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Permeability Prediction Enhancement in Carbonate Reservoirs by Proposing a New Fuzzy Logic Approach



S. Alfaouri, M. Ali Riahi, N. Alizadeh and M. Rezaei
 
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ABSTRACT

The aim of this study was to modify some previous Fuzzy based models for developing a convenient and robust method for permeability problem solving in carbonates. The proposed technique is tested in two complex giant Iranian oil fields for justification; which are Sarvak and Asmari formations. The results were much more precise than previous similar Fuzzy studies which were in high agreement with core measured values. Permeability values estimation using core-derived information of wells with just electric logs is an old problem in reservoir characterization. In essence, the problem consists in finding some explicit relation between log and core data in those wells that contain both types of information. Then, describe reservoir features (derived from core data) of wells with log information only. Fuzzy logic is one of the intelligent techniques that have been applied extensively nowadays, but all the previous researches in this subject have been applied in Sandy reservoir cases. In this study, besides the previous studies a new Fuzzy model has been testified to estimate permeability values in two carbonate reservoirs. Moreover, the accuracy of the predicted results will be considered comparing with the measured core values. During this study a new modification in defuzzification stage will be introduced to make the method much more accurate and flexible in predicting permeability values in carbonates. Results show that the new proposed method yields better estimations than similar previous techniques in carbonate reservoirs. Furthermore, the predicted results represented in the actual range of core plugs permeability measures.

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  How to cite this article:

S. Alfaouri, M. Ali Riahi, N. Alizadeh and M. Rezaei, 2009. Permeability Prediction Enhancement in Carbonate Reservoirs by Proposing a New Fuzzy Logic Approach. Journal of Applied Sciences, 9: 3263-3274.

DOI: 10.3923/jas.2009.3263.3274

URL: https://scialert.net/abstract/?doi=jas.2009.3263.3274
 

INTRODUCTION

Permeability controls how fluid can migrate through the reservoir. The permeability is a key parameter in reservoir development and management because it controls the production rate (Altunbay et al., 1997). In general, the permeability increases with increasing porosity, increasing grain size and improved sorting. In carbonates connectivity between pores is the main control for the permeability. Heterogeneity occurs in carbonate reservoirs due to variation in depositional environments and subsequent diagenetic processes. Depositional environment is important for creating primary porosity. Generally high energy deposits give high porosity and permeability, while low energy deposits give low permeable intervals. Often low energy deposits may have high porosity, but if the pore throat sizes are too small, permeability may also be low. Diagenesis both constructs and destruct porosity. For example, cementation decreases porosity and permeability, but early cementation may prevent compaction and thereby preserve primary porosity, while dissolution mainly increases porosity except in case like some satellites which may form barriers (Altunbay et al., 1997; Babadagli and Al-Salmi, 2003; Carlos, 2004; Jennings and Lucia, 2003; Kolodzie, 1980; Lucia, 1999; Mohagheh et al., 1997).

The permeability prediction is a challenge in formation evaluation and reservoir modeling because of difficulty to measure it directly. Knowledge of permeability is important in building 3D reservoir models and understanding production of oil and gas and finally development strategy. The best method for direct permeability measurement is obtained from core plug analysis. It is measured in both vertical and horizontal directions, commonly every 30 cm (Altunbay et al., 1997; Babadagli and Al-Salmi, 2003; Carlos, 2004; Cuddy and Putnam, 1998; Hambalek and González, 2003; Jennings and Lucia, 2003; Lim and Kim, 2004; Mohagheh et al., 1997; Taghavi, 2005).

Coring is very expensive and time consuming limiting such measurements. In addition, in some cases such as horizontal wells it is technically impossible. Small scale heterogeneities that might not affect flow on a reservoir scale are measured and these need to be upscaled. An alternative way to estimate the permeability is from electrical logs. The challenge in permeability prediction is that permeability is related more to the pore throat size rather than pore size, which is difficult to measure by logging tools. Determining permeability from well logs is also complicated by the problem of scale, well logs having a vertical resolution of typically 1/2 m compared to the 5 cm diameter of core plugs.

Fuzzy logic was introduced by Zadeh (1965) and is an extension of conventional Boolean logic (0 and 1) developed to handle the concept of partial truth values between completely true and completely false values. In Fuzzy sets, everything is a matter of degrees. Therefore, an object belongs to a set to a certain degree. The Fuzzy logic can be used as a simple and useful predictor method in un-cored wells (Cuddy and Putnam, 1998; Hambalek and González, 2003; Lim and Kim, 2004; Mohagheh, 2000; Saggaf and Nebrija, 2003; Saggaf and Nebrija, 2000; Taghavi, 2005).

In essence, Fuzzy logic maintains that any interpretation is possible but some are more likely than others. One advantage of Fuzzy logic is that we never need to make a specific decision. Other benefits of using Fuzzy logic is that it can be described by established statistical algorithms; and computers, which themselves work in ones and zeros, can do this effortlessly for us. Conventional techniques try to minimize or ignore the error. Fuzzy logic asserts that there is useful information in this error. The error information can be used to provide a powerful predictive tool for the geoscientist to complement conventional techniques (Cuddy and Putnam, 1998; Hambalek and González, 2003; Lim and Kim, 2004; Mohaghegh, 2000; Saggaf and Nebrija, 2003; Saggaf and Nebrija, 2000; Taghavi, 2005).

Fuzzy mathematical techniques have been applied to solve various petroleum engineering and geological problems in the past, involving mainly classification, identification, or clustering. Cuddy and Putnam (1998) and Cuddy and Glover (2002) used Fuzzy logic to predict permeability and lithofacies in uncored wells to improve well-to-well log correlations and 3-D geological model building. In Hambalek and González (2003) made some modification to the cuddy’s works in a more or less similar study. In addition, Saggaf and Nebrija (2003) used Fuzzy logic approach for the estimation of facies from wire-line logs in a field in Saudi Arabia. Taghavi (2005) applied Fuzzy logic to Improve Permeability Estimation in a complex Carbonate Reservoir in Southwest of Iran.

In this study, we apply the Fuzzy Logic inference method to determine the permeability values in uncored wells based on data from wire-line logs in two heterogeneous sandy oil-bearing reservoirs in Persian Gulf. For this purpose a Fuzzy model based on the method proposed by Hambalek and González (2003) was developed to predict permeability values in two Iranian huge heterogeneous carbonate reservoirs. It should be mentioned that Hambalek and González (2003) implemented their model in a Sandy deposit reservoir, but in this study it has been tried to apply their concept for carbonates which are much more complex.

In addition, during this study a modification to defuzzification stage of the Hambalek and González’s technique will be proposed. This new approach will diminish the high amount if uncertainty in predicted permeability values of carbonates. Moreover, the proposed approach will be justified by testifying the model in two studied carbonate reservoirs named Sarvak and Asmari formations.

It should be mentioned that definition of Fuzzy membership functions is fundamentally based on the probability theory. Probability theory has been implemented in some previous studies to quantify grayness of fuzziness. Although, the reason behind random events might hardly be understood, but it has been shown in previous studies that how Fuzzy logic could be beneficial for bring meaning to its concept. All the studies have accepted the premise that any interpretation is possible although some are more likely than others (Hambalek and González, 2003).

STUDIED RESERVOIR CASES DESCRIPTION

Sarvak formation: Sarvak formation hosts huge oil reserves in Southwest Iran. It is composed mainly of limestone with occasional dolomite intervals. The formation is divided into two parts by a thick interval of argillaceous carbonates. The upper Sarvak Formation which is used in this study has been deposited in a carbonate ramp setting during mid Cenomanian to early Turoninan (mid-Cretaceous) (IOOC, 2003).

Upper sarvak formation is a very heterogeneous reservoir where heterogeneity results from both depositional environment and diagenetic processes. Depositional setting forms different faces as an effect of sea level fluctuation and energy during sedimentation. Low energy environments forms low porosity sediments such as in lagoons and in the shallow open marine, outer shelf and intrashelf basin. These environments are dominated by wackestone and mud dominated packstones. High energy environments form high porosity sediments such as reefs and shoals with mainly grain dominated packstones, grainstones, floatstones and rudstones.

The diagenetic processes in upper Sarvak have both constructed and destructed porosity. Dissolution and karstification (uppermost part of the reservoir) produce porosity in both mud-and grain-supported intervals during exposure because of sea level fall. They occur as vuggy and more rarely moldic porosities. Cementation diminishes primary porosity during early and burial diagenesis. Early and late cements fill the primary intergranular porosity in the high energy deposits and may create barrier for hydrocarbon movement. The effect of dolomitization in altering porosity depends on dolomite types. Generally dolomitization associated with dissolution marks high porosity and permeability, while dolomite within lagoonal and intrashelf basin deposits did not change porosity. Compaction has been characterized by core studies. It has destructed porosity by decreasing pore space in both mud- and grain supported deposits. Fracturing as recognized in cores and by mud loss has increased permeability in some of the intervals (IOOC, 2003) (Fig. 1).

In this area of study five continuous cored wells were available. Porosity and permeability data are measured from plugs of these wells and these core data were used for validation of the predicted data. However, core and log data from three wells used to derive a model and this model used to predict permeability in two blind testing wells with available core data to check the accuracy of prediction. The conventional well logs used besides the core permeability information to develop models are Sonic and Neutron logs which are available in all wells of studied cases.

Asmari formation: Another giant petroleum reservoir in Persian Gulf which was used in this study is Asmari Carbonate Reservoir with an average thickness of 395 meters in South-West of Iran. The reservoir is isolated from adjacent reservoirs by sealing faults in south and west flanks.

Petrographycally point of view, Asmari formation composed mainly of Carbonates which include Dolomites, Shale and Marls. Generally, Dolomitization in Asmari and Sarvak formations follow the Sabkha Dolomitization System of Persian Gulf. Productivity of Asmari reservoir systems is affected mainly by secondary parameters (Secondary Porosity and Permeability) and diagensis processes such as Dolomitization, Techtonic activities (Fractures and Micro fractures) and salt dome activity of underlying gachsaran (IOOC, 2003).

Image for - Permeability Prediction Enhancement in Carbonate Reservoirs by Proposing a New Fuzzy Logic Approach
Fig. 1: Schematic Location of two studied cases; Sarvak and Asmari formation which are two huge Iranian carbonates reservoirs in Persian Gulf (IOOC, 2003)

Same as the previous studied reservoir case, there are five continuous cored wells for Sarvak reservoir in this study, all with available well logs information; in which three of them used as model description whereas other two wells used as a blind testing for testifying the developed Fuzzy models. The input data are selected to be the same as the previous studied case.

Permeability prediction applyingHhambalek and González approach: It was Cuddy in 2000-2003 that first used Normal Distribution concept for membership function definition in constructing Fuzzy Logic model for the purpose of permeability estimation. Cuddy applied his model in a Sandy Reservoir with almost acceptable results. Later, Hambalek and González (2003) also employed Cuddy’s approach with some modification in defuzzification stage with much more reliable results. That study was also testified in Sandy Deposits.

Although, that technique was so flexible in sandy deposits but due to high complexity of carbonates it is not so efficient when subjects to carbonate deposits. To show that, we applied that technique in two carbonate reservoirs of Iran in Persian Gulf. In addition, a modification to this technique would be proposed in the next stage to transform this technique to a much more reliable technique in carbonate deposits.

It should be mentioned that normal distribution is completely determined by two parameters: mean and variance. Its bell shape is very familiar to all us and its application is often justified with symmetric histograms derived from the sample data. The variance (the standard deviation squared) depends on the hidden factors and measurement errors and it can be seen like the fuzziness (spread) about a most probably value of occurrence (the mean). This interpretation is a key to the method because it allows to consider the possibility of observing any particular value of the analyzed variable but equally to accept that some observations are more probable than others (Hambalek and González, 2003).

The probability density that an is measured observation x occurred in a data set which is described by a mean μ and standard deviation σ will be determine by the normal distribution function:

Image for - Permeability Prediction Enhancement in Carbonate Reservoirs by Proposing a New Fuzzy Logic Approach
(1)

This curve is used to estimate the relative probability or Fuzzy possibility that a data value belongs to a particular data set. For example if a permeability Geocategory has a porosity distribution with a mean μΦ and standard deviation σΦ (these values are simply derived from the calibrating or conditioning data set, usually core data), the Fuzzy possibility that a well-log porosity value Φeff., x is measured in this Permeability Geo-Category type can be estimated using Eq. 2:

Image for - Permeability Prediction Enhancement in Carbonate Reservoirs by Proposing a New Fuzzy Logic Approach
(2)

Fuzzy logic applied in this study was based on establishing the Fuzzy relation between Permeability Geocategories (Let’s call it Bin) derived from core data and some associated electrical well-logs. Then, using this Fuzzy relation we can predict these permeability values in those wells without core information but with coincident well logs. It should be mentioned that each Permeability Geocategory (Bin) is defined in such way that have same characteristic.

For instance, one may define one bin as very high permeability values which is belong to values of permeabilities grater than 1500 md. Defining permeability values boundaries are of important factors in establishing a perfect Fuzzy model. In this study log reading characteristics are considered besides the permeability values to in defining bin boundaries. However, in this study the Permeability geocategories with different biz sizes (number of data in each bin) are used. Table1 shows the summarized information related to bin boundaries used in this study for each studied case.

Where, there are several permeability geocategories (Bins) in a well, the porosity value Φeff., x may belong to any of these Bins, but some are more likely than others. Each of these bins has its own mean and standard deviation such that for N Permeability Geocategory there are N pairs of μ and σ.

Table 1: Permeability Geocategories information used for Fuzzy model description in each reservoir case. Permeability boundaries and corresponding bin size also mentioned
Image for - Permeability Prediction Enhancement in Carbonate Reservoirs by Proposing a New Fuzzy Logic Approach

If the porosity measurement is assumed to belong to Bin fi, the Fuzzy possibility that porosity Φeff., x is measured (logged) can be calculated similarly using Eq. 2 by substituting μi and σi, corresponding to porosity, the Fuzzy possibilities can be computed for all N Bins. These Fuzzy possibilities refer only to particular bins fi and cannot be compared directly, as they are not additive and do not add up to 1. The ratio of the Fuzzy possibility for each Permeability Geocategory with the Fuzzy possibility of the mean or most likely observation could be achieved by de-normalizing Eq. 2.

The relative Fuzzy possibility R (x) of porosity Φeff., x belonging to fi-th Geocategory compared to the Fuzzy possibility of measuring the mean value μΦσ calculated as:

Image for - Permeability Prediction Enhancement in Carbonate Reservoirs by Proposing a New Fuzzy Logic Approach
(3)

Each Fuzzy possibility is now self-referenced to possible bins. To compare these Fuzzy possibilities between bins, the relative occurrence of each Geocategory in the well must be taken into account. This is achieved by multiplying Eq. 3 by the square root of the expected occurrence of geocategory fi. If this is denoted by nfi, the Fuzzy possibility of measured effective porosity Φeff, x belonging to permeability geocategory μΦc is:

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(4)

The Fuzzy possibility Ffi, Φeff, (Φeff, x) is based on the effective porosity logs alone. This process is repeated for a second parameter for example Neutron Porosity Log. This will give:

Image for - Permeability Prediction Enhancement in Carbonate Reservoirs by Proposing a New Fuzzy Logic Approach
(5)

where, Nphix is the Neutron Porosity log reading value in a specific horizon and μ1Nphi, σ1Nphi are respectively the Mean and standard deviation values of the Neutron Porosities Distribution belonging to Permeability Geocategory fi. Therefore, Ff1Nphi (Nphix), will be the Fuzzy possibility of measured Neutron Porosity value Nphix belonging to Permeability Geocategory fi with mean μ1Nphi and standard deviation value σ1Nphi.

As in this study Sonic Porosity and Neutron Porosity logging data are used as input parameters, the Fuzzy possibility of measured Sonic Porosity log values Ff1ΔT belonging to Permeability Geocategory fi with mean μ1ΔT and standard deviation σ1ΔT is calculated as follow:

Image for - Permeability Prediction Enhancement in Carbonate Reservoirs by Proposing a New Fuzzy Logic Approach
(6)

Finally, these Fuzzy possibilities are combined harmonically to give a “combined Fuzzy possibility”. In this example for a measurement x in a specific horizon for Neutron Porosity and Sonic Porosity, the combined Fuzzy possibility for these measurements to belong to a data set, let say Permeability Geocategory fi will be:

Image for - Permeability Prediction Enhancement in Carbonate Reservoirs by Proposing a New Fuzzy Logic Approach
(7)

This process is then repeated similarly for other defined Bins. Note that, in defuzzification stage a value should be assigned to precede fuzzified input values. These values are highly dependent with the method used for defuzzification. As the defuzzification technique gives much more flexible values to each fuzzified output processed value, the model will be more flexible to predict an accurate result values.

For defuzzification stage Hambalek and González (2003) proposed a technique as follow: the two highest Fuzzy possibilities are taken as the most probable categories for that log measurements for that depth. The simulated horizontal permeability value is proposed as a weighted mean of the representative values of the two most probable categories of permeability inferred through the Fuzzy procedure (Hambalek and González, 2003).

Image for - Permeability Prediction Enhancement in Carbonate Reservoirs by Proposing a New Fuzzy Logic Approach
(8)

where, KH (h) Simulated is Simulated horizontal permeability value for specific log measurements in depth, Image for - Permeability Prediction Enhancement in Carbonate Reservoirs by Proposing a New Fuzzy Logic Approach are respectively Representative horizontal permeability values of the first and second most probable predicted i-th Geocategory, FT, I, (1), FT, I, (2) are respectively Combined Fuzzy possibilities associated with the first and second most probable predicted i-th Geocategory calculated for a specific depth h.

Another consideration should be also taken into account in which the representative permeability values, corresponded to each permeability bin defines (Hambalek and González, 2003), considered each mean, median, maximum and minimum values of each permeability bins as the representative permeability value for each bin. Finally they proposed the minimum value as the best representative permeability value that results in lowest amount of error (Table 2, 3).

Table 2: Permeability representative values for each permeability geocategory (Bin) for studied reservoir case number 1; Sarvak Formation
Image for - Permeability Prediction Enhancement in Carbonate Reservoirs by Proposing a New Fuzzy Logic Approach

Table 3: Permeability representative values per each permeability geocategory (Bin) for studied reservoir case number 2; Asmari Formation
Image for - Permeability Prediction Enhancement in Carbonate Reservoirs by Proposing a New Fuzzy Logic Approach

Determining number of Permeability Bines is directly related to the amount of the available data. As it was explained, to avoid statistical errors there should be at least 30 readings in each Geocategory (Bin Size). In this study different number of Permeability Geocategories was tested and results from the model with four bins were much more precise.

Furthermore, to quantify each point error in permeability determination Hambalek and González (2003) introduced the Relative Absolute Error concept, denoted by RAE. The RAE is defined by the difference between the simulated value and the core reported one divided by the core derived referenced value in each specific depth. This value could be presented as percentage.

Image for - Permeability Prediction Enhancement in Carbonate Reservoirs by Proposing a New Fuzzy Logic Approach
(9)

Where:
RAE (h) : Relative absolute error at depth h
KC (h) : Calculated core-permeability value at depth h
KS (h) : Calculated simulated-permeability value at depth h

As it was mentioned, there are two testing wells per each studied reservoir case; therefore the RAE in each testing well should be calculated separately applying different representative values. Table 4 and 5 represent RAE values corresponding to apply Hambalek and González (2003) approach in Sarvak and Asmari formation, respectively.

Based on the detailed information above (Table 4, 5) total minimum errors occurred in case of selecting Minimum Values of each Permeability Geocategory (Bin) as Representative Value. Therefore, in this study the minimum values of each bin are selected as permeability representative values for the constructed Fuzzy model. Figure 2-5 show the predicted values versus core reposted ones in two reservoir cases applying this approach by selecting minimum values as representative values.

New formula, defuzzification modification: The complexity of permeability trends in carbonates due to secondary parameters makes it much more difficult to estimate permeability values in comparison with Sandy reservoirs. In this study, a modification in defuzzification stage of Hambalek and González (2003) approach is proposed to make this technique much more convenient and accurate for carbonates. As it was mentioned, different Permeability Geocategory numbers were testified and finally the result of four permeability bins was found to be much more reliable with lowest amount of errors. Thus, in this study four permeability Geocategories was proposed.

In this stage, the permeability Geocategories are defined same as the previous stage. But during defuzzification stage, the formula below is proposed. This is in such way that guaranties all Geocategories contribution in defining final simulated permeability values. This formula could be achieved from the equation below:

Image for - Permeability Prediction Enhancement in Carbonate Reservoirs by Proposing a New Fuzzy Logic Approach
(10)

In which the values of A and B are defined as below:

Image for - Permeability Prediction Enhancement in Carbonate Reservoirs by Proposing a New Fuzzy Logic Approach
(11)

Image for - Permeability Prediction Enhancement in Carbonate Reservoirs by Proposing a New Fuzzy Logic Approach
(12)

and the parameters are defined as:

KH (h)simulated is Simulated horizontal permeability value for specific log measurements in depth h, Fi (k) (h):(where: k=1, 2) are relatively the first and second biggest combined Fuzzy possibility values (Eq. 7) associated with the first and second most probable predicted i-Geocategory for log measurement vales in depth h, Gi (k) (h): (where: k=1, 2) are relatively the first and second lowest combined Fuzzy possibility values (Eq. 7) associated with the first and second most probable predicted i-Geocategory for log measurement values in depth h,Image for - Permeability Prediction Enhancement in Carbonate Reservoirs by Proposing a New Fuzzy Logic Approach are, respectively representative horizontal permeability values of the first and second most probable predicted I-th Geocategory, Image for - Permeability Prediction Enhancement in Carbonate Reservoirs by Proposing a New Fuzzy Logic Approachare, respectively the two lowest representative horizontal permeability values regarding to Minimum values of each Permeability Bin, Image for - Permeability Prediction Enhancement in Carbonate Reservoirs by Proposing a New Fuzzy Logic Approachare, respectively the two lowest representative horizontal permeability values regarding to Maximum values of each Permeability Bin.

Table 4: Relative absolute error values in two testing wells applying hambalek and gonzález approach by different representative values in studied case number 1; sarvak formation
Image for - Permeability Prediction Enhancement in Carbonate Reservoirs by Proposing a New Fuzzy Logic Approach

Table 5: Relative absolute error values in two testing wells applying hambalek and gonzález approach by different representative values in studied case number 2; asmari formation
Image for - Permeability Prediction Enhancement in Carbonate Reservoirs by Proposing a New Fuzzy Logic Approach

Table 6: Representative permeability values for each permeability geocategory
Image for - Permeability Prediction Enhancement in Carbonate Reservoirs by Proposing a New Fuzzy Logic Approach

Note that, this formula guaranty that the most probable category receives the heaviest weight. Moreover, using a combination of representative values from different Geocategories with different defined weights will results much more precise simulated permeability values in which data distribution characteristics were comprehensively considered. However, any classification must be sure of having enough sample observations inside each class for guarantying the statistical robustness of the results. A reasonable statistical sample size is around 30. The distribution of bin boundaries depends on the range of expected permeabilities, same as described by Hambalek and González (2003), an example:

To show the calculation procedure for a considered specific horizon h, permeability prediction demonstration has been shown in this section. Suppose for the four permeability Geocategories (Bins) the different representative values are as Table 6. Thus, according to sthe formulas of Image for - Permeability Prediction Enhancement in Carbonate Reservoirs by Proposing a New Fuzzy Logic Approach, the values of A and B would be:

Image for - Permeability Prediction Enhancement in Carbonate Reservoirs by Proposing a New Fuzzy Logic Approach

Finally, the calculated permeability value for the horizon h would be estimated.

RESULTS AND DISCUSSION

According to the Table 7, relative absolute errors of predicted permeability values in all four blind testing wells belonging to either Sarvak or Asmari formation show lowest amount of error when comparing to core reported permeabilities. Thus, the precision of the model will increase significantly by defuzzification proposed in this study. The results could be seen in Fig. 2-5.

Although, the predicted results have a perfect match in almost all part of the wells sections Fig. 2 and 3, but to see how accurate is the new model in prediction of permeability values in un-logarithmic scales we select some sections of the wells with the predicted values by two different approaches mentioned in this article versus core reported values.

Table 7: Relative absolute error values in two testing wells of each reservoir case by new proposed Fuzzy approach RAE from the Hambalek and Gonzalez approach are also mentioned for comparison
Image for - Permeability Prediction Enhancement in Carbonate Reservoirs by Proposing a New Fuzzy Logic Approach

Image for - Permeability Prediction Enhancement in Carbonate Reservoirs by Proposing a New Fuzzy Logic Approach
Fig. 2:
The calculated permeability values versus depth of well 1 and well 2, obtained from different methods for the Sarvak formation: (A) Hambalek and González method, (B) New introduced Fuzzy method. In all diagrams, continues line shows the predicted permeability and solid circles indicate the core reported permeability. Note that, the results obtained from new introduced Fuzzy method shows a better match in almost all parts of the well sections than Hambalek and Gonzalez’s method

Image for - Permeability Prediction Enhancement in Carbonate Reservoirs by Proposing a New Fuzzy Logic Approach
Fig. 3:
The calculated permeability values versus depth of well 1 and well 2, obtained from different methods for the Asmari formation: (A) Hambalek and González method, (B) New introduced Fuzzy method. In all diagrams, continues line shows the predicted permeability and solid circles indicate the core reported permeability. Note that, the results obtained from new introduced Fuzzy method shows a better match in almost all parts of the well sections than Hambalek and González’s method

As it is clear in Table 8, the permeability values predicted by new proposed technique are much more close to the reported core values which are considered as exact values.

As it was mentioned Sarvak and Asmari formations, two huge carbonate petroleum bearing reservoirs, are selected for case studies in this article. In each case, two wells with core and log information used as blind testing to testify the accuracy of each Fuzzy logic model constructed by two different approaches described above.

Simulated permeability values from the new modified Fuzzy model are plotted versus depth in Fig. 2 and 3 for both studied reservoir cases. The results for the first studied reservoir case of Sarvak formation is presented in Fig. 4, whereas Fig. 5 is related to another studied case of Asmari formation.

In addition, core reported values are also plotted which are considered to be the actual and exact values. According to the graph, although the general trend of simulated values follows the actual core values, there are some horizons in which the model is not so flexible in prediction and the simulated values tend to follow a straight line through the average actual core reported ones.

Table 8:Predicted permeability values versus core reported ones applying two different approaches. Data are belonging to some selective horizon of four blind testing wells
Image for - Permeability Prediction Enhancement in Carbonate Reservoirs by Proposing a New Fuzzy Logic Approach
Predicted permeability values versus core reported ones in Sarvak Formation applying Hambalek and González approach (Method 1) and New Proposed technique (Method 2)

Image for - Permeability Prediction Enhancement in Carbonate Reservoirs by Proposing a New Fuzzy Logic Approach
Fig. 4:
Simulated permeability values versus core reported ones for each applied technique. Results from the Fuzzy model mounted with new defuzzification algorithm occur in a wider range just close to core reported range. Furthermore, the general trend is close to line of 45 degree which represents the high precision of the simulated values. The graph is related to the testing wells of the first studied case, Sarvak formation

Image for - Permeability Prediction Enhancement in Carbonate Reservoirs by Proposing a New Fuzzy Logic Approach
Fig. 5:
Simulated permeability values versus core reported ones for each applied technique. Results from the Fuzzy model mounted with new defuzzification algorithm occur in a wider range just close to core reported range. Furthermore, the general trend is close to line of 45 degree which represents the high precision of the simulated values. The graph is related to the testing wells of the first studied case, Asmari formation

This pattern could be observed in some parts of both Sarvak and Asmari formations (Fig. 2, 3).

Furthermore, to have a better understanding of the accuracy of the predicted results the simulated values versus core reported ones are plotted in Fig. 4 and 5. As it is clear, the predicted values occur by new method in the actual range of core derived ones whereas the result from coarser bins definition will occur in a narrower range (Fig. 4B, 5B).

CONCLUSION

In this study we introduced a modification in defuzzification stage of the model provided by Hambalek and González (2003) to propose a new Fuzzy based method which is much more convenient and precise for carbonates. In addition, we used two studied carbonate reservoir cases to justify our proposed technique and compared its results with the previous Fuzzy technique.

The method simply uses some basic selected Porosity well log data sets such Neutron and Sonic porosity well logs rather than depending on new complicated logging technologies. The reason behind using porosity logs as input parameters is the close relationship between permeability and porosity. This relationship is a function of particle sizes, shapes, sorting, compaction and degree of cementation etc.

The results of permeability values by Hambalek and González (2003) approach in both carbonate studied cases showed an acceptable correspondence with measured core permeability in general trend but there were some horizon in which the model was not so flexible in prediction. However, applying Fuzzy model with the proposed modification increased the accuracy of predicted permeability values and makes the predicted values to follow the more complex fluctuation trends in almost all horizons of both case studies.

In this study, we used a spatial algorithm for assigning representative value to each permeability geo-category, in which permeability geo-categories classified in four group and a combined Fuzzy possibility with special averaging was proposed in a way that characteristics of all Geocategories are considered to predict much more precise results.

In this study, two huge carbonate reservoirs used as case study which are Sarvak and Asmari formations in Persian Gulf located in south west of Iran. To develop Fuzzy logic model in each case three wells with available core and log information were used. Moreover, two wells with core and log information were used as blind testing in each reservoir case for testifying model’s predictions.

Cross correlation between simulated permeability values versus cored reported ones confirms the increase in accuracy of predictions when applying new approach in defuzzification. As it is clear, the general trend of the plotted values follow the line of 45 degree line which means that the predicted values are very close to the actual core reported ones.

ACKNOWLEDGMENTS

This study was prepared under the supervision and permission of NIOC-Exploration Directorate in cooperation with Amir Kabir University of Technology. The authors would like to thank Dr.A.R.Rabani, Mr. N. Sabeti, Mr. S.A. Miri, for their support and permissions to publish this paper. We are also especially grateful to Amir Kabir University staff, Dr. M. Irannajad, Dean of Mining, Metallurgical and Petroleum Engineering for help and close cooperation. The authors greatly appreciate the financial supports of the Institute of Geophysics and the Research Council of the University of Tehran which enabled the second author for this research. We appreciate the critical reading by the arbitration committee and we would greatly appreciate enlightening suggestion and insightful comments.

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8:  Kolodzie, S.R., 1980. Analysis of pore throat size and use of the Waxman-Smits equation to determine OOIP in spindle field. Proceedings of the SPE 9832 Annual Conference and Exhibition, September 21-24, 1980, Dallas -.

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15:  Taghavi, A.A., 2005. Improved permeability estimation through use of fuzzy logic in a carbonate reservoir from Southwest Iran, SPE 93269. Proceedings of the 14th SPE Middle East Oil and Gas Show Conference, March 12-15, 2005, Bahrain International Exhibition Centre, Bahrain, pp: 1-9.

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17:  IOOC., 2003. Report geology and reservoir engineering of Asmari and Sarvak formation. Iranian Offshore Oil Company. http://www.iooc.co.ir/english/default.asp.

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