do not submit this orientation sheet with your · pdf filedo not submit this orientation sheet...

DO NOT Submit this Orientation Sheet with your assignment

Petroleum Engineering 663 — Summer 2012 Formation Evaluation and Analysis of Reservoir Performance

Analysis of Reservoir Performance [Blasingame] Orientation to Assignment Set

Commands: ● You must submit a SINGLE .pdf file on 07 August 2012 to:

— [email protected] (the course instructor) — [email protected] (the Distance Learning staff)

● The name of the file MUST be: P663_12B_Assgn_YOURLASTNAME.pdf ● You must only work on the given assignment sheets. ● You must only write on the front of any page (obvious, but has to be mentioned). ● The assignment must be submitted EXACTLY AS RECEIVED (same number of pages). ● Write your name in the "Name: ______________" space (EVERY page!).

Suggestions: ● Print the assignment on a color printer (immediately). ● Read the assignment in its entirety:

— Print and sign your name as required on the coversheet. — Write your name in the "Name: ______________" space.

● Read the assignment again, carefully reviewing what is asked and what is given. ● Read the references provided BEFORE starting work on the assignment.

Last Words: ● Follow instructions (please!). ● ALL work must be performed by HAND (this is stated repeatedly). ● ALL work must be performed on the assignment sheets (this is stated repeatedly). ● No computer-aided/assisted work/solutions/etc. of any kind are permitted. ● No collaborations of any kind are permitted.

________________________________________________________________________________________________________________________________________________________________________

Notes:

— You MUST submit ALL assignments in a SINGLE .pdf file — P663_12B_Assgn_YOURLASTNAME.pdf — You MUST perform all work BY HAND, on the sheets provided in this handout. (no computer analyses allowed) — You MUST ensure that all pages are correctly ordered and scanned legibly. (poorly constructed/assembled work will not be graded) — Treat this assignment as an EXAMINATION, no collaboration is allowed, submit only your best work!

(Page 1 of 29)

Name: ______________________________

Assigned: Saturday 28 July 2012

Due: Tuesday 07 August 2012 by Midnight (23:59:59 US CDT)

Send a SINGLE .pdf file (no .doc, .xls, .??? — no exceptions) to: [email protected], [email protected]

Petroleum Engineering 663 — Formation Evaluation and Analysis of Reservoir Performance Assignment Set — Analysis of Reservoir Performance [Blasingame]

Assigned: Saturday 28 July 2012 — Due: Tuesday 07 August 2012 [by Midnight (23:59:59 US CDT)]

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."

________________________________________________________________________________________________________________________________________________________________________

Notes:


(Page 2 of 29)

Name: ______________________________






Instructions:

You must follow the following instructions for the submission of your assignments for this portion of the course:

● You must submit a SINGLE .pdf file: — BOTH assignments must be in the same .pdf file. — The name of the file MUST be: P663_12B_Assgn_YOURLASTNAME.pdf (name in ALL CAPS). ● You must include all assignment sheets, including the SIGNED coversheet (i.e., the honor statement). ● You must submit to "[email protected]" (this address accepts attachments up to (approximately) 50 MB): — All submissions will be confirmed with a personal receipt reply (instructor acknowledgement). — Please submit the smallest practical-sized file to avoid issues with receiving and downloading. ● Your scanned submission MUST BE LEGIBLE: — You should check a sample of your submission, if it cannot be read, it will not be graded. ● If your submission is received late (i.e., after 23:59:59 US CDT on Tuesday 07 August 2012), then your submission

will likely be graded after the grade submission deadline, you will receive an "I" or "incomplete" grade in this case. Your grade will be resolved once your submission is received and graded.

Work Requirements: (layout/format/etc.)

You must prepare your work as instructed below, or you will be assessed SEVERE grading penalties.

● You must only work on the assignment sheets: — NO insert or extra pages allowed, the assignment must be submitted EXACTLY AS RECEIVED. — You must write on the assignment by hand, no computer-based work will be permitted. — You must properly reassemble your assignment. — You must only write on the FRONT of any page.

● You must show ALL work — in particular, YOU MUST: — Write your name in the "Name: ______________" space given on the upper right corner of EVERY page. — Show all details in your calculations (no skipped steps). — Show all units in each calculation. ● Work layout: — NEATNESS: You will be graded on the neatness of your work. — LABELS: All plots, trends, features MUST be appropriately labeled — no exceptions. — 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.

Scholastic Dishonesty:

THE STUDENT IS HEREBY WARNED THAT ANY/ALL ACTS OF SCHOLASTIC DISHONESTY WILL RESULT IN AN "F" GRADE FOR ALL ASSIGNMENTS IN THIS PORTION OF THE COURSE. As a definition, "scholastic dishonesty" will include any or all of the following acts:

● Unauthorized collaborations — you are explicitly forbidden from working together. ● Using work of others — you are explicitly forbidden from using the work of others — "others" is defined as students

in this course, as well as any other person. You are required to perform your own work. ● Using software — you are explicitly forbidden from using commercial and/or non-commercial software packages for

well test and production data analysis. No computer-based solutions are permitted, only "hand work."

This is a zero-tolerance policy, there will be no exceptions.

Work Standard:

Simply put, the expectation of the instructor (Blasingame) is that "perfection is the standard" — in other words, your work will be judged against a perfect standard. If your submission is not your very best work, then don't submit it. You have an OBLIGATION to submit only your very best work.

________________________________________________________________________________________________________________________________________________________________________

Notes:


(Page 3 of 29)

Name: ______________________________






Problem 1: Analysis of Water Well Test Data (2003) (Texas A&M University)

Orientation: This problem consists of a pressure drawdown/buildup test sequence performed on a pumping WATER well (our campus water well). There are no "tricks" involved — this should be a straightforward analysis/interpretation sequence. Be sure to perform all analyses — and cross-check/double-check your work whenever possible.

Given: These attached data were taken from a pressure drawdown/buildup test sequence performed on our campus water well. The reservoir interval is a water sand at about 450 ft — the well is not stimulated and should not be damaged — however, the well is completed "open hole," so some evidence of stimulation is possible. The reservoir should be assumed to be homogeneous and infinite-acting.

Reservoir properties:

=0.25 rw=0.36 ft ct=6.5x10-6 psia-1 h=23 ft

Water properties:

Bw=1.0 RB/STB w=1.0 cp

Production parameters:

Event

Duration of Event

(hr)

Pressure at start of Event

(psia)

Water Flowrate (STB/D)

1. Drawdown Test ≈ 2.054 pi=147.29 60 2. Buildup Test ≈ 2.25 pwf(t=0)=139.3 0

Summary Plot: (Drawdown/Buildup Test Sequences)

________________________________________________________________________________________________________________________________________________________________________

Notes:


(Page 4 of 29)

Name: ______________________________







Governing Equations: Drawdown

Early-Time Cartesian Analysis: Wellbore Storage Domination Regime

The governing relation for the wellbore storage domination regime is:

swbswbsiwf C

qBmtmpp

24 where, — Cs, is given by: .

24 wbss m

qBC

Semilog Analysis: Infinite-Acting Radial Flow Regime (IARF)

The governing relation for the infinite-acting radial flow regime (IARF) is:

. 8686.02275.32

log and6.162 where, )log( 11

prs

wrtc

kmpp

kh

qBmtmpp slihrslslhrwf

The formation permeability, k, is given as:

hm

qBk

sl

6.162

The pseudoradial skin factor, spr, is given by:

hr)] 1([ 2275.32

loghr)] 1([

1513.1 1

tpp

wrtc

k

slm

twfpipprs wfhr

"Preliminary" Log-log Analysis:

The governing relation for the wellbore storage domination regime (unit slope line):

swbswbs C

qBmtm

dt

pdtp'

24 where,


slmkh

qB

dt

pdtp'

303.2

16.70

Type Curve Analysis Relations: "Advanced" Log-Log Analysis

"Bourdet -Gringarten" Type Curves: (Unfractured Vertical Well with Wellbore Storage and Skin Effects)

Family Parameter:

CDe2s

Formation Permeability:

]or [

]or [ 2.141

MP'

MP'wDwD

pp

pp

h

qBk

Dimensionless Wellbore Storage Coefficient:

]/[

][ 0002637.0

2 MPDD

MP

wtD Ct

t

rc

kC

Pseudoradial Flow Skin Factor:

][

ln2

1

2

D

MPs

Dpr C

eCs

________________________________________________________________________________________________________________________________________________________________________

Notes:


(Page 5 of 29)

Name: ______________________________







Governing Equations: Buildup

Early-Time Cartesian Analysis: Wellbore Storage Domination Regime


swbswbswfws C

qBmtmtpp

24 where, 0)( — Cs, is given by: .

24 wbss m

qBC

Semilog Analysis: Infinite-Acting Radial Flow Regime (IARF)

Horner Time: (includes the rate history)


kh

qBm

t

ttmpp sl

psliws

6.162 where, log

— k, is given as:

hm

qBk

sl

6.162


2275.3

2log

1log

0)](hr) 1([ 1513.1

wrtc

k

t

t

slm

twfptwspprs

p

p

MDH: (does NOT include the rate history)

The (approximate) governing relation for the infinite-acting radial flow regime (IARF) is:

.6.162 where, 8686.02275.32

log )log( 0)(kh

qBmprs

wrticgi

kmtmtpp slslslwfws


hm

qBk

sl

6.162


2275.3

2log

0)](hr) 1([ 1513.1

wrtc

k

slm

twfptwspprs

Agarwal Effective Time: (includes the rate history)


tt

tttprs

wrtc

kmtpp

kh

qBmtmpp

p

peslwfhrsleslhrws

8686.02275.3

2log 0)( and6.162 ; )log( 11


hm

qBk

sl

6.162


hr)] 1([ 2275.32

log1

log0)](hr) 1([

1513.1 1

tpp

wrtc

k

t

t

slm

twfptwspprs wshr

p

p

________________________________________________________________________________________________________________________________________________________________________

Notes:


(Page 6 of 29)

Name: ______________________________







Governing Equations: Buildup (Continued)

"Preliminary" Log-log Analysis:


swbswbs C

qBmtm

td

pdtp'

24 where,


slmkh

qB

td

pdtp'

303.2

16.70

Type Curve Analysis Relations: "Advanced" Log-Log Analysis

"Bourdet -Gringarten" Type Curves: (Unfractured Vertical Well with Wellbore Storage and Skin Effects)

Family Parameter:

CDe2s

Formation Permeability:

]or [

]or [ 2.141

MP'

MP'wDwD

pp

pp

h

qBk

Dimensionless Wellbore Storage Coefficient:

]/[

]or [ 0002637.0

2 MPDD

MPe

wtD Ct

tt

rc

kC

Pseudoradial Flow Skin Factor:

][

ln2

1

2

D

MPs

Dpr C

eCs

Modified Muskat/Muskat-Arps Plot: (ONLY valid for late-time boundary-dominated flow)

The governing relation for the late-time "Muskat" flow regime is given as:

tbatrc

k

kh

qBp-p

etws

exp 00388.0exp 6.118

2

Solving for the "Muskat-Arps" plotting function, we have:

. is 0at intercept ted)(extrapola the where,1

ptd

dp

td

dp

b-pp wsws

ws

________________________________________________________________________________________________________________________________________________________________________

Notes:


(Page 7 of 29)

Name: ______________________________







Required: Pressure Drawdown Analysis of Water Well Test Data (Texas A&M University — 2003)

You are to estimate the following:

● Preliminary log-log analysis: a. The wellbore storage coefficient, Cs. b. The formation permeability, k.

● Cartesian analysis of "early" time (wellbore storage distorted) data: a. The pressure at the start of the test, pi. b. The wellbore storage coefficient, Cs.

● Semilog analysis of "middle" time (radial flow) data: a. The formation permeability, k. b. The near well skin factor, s.

● Log-log type curve analysis: a. The formation permeability, k. b. The dimensionless (pseudoradial flow) skin factor, spr. c. The wellbore storage coefficient, Cs. d. The dimensionless wellbore storage coefficient, CD. Results: Pressure Drawdown Analysis of Water Well Test Data (Texas A&M University — 2003)

Preliminary Log-Log Analysis:

Wellbore storage coefficient, Cs = RB/psi

Formation permeability, k = md

Cartesian Analysis: Early Time Data

Pressure at start of test, pi = psia


Dimensionless wellbore storage coefficient, CD =

Semilog Analysis:


Dimensionless (pseudoradial flow) skin factor, spr =

Log-Log Type Curve Analysis:


Dimensionless (pseudoradial flow) skin factor, spr =



________________________________________________________________________________________________________________________________________________________________________

Notes:


(Page 8 of 29)

Name: ______________________________







Required: Pressure Buildup Analysis of Water Well Test Data (Texas A&M University — 2003)

You are to estimate the following:

● Preliminary log-log analysis: a. The wellbore storage coefficient, Cs. b. The formation permeability, k.

● Cartesian analysis of "early" time (wellbore storage distorted) data: a. The pressure at the start of the test, pwf(t=0). b. The wellbore storage coefficient, Cs.

● Semilog analysis of "middle" time (radial flow) data: a. The formation permeability, k. b. The near well skin factor, s.

● Log-log type curve analysis: (use both t and te methods) a. The formation permeability, k. b. The dimensionless (pseudoradial flow) skin factor, spr. c. The wellbore storage coefficient, Cs. d. The dimensionless wellbore storage coefficient, CD.

● Cartesian analysis of "late" time (boundary-dominated) data: "Muskat Plot" a. Average pressure, p . Results: Pressure Buildup Analysis of Water Well Test Data (Texas A&M University — 2003)

Preliminary Log-Log Analysis: (te and t (MDH) analysis) te t (MDH)

Wellbore storage coefficient, Cs = RB/psi = RB/psi

Formation permeability, k = md = md


Pressure at start of test, pwf(t=0) = psia



Semilog Analysis: (Horner and MDH analysis) Horner te t (MDH)

Formation permeability, k = md = md = md

Dim-less (psd. rad, flow) skin factor, spr = = =

Log-Log Type Curve Analysis: te t

Formation permeability, k = md = md

Dimensionless (pseudoradial flow) skin factor, spr = =

Wellbore storage coefficient, Cs = RB/psi = RB/psi

Dimensionless wellbore storage coefficient, CD = =

Cartesian Analysis: Late Time Data ("Muskat Plot")

Average pressure, p (if applicable) = psia

________________________________________________________________________________________________________________________________________________________________________

Notes:


(Page 9 of 29)

Name: ______________________________







Data Functions: Pressure Drawdown Case [Analysis of Water Well Test Data (2003) (Texas A&M University)]

Point

t (hr)

pwf (psia)

p (psi)

p' (psi)

1 0.0042 146.98 0.307 0.3117 2 0.0083 146.68 0.613 0.4685 3 0.0125 146.50 0.794 0.7677 4 0.0167 146.24 1.046 0.8560 5 0.0208 145.92 1.371 0.8609 6 0.0250 145.74 1.552 1.2644 7 0.0292 145.63 1.660 1.3669 8 0.0333 145.45 1.840 1.4444 9 0.0375 145.31 1.985 1.3695

10 0.0417 145.16 2.129 1.4228 11 0.0458 144.95 2.345 1.4908 12 0.0542 144.58 2.706 1.7374 13 0.0625 144.33 2.959 1.8189 14 0.0708 144.08 3.211 1.8992 15 0.0792 143.95 3.338 1.8622 16 0.0875 143.86 3.428 1.7132 17 0.0958 143.77 3.518 1.6968 18 0.1042 143.57 3.717 1.5785 19 0.1125 143.36 3.933 1.5360 20 0.1208 143.16 4.132 1.5626 21 0.1375 143.05 4.240 1.4033 22 0.1542 142.91 4.384 1.3954 23 0.1708 142.78 4.510 1.4944 24 0.1875 142.67 4.619 1.3573 25 0.2042 142.60 4.691 1.2162 26 0.2208 142.46 4.835 1.1080 27 0.2375 142.40 4.889 1.1431 28 0.2542 142.35 4.943 1.1826 29 0.2708 142.26 5.034 1.2060 30 0.2875 142.22 5.070 1.1989 31 0.3042 142.13 5.160 1.2172 32 0.3208 142.09 5.196 1.2415 33 0.3375 142.04 5.250 1.2473 34 0.3542 142.00 5.286 1.2884 35 0.3708 141.93 5.358 1.2225 36 0.3875 141.90 5.394 1.2358 37 0.4042 141.84 5.449 1.1947 38 0.4208 141.81 5.485 1.1808 39 0.4375 141.70 5.593 1.2256 40 0.4542 141.64 5.647 1.2847

________________________________________________________________________________________________________________________________________________________________________

Notes:


(Page 10 of 29)

Name: ______________________________







Data Functions: Pressure Drawdown Case [Analysis of Water Well Test Data (2003) (Texas A&M University)]

Point

t (hr)

pwf (psia)

p (psi)

p' (psi)

41 0.4708 141.61 5.683 1.2911 42 0.4875 141.54 5.755 1.2893 43 0.5042 141.50 5.791 1.3508 44 0.5208 141.45 5.845 1.3988 45 0.5375 141.39 5.900 1.4110 46 0.5542 141.34 5.954 1.3888 47 0.5708 141.28 6.008 1.4318 48 0.5875 141.25 6.044 1.4324 49 0.6042 141.19 6.098 1.4537 50 0.6208 141.16 6.134 1.4516 51 0.6375 141.08 6.206 1.4909 52 0.7208 141.03 6.260 1.5017 53 0.8042 140.90 6.387 1.4604 54 0.8875 140.72 6.567 1.4392 55 0.9708 140.51 6.784 1.4745 56 1.0542 140.40 6.892 1.4602 57 1.1375 140.29 7.000 1.4555 58 1.2208 140.15 7.144 1.5477 59 1.3042 140.07 7.217 1.7314 60 1.3875 139.98 7.307 1.7255 61 1.4708 139.91 7.379 1.7646 62 1.5542 139.86 7.433 1.7110 63 1.6375 139.79 7.505 1.6359 64 1.7208 139.71 7.577 1.6371 65 1.8042 139.62 7.668 1.5155 66 1.8875 139.55 7.740 1.5420 67 1.9708 139.51 7.776 1.4999 68 2.0542 139.46 7.830 1.4844

________________________________________________________________________________________________________________________________________________________________________

Notes:


(Page 11 of 29)

Name: ______________________________







Data Functions: Pressure Buildup Case [Analysis of Water Well Test Data (2003) (Texas A&M University)]

Point

t (hr)

te (hr)

Horner Time

pws (psia)

p (psi)

p'(t) (psi)

p'(te) (psi)

1 0.00417 0.00416 494.00 139.55 0.2500 0.4465 0.4482 2 0.00833 0.00830 247.50 139.78 0.4847 0.4761 0.5863 3 0.01250 0.01242 165.33 140.04 0.7372 0.6496 0.7524 4 0.01667 0.01653 124.25 140.25 0.9537 0.8573 0.9280 5 0.02083 0.02062 99.60 140.47 1.1702 1.0077 1.1101 6 0.02500 0.02470 83.17 140.65 1.3507 1.1831 1.2773 7 0.02917 0.02876 71.43 140.87 1.5672 1.3363 1.3882 8 0.03333 0.03280 62.63 141.07 1.7656 1.4840 1.4466 9 0.03750 0.03683 55.78 141.23 1.9280 1.5453 1.5409

10 0.04167 0.04084 50.30 141.34 2.0363 1.5922 1.6488 11 0.04583 0.04483 45.82 141.57 2.2708 1.7493 1.6789 12 0.05000 0.04881 42.08 141.68 2.3790 1.8102 1.7006 13 0.05417 0.05278 38.92 141.88 2.5775 1.8593 1.8375 14 0.05833 0.05672 36.21 142.00 2.7038 1.8630 1.8636 15 0.06250 0.06065 33.87 142.17 2.8662 1.9784 1.8951 16 0.06667 0.06457 31.81 142.26 2.9564 1.9843 1.9121 17 0.07083 0.06847 30.00 142.35 3.0466 2.0171 1.9460 18 0.07500 0.07236 28.39 142.45 3.1548 2.0352 1.9832 19 0.07917 0.07623 26.95 142.56 3.2631 2.1403 2.0224 20 0.08333 0.08008 25.65 142.65 3.3533 2.0667 2.0220 21 0.09167 0.08775 23.41 142.89 3.5878 2.1739 2.0777 22 0.10000 0.09536 21.54 143.03 3.7322 2.1005 2.0849 23 0.10833 0.10291 19.96 143.14 3.8404 2.1185 2.0994 24 0.11667 0.11040 18.61 143.39 4.0930 2.1298 2.0805 25 0.12500 0.11783 17.43 143.52 4.2193 2.1778 2.0746 26 0.13333 0.12521 16.41 143.65 4.3456 2.2077 2.0360 27 0.14167 0.13253 15.50 143.75 4.4538 2.1873 2.0586 28 0.15000 0.13979 14.69 143.88 4.5801 2.2009 2.0776 29 0.15833 0.14700 13.97 144.01 4.7064 2.1845 2.0554 30 0.16667 0.15416 13.33 144.11 4.8147 2.1729 2.0496 31 0.17500 0.16126 12.74 144.19 4.8868 2.1184 2.0454 32 0.18333 0.16831 12.20 144.31 5.0131 2.1219 2.0263 33 0.20000 0.18226 11.27 144.44 5.1394 2.1012 1.9580 34 0.21667 0.19599 10.48 144.64 5.3379 2.1551 1.9553 35 0.23333 0.20953 9.80 144.73 5.4281 1.9794 1.9450 36 0.25000 0.22288 9.22 144.87 5.5724 1.9673 1.8406 37 0.26667 0.23603 8.70 144.96 5.6626 1.9282 1.8017 38 0.28333 0.24899 8.25 145.09 5.7889 1.8812 1.7567 39 0.30000 0.26177 7.85 145.14 5.8430 1.7986 1.7336 40 0.31667 0.27437 7.49 145.23 5.9332 1.7516 1.7112

________________________________________________________________________________________________________________________________________________________________________

Notes:


(Page 12 of 29)

Name: ______________________________







Data Functions: Pressure Buildup Case [Analysis of Water Well Test Data (2003) (Texas A&M University)]

Point

t (hr)

te (hr)

Horner Time

pws (psia)

p (psi)

p'(t) (psi)

p'(te) (psi)

41 0.33333 0.28679 7.16 145.32 6.0235 1.7562 1.6772 42 0.41667 0.34640 5.93 145.63 6.3302 1.5923 1.4899 43 0.50000 0.40212 5.11 145.85 6.5467 1.4051 1.3659 44 0.58333 0.45432 4.52 145.99 6.6910 1.2938 1.2703 45 0.66667 0.50332 4.08 146.10 6.7992 1.2218 1.1940 46 0.75000 0.54941 3.74 146.21 6.9075 1.1551 1.1885 47 0.83333 0.59283 3.47 146.30 6.9977 1.1114 1.1519 48 0.91667 0.63382 3.24 146.37 7.0699 1.2932 1.1323 49 1.00000 0.67258 3.05 146.39 7.0879 1.2078 1.0924 50 1.08333 0.70927 2.90 146.46 7.1601 1.2309 1.0585 51 1.16667 0.74407 2.76 146.50 7.1962 1.1061 1.0424 52 1.25000 0.77711 2.64 146.53 7.2322 1.0933 1.0320 53 1.33333 0.80853 2.54 146.59 7.2864 1.0775 1.0076 54 1.41667 0.83844 2.45 146.60 7.3044 1.0457 0.9921 55 1.50000 0.86694 2.37 146.62 7.3225 1.0220 0.9807 56 1.58333 0.89414 2.30 146.66 7.3585 1.0336 0.9837 57 1.66667 0.92012 2.23 146.68 7.3766 0.9965 0.9628 58 1.75000 0.94496 2.17 146.69 7.3946 0.9854 0.9571 59 1.83333 0.96874 2.12 146.73 7.4307 1.0079 0.9651 60 1.91667 0.99152 2.07 146.75 7.4487 0.9518 0.9619 61 2.00000 1.01336 2.03 146.77 7.4668 0.9496 0.9538 62 2.08333 1.03432 1.99 146.78 7.4848 0.9497 0.9527 63 2.16667 1.05446 1.95 146.80 7.5029 0.9082 0.9524 64 2.25000 1.07381 1.91 146.82 7.5209 0.9129 0.9529

________________________________________________________________________________________________________________________________________________________________________

Notes:


(Page 13 of 29)

Name: ______________________________








Pressure at start of test, pi = psia Wellbore storage coefficient, Cs = RB/psi Dimensionless wellbore storage coefficient, CD =

Show ALL work below: (no insert work/pages permitted)

________________________________________________________________________________________________________________________________________________________________________

Notes:


(Page 14 of 29)

Name: ______________________________







Semilog Analysis: "MDH" Plot — Pressure Data versus Shut-In Time

Formation permeability, k = md Dimensionless (pseudoradial flow) skin factor, spr =


________________________________________________________________________________________________________________________________________________________________________

Notes:


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Log-log Plot: Pressure Drop and Pressure Drop Derivative Data versus Shut-In Time (t) (1 inch x 1 inch)

Formation permeability, k = md (k from prf': = _________ md) Dimensionless (pseudoradial flow) skin factor, spr = Wellbore storage coefficient, Cs = RB/psi (Cs Unit Slope Line: = _________ RB/psi) Dim. wellbore storage coefficient, CD =


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Pressure at start of test, pwf(t=0) = psia Wellbore storage coefficient, Cs = RB/psi Dimensionless wellbore storage coefficient, CD =


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Semilog Analysis: "MDH" Plot — Pressure Data versus Shut-In Time



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Semilog Plot: "Horner" Plot — Pressure Data versus Horner Time



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Semilog Plot: "Agarwal" Plot — Pressure Data versus Effective Shut-In Time



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Log-log Plot: Pressure Drop and Pressure Drop Derivative Data versus Shut-In Time (t) (1 inch x 1 inch)



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Log-log Plot: Pressure Drop and Pressure Drop Derivative Data vs. Effective Shut-In Time (te) (1 inch x 1 inch)



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Late-Time Cartesian Plot ("Muskat Plot"): Pressure Buildup Case

Average pressure, p (if applicable) = psia


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Problem 2: Analysis of Production Data — Fetkovich Gas Case (Well A — SPE 13169)

Given: In this problem you are to provide a complete analysis of the production data set referenced by Fetkovich et al (SPE 13169 — West Virginia Well A) using the Fetkovich "decline type curve" approach. Plots are included.

Required: You are to perform the following specific tasks:

1. Using the Arps relations given below:

Exponential Rate-Time Relation: Hyperbolic Rate-Time Relation: (0<b<1)

) exp( tDqq igig b

i

gig

tbD

qq

/1 )1(

Exponential Cumulative-Time Relation: Hyperbolic Cumulative-Time Relation: (0<b<1)

]) exp(1[ tDD

qG i

i

gip ] )1(1 [

)1( /11

b

ii

gip tbD

Db

qG

Exponential Rate-Cumulative Relation: Hyperbolic Rate-Cumulative Relation: (0<b<1)

i

gi

D

qGpGiDgiqgq

i

gibpgig Db

qG

G

Gqq

)(1 1 )1(

1

You are to:

1.1 Use a plot of qg versus Gp to estimate the maximum cumulative gas production, (Gp)max, using the exponential rate decline relation. (Gp)max = BSCF

1.2 Use a plot of log(qg) versus t to develop a production forecast using both the hyperbolic and exponential rate decline relations. You are to sketch trends by HAND and record your results below:

Exponential Trend: Hyperbolic Trend:

qi = MSCFD qi = MSCFD

Di = 1/D Di = 1/D

b =

1.3 Estimate the maximum cumulative gas production using the reciprocal rate method as described in the reference by Reese et al. (Gp)max = BSCF

2. You are to estimate the following properties using decline type curve matching techniques — specifically, the Fetkovich et al methodology (the analysis relations and data can be found in the Fetkovich, et al reference).

2.1 The formation permeability, k. k = md 2.2 The near well skin factor, s s = 2.3 The gas-in-place, G. G = BSCF

References:

● Fetkovich, M.J.: "Decline Curve Analysis Using Type Curves," JPT (March 1980) 1065-1077.

● Fetkovich, M.J., et al: "Decline Curve Analysis Using Type Curves — Case Histories, " SPEFE (December 1987) 637-656.

● Reese, P.D., Ilk, D., and Blasingame, T.A.: "Estimation of Reserves Using the Reciprocal Rate Method," paper SPE 107981 presented at the 2007 SPE Rocky Mountain Oil & Gas Technology Symposium held in Denver, CO, U.S.A., 16-18 April 2007.

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Cartesian Plot: qg versus Gp (use to estimate the maximum cumulative gas production, (Gp)max)

Estimate (Gp)max using the exponential rate decline relation. (Gp)max = BSCF


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Semi-log Plot: log(qg) versus t (use to define hyperbolic and exponential decline trends for this case)

Develop a production forecast using both the hyperbolic and exponential rate decline relations.

Exponential Trend: Hyperbolic Trend:

qi = MSCFD qi = MSCFD

Di = 1/D Di = 1/D

b =


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Cartesian Plot: 1/qg versus Gp/qg (use to estimate the maximum cumulative gas production, (Gp)max)

Estimate (Gp)max using reciprocal rate method (as described in the reference by Reese et al.). (Gp)max = BSCF


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Data Plot for Fetkovich Decline Type Curve Match:

Log-log Plot: Gas Rate vs. Production Time (1 inch x 1 inch)

Formation permeability, k = md The near well skin factor, s = The gas-in-place, G. = BSCF


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Fetkovich Decline Type Curve: Circular Radial Flow System (constant pwf production)

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