Society of Petroleum Engineers. SPE 17791 ... The application of an Artificial Intelligence (AI) technique ... to find all the EOR processes applicable to the oil field.
SPE Society of Petroleum Engineers
SPE 17791 EOR Screening With an Expert System by D.R. Guerillot, lnst. Franc;ais du Petrole SPE Member
Copyright 1988, Society of Petroleum Engineers This paper was prepared for presentation at the SPE Symposium on Petroleum Industry Applications of Microcomputers held in San Jose, California June 27-29, 1988. This paper was selected for presentation by an SPE Program Committee following review of information contained in an abstract submitted by the author(s) . Contents of the paper, as presented, have not been reviewed by the Society of Petroleum Engineers and are subject to correction by the author(s) . The material, as presented, does not necessarily reflect any position of the Society of Petroleum Engineers, its officers, or members. Papers presented at SPE meetings are subject to publication review by Editorial Committees of the Society of Petroleum Engineers. Permission to copy is restricted to an abstract of not more than 300 words. Illustrations may not be copied . The abstract should contain conspicuous acknowledgment of where and by whom the paper is presented. Write Publications Manager, SPE, P.O. Box 833836, Richardson, TX 75083·3836. Telex, 730989 SPEDAL.
Then, the architecture of the system is described, and the method for formalizing the knowledge is indicated using . 11 f uzzy l oglC concepts . THE DIAGNOSIS PROBLEM
ABSTRACT The application of an Artificial Intelligence (AI) technique to assist in the selection of an Enhanced Oil Recovery process (EOR) is described. The aim of this Expert System (ES) is to provide reasoned comments on the applicability of such processes on the basis of reservoir characteristics. The knowledge base has been developed using a professional inference engine. To be closer to the type of reasoning used by experts, fuzzy logic concepts have been introduced in the knowledge representation. This approach leads to a methodology for selecting EOR processes and for intproving know-how by checking the criteria used by comparison with practical experience, and it helps to transfer the expert's knowledge to the users of the system. Moreover, estimations of additional field cases makes it possible to continuously refine the screening procedure.
EOR methods or processes have as their objectives to increase recovery from reservoirs which would not respond floodi . . . 12, 13, 16, 18,20,2 ,24 . al to convention water ng or gas InJeCtiOn . The choice of enhanced recovery processes is based on 12 24 technical and economic criteria - • The problem involved is to find all the EOR processes applicable to the oil field concerned, or to check the suitability of a particular process in the light of the information available about the reservoir. In this application, we considered only the technical criteria of process application, since economic criteria are too subject to change from one company to another, but they could be easily added taking into account each petroleum company strategy.
INTRODUCTION
Another very important aspect in the choice of a process is the possibility of obtaining precise documentation on reservoirs similar to the reservoir studied.
Expert systems (ES) are sophisticated computer programs that manipulate knowledge to solve problems efficiently and effectively in a narrow problem area. Like real human experts, these systems use symbolic logic and heuristics/rules-of-thumb to find solutions 1.2. This kind of software, also called Knowledge-Based System (KBS), today constitutes the most operational aspect of AI methods.
Why an Expert System? An Expert System to solve this problem has been chosen in the light of the difficulties following:
Various problems occurring in production are solved using 3 10 a KBS approach - • This article discusses the construction of an advisor system for selecting possible EOR processes in account of reservoir characteristics.
• Decision-making rules are numerous. These rules are related to the reservoir data, which themselves are numerous. The type of reservoir, its depth, its pressure, the permeability and porosity of the rock, etc., must be known. Moreover, we do not always need the same data to assess the applicability of a particular process. For example, the acid number of the oil in place is a screening criterion only for certain chemical processes.
First, the diagnosis problem is defined and some of its difficulties are stressed. The type of reasoning is illustrated by the example of carbon dioxide (C02) flooding. References and illustrations at end of paper. 137
2
EOR Screenina With An • Few experts who know about all the processes are available. The multidisciplinary knowledge is very vast, and few persons have the background required for a critical evaluation of all the mechanisms involved in EOR processes. This knowledge is both theoretical (physical laws of multiphase flows, thermodynamic laws of interphase exchanges, etc.) and practical (surface facilities, injection and production conditions, etc.). An attempt is made here to obtain a diagnosis, even an approximate one, of the overall processes rather than a detailed diagnosis of one of the processes.
Exnflrt
Svstem
SPE 17 791
Brief Description of EOR Processes Selected The term "Enhanced Oil Recovery" covers all reservoir treatment processes designed to recover the "trapped" fraction of the oil in place, namely the fraction that has not been able to move under the natural effect of the pressure gradient, imbibition and expansion of the dissolved gas, pressure maintenace by water or gas injection. Here, the rule base has been developed for nine processes, classified in three families: • four thermal processes: hot water injection, steam stimulation, steam injection, in situ combustion;
• This area is in a constant state of development. In the past twenty five years, scientists have investigated methods for recovering more hydrocarbons from depleted reservoirs which often still contain more than half of the hydrocarbons originally in place. Many experiments performed on oil fields are now available, renewing the criteria for application of the processes.
• two dissolution processes: carbon dioxide injection, hydrocarbon gas injection; • three chemical processes: polymer injection, injection
of a surfactant solution followed by polymers, injection of an alkaline solution.
• Field data are poorly known. They are obtained by various means: geological surveys, petrophysical measurements, core displacement tests, well tests, numerical modelling. They are often imprecise due to measurement difficulties.
The influence of reservoir chara~teristics on the choice of a process can already be indicated qualitatively: . for a carbonate reservoir, polymer and surfactant solutions cannot be injected without precautions;
• Expertise rules are not strict rules such as may be found, for example, in problems of diagnosing machine breakdowns. The latter are related to an area of "hard" knowledge. These are fields in which the reactions to an external action can be predicted exactly and deterministically. Here, the knowledge is "soft" such as in the case of a medical diagnosis, for example. In fact, when we say that the permeability of the rock must be 2 greater than 10 mD (0.010 tJm ) for C02 flooding, we cannot categorically exclude a reservoir with a 2 permeability of 8 mD (0.008 tJm ).
. the reservoir depth is limited for steam injection for various reasons (surface equipment, heat losses in wells); . the reservoir pressure must be sufficient for carbon dioxide injection in order for phase exchanges with the oil to have significant effects; . polymer and surfactant solutions cannot withstand high temperatures, etc. Let us detail expertise rules for a specific process, i.e. carbon dioxide injection.
• Expertise is not completely formalized. Much of the literature offers rather general rules for process application, but in making a choice on an actual scale, it emerges that experts actually use many rules which are not clarified in the literature. Moreover, these rules are closely linked to the experience of these experts with a few processes, and can sometimes lead to a lack of objectivity. We need not only the conditions for the application of each process but also comparative studies of the effectiveness of a process compared with the other processes.
Rules and Reasoning for Carbon Dioxide Injection A simplified case is described here illustrating the procedure of evaluation of carbon dioxide (C02) injection into a hydrocarbon reservoir. The term C02 injection applies to the following two processes: 1) C02 injection without dynamic miscibility which concerns heavy oils and takes benefit of oil swelling and viscosity reduction associated to C02 dissolution into the oil,and 2) C02 injection with dynamic miscibility wich can be reached with light oils and permits very high displacement efficiencies to be achieved.
The idea of developing an expert system for this problem 23 started at the end of 1983. • A first version using an 26 27 inference engine developed at IFP ' ("lnstitut Fran~ais du Petrole ") in a LISP dialect has shown the feasibility of this way of helping to select EOR processes. This prototype has enabled us to specify an industrial system with a better 28 knowledge representation , with refined expertise rules and with more processes considered. This operational system is described here.
The primary criterion is pressure. Pressure must sufficient for carbon dioxide to have a significant effect the oil in place. It can be estimated that below 725 psi 6 10 Pa), C02 injection is ineffective, giving rise to following rule: 138
be on (5. the
D. GUERILLOT
SPE 17 791
2. An aquifer may exist which maintains the pressure.
6
IF the pressure is lower than 725 psi (5. 10 Pa), THEN C02 may not be injected.
3. The gas cap must not be too large in consideration the high compressibility of the gas.
The layer treated must not be too thick. It can be stated that, for both C02 injection processes, the thickness must be less than 60 ft (20 m).
Finally, for the variation in reservoir pressure, following rule is applied:
IF the thickness is higher than 60ft (20m), THEN C02 may not be injected.
the
IF there is no risk of fracturing the rock and IF nothing else opposes the increase in reservoir pressure, THEN the quantity of fluid to be injected to reach MMP is estimated.
To distinguish between the foregoing two C02 injection processes, it is also necessary to know the Minimum Miscibility Pressure (MMP). Nevertheless, without knowing this pressure, one can already sort out the extreme cases with the following two rules:
The quantity of fluid to be injected can be estimated by using an average compressibility factor. Moreover, for immiscible as well for miscible C0 2 flooding, several rules are applied that are essentially extracted from tables for selecting the main enhanced recovery methods C'screenin~ criteria"). Many authors have 12 16 18 2 furnished such tables ' ' ' •
IF the pressure is lower than 1450 psi (1. 1d Pa) and IF the oil gravity is lower than 25 oAPI (specific gravity higher than 0.904), THEN immiscible C02 injection is feasible. IF the pressure is higher than 3600 psi (2.5 1d Pa) and IF the oil gravity is higher than 40 oAPI (specific gravity lower than 0.825), THEN miscible C02 injection is feasible.
This example illustrates the type of reasoning involved in this problem. In the rules written above, difficulties also arise from the fact that it is very difficult to draw clear frontiers between admissible values and nonadmissible ones for a parameter for a given process. The terms "higher than" or "lower than" are not well suited. To avoid this jump between "good" and "bad" values, determination functions have been introduced to ~odulate this jump. Exgertise ~ules. have been implemented usmg "fuzzy" set theory . Modtficatwns of the inference engine have been made for this better knowledge representation. This technical point will be detailed in Appendix A.
In other cases, the MMP is calculated, as described hereafter.
The MMP is rarely known for the field to be investigated. However, laboratory data are available for estimating the MMP versus temperature for different oils. Correlation~have 29 been published by Holm and Josendal and extended by 30 Mungan to predict the MMP of C02 -oil systems, knowing the molecular weight of the C5+ fraction · of the oil and the temperature. If the molecular weight of the C5 + fraction of 12 the oil is unknown, other correlations can be used to obtain it from the oil gravity. Two cases are distinguished according to the relative values of the MMP and the reservoir pressure, yielding the following rules:
DESCRIPTION OF THE SYSTEM Software from outside The software, called SARAH (for "Systeme d' Aide en Recuperation Assisree d'Hydrocarbures"), is a diagnosis expert system. Using reservoir characteristics, it assesses all the processes considered, or a subset of these processes.
IF the MMP is lower than the reservoir pressure, THEN
C02 injection with dynamic miscibility is feasible, and IF NOT, can this pressure be varied? It may be of great interest to increase reservoir pressure to reach dynamic miscibility pressure. It must be emphasized that in this case the reasoning is carried out in relation to conditions which are not those of the reservoir at the time of the diagnosis. However, increasing pressure raises several problems such as:
It is an interactive system. The user is queried on the value of some parameters (different unit systems could be used), but could himself interrogate the system to know the whole set of possible answers, the justification of a question and the correlation used to determine the parameter. It is also possible to obtain, at any time, the history and current value of a parameter.
1. Fracturing the layer to be treated must be avoided. To check this, the MMP can be compared with the initial pressure as follows:
Consultation is very quick. Answers are given nearly without delay. A whole interactive session takes less than half an hour of dialog with the system and costs only a few seconds of CPU time with a microcomputer.
IF the initial pressure is higher than the MMP, THEN there is no risk of fracturing, and IF NOT, the user is without further user's warned of this risk and, recommendation, immiscible C02 injection is considered.
The diagnosis determined by SARAH is argued. It is justified by a report generated automatically at the request of the user, including: 139
EOR Screening With An Expert System
4
1. A review of the values of the parameters considered for the expertise, expresse 1 in the unit system chosen by the user.
SPE 17 791
It accepts the attachment of outside functions written in C language to enrich the structures available to the interface (writing in a file, consulting of tables or data bases, etc.).
2. For each process examined, a general text on the enhanced recovery mechanism and then a summary of the judgment criteria compared to the consultation data. An effort has been made to make this part "dynamic".
Notice that other shells including the features described above could also be used for our problem. The advantage to use a professionnal shell to develop expert systems are numerous: a better reliability (it is used for several applications), a good portability (the shell builder generally proposes it for many computers), a good documentation, a support course, etc.
3. Possibly, bibliographical references on reservoirs having similar characteristics. Indeed, a data base is simulated that contains the characteristics of well-known reservoirs on which at least one of the processes being investigated has been tried out, successfully or not.
Some reservoir data concern the rock, others the oil in place, etc. All parameters required for consulting have thus been grouped by concepts defining the classes: field, reservoir, rock, oil, formation water, gas, process. An example of the definition of CLASS is given in TABLE 1.
4. A general bibliography on EOR methods and on the SARAH system itself. This report contains formatting orders for text processing. The user merely has to print out the formatted file, which amounts to an average of about 20 pages.
A set of real, entire, Boolean or text attributes is assigned to each of these concepts. These attributes will be determined during the query, either by a question asked to the user or by being deduced from other attributes (mathematical formula, correlation, deduction by testing the values of the attributes). As in any expert system, an attempt is made to make the dialogue as user-friendly as possible. For example, the system will only ask useful questions on physical parameters of the reservoir (depth, thickness, etc.), of the oil (viscosity, specific gravity, etc.), of the water and gas, etc. An example of the definition of ATTRIBUTE is given in TABLE 2.
The Inference Engine The expert system has been developed with a professional 31 she11 • Because it is written in the C programming language, it enables the same knowledge base to be used through various computing environments (PCs, workstations and mainframes). Knowledge is organized in the form of "subject-attribute-value" triplets. Classes can be defined and possibly grouped in types of classes, attributes belonging to a class or a type of class and hierarchies of values.
There are formulas definitively linking some parameters. For example, the transmissivity is computed from layer permeability and thickness and oil viscosity. When this parameter has to be determined, the engine triggers the rule determining the transmissivity and does the computing. An example of the calculation of an attribute by a mathematical formula is given in TABLE 3.
This inference engine does not fall into any standard classification (engine using 0 or 0+ proposal logic, or first-order logic). It contains a variable concept represented by instances of classes, but the syntax of its rules is close to that of a 0 + engine.
For complex formulas or ones requmng high arithmetic precision, it may be useful to make use of outside functions.
It operates mainly by backward chaining. A rule is triggered by an attempt to determine one of its conclusions. Rules can be structured in packets, so that the search can be guided and limited to the set of candidate rules. An attribute can be determined by triggering a rule containing this attribute in its concluding part, by execution of a procedure or by questioning the user. At any time in the query, the justification can be requested of a question, the value of an attribute, its history, etc.
Experiments have determined relations among different parameters to give an approximate value to a given factor. For example, the temperature inside the reservoir can be estimated from the depth of the reservoir. But this value has to be checked by being confirmed by the user. These attributes may thus be determined either by a rule, if the value is accepted, or by questioning the user if it is not accepted.
The declarative part is assisted and supervised by a consequential procedural part. Procedures can be defined to check the order for triggering rules and determining attributes.
Reasoning Expertise is performed by examining the parameters:
It also has a developed user interface for associating a
message with each attribute (its meaning in natural language) and for displaying messages and results in a user-friendly way.
following
• for the reservoir: depth, lithology (nature), bubble pressure, fracturing pressure, etc.;
140
SPE
17 791
D. GUERILLOT
• for the rock: thickness, porosity, permeability, oil saturation, etc. ;
Simulation test of reasoning by analogy We have tried to represent the reasoning by analogy of an expert by simulating a data base for well-known reservoirs. At the end of a query, we look to see whether there is a reservoir in memory having similar characteristics to the reservoir being examined. The originality of our approach is to use production rules to find these reservoirs. Note that this rules of proximity between the reservoir being examined and the reference reservoirs depends on the EOR process.
• for the fluids in place: oil properties (viscosity, specific gravity, acid number, etc.), presence of a gas cap, of an aquifer, formation water (salinity, viscosity), etc. These parameters are acquired by the methods described above. A query of the expert system is thus divided into several parts. Each part corresponds to the forming of an opinion about the process. The expert system can be queried for one or several processes. Since chaining is of the backward type, the inference engine tries to evaluate the processes. It searches in the rule base for the rules that would enable it to assess the pertinence of a process. To trigger the premises for these rules, it begins by ascertaining whether it already has the information required. If it does not, it tries to obtain it by a new rule, a correlation, a formula or, as a last resort, by asking the user a question. Hence there is almost never the same dialogue with the system. Each investigation may lead to an examination of data suited to the situation. This is an important difference compared to an interactive system, which systematically asks the same questions while adapting itself with great difficulty to the case at hand.
At present, about ten typical reservoirs have been input for each EOR process, but this proportion can very easily be increased. We could also connect on already existing data bases. In this case, the expert system itself queries the data base to obtain useful information. Validation and example of consulting The rule base was tested on many cases taken from published articles as well as from IFP experience. To obtain a knowledge system capable of performing the given diagnosis problem, three important activities are depicted in figure 3: knowledge acquisition, knowledge system construction, and knowledge system execution and testing:
• Knowledge acquisition involves a dialogue between the expert and the knowledge engineer. The knowledge engineer uses also written information (books, articles, etc.) to learn problem solving principles specific to the
To assess the pertinence of a process, an original method has been developed. This method prevents the number of conditions for which a process is applied from having consequences on the result of the diagnosis.
task. In the first phase, a numerical coefficient between -1 and
• Knowledge system construction is the process of expressing the knowledge acquired in a knowledge base.
+ 1 is determined, characterizing the compatibility of the reservoir, rock and fluid characteristics with the judgement criteria for the process. The same importance is assigned to each family of characteristics.
• Knowledge system execution and testing involve running the system on cases to test its performance and the validity of the answer. The methodology followed here was to compare the expert and the system diagnosis on well known cases. After analysis, differences between these two answers allowed us improving the knowledge representation of the expert system. Now, the system gives good results, especially for thermal processes. For other processes, tests still remain to be performed, because there are not yet enough actual data.
From these three real numbers, a new coefficient is determined between - 1 and + 1, representing the feasibility of the process for the reservoir examined. Then from this "grade," an assessment is determined which is the result sent to the user. A schematic diagram representing the reasoning is given in Figure 1. Two different composition rules are used to obtain these coefficients. These two stages in this "grading" method for a process are described in Appendix A.
An example of consulting is given in figure 4. It illustrates some features of the expert system:
Rule Base • The consultation phase is initiated by issuing the start.consulation command. In order to start a consultation, you must have loaded a knowledge base, and this knowledge base must be consistent;
Most rules test the value of several pertinent attributes to judge the reservoir, rock or fluids for a process. They are expertise rules such as the rules described above.
• The name of the field is used to give a name of the paper report file (question 1);
Other rules are established and grouped by packets, so that calculations and unit conversions can be performed. These are utilitarian rules for determining the value of an attribute by a mathematical formulation or correlation. (For example, the oil content of the rock is computed from the porosity and initial oil saturation).
• The choice between the three process families considered is done using the procedural part of the inference engine (question 2). 141
EOR Screening With An Expert System
6
SPE 17 791
4. Courteille, J.M., Fabre, M. and Hollander, C.R.: "An Advanced Solution: The Drilling Adviser," JPT (Aug. 1986) 899-904.
• Three unit systems could be chosen (question 3). This choice modifies the units written in the question (see for instance "ft" in question 5).
5. Gani, R. and Fredenslund, A.: "Thermodynamic of Petroleum Mixtures Containing Heavy Hydrocarbons: An Expert Tuning System," Ind. lng. Chern. Res . V.26, No.7, (July 1987) 1304-1312.
• Parameter values are proposed using correlations wich can be commented (question 6). Here, reservoir pressure is correlated with the depth of the reservoir. Display is requested, and the value is accepted; • Having enough information, the system can now conclude after question 15 for the "steam drive" process.
"OPUS: An Integrated Assistance System for Oil Production", Expert Systems V.4, No.4, (nov. 1987) 242-250 .
CONCLUSIONS
7. Kuo,
6. Hoffmann, F.C. and Valentin, E.P.:
T.-B.: Well Log Correlation Using Artificial Intelligence, PhD. Thesis, Texas A&M Univ. (Jan. 1987) 150.
This operational system of about 300 expertise rules has led to the following results:
8. Kuo, T.-B. and Startzman, R .A.: Stratigraphic Correlation Using Artificial Geobyte V.2, No.2, (1987) 30-35.
1. Confirming the feasibility of an expert system for assisting in the selection of EOR processes.
9. Leblanc, L.: "Integrated Data Aids Rig Management," Offshore V.47, No.4, (Apr. 1987) 36-38 .
2. Enabling quick screening criteria to be determined on the basis of reservoir characteristics for editing a reasoned paper report.
10. Startzman, R.A. and Kuo, T.-B.: "A Rule-Based System for Well Log Correlation," SPE Formation Evaluation (sep. 1987) 311-319.
3. Instructing the expertise rules used for choosing an EOR process and helping to transfer the expert's knowledge to the user of the system.
11. Turner ,R.: Logics For Artificial Intelligence, Horwood Ltd., Chichester (1984) 121.
4. Giving references to similar reservoirs.
5. Enabling the expert to
constantly
refine
process
6. Justifying sensitivity tests to different parameters.
13. Bardon, C.: "Recuperation assistee du petrole - Injection de gaz carbonique", (in French), Course at the "Ecole Nationale Superieure du Petrole et des Moteurs" (Jan. 1985).
7. Being of particular interest when there are numerous cases to be examined. ACKNOWLEDGMENTS
14. Burger, J. and Champion, D.: "How to estimate production cost by steam drive?," Petroleum Engineer International (June 1983) 66-70.
The author thanks the management of the Institut Fran~ais du Petrole (IFP) for permission to publish this paper. He also thanks Murielle Roussel for her contribution to the development of this knowledge-based system as well as all the IFP experts in EOR for their continuous help.
15. Burger, J. and Champion, D.: "How to estimate in situ combustion cost?" Petroleum Engineer International (Nov. 1983) 32-44.
REFERENCES
1 Hayes-Roth,
16. Burger, J., Sourieau, P . and Combarnous, M.: Thermal Methods of Oil Recovery, Editions Technip, Paris, (1985).
F.,
Waterman, D.A. and Lenat, D.B.: Addison-Wesley Publishing Company Inc., Massachusetts, (1983) 445.
Expert
Ellis
12. Bailey, R .E. and Curtis, L.B.: Enhanced Oil Recove1y, National Petroleum Council (June 1984).
selection procedures.
Building
"Field-Scale Intelligence,"
17. Chauvel, A., Franckowiak, S. and Vacelet, 0.: "Recuperation assistee du petrole par le C02 : disponibilites et coOts en Europe de l'Ouest," (in French), Revue de l'Institut
Systems,
Fran~ais
2 Waterman, D.A.: A Guide to Expert Systems, Addison-Wesley Publishing Company Inc., Massachussets, (1985) 420.
du Petrole, No.1, (Jan./Feb. 1984).
18. Dafter, R.: Scrapping the barrel - The worlwide potential for enhanced oil recovery, The Financial Times Business Information Ltd. (1980).
3. Affieck, N. and Zamora, M.: "PC-Based Expert System Aids Optimum Mud Selection," Petroleum Engineer International (Jan. 1987) 38-42.
19. Denoyelle, L. and Champion, D .: "Study show cost of EOR by C02 , " Petroleum Engineer International (July 1985) 46-54. 142
SPE 17 791
D. GUERILLOT
7
Appendix A: Fuzzy Logic for Assessing the System on a Process
20. Haynes, H.J., Thrasher, L.W., Katz, M.L. and Eck, T .R.: Enhanced Oil Recovery - An Analysis of the Potential for Enhanced Oil Recovery from Known Fields in the United States - 1976 to 2000, National Petroleum Council (Dec. 1976).
Assessing the Influence of a Parameter for a Process For each numerical parameter, there is a range of unfavorable values for the choice of the process. This range is difficult to quantify. A strict threshold cannot be determined in relation to which a given factor can be said to be favorable or unfavorable for the process in question. This is why we decided to deal with the problem by a fuzzy logic approach.
21. Latil, M.: Enhanced Oil Recovery, Editions Technip, Paris, (1980). 22. Simandoux, P., Burger, J., Chauveteau, G., Champion, I., Combe, J., Denoyelle, L. and Labrid, J.: "Etude economique des prmclpaux procedes de recuperation assisree," (in French), IFP report No. 31872 (Feb. 1984).
Two cases are to be considered: 1) numerical parameter, 2) non-numerical parameter.
23. Simandoux, P., Bardon, C., Denoyelle, L. and Vacelet, 0.: "Recuperation assisree des hydrocarbures par injection de C0 : aspects techniques et economiques", (in French), Revue 2 de l'lnstitut Fran~ais du Petrole, No. 4, (July/Aug. 1984).
Case 1: Let us then define three types of intervals in the range of acceptable values:
24. Van Poollen, H.K. and Associates, Inc.: Fundamentals of Enhanced Oil Recovery, PennWell Publishing Company (1980).
• a range in which the parameter would be favorable to the process;
25. Guerillot, D.: "Maquette d'un systeme en recuperation assisree des hydrocarbures," (in French), IFP note No.7740/1399 (Dec. 1984).
• a range in which the parameter would be moderately favorable to the process;
26. Guerillot D.: "Maquette d'un systeme de diagnostic en recuperation assisree d'hydrocarbures," (in French), IFP report No. 33511 (Sep. 1985).
• the remaining part of the interval in which the parameter would be unfavorable.
27. Guerillot, D. and Bessis, F.: "Sarah-Diezol: un systeme de diagnostic en recuperation assistee d 'hydrocarbures"' (in French), Revue de 1' Institut Fran~ais du Petrole, V .41 , Na. 6, (Nov./Dec. 1986) 759-771.
For a given process, a real value between -1 and + 1 is associated with each parameter: -1: unfavorable from - 1 to + 1: moderately favorable (with nuances between these two values), + 1: favorable.
28. Roussel, M.: "Etude par un systeme expert de la pertinence de procedes de recuperation assistee d'hydrocarbures pour un gisement," (in French), IFP report No. 35425 (Aug. 1987).
Example: For the "polymer flooding" process, the temperature factor is:
29. Holm, L.W. and Josendal, V.A.: "Mechanisms of oil displacement by carbon dioxide," JPT (Dec. 1974).
. favorable if it is less than 340 °K, . moderately favorable if it is between 340 and 360 °K, . unfavorable if it is over 360 °K;
30. Mungan, N.: "Carbon Dioxide Flooding Fundamentals," JPT (Jan./Mar. 1981).
Let ~ be the estimation function of the temperature T (fig. 2): ~: T-. ~(T) e [ -1,+1]
31. Framentec: S.l Reference manual, (1986)
so that: ~(T)= + 1 for T
