ALL features. Filename: P324_23A_Hwk_05_YOURLASTNAME.pdf Collaboration is expressly forbidden.(Submit in Class and to Canvas) (Page 2 of 10) Name: ___________________________ Signature: ___________________________ Guidance: "BEFORE YOU START"
Petroleum Engineering 324/648 — Well Testing / Pressure Transient Testing Homework 5 — [PTA] History Matching of a Pressure Drawdown Test — Lee Text Example 3.1 Sunday 23 April 2023 — Due: Thursday 27 April 2023 (Turn in paper copy at the start of class, submit e-copy to Canvas) You MUST hand-write all of your work on this page for this problem. Due Date: Thursday 27 April 2023 at 14:59:59 US CDTYou MUST show all work and clearly identify/label ALL features. Filename: P324_23A_Hwk_05_YOURLASTNAME.pdf Collaboration is expressly forbidden.(Submit in Class and to Canvas) (Page 3 of 10) Name: ___________________________ Signature: ___________________________ Grading Summary: You must provide source code of your software as an electronic submission: ●You are to (also) submit your work via Canvas in a file named: P324_23A_Hwk_05_YOURLASTNAME_(software).zip ●Failure to submit your code will result in a zero grade for this assignment Component Scores: (_____/20 pts) Combined log-log and semi-log DIAGNOSTIC plot. (see requirement on p. 7) (_____/20 pts) Working Table for Analysis plot. (see requirement on p. 8) (_____/20 pts) Combined log-log and semi-log ANALYSIS plot. (see requirement on p. 9) (_____/20 pts) Discussion of RESULTS. (see requirement on p. 10) (_____/20 pts) Miscellaneous: ●Results (state your results on p. 4) ●Neatness, construction of work, layout, etc. (discretion of instructor) ●Work quality (accuracy, correctness of structure, etc.) _________________________________________________________________________________________________________________________________________________________________________________ (_____/100 pts) Total
Petroleum Engineering 324/648 — Well Testing / Pressure Transient Testing Homework 5 — [PTA] History Matching of a Pressure Drawdown Test — Lee Text Example 3.1 Sunday 23 April 2023 — Due: Thursday 27 April 2023 (Turn in paper copy at the start of class, submit e-copy to Canvas) You MUST hand-write all of your work on this page for this problem. Due Date: Thursday 27 April 2023 at 14:59:59 US CDTYou MUST show all work and clearly identify/label ALL features. Filename: P324_23A_Hwk_05_YOURLASTNAME.pdf Collaboration is expressly forbidden.(Submit in Class and to Canvas) (Page 4 of 10) Name: ___________________________ Signature: ___________________________ Given: Pressure Drawdown (Lee Ex. 3.1) [Lee, W.J.: Well Testing, SPE (1982) (ISBN: 978-089520-317-5)] These data are taken from Example 3.1 (drawdown) in the Lee text, Well Testing. Reservoir and Fluid Properties: Production Properties: φ= 0.039 (fraction) Swi= 0 (fraction) rw= 0.198 ft h= 69 ft qo= 250 STBOD(final rate) Βo= 1.136 RB/STB µo= 0.8 cpct= 17x10-6psia-1pi= 4412 psia (pressure at start of production) Pressure Drawdown Functions:(pi= 4412 psia) tpwf∆p∆p'Point (hr) (psia) (psi) (psi) 1 1.12 3812 600 205.69 2 1.94 3699 713 154.47 3 2.79 3653 759 107.58 4 4.01 3636 776 74.73 5 4.82 3616 796 54.89 6 5.78 3607 805 49.01 7 6.94 3600 812 53.34 8 8.32 3593 819 39.30 9 9.99 3586 826 36.49 10 14.4 3573 839 34.66 11 17.3 3567 845 33.85 12 20.7 3561 851 32.44 13 24.9 3555 857 32.91 14 29.8 3549 863 32.09 15 35.8 3544 868 32.00 16 43 3537 875 31.14 17 51.5 3532 880 31.04 18 61.8 3526 886 31.97 19 74.2 3521 891 31.17 20 89.1 3515 897 31.95 21 107 3509 903 32.84 22 128 3503 909 36.47 23 154 3497 915 39.32 24 185 3490 922 44.91 25 222 3481 931 52.12 26 266 3472 940 62.11 27 319 3460 952 66.75 28 383 3446 966 71.33 29 460 3429 983 78.51 Required: You are to estimate the parameters in the Results section below using a computational tool of your own construction. Your tool can be constructed in any language/environment/etc. (e.g., MS Excel, Python, C, Java, FORTRAN, etc.). HOWEVER, this tool must be of your own construction — no sharing of codes(sharing = "F" grade in course) and no commercial or research software are permitted, specifically no software for pressure transient or production data analysis are permitted. DO YOUR OWN WORK. Results: (You must complete all analyses and put your answers in the appropriate locations provided below) History Analysis: Formation permeability, k= md (from history-match) Pseudoradial flow skin factor, spr= (dim-less) (from history-match) Wellbore storage coefficient, Cs= RB/psi (from history-matchReservoir drainage Area, A= acre (from history-match
Petroleum Engineering 324/648 — Well Testing / Pressure Transient Testing Homework 5 — [PTA] History Matching of a Pressure Drawdown Test — Lee Text Example 3.1 Sunday 23 April 2023 — Due: Thursday 27 April 2023 (Turn in paper copy at the start of class, submit e-copy to Canvas) You MUST hand-write all of your work on this page for this problem. Due Date: Thursday 27 April 2023 at 14:59:59 US CDTYou MUST show all work and clearly identify/label ALL features. Filename: P324_23A_Hwk_05_YOURLASTNAME.pdf Collaboration is expressly forbidden.(Submit in Class and to Canvas) (Page 5 of 10) Name: ___________________________ Signature: ___________________________ Governing Relations: Approximate(Bounded Reservoir) Full Solution: (Horner, 1950's) 222112211111(,) EE2 expexp24244442eDeDeDDD eD DDDDDeDeDrrrtprtttttrr−−≈−++−......................................(1) Adding the Skin Factor: (s) ()(,) sD DD eD Dptprts=+..........................................................................................................................................................(2) Adding Wellbore Storage: (CD) (Approximate Solution) (, ,,)() 1exp()DwD DD eDsD DD sD Dtpts CrptCpt−≈−............................................................................................................(3) Definition of Dimensionless Variables: 422.637x10Dt wtktc rφµ−=........................................(4a) ()= = 141.2iwfwDwDpppqBppkhµ−∆....................................(4b) eeDwrrr=...................................................................(4c) 20.894sDt wCChc rφ=...........................................................(4d) Solution Layout: (suggest using at least 1000 logarithmically even-spaced points in order to estimate ∆p'accurately) [Eq. 4a][Eq. 1] [Eq. 2][Eq. 3][Eq. 4b] tgridtD,gridpD,gridpsD,gridpwD,grid∆pgrid∆p'gridPoint (hr) (dim-less) (dim-less) (dim-less) (dim-less) (psi) (psi) 1 #### #### #### #### #### #### #### 2 #### #### #### #### #### #### #### 3 #### #### #### #### #### #### #### … … … … … … … … … … … … … … … … … … … … … … … … npoints#### #### #### #### #### #### #### Comments: ●The "grid" terminology means that you will calculate a "grid" of values (like a "type curve"). ●It may be best to set up a function statement in VBA to calculate Eqs. 1, 2, and 3 — this is not "necessary," but may be convenient. ●A finite-difference derivative formulation should be fine for this application.
Petroleum Engineering 324/648 — Well Testing / Pressure Transient Testing Homework 5 — [PTA] History Matching of a Pressure Drawdown Test — Lee Text Example 3.1 Sunday 23 April 2023 — Due: Thursday 27 April 2023 (Turn in paper copy at the start of class, submit e-copy to Canvas) You MUST hand-write all of your work on this page for this problem. Due Date: Thursday 27 April 2023 at 14:59:59 US CDTYou MUST show all work and clearly identify/label ALL features. Filename: P324_23A_Hwk_05_YOURLASTNAME.pdf Collaboration is expressly forbidden.(Submit in Class and to Canvas) (Page 6 of 10) Name: ___________________________ Signature: ___________________________ Exponential Integral: [E1(x)] Definition: 11( 1)E () ln( )( >0) !kkkxxxxkkγ∞=−= −−−∑[γ= 0.577216 … (Euler's constant)] .........................................................................(5) Numerical Approximations:Handbook of Mathematical Functions, M. Abramowitz and I. Stegun, Dover Pub. (1972). MS Excel Solution: [(MSXL)_VB_Spc_Fcns_(xlsm).xlsm file]
Petroleum Engineering 324/648 — Well Testing / Pressure Transient Testing Homework 5 — [PTA] History Matching of a Pressure Drawdown Test — Lee Text Example 3.1 Sunday 23 April 2023 — Due: Thursday 27 April 2023 (Turn in paper copy at the start of class, submit e-copy to Canvas) You MUST hand-write all of your work on this page for this problem. Due Date: Thursday 27 April 2023 at 14:59:59 US CDTYou MUST show all work and clearly identify/label ALL features. Filename: P324_23A_Hwk_05_YOURLASTNAME.pdf Collaboration is expressly forbidden.(Submit in Class and to Canvas) (Page 7 of 10) Name: ___________________________ Signature: ___________________________ Combined log-log and semi-log DIAGNOSTIC plot: (cut and tape your Combined log-log and semi-log DIAGNOSTIC plot in the box below)
Petroleum Engineering 324/648 — Well Testing / Pressure Transient Testing Homework 5 — [PTA] History Matching of a Pressure Drawdown Test — Lee Text Example 3.1 Sunday 23 April 2023 — Due: Thursday 27 April 2023 (Turn in paper copy at the start of class, submit e-copy to Canvas) You MUST hand-write all of your work on this page for this problem. Due Date: Thursday 27 April 2023 at 14:59:59 US CDTYou MUST show all work and clearly identify/label ALL features. Filename: P324_23A_Hwk_05_YOURLASTNAME.pdf Collaboration is expressly forbidden.(Submit in Class and to Canvas) (Page 8 of 10) Name: ___________________________ Signature: ___________________________ Example of Working Table: (cut and tape your Example of Working Table in the box below)
Petroleum Engineering 324/648 — Well Testing / Pressure Transient Testing Homework 5 — [PTA] History Matching of a Pressure Drawdown Test — Lee Text Example 3.1 Sunday 23 April 2023 — Due: Thursday 27 April 2023 (Turn in paper copy at the start of class, submit e-copy to Canvas) You MUST hand-write all of your work on this page for this problem. Due Date: Thursday 27 April 2023 at 14:59:59 US CDTYou MUST show all work and clearly identify/label ALL features. Filename: P324_23A_Hwk_05_YOURLASTNAME.pdf Collaboration is expressly forbidden.(Submit in Class and to Canvas) (Page 9 of 10) Name: ___________________________ Signature: ___________________________ Combined log-log and semi-log ANALYSIS plot: (cut and tape your Combined log-log and semi-log ANALYSIS plot in the box below)
Petroleum Engineering 324/648 — Well Testing / Pressure Transient Testing Homework 5 — [PTA] History Matching of a Pressure Drawdown Test — Lee Text Example 3.1 Sunday 23 April 2023 — Due: Thursday 27 April 2023 (Turn in paper copy at the start of class, submit e-copy to Canvas) You MUST hand-write all of your work on this page for this problem. Due Date: Thursday 27 April 2023 at 14:59:59 US CDTYou MUST show all work and clearly identify/label ALL features. Filename: P324_23A_Hwk_05_YOURLASTNAME.pdf Collaboration is expressly forbidden.(Submit in Class and to Canvas) (Page 10 of 10) Name: ___________________________ Signature: ___________________________ Discussion of RESULTS: (cut and tape your Discussion of RESULTS in the box below)