- Email: [email protected]
Anappres V2.0: A computerized expert system for well-test analysis
Computers & Geosciences Vol. 16. No. 8. pp. I 105--I I 15. 1990 Printed in Great Britain
0098-300490 $3.00 + 0.00 Pergamon Press plc
ANAPPRES V2.0: A COMPUTERIZED EXPERT SYSTEM FOR WELL-TEST ANALYSIS V. M. ARELLANO, E. IGLESIAS, and J. ARELLANO Instituto de Investigaciones Elfctricas, Departamento de Geotermia. Apdo. Postal 475, Cuemavaca, Mor., Mrxico (Receiced 27 June 1989; accepted 20 March 1990) Abstract--This paper presents ANAPPRES V2.0, the second version of a computerized expert system that interprets data of constant and variable-flowrate interference tests which include arbitrary numbers of active and observation wells. From the analysis, the transmissivity (permeability,reservoirthickness/fluid viscosity), storativity (porosity*composite fluid-rock compressibility,reservoirthickness), and hydrologic boundaries (existence, type. and location) are obtained. ANAPPRES successfully couples a mathematical model, an optimization technique, and heuristic knowledge, an unusual combination for a published expert system. The main advantages of ANAPPRES as compaed to standard type-curve and earlier computerized methods are: it can analyze variable flowrate interference tests; it allows analysis of tests including an arbitrary number of observation and production wells; it can obtain 4-5 parameters (transmissivity, storativity, type of boundary, distance, and angle to boundary) in one computer run; and it is considerably faster than a human expert. Key Word~: Expert system, FORTRAN. Hydrologic boundaries, Storativity, Transmissivity, Variable flowrate interference tests.
INTRODUCTION For interference test analysis, a type-curve graphical technique (e.g. Earlougher, 1977) has been the standard of the trade for many years. This technique has the disadvantages of being restricted to relatively simple situations and of requiring subjective judgement for curve fitting. The popularization of digital computers brought about computerized analysis techniques (e.g. Earlougher and Kersch, 1972; McEdwards and Benson, 1981). These techniques, by use of regression and least-squares linear programming, eliminated the subjectivity previously associated with fitting a model to the observations, and provided the possibilities to study complicated systems and handle large quantities of data. However, the application of these techniques requires extensive experience on the part of the analyst and, except in the simpler situations, is laborious. The labor is associated mainly with running the program(s) several to many times, in cleverly selected sequences, with different subsets of data. The experience is required, for example, to provide initial guesses of the parameter solutions to start the program(s), provide and apply quantitative criteria to accept computed fits to the data, be able to decide the proper sequence in which to run the program(s) and the corresponding data subsets, etc. This work describes ANAPPRES V2.0 (ANAlizador de Pruebas de PRESion, Spanish for "Well Test Analyst") a computerized expert system developed to analyze interference tests in homogeneous reservoirs. An earlier version of this system,
with lesser capabilities, has been described elsewhere (Arellano and others, 1989). ANAPPRES is user friendly, requires limited experience on the part of the analyst, eliminates subjectivity, and can handle complex situations and large data sets. In the current version ANAPPRES can analyze interference tests which include an arbitrary number of active wells and an arbitrary number of observation wells. The user could even be a beginner, as long as he (she) can create ASCII files, with the test data, for input. If required by the user, ANAPPRES can explain how and why it arrived at the current conclusion. This feature has didactic advantages for nonexpert users, provides verification capabilities for expert analysts and increases confidence in the expert system. These characteristics of ANAPPRES were obtained applying artificial intelligence techniques, mathematical models, optimization techniques, heuristic knowledge, and graphics software.
HARDWARE AND SOFTWARE
ANAPPRES was developed and is used in a VAX-II/780, a computer system widely used in universities and R&D institutions. As any other application developed on a VAX platform, it will run unmodified on any other VAX platform (including workstations), because of the built-in binary-level compatibility of this line of computers. For input-output ANAPPRES uses any graphics terminal that can emulate a Digital VT241 color graphics terminal. For hardcopy output it currently
1105
1106
V M. ,,.M~LLx.~O,E. IGLr.SIA.S.and J. ,A..RELLANO
uses the Digatal LA120 or LA210 matrix printers, the QMS KISS laser printer and the Hewlett-Packard HP-7585A pen plotter (most HP pen plotters are compatible). With the exception of its graphics modules, ANAPPRES is written in F O R T R A N 77, for portability, For expedience, we opted to use an existing graphics package (Rodriguez and others. 1987), developed in-house, which is written in Pascal. In a future version we plan to include an ad-hoc, smaller, faster graphics package. ARCHITECTURE OF ANAPPRES
t
Its main goal is to provide a friendly environment for communication with the user. The main functions of this module are to generate menus, to display diagnostics and numerical results, to generate graphics, and to display explanations (Fig. 1). Figures in the Application Example section, illustrate the presentation of the menus, results, graphics, and explanations, respectively. The screens of the current version actually are presented in Spanish: for this reason we resorted to translated drawings to illustrate them in this paper.
Computational Module
The architecture of ANAPPRES is presented in Figure I. There are five main modules, with four of them (the User Interface, the Computational Module, the Knowledge Base, and the Explanatory Module) linked to the central Inference Engine which drives the analysis. The functions of the different modules are described next. The user must provide two ASCII data files, corresponding to the active and observation wells (Fig. I). These files must conform to specified formats, and are read directly by the Computational Module.
menu function
User Inter/ace
This is a modified version of the program ANALYZE (McEdwards and Benson, 1981). The modifications to the original code include refreshing the memory in successive calls to this module, automatic handling of error conditons, and the inclusion of criteria to decide whether a run with given reservoir parameter initial guesses will converge. ANALYZE was developed for an analysis of interference tests in single (liquid) phase, homogeneous, isotropic reservoirs. This program determines reservoir parameters by minimizing the differences
~user function graphics ]
userinterface display explanations i display results ] function function
T
1
explanatoryI ~ modue l ....
I
~
I.
knowledge as,
Figure I. Architecture of ANAPPRES
.~',
Computerized expert system for well-test analysis between observed and calculated pressure histories. Pressure histories are calculated with the Theis (1935) solution, and the principle of superposition (e.g. Earlougher, 1977). Minimization is achieved by a nonlinear least-squares routine. A chi-squared statistic, normalized to the observed pressures, provides a quantitative measure of the quality of the fit.
Knowledge Base The Knowledge Base is organized in production rules (Arellano, 1987), with the well-known IFTHEN format. It contains the knowledge necessary to perform the analysis of interference tests. This knowledge includes quantitative criteria to decide whether there is a hydrologic boundary and its type, what initial guesses to use in order to start the Computational Module, etc. For example Figure 2 is a map in the transmissivity-storativity plane, illustrating sixteen trigger points, and the corresponding areas of convergence. ANAPPRES will use the trigger points as initial guesses to start the Computational Module, if the user chooses not to provide an initial guess, or if the initial guess provided by the user failed to promote convergence. This map was obtained by the analysis of the solution domain of more than 230 synthesized well tests. Production rules may be illustrated by the following pseudo code I F[TRA NSM ISSIVITY( I ) < TRANSM 1SSIVITY(2) AND TRANSMISSIVITY(2) < TRANSMISSIVITY(3) AND CilI-SQUARED(3) > CHI-SQUARED(2) AND CHI-SQUARED(2) > CHI-SQUARED(I)] TItEN A NO-FLOW BOUNDARY IS INDICATED
I°~ ~
~
Q.
E I0-~
10.7 03 0
iO-9 .O O
IO'~1 4 10-12 iO-~Z
lo-IO
lO-e
10 -6
Tronsmis$ivily ( m3/Po-s )
Figure 2. Trigger points and their corresponding convergence regions.
1107
which provides the Inference Engine with information related to diagnosing the existence of a boundary.
Inference Engine This module drives the analysis of the test, on the basis of the options selected and the input data given by the user, the partial results provided by the Computational Module and the information provided by the Knowledge Base. Its mode of operation is forward-chaining (e.g. Sell, 1985). The Inference Engine controls the operation of the Computational Module, and gets results, such as chisquared and reservoir parameter values, from it. With this information, the Inference Engine interacts, with the Knowledge Base in order to reach conclusions. Every time the Inference Engine reaches a conclusion, it commands the User Interference to display it in the screen of the graphics terminal and ask the user if an explanation is requested.
Explanatory Module It contains preformatted explanations for all the diagnostics and conclusions that ANAPPRES can reach. These explanations are supplemented with information provided by the Inference Engine each time it reaches a conclusion or diagnostic. If the user requests an explanation, the Explanatory Module passes the corresponding explanation to the User interface, which displays it through its Display Explanation function (Fig. I). METHOD OF ANALYSIS ANAPPRES performs a totally automatic interference tests analysis in a single run. That is, it determines whether there is evidence of a hydrologic boundary in the test data and determines its type, computes storativity and transmissivity values, and (if warranted) distance and angle from an arbitrary origin to the hydrologic boundary. Figure 3 illustrates the general logic of the analysis. The analytical process consists of three main stages: interference verification, search for hydrologic boundaries, and location of hydrologic boundaries. ANAPPRES determines for each observation well which of the production wells do interfere with it, using the principle of superposition (e.g. Earlougher, 1977), and the Theis (1935) solution. After that, for each observation well ANAPPRES determines if the corresponding data indicate the existence of a boundary, and if there is one, its type (either no-flow or constant-pressure). At this stage, estimates of the storativity and transmissivity associated with the well are obtained; these are taken as final results for the well if no boundary is detected. If a boundary is detected, the values of the transmissivity, storativity, and distance of the boundary to the origin are determined simultaneously. This is done sequentially for each and all the observation
V. M. Ag~t.x.~o, E. IGI_ELSIA.S,and J AKELLANO
t 108 INTERFER[NCE
VERIFICATION
For each observation well the interfering DrOduCtion wells ore identified utilizing superposltlon. AI 0 result of the O~'lalysil an estimation of tronsmis$ivity and storativity are obtained. The production wells that do not interfere with the observation well ore eliminated through this analysis.
SEARCH FOR HYDROLOGIC BOUNDARIES
I
I - T h e data ore analysed for existence of o boundary. :[f o boundary is found, it's type is determined and estimates of tronsmissivity and efo¢otivity are obtained. 2:- Tf no boundary is detected,the final values of tronsmissivity and storativity ore obtained.
1 /
! J J J J [ [ ]
Another well J
~
YES
LOCATION OF HYDROLOGIC BOUNDARIES The values of tronsm~ssiwty, sforotivify and distance to the boundary ore simultaneously determined using the i s t i m o fee of tranlmissivity and storahvity obtained before as guesses
Final values for fronsmissivify and storotivity ate obtained
I
!
End of the analysis of the present well
] I
A final analysis including only the wells that contain information about that boundary is performed,in which the average values of the tronsmlsstvity and storOtivdy Ore determined simultaneously with the values of the distance and the angle to the boundary.
A final analysis including both wells is performed, in whiCh the overage values of the transmiesivity and storat*vify ore determined simultoneoully with the values of the dlstonce and the angle. However, in the ease the solution for the angle is not unique: It iS either m o t 21T-¢x
Figure 3. Logic flowchart of analysis performed by ANAPPRES.
wells participating in the test. If exactly two wells detect a boundary, a final analysis simultaneously including both wells is performed to obtain the average values of storativity and transmissivity, the distance of the boundary to the origin and ,8, the angular location of the boundary. However, in this case ,8 is not determined uniquely and the true angular location could be 2n-//. If more than two wells detect a boundary, a final analysis simultaneously including all these wells is performed to obtain storativity, transmissivity. distance, and angle: in this situation the angle is determined uniquely. VALIDATION At the time of this writing ANAPPRES V2.0 had been validated against a number of published and unpublished problems with known solutions, The former include: (a) A constant-flowrate match of the Theis curve, modeling the simplest interference example in an infinite reservoir (McEdwards and Benson, 1981); (b) A constant-flowrate, production interference test between wells RRGE-I and RRGE-2 in the Raft River, Idaho, geothermal project that detected a no-flow boundary (Narasimhan and Witherspoon, 1977); (c) A constant-flowrate production interference test between wells 6-2 and 6-1 at the East Mesa geothermal field that detected a constant-pressure boundary (Narasimhan, McEdwards, and Witherspoon, 1977); (d) A constant-flowrate production interference test between wells 31-1 and 38-30 at the East Mesa geothermal field that detected a no-flow boundary (Narasimhan, McEdwards, and Witherspoon, 1977); (e) A highly variable-flowrate, five-spot pattern, injection test in a shallow groundwater aquifer under consideration for an aquifer thermal energy storage project, in which the central well was active and the peripheral wells were monitored (McEdwards and Benson, 1981 ); (f) A highly variable-flowrate, multiple-production-well intereference test in the Cerro PriseD, Mexico, geothermal reservoir which is being used currently for electric power generation (McEdwards and Benson, 1981); (g) A constant-flowrate, injection interference test between two wells, which did not detect a boundary (Earlougher, 1977, example 9.1); and (h) A constant-flowrate injection test in a nine-spot pattern, where the central well is the injector and the peripheral wells are observation wells, which did not detect a boundary (Ramey, 1975). In all situations ANAPPRES obtained the correct diagnoses and quantitative results, as shown in Table 1, whether initial guesses were provided by the user. The r.m.s, normalized relative differences are 11.7% for transmissivity and 5.01% for storativity. The
Computerized expert system for well-test analysis
1109
Table 1. Comparison with published results Test
Literature results k.h/p ech boundary
ANAPPRES results kh/~ ech boundary
(a) (b) (¢)
1.0 3.81E-7 3.37E-8 8.87E-9 8.23E-7 3.85E-7 6.90E-II 1.27E-I0
1.000 4.10E-7 3.46E-8 1.lIE-8 7.90E-7 4.15E-7 8.10E-11 1.24E-10
(d)
(e) (f) (g) (h)
Notes to Table normalized with no flow; C.P. = cases mentioned
1.0 5.20E-8 2.60E-7 9.30E-8 1.72E-7 1.00E-6 1.97E-9 1.77E-9
N.B. N.F. C.P. N.F. N.F. N.B. N.B. N.B.
1:Ekhlg3
= n3pa-ls-1;
0.9999 5.00E-8 2.50E-7 9.28E-8 1.70E-7 1.02E-6 2.00E-9 1.54E-9
[ech3
magnitudes of these differences are negligible for all practical purposes. Furthermore, the analysis of the tests identified as (b), (c), (d), (g), and (h) were done by highly recognized international experts, using the traditional typecurve graphical technique, whereas the rest of the tests where analyzed by least-squares computerized techniques. As mentioned in the "Introduction", the type-curve technique has the disadvantage of requiring subjective judgement for curve fitting. This handicap may be reflected by the r.m.s, relative differences corresponding to the former set of tests (transmissivity = 14.28%, storativity = 6.25*/,) which far exceed the r.m.s, relative differences of the rest of the tests (transmissivity = 5.06%, storativ-
016
M-91
N.B. N.F. C.P. N.F. N.F. N.B. N.B. N.B.
= pa-lm;
respect to the literature constant pressure boundary; in the V a l t d a t l o n section.
Relative difference khl~ ech boundary
results; letters
0.0 8.4 2.7 25.1 -4.0 7.8 17.5 -2.4
-0.0001 -4.1 -3.1 -0.2 -1.1 2.1 -1.5 -12.9
Relative
difference
N .B . = no b o u n d a r y ; in parenthesis refer
None
None None None None None None None in
4,
N.F. • to the
ity = 1.37%). Unfortunately, the small size of the sample does not warrant a firm statistical conclusion in this respect. We also have tested ANAPPRES against a few hundred real and synthetic interference tests with known but unpublished results. These tests span all types of situations and combinations of parameters relevant to the capabilities of this expert system. Our results will be the subject of another paper, but agree well with the statistics of the preceding paragraphs. EXAMPLE APPLICATION To illustrate the uses of ANAPPRES V2.0 we selected example (f) from the preceding section,
M-51
7 M-90
012
o o
M-50
I
o0e
cJ 0 0 4
00C 276
O OO
]
,
I
a
I B
OgO OO@
275
g. 274
O0° ~. 273
272
O00~O o O 0°
O0oo°
OoooO = 0
1 200
=
I 400
,
I 600 Time
,
I 800
,
I 1000
J
I 1200
,
I 1400
( hr )
Figure 4. A--Measured flowrates of the active wells; B--measured pressure response at observation well M-101.
[110
V, M. A~LLANO. E. IGLESL~S,and J, ,'~.P,ELLANO
{412 m.1219rn) ®
ya
(914
M-5~
m, H43"m )
I
(Ore,
®
M-91 IOOO m)
® M:5o
( - 34 m. 494. m I
®
M-90
(Ore,Ore) . . . . ® . . . . . . . . . . . . . . . . . . . . M
-i101
x
I
Figure 5. Location of wells participating in lest. because it demonstrates the ability of this expert system to handle a complex situation. This example includes four active wells, each with a highly variable llowrate, which overlaps in time with at least another flowrate (Fig. 4A). The pressure response at observation well M-101 is shown in Figure 4B. The location of the wells is presented in Figure 5. After setting up the active-wells and observationwell input data files, the user runs ANAPPRES. A series of screens will appear in succcssion, depending on the user's selections. For brevity, wc will illustrate only a fraction of the screens that are
EXPERT
What
SYSTEM
type of
I-One
presented in an actual session. In this example, after selecting option No. 2 early on the screen (Fig. 6). the user is presented information about which of the active wells, if any, interferes with the observation well (Fig. 7). This is done sequentially in several screens (Fig. 8), each updating the effects of adding one more active well to the superposition trial solution, on transmissivity, storativity, and chisquared (see Fig. 3). Eventually. all the active wells are tried, and a diagnostic about which of them do interfere with the observation v~ell is reached; the corresponding screen (Fig. 9) also provides the history of the successive matches that underlie this diagnostic. At this point, the user may ask how the conclusion was arrived at; if so an explanation will be presented (Fig. 10), Next. A N A P P R E S sets out to determine whether the data indicate the existence of a boundary. The rationale tbr this search is that the effects of boundaries on pressure response are more noticeable in the late pressure data, which may depart significantly from the infinite-reservoir solution. For that reason, successive screens (Figs. 11, 12) inform the user how well the trial solution fits the observed pressure response for progressively earlier times. In this situation the lit does not improve at earlier times, indicating that no boundary information is contained in thc data. This conclusion is presented in the following scrcen (Fig. 13), along ~ith the history of the successive matches; again, an explanation can be requested by the user. Thc next screcn (not shown) offers to present a graph of the final fit in the monitor screen (Fig. 14). There also is the option of creating a plot file for hardcopy output ,,i~t printer or plotter. The final screen (Fig. 15) offers :~ ,;urnmary of the results.
FOR W E L L - T E S T
test do you want
active well -
N
ANALYSIS
to analyze 2
observation wells
2--N active w e l l s - N observation wells
OPTION > [-'I
Figure 6. Example of menu screen.
Computerized exixrt system for well-test analysis
1111
OPTION: N ACTIVE W E L L S - N OBSERVATION WELLS
1
FOR OBSERVATION WELL M-lOI
I FINOING WHICH WELLS DO INTERFERE I Number of active
(K.h)/Mu
FT e C * h
X**2
I
0.4137 E-07
0.2381 E - 0 6
0 . 4 9 6 0 E-OI
2
0.1233 E - 0 6
0.4981 E - 0 6
0.2778 E-Of
wells considered
/
Figure 7. Presentation of partial results when system is assessing which wells do interfere.
\ OPTION" N ACTIVE W E L L S - N
OBSERVATION WELLS
\
FOR OBSERVATION WELL M-IOI I FINDING WHICH WELLS DO INTERFERE ]
Number of active
(K~h)IMu
F'r . C . h
X** 2
wells considered
| 2 :5 4
0.4137 0.1233 0.3470 0.4152
E-07 E-06 E-06 E-06
0.2:581 E - 0 6 0.4981 E - 0 6 0.9689 E - 0 6 0.1025 E - 0 5
0.4960 0.2778 0.2:564 0.1434
E-01 E-01 E-02 E-02
ORDER OF ACTIVE WELLS CONSIDERED: M-9!, M-51,M-90,
/
M-50
< RETURN > [7
Figure 8. Update of screen of Figure 7.
II 12
V . M . AII.ELL.~,',;O, E. IGLESlAS, and J ,'-%LELLxXO
/
OPTION
N
ACTIVE
WELLS
- N
OBSERVATION
FOR OBSERVATION WELL
WELLS
M-lOl
FOUND THAT THE FOLLOWING WELLS DO INTERFERE
M-91 HISTORY
M-51
M-90
M-50
OF" S U C C E S S I V E
Number of active wells considered 1
(K *h)/Mu
MATCHES FZ.
C* h
X**
2
04137
E-07
02381
E-06
04960
E-O1
2
O 1233
E-06
04981 E-D6
02778
E-O1
3
O 3470
E-06
0 9689 E - 0 6
02364
E-02
4
04152
E-06
0 1025E-05
01434
E-02
/ •
7
/
Figure 9, [-xample of screen presenting conclusion
I
OPTION I N ACTIVE
WELLS
-
N OBSERVATION
WELLS
EXPLANATION FOR OBSERVATION WELL M - I O 1 - A l l active wells were included in trial superposifion soluhons, which were fit to the observed pressures The quality of the f~t wos measured by Chi-squored statistics.
- Excluding wells NONE from the superpoiition solution, eHher left unchanged or =reproved the qualify of the fit to the observed pressures - 1"he value of the Chi-squared corresponding to the superpos~t~on solution that includes the remaining wells ~s consistent with the
current toJeronce, t
-- Therefore, one concludes that the following wells do interfere M-91, M-51, M-90, M - 5 0 1 Go back one screen
/
/
/
2 Resume analysis
/ Figure 10. Example of explanauon screen
t t
Computerized expert system for well-test analysis
OPTION:
N ACTIVE
WELLS-N
OBSERVATION
I l 13
WELLS
FOR OBSERVATION WELL M-101
. . .[ . FINDING WHETHER A BOUNDARY IS INDICATED 1
Max lime considered
(Keh]/Mu
FT~,C~h
0.4234 E + 0 7 0.2823 E + 0 7
0.4152 E - 0 6 0.4022 E - 0 6
0.1025 E - 0 5 0.1012 E - 0 5
X~Z 0.1434 E - 0 2 0.1510 E - 0 2
l Figure I I. Prcsentation of partial results when system is assessing whether boundary is indicated by data.
OPTION:
N ACTIVE
WELLS-N
OBSERVATION
WELLS
FOR OBSERVATION WELL M - l O S
[ FINDING WHETHER A BOUNDARY IS INDICATED]
Mox lime considered
(Keh]IMu
0.4234 E + 0 7 0.2823 E + 0 7 0.1411 E + 0 7
0.415Z E - 0 6 0.4022 E - 0 6 0.3241 E - 0 6
FI ~Ceh O. lOZ5 E - 0 5 O.lOIZ E - O 5 0.9223 E - 0 5
X¢~¢~ 2 0 1 4 3 4 E-OZ 0.1510 E - O 2 0.2128 E - 0 2
Figure 12. Update of screen of Figure I I.
/
II 14
', M. ARELLANO. E. IGLESIAS, and J. ARELLANO
OPTION
N
ACTIVE
WELLS
- N
OBSERVATION
FOR OBSERVATION WELL
WELLS
M-101
THE DATA DO NOT CONTAIN BOUNDARY INFORMATION
HISTORY OF SUCCESSIVE MATCHES Max
time
(K*h)lMu
FIiC.h
X~.2
considered 0.4234 E+07
0 4152 E-06
0 1025 E - 0 5
01434
02823
E+07
04022
E-06
01012
E-05
01510
E-02 E-02
01411
E+07
05241
E-06
0.9223 E-06
02128
E-02
/ J
I"igurc 13. S>stcm concluded that no boundl, ry is indicated by to,4 daL~
\
/ E+3
ANAPPRES
50
40
'~ n
•
Calculated
o
Observed
30
D_ <3 20 F
0 '
0
I0
20
30
Time
(s )
40
50 E+5
Figure 14 Final ti1 or model results to observed pressure response, as deployed b) Graphics Function or User Interface
Computerized expert system for well-test analysis
OPTION:
N ACTIVE
WELLS-N
OBSERVATION
FOR OBSERVATION WELL
1115
WELLS
M-IOl
SUMMARY
•)6
INTERFERING WELLS: NO BOUNDARY I S
")(" ( K e h l / M u =
")(" F I * C * h X,~. 2 ~
M-91,M-51,
M-90, M-50
INDICATED
0.415:>E-06 =0.1025E-05
")6
(m*'~3)(PoS)**-I
K"
(9a**-ll(m)
=0.1454E-02
-R- -1(- "R- -)(.
-)6 *
~
~ -t4" *
-)6 ,)(. Yr
-)6 ~
< RETURN
>
o
/ /
Figure 15. Summary of analysis' results CONCLUSIONS AND FUTURE WORK We have developed and validated the second version of a computerized expert system capable of analyzing constant and variable flowrate interference tests, in which there are an arbitrary number of production wells and an arbitrary n u m b e r of observation wells, in liquid-saturated homogenous reservoirs. The main advantages of this system are that it is user friendly, requires limited experience on the part of the analyst, eliminates subjectivity associated with earlier techniques of analysis, can handle complex cases and large data sets, completes the analysis of even the most complex situations (including plotting the results) in one run and is significantly faster than a human expert. The next version of A N A P P R E S , which already is in an advanced stage of development, will include, in addition to the current capabilities, the possibility of analyzing single-well pressure tests.
Acknowledgments--We thank two anonymous referees for comments that helped improve the presentation of this paper. REFERENCES
Arellano, V, M., 1987. DesarroUo de un sistema experto para el an:ilisis de pruebas de presi6n: unpubl, masters thesis. Universidad Aut6noma del Estado de Morelos. Cuernavaca, Mor., M6xico, 137 p.
CAGEO 1 6 , ~
Arellano, V. M., Iglesias, E. R.. Arellano, J., and Schwarzblat, M., 1989. Developments in geothermal energy in Mexico--Part twenty-one. ANAPPRES VI.0: a computerized expert system for interference well-test analysis in geothermal reservoirs: Heat Recovery Systems & CHP, v. 9. p. 101-113. Earlougher, R. C., 1977, Advances in well test analysis: Soc. Petroleum Engineers Mon. 5, 264 p. Earlougher. R. C., and Kersch, K. M., 1972, Field examples of automatic transient test analysis: Jour. Pet. Tech., October, p, 1271-1277. McEdwards, D. G., and Bcnson, S. M.. 1981, User's manual for ANALYZE, a multiple-well, least squares matching routine for well-test analysis: Rept. LBL-10907, Lawrence Berkeley Laboratory. 70 p. Narasimhan, T. N., and Witherspoon, P. A., 1977, Reservoir evaluation tests on RRGE-I and RRGE-2, Raft River geothermal project, Idaho: Rept. LBL-5958, Lawrence Berkeley Laboratory, 50 p. Narasimhan, T. N., McEdwards, D. G., and Witherspoon, P. A., 1977, Results of reservoir evaluation tests, 1976, East Mesa geothermal field, California: Rept. LBL-5973, Lawrence Berkeley Laboratory, 48 p. Ramey, H. J., Jr., 1975, Interference analysis for anisotropic formations--a case history: Jour. Pet. Tech., October, p. 1290-1298. Rodriguez A., Angeles M., Pineda A., and Santana J., 1987, DIGRAF: Disefio de grhficas, Conferencia National D.E.C.U.S., M6xico D.F. 5--6 November, 8 p. Sell, P. S., 1985, Expert systems---A practical introduction, Macmillan Publ. Ltd., London, 99 p. Theis, C. V., 1935, The relation between the lowering of the piezometric surface and the rate and duration of discharge of a well using groundwater storage, Trans. A.G.U., p. 519-524.
0098-300490 $3.00 + 0.00 Pergamon Press plc
ANAPPRES V2.0: A COMPUTERIZED EXPERT SYSTEM FOR WELL-TEST ANALYSIS V. M. ARELLANO, E. IGLESIAS, and J. ARELLANO Instituto de Investigaciones Elfctricas, Departamento de Geotermia. Apdo. Postal 475, Cuemavaca, Mor., Mrxico (Receiced 27 June 1989; accepted 20 March 1990) Abstract--This paper presents ANAPPRES V2.0, the second version of a computerized expert system that interprets data of constant and variable-flowrate interference tests which include arbitrary numbers of active and observation wells. From the analysis, the transmissivity (permeability,reservoirthickness/fluid viscosity), storativity (porosity*composite fluid-rock compressibility,reservoirthickness), and hydrologic boundaries (existence, type. and location) are obtained. ANAPPRES successfully couples a mathematical model, an optimization technique, and heuristic knowledge, an unusual combination for a published expert system. The main advantages of ANAPPRES as compaed to standard type-curve and earlier computerized methods are: it can analyze variable flowrate interference tests; it allows analysis of tests including an arbitrary number of observation and production wells; it can obtain 4-5 parameters (transmissivity, storativity, type of boundary, distance, and angle to boundary) in one computer run; and it is considerably faster than a human expert. Key Word~: Expert system, FORTRAN. Hydrologic boundaries, Storativity, Transmissivity, Variable flowrate interference tests.
INTRODUCTION For interference test analysis, a type-curve graphical technique (e.g. Earlougher, 1977) has been the standard of the trade for many years. This technique has the disadvantages of being restricted to relatively simple situations and of requiring subjective judgement for curve fitting. The popularization of digital computers brought about computerized analysis techniques (e.g. Earlougher and Kersch, 1972; McEdwards and Benson, 1981). These techniques, by use of regression and least-squares linear programming, eliminated the subjectivity previously associated with fitting a model to the observations, and provided the possibilities to study complicated systems and handle large quantities of data. However, the application of these techniques requires extensive experience on the part of the analyst and, except in the simpler situations, is laborious. The labor is associated mainly with running the program(s) several to many times, in cleverly selected sequences, with different subsets of data. The experience is required, for example, to provide initial guesses of the parameter solutions to start the program(s), provide and apply quantitative criteria to accept computed fits to the data, be able to decide the proper sequence in which to run the program(s) and the corresponding data subsets, etc. This work describes ANAPPRES V2.0 (ANAlizador de Pruebas de PRESion, Spanish for "Well Test Analyst") a computerized expert system developed to analyze interference tests in homogeneous reservoirs. An earlier version of this system,
with lesser capabilities, has been described elsewhere (Arellano and others, 1989). ANAPPRES is user friendly, requires limited experience on the part of the analyst, eliminates subjectivity, and can handle complex situations and large data sets. In the current version ANAPPRES can analyze interference tests which include an arbitrary number of active wells and an arbitrary number of observation wells. The user could even be a beginner, as long as he (she) can create ASCII files, with the test data, for input. If required by the user, ANAPPRES can explain how and why it arrived at the current conclusion. This feature has didactic advantages for nonexpert users, provides verification capabilities for expert analysts and increases confidence in the expert system. These characteristics of ANAPPRES were obtained applying artificial intelligence techniques, mathematical models, optimization techniques, heuristic knowledge, and graphics software.
HARDWARE AND SOFTWARE
ANAPPRES was developed and is used in a VAX-II/780, a computer system widely used in universities and R&D institutions. As any other application developed on a VAX platform, it will run unmodified on any other VAX platform (including workstations), because of the built-in binary-level compatibility of this line of computers. For input-output ANAPPRES uses any graphics terminal that can emulate a Digital VT241 color graphics terminal. For hardcopy output it currently
1105
1106
V M. ,,.M~LLx.~O,E. IGLr.SIA.S.and J. ,A..RELLANO
uses the Digatal LA120 or LA210 matrix printers, the QMS KISS laser printer and the Hewlett-Packard HP-7585A pen plotter (most HP pen plotters are compatible). With the exception of its graphics modules, ANAPPRES is written in F O R T R A N 77, for portability, For expedience, we opted to use an existing graphics package (Rodriguez and others. 1987), developed in-house, which is written in Pascal. In a future version we plan to include an ad-hoc, smaller, faster graphics package. ARCHITECTURE OF ANAPPRES
t
Its main goal is to provide a friendly environment for communication with the user. The main functions of this module are to generate menus, to display diagnostics and numerical results, to generate graphics, and to display explanations (Fig. 1). Figures in the Application Example section, illustrate the presentation of the menus, results, graphics, and explanations, respectively. The screens of the current version actually are presented in Spanish: for this reason we resorted to translated drawings to illustrate them in this paper.
Computational Module
The architecture of ANAPPRES is presented in Figure I. There are five main modules, with four of them (the User Interface, the Computational Module, the Knowledge Base, and the Explanatory Module) linked to the central Inference Engine which drives the analysis. The functions of the different modules are described next. The user must provide two ASCII data files, corresponding to the active and observation wells (Fig. I). These files must conform to specified formats, and are read directly by the Computational Module.
menu function
User Inter/ace
This is a modified version of the program ANALYZE (McEdwards and Benson, 1981). The modifications to the original code include refreshing the memory in successive calls to this module, automatic handling of error conditons, and the inclusion of criteria to decide whether a run with given reservoir parameter initial guesses will converge. ANALYZE was developed for an analysis of interference tests in single (liquid) phase, homogeneous, isotropic reservoirs. This program determines reservoir parameters by minimizing the differences
~user function graphics ]
userinterface display explanations i display results ] function function
T
1
explanatoryI ~ modue l ....
I
~
I.
knowledge as,
Figure I. Architecture of ANAPPRES
.~',
Computerized expert system for well-test analysis between observed and calculated pressure histories. Pressure histories are calculated with the Theis (1935) solution, and the principle of superposition (e.g. Earlougher, 1977). Minimization is achieved by a nonlinear least-squares routine. A chi-squared statistic, normalized to the observed pressures, provides a quantitative measure of the quality of the fit.
Knowledge Base The Knowledge Base is organized in production rules (Arellano, 1987), with the well-known IFTHEN format. It contains the knowledge necessary to perform the analysis of interference tests. This knowledge includes quantitative criteria to decide whether there is a hydrologic boundary and its type, what initial guesses to use in order to start the Computational Module, etc. For example Figure 2 is a map in the transmissivity-storativity plane, illustrating sixteen trigger points, and the corresponding areas of convergence. ANAPPRES will use the trigger points as initial guesses to start the Computational Module, if the user chooses not to provide an initial guess, or if the initial guess provided by the user failed to promote convergence. This map was obtained by the analysis of the solution domain of more than 230 synthesized well tests. Production rules may be illustrated by the following pseudo code I F[TRA NSM ISSIVITY( I ) < TRANSM 1SSIVITY(2) AND TRANSMISSIVITY(2) < TRANSMISSIVITY(3) AND CilI-SQUARED(3) > CHI-SQUARED(2) AND CHI-SQUARED(2) > CHI-SQUARED(I)] TItEN A NO-FLOW BOUNDARY IS INDICATED
I°~ ~
~
Q.
E I0-~
10.7 03 0
iO-9 .O O
IO'~1 4 10-12 iO-~Z
lo-IO
lO-e
10 -6
Tronsmis$ivily ( m3/Po-s )
Figure 2. Trigger points and their corresponding convergence regions.
1107
which provides the Inference Engine with information related to diagnosing the existence of a boundary.
Inference Engine This module drives the analysis of the test, on the basis of the options selected and the input data given by the user, the partial results provided by the Computational Module and the information provided by the Knowledge Base. Its mode of operation is forward-chaining (e.g. Sell, 1985). The Inference Engine controls the operation of the Computational Module, and gets results, such as chisquared and reservoir parameter values, from it. With this information, the Inference Engine interacts, with the Knowledge Base in order to reach conclusions. Every time the Inference Engine reaches a conclusion, it commands the User Interference to display it in the screen of the graphics terminal and ask the user if an explanation is requested.
Explanatory Module It contains preformatted explanations for all the diagnostics and conclusions that ANAPPRES can reach. These explanations are supplemented with information provided by the Inference Engine each time it reaches a conclusion or diagnostic. If the user requests an explanation, the Explanatory Module passes the corresponding explanation to the User interface, which displays it through its Display Explanation function (Fig. I). METHOD OF ANALYSIS ANAPPRES performs a totally automatic interference tests analysis in a single run. That is, it determines whether there is evidence of a hydrologic boundary in the test data and determines its type, computes storativity and transmissivity values, and (if warranted) distance and angle from an arbitrary origin to the hydrologic boundary. Figure 3 illustrates the general logic of the analysis. The analytical process consists of three main stages: interference verification, search for hydrologic boundaries, and location of hydrologic boundaries. ANAPPRES determines for each observation well which of the production wells do interfere with it, using the principle of superposition (e.g. Earlougher, 1977), and the Theis (1935) solution. After that, for each observation well ANAPPRES determines if the corresponding data indicate the existence of a boundary, and if there is one, its type (either no-flow or constant-pressure). At this stage, estimates of the storativity and transmissivity associated with the well are obtained; these are taken as final results for the well if no boundary is detected. If a boundary is detected, the values of the transmissivity, storativity, and distance of the boundary to the origin are determined simultaneously. This is done sequentially for each and all the observation
V. M. Ag~t.x.~o, E. IGI_ELSIA.S,and J AKELLANO
t 108 INTERFER[NCE
VERIFICATION
For each observation well the interfering DrOduCtion wells ore identified utilizing superposltlon. AI 0 result of the O~'lalysil an estimation of tronsmis$ivity and storativity are obtained. The production wells that do not interfere with the observation well ore eliminated through this analysis.
SEARCH FOR HYDROLOGIC BOUNDARIES
I
I - T h e data ore analysed for existence of o boundary. :[f o boundary is found, it's type is determined and estimates of tronsmissivity and efo¢otivity are obtained. 2:- Tf no boundary is detected,the final values of tronsmissivity and storativity ore obtained.
1 /
! J J J J [ [ ]
Another well J
~
YES
LOCATION OF HYDROLOGIC BOUNDARIES The values of tronsm~ssiwty, sforotivify and distance to the boundary ore simultaneously determined using the i s t i m o fee of tranlmissivity and storahvity obtained before as guesses
Final values for fronsmissivify and storotivity ate obtained
I
!
End of the analysis of the present well
] I
A final analysis including only the wells that contain information about that boundary is performed,in which the average values of the tronsmlsstvity and storOtivdy Ore determined simultaneously with the values of the distance and the angle to the boundary.
A final analysis including both wells is performed, in whiCh the overage values of the transmiesivity and storat*vify ore determined simultoneoully with the values of the dlstonce and the angle. However, in the ease the solution for the angle is not unique: It iS either m o t 21T-¢x
Figure 3. Logic flowchart of analysis performed by ANAPPRES.
wells participating in the test. If exactly two wells detect a boundary, a final analysis simultaneously including both wells is performed to obtain the average values of storativity and transmissivity, the distance of the boundary to the origin and ,8, the angular location of the boundary. However, in this case ,8 is not determined uniquely and the true angular location could be 2n-//. If more than two wells detect a boundary, a final analysis simultaneously including all these wells is performed to obtain storativity, transmissivity. distance, and angle: in this situation the angle is determined uniquely. VALIDATION At the time of this writing ANAPPRES V2.0 had been validated against a number of published and unpublished problems with known solutions, The former include: (a) A constant-flowrate match of the Theis curve, modeling the simplest interference example in an infinite reservoir (McEdwards and Benson, 1981); (b) A constant-flowrate, production interference test between wells RRGE-I and RRGE-2 in the Raft River, Idaho, geothermal project that detected a no-flow boundary (Narasimhan and Witherspoon, 1977); (c) A constant-flowrate production interference test between wells 6-2 and 6-1 at the East Mesa geothermal field that detected a constant-pressure boundary (Narasimhan, McEdwards, and Witherspoon, 1977); (d) A constant-flowrate production interference test between wells 31-1 and 38-30 at the East Mesa geothermal field that detected a no-flow boundary (Narasimhan, McEdwards, and Witherspoon, 1977); (e) A highly variable-flowrate, five-spot pattern, injection test in a shallow groundwater aquifer under consideration for an aquifer thermal energy storage project, in which the central well was active and the peripheral wells were monitored (McEdwards and Benson, 1981 ); (f) A highly variable-flowrate, multiple-production-well intereference test in the Cerro PriseD, Mexico, geothermal reservoir which is being used currently for electric power generation (McEdwards and Benson, 1981); (g) A constant-flowrate, injection interference test between two wells, which did not detect a boundary (Earlougher, 1977, example 9.1); and (h) A constant-flowrate injection test in a nine-spot pattern, where the central well is the injector and the peripheral wells are observation wells, which did not detect a boundary (Ramey, 1975). In all situations ANAPPRES obtained the correct diagnoses and quantitative results, as shown in Table 1, whether initial guesses were provided by the user. The r.m.s, normalized relative differences are 11.7% for transmissivity and 5.01% for storativity. The
Computerized expert system for well-test analysis
1109
Table 1. Comparison with published results Test
Literature results k.h/p ech boundary
ANAPPRES results kh/~ ech boundary
(a) (b) (¢)
1.0 3.81E-7 3.37E-8 8.87E-9 8.23E-7 3.85E-7 6.90E-II 1.27E-I0
1.000 4.10E-7 3.46E-8 1.lIE-8 7.90E-7 4.15E-7 8.10E-11 1.24E-10
(d)
(e) (f) (g) (h)
Notes to Table normalized with no flow; C.P. = cases mentioned
1.0 5.20E-8 2.60E-7 9.30E-8 1.72E-7 1.00E-6 1.97E-9 1.77E-9
N.B. N.F. C.P. N.F. N.F. N.B. N.B. N.B.
1:Ekhlg3
= n3pa-ls-1;
0.9999 5.00E-8 2.50E-7 9.28E-8 1.70E-7 1.02E-6 2.00E-9 1.54E-9
[ech3
magnitudes of these differences are negligible for all practical purposes. Furthermore, the analysis of the tests identified as (b), (c), (d), (g), and (h) were done by highly recognized international experts, using the traditional typecurve graphical technique, whereas the rest of the tests where analyzed by least-squares computerized techniques. As mentioned in the "Introduction", the type-curve technique has the disadvantage of requiring subjective judgement for curve fitting. This handicap may be reflected by the r.m.s, relative differences corresponding to the former set of tests (transmissivity = 14.28%, storativity = 6.25*/,) which far exceed the r.m.s, relative differences of the rest of the tests (transmissivity = 5.06%, storativ-
016
M-91
N.B. N.F. C.P. N.F. N.F. N.B. N.B. N.B.
= pa-lm;
respect to the literature constant pressure boundary; in the V a l t d a t l o n section.
Relative difference khl~ ech boundary
results; letters
0.0 8.4 2.7 25.1 -4.0 7.8 17.5 -2.4
-0.0001 -4.1 -3.1 -0.2 -1.1 2.1 -1.5 -12.9
Relative
difference
N .B . = no b o u n d a r y ; in parenthesis refer
None
None None None None None None None in
4,
N.F. • to the
ity = 1.37%). Unfortunately, the small size of the sample does not warrant a firm statistical conclusion in this respect. We also have tested ANAPPRES against a few hundred real and synthetic interference tests with known but unpublished results. These tests span all types of situations and combinations of parameters relevant to the capabilities of this expert system. Our results will be the subject of another paper, but agree well with the statistics of the preceding paragraphs. EXAMPLE APPLICATION To illustrate the uses of ANAPPRES V2.0 we selected example (f) from the preceding section,
M-51
7 M-90
012
o o
M-50
I
o0e
cJ 0 0 4
00C 276
O OO
]
,
I
a
I B
OgO OO@
275
g. 274
O0° ~. 273
272
O00~O o O 0°
O0oo°
OoooO = 0
1 200
=
I 400
,
I 600 Time
,
I 800
,
I 1000
J
I 1200
,
I 1400
( hr )
Figure 4. A--Measured flowrates of the active wells; B--measured pressure response at observation well M-101.
[110
V, M. A~LLANO. E. IGLESL~S,and J, ,'~.P,ELLANO
{412 m.1219rn) ®
ya
(914
M-5~
m, H43"m )
I
(Ore,
®
M-91 IOOO m)
® M:5o
( - 34 m. 494. m I
®
M-90
(Ore,Ore) . . . . ® . . . . . . . . . . . . . . . . . . . . M
-i101
x
I
Figure 5. Location of wells participating in lest. because it demonstrates the ability of this expert system to handle a complex situation. This example includes four active wells, each with a highly variable llowrate, which overlaps in time with at least another flowrate (Fig. 4A). The pressure response at observation well M-101 is shown in Figure 4B. The location of the wells is presented in Figure 5. After setting up the active-wells and observationwell input data files, the user runs ANAPPRES. A series of screens will appear in succcssion, depending on the user's selections. For brevity, wc will illustrate only a fraction of the screens that are
EXPERT
What
SYSTEM
type of
I-One
presented in an actual session. In this example, after selecting option No. 2 early on the screen (Fig. 6). the user is presented information about which of the active wells, if any, interferes with the observation well (Fig. 7). This is done sequentially in several screens (Fig. 8), each updating the effects of adding one more active well to the superposition trial solution, on transmissivity, storativity, and chisquared (see Fig. 3). Eventually. all the active wells are tried, and a diagnostic about which of them do interfere with the observation v~ell is reached; the corresponding screen (Fig. 9) also provides the history of the successive matches that underlie this diagnostic. At this point, the user may ask how the conclusion was arrived at; if so an explanation will be presented (Fig. 10), Next. A N A P P R E S sets out to determine whether the data indicate the existence of a boundary. The rationale tbr this search is that the effects of boundaries on pressure response are more noticeable in the late pressure data, which may depart significantly from the infinite-reservoir solution. For that reason, successive screens (Figs. 11, 12) inform the user how well the trial solution fits the observed pressure response for progressively earlier times. In this situation the lit does not improve at earlier times, indicating that no boundary information is contained in thc data. This conclusion is presented in the following scrcen (Fig. 13), along ~ith the history of the successive matches; again, an explanation can be requested by the user. Thc next screcn (not shown) offers to present a graph of the final fit in the monitor screen (Fig. 14). There also is the option of creating a plot file for hardcopy output ,,i~t printer or plotter. The final screen (Fig. 15) offers :~ ,;urnmary of the results.
FOR W E L L - T E S T
test do you want
active well -
N
ANALYSIS
to analyze 2
observation wells
2--N active w e l l s - N observation wells
OPTION > [-'I
Figure 6. Example of menu screen.
Computerized exixrt system for well-test analysis
1111
OPTION: N ACTIVE W E L L S - N OBSERVATION WELLS
1
FOR OBSERVATION WELL M-lOI
I FINOING WHICH WELLS DO INTERFERE I Number of active
(K.h)/Mu
FT e C * h
X**2
I
0.4137 E-07
0.2381 E - 0 6
0 . 4 9 6 0 E-OI
2
0.1233 E - 0 6
0.4981 E - 0 6
0.2778 E-Of
wells considered
/
Figure 7. Presentation of partial results when system is assessing which wells do interfere.
\ OPTION" N ACTIVE W E L L S - N
OBSERVATION WELLS
\
FOR OBSERVATION WELL M-IOI I FINDING WHICH WELLS DO INTERFERE ]
Number of active
(K~h)IMu
F'r . C . h
X** 2
wells considered
| 2 :5 4
0.4137 0.1233 0.3470 0.4152
E-07 E-06 E-06 E-06
0.2:581 E - 0 6 0.4981 E - 0 6 0.9689 E - 0 6 0.1025 E - 0 5
0.4960 0.2778 0.2:564 0.1434
E-01 E-01 E-02 E-02
ORDER OF ACTIVE WELLS CONSIDERED: M-9!, M-51,M-90,
/
M-50
< RETURN > [7
Figure 8. Update of screen of Figure 7.
II 12
V . M . AII.ELL.~,',;O, E. IGLESlAS, and J ,'-%LELLxXO
/
OPTION
N
ACTIVE
WELLS
- N
OBSERVATION
FOR OBSERVATION WELL
WELLS
M-lOl
FOUND THAT THE FOLLOWING WELLS DO INTERFERE
M-91 HISTORY
M-51
M-90
M-50
OF" S U C C E S S I V E
Number of active wells considered 1
(K *h)/Mu
MATCHES FZ.
C* h
X**
2
04137
E-07
02381
E-06
04960
E-O1
2
O 1233
E-06
04981 E-D6
02778
E-O1
3
O 3470
E-06
0 9689 E - 0 6
02364
E-02
4
04152
E-06
0 1025E-05
01434
E-02
/ •
7
/
Figure 9, [-xample of screen presenting conclusion
I
OPTION I N ACTIVE
WELLS
-
N OBSERVATION
WELLS
EXPLANATION FOR OBSERVATION WELL M - I O 1 - A l l active wells were included in trial superposifion soluhons, which were fit to the observed pressures The quality of the f~t wos measured by Chi-squored statistics.
- Excluding wells NONE from the superpoiition solution, eHher left unchanged or =reproved the qualify of the fit to the observed pressures - 1"he value of the Chi-squared corresponding to the superpos~t~on solution that includes the remaining wells ~s consistent with the
current toJeronce, t
-- Therefore, one concludes that the following wells do interfere M-91, M-51, M-90, M - 5 0 1 Go back one screen
/
/
/
2 Resume analysis
/ Figure 10. Example of explanauon screen
t t
Computerized expert system for well-test analysis
OPTION:
N ACTIVE
WELLS-N
OBSERVATION
I l 13
WELLS
FOR OBSERVATION WELL M-101
. . .[ . FINDING WHETHER A BOUNDARY IS INDICATED 1
Max lime considered
(Keh]/Mu
FT~,C~h
0.4234 E + 0 7 0.2823 E + 0 7
0.4152 E - 0 6 0.4022 E - 0 6
0.1025 E - 0 5 0.1012 E - 0 5
X~Z 0.1434 E - 0 2 0.1510 E - 0 2
l Figure I I. Prcsentation of partial results when system is assessing whether boundary is indicated by data.
OPTION:
N ACTIVE
WELLS-N
OBSERVATION
WELLS
FOR OBSERVATION WELL M - l O S
[ FINDING WHETHER A BOUNDARY IS INDICATED]
Mox lime considered
(Keh]IMu
0.4234 E + 0 7 0.2823 E + 0 7 0.1411 E + 0 7
0.415Z E - 0 6 0.4022 E - 0 6 0.3241 E - 0 6
FI ~Ceh O. lOZ5 E - 0 5 O.lOIZ E - O 5 0.9223 E - 0 5
X¢~¢~ 2 0 1 4 3 4 E-OZ 0.1510 E - O 2 0.2128 E - 0 2
Figure 12. Update of screen of Figure I I.
/
II 14
', M. ARELLANO. E. IGLESIAS, and J. ARELLANO
OPTION
N
ACTIVE
WELLS
- N
OBSERVATION
FOR OBSERVATION WELL
WELLS
M-101
THE DATA DO NOT CONTAIN BOUNDARY INFORMATION
HISTORY OF SUCCESSIVE MATCHES Max
time
(K*h)lMu
FIiC.h
X~.2
considered 0.4234 E+07
0 4152 E-06
0 1025 E - 0 5
01434
02823
E+07
04022
E-06
01012
E-05
01510
E-02 E-02
01411
E+07
05241
E-06
0.9223 E-06
02128
E-02
/ J
I"igurc 13. S>stcm concluded that no boundl, ry is indicated by to,4 daL~
\
/ E+3
ANAPPRES
50
40
'~ n
•
Calculated
o
Observed
30
D_ <3 20 F
0 '
0
I0
20
30
Time
(s )
40
50 E+5
Figure 14 Final ti1 or model results to observed pressure response, as deployed b) Graphics Function or User Interface
Computerized expert system for well-test analysis
OPTION:
N ACTIVE
WELLS-N
OBSERVATION
FOR OBSERVATION WELL
1115
WELLS
M-IOl
SUMMARY
•)6
INTERFERING WELLS: NO BOUNDARY I S
")(" ( K e h l / M u =
")(" F I * C * h X,~. 2 ~
M-91,M-51,
M-90, M-50
INDICATED
0.415:>E-06 =0.1025E-05
")6
(m*'~3)(PoS)**-I
K"
(9a**-ll(m)
=0.1454E-02
-R- -1(- "R- -)(.
-)6 *
~
~ -t4" *
-)6 ,)(. Yr
-)6 ~
< RETURN
>
o
/ /
Figure 15. Summary of analysis' results CONCLUSIONS AND FUTURE WORK We have developed and validated the second version of a computerized expert system capable of analyzing constant and variable flowrate interference tests, in which there are an arbitrary number of production wells and an arbitrary n u m b e r of observation wells, in liquid-saturated homogenous reservoirs. The main advantages of this system are that it is user friendly, requires limited experience on the part of the analyst, eliminates subjectivity associated with earlier techniques of analysis, can handle complex cases and large data sets, completes the analysis of even the most complex situations (including plotting the results) in one run and is significantly faster than a human expert. The next version of A N A P P R E S , which already is in an advanced stage of development, will include, in addition to the current capabilities, the possibility of analyzing single-well pressure tests.
Acknowledgments--We thank two anonymous referees for comments that helped improve the presentation of this paper. REFERENCES
Arellano, V, M., 1987. DesarroUo de un sistema experto para el an:ilisis de pruebas de presi6n: unpubl, masters thesis. Universidad Aut6noma del Estado de Morelos. Cuernavaca, Mor., M6xico, 137 p.
CAGEO 1 6 , ~
Arellano, V. M., Iglesias, E. R.. Arellano, J., and Schwarzblat, M., 1989. Developments in geothermal energy in Mexico--Part twenty-one. ANAPPRES VI.0: a computerized expert system for interference well-test analysis in geothermal reservoirs: Heat Recovery Systems & CHP, v. 9. p. 101-113. Earlougher, R. C., 1977, Advances in well test analysis: Soc. Petroleum Engineers Mon. 5, 264 p. Earlougher. R. C., and Kersch, K. M., 1972, Field examples of automatic transient test analysis: Jour. Pet. Tech., October, p, 1271-1277. McEdwards, D. G., and Bcnson, S. M.. 1981, User's manual for ANALYZE, a multiple-well, least squares matching routine for well-test analysis: Rept. LBL-10907, Lawrence Berkeley Laboratory. 70 p. Narasimhan, T. N., and Witherspoon, P. A., 1977, Reservoir evaluation tests on RRGE-I and RRGE-2, Raft River geothermal project, Idaho: Rept. LBL-5958, Lawrence Berkeley Laboratory, 50 p. Narasimhan, T. N., McEdwards, D. G., and Witherspoon, P. A., 1977, Results of reservoir evaluation tests, 1976, East Mesa geothermal field, California: Rept. LBL-5973, Lawrence Berkeley Laboratory, 48 p. Ramey, H. J., Jr., 1975, Interference analysis for anisotropic formations--a case history: Jour. Pet. Tech., October, p. 1290-1298. Rodriguez A., Angeles M., Pineda A., and Santana J., 1987, DIGRAF: Disefio de grhficas, Conferencia National D.E.C.U.S., M6xico D.F. 5--6 November, 8 p. Sell, P. S., 1985, Expert systems---A practical introduction, Macmillan Publ. Ltd., London, 99 p. Theis, C. V., 1935, The relation between the lowering of the piezometric surface and the rate and duration of discharge of a well using groundwater storage, Trans. A.G.U., p. 519-524.