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## New Method for Predicting Production Boosts Accuracy for Carbonate Reservoirs

#### Topics

The widely developed karst caves and fractures in carbonate reservoirs result in strong spatial heterogeneity. Consequently, the parameters obtained from cores and numerical simulation are limited in their ability to reflect the production possibility of the entire reservoir. To solve this problem, this paper proposes a new method of economic prediction on the basis of expert library and oilfield databases. The method takes into account geological factors and the effect of production factors on the economic prediction.

Introduction
The key parameters used for the economic prediction of a carbonate reservoir include well spacing, oil production, and annual decline rate. These parameters are mainly from core experiments in the laboratory or from the numerical simulation of wells, but caves and fractures are dispersed throughout the carbonate reservoir. This heterogeneity means the properties of a carbonate reservoir can be very different in different regions. Consequently, the commonly used parameters are limited in their ability to represent the whole reservoir, which leads to high risk in economic prediction.

The method proposed in this paper combines the Delphi method, the analytic hierarchy process (AHP), the technique for order preference by similarity to ideal solution (TOPSIS), the moving least-squares (MLS) method, and future net present value (FNPV) to create the DATMF method in an attempt to overcome these shortcomings. Through classical mathematics methods, the DATMF method combines expert library and oilfield databases to predict the economy of carbonate reservoirs. This prediction method reduces the size of the required database greatly, and its calculation process is based on professional geology theory and reservoir engineering. In addition, the DATMF economic prediction method can be applied directly to the stage of geological exploration, which removes the barrier between geologists and reservoir engineers and simplifies the procedure of economic prediction.

DATMF Work Flow
Delphi Method.
The Delphi method is a management strategy for dealing with complex task problems. Here, it aims to quantify experience and ensure the reliability of results in theory. After experts learn the purpose and background of research, they compare the effect of factors of the same level. Two factors are compared each time. After repeated inquiry and feedback, the experts finally reach an agreement of opinion and a final expert judgment matrix is established and expressed as Matrix A. Because of the independent judgment environment, the objectivity of the Delphi method is strong and reliable.

AHP. AHP is a powerful method used for system analysis and operational research. The method divides the decision process into three layers: the goal layer, the criterion layer, and the scheme layer. It obtains a weight vector for each level by solving the matrix’s eigenvector for each layer.

In the DATMF method, the AHP method is used to calculate the weight vectors by solving the eigenvector for each layer of Matrix A with the aim of obtaining the weight vector of all subfactors describing a carbonate reservoir.

TOPSIS. The mathematical principle of the TOPSIS method is to calculate the distance between the evaluated object and the positive ideal solution and the negative ideal solution. The evaluated object is the optimal solution in all existing schemes if it is closest to the positive ideal solution and furthest from the negative ideal solution. The coordinates for calculating the distance in the TOPSIS method are multivariate indices, and each index has a relative weight used when calculating the distance.

In the TOPSIS method, the indices and their weights are derived from the AHP method and the distance represents the degree of similarity between the reservoir being analyzed and reservoirs in the database. Therefore, their similarity can be quantified by the TOPSIS method. Then, the most valuable reservoirs can be selected to optimize the database and obtain the reference weight of each reservoir.

MLS. The least-squares (LS) method is a classic mathematical optimization method that finds an optimal equation by minimizing the sum of the squared error. In the LS method, the importance of all data is the same, but the weighted least squares (WLS) method adds a weight vector to reflect the different importance of each point in the fitting process, which results in a different fitting equation.

In the MLS method, the fitting points are the data from the selected reservoirs and the weight of each point is the similarity vector calculated by the TOPSIS method.

On the basis of existing geological and development databases, the MLS method analyzes these data to find the relationship between the parameters in the two databases. The new reservoir’s geological parameters can then be used to predict development parameters that will be used for economic prediction.

FNPV. Net present value (NPV) is the difference between income and investment and is a common method to evaluate an investment scheme. In the NPV method, the time of the evaluation is now, but the FNPV method uses a future time point, converting the income and expenditure of a project into the future.

DATMF Methodology
Quantify the Importance of Factors: Delphi Method.
Four methods exist for quantitative comparison of two factors: classification, scoring, sorting, and scaling. The DATMF method uses a scale method to evaluate the importance of two factors. This scaling method is based on psychology, and its accuracy has been verified by thousands of experiments in many fields. The Delphi method establishes a pairwise comparison matrix until expert opinions are unified and the matrix is consistent.

Framework for Describing Carbonate Reservoirs: AHP Method. Taking into account various characteristics of carbonate reservoirs, an evaluation system that includes five factors and 26 subfactors is set up to describe and identify every carbonate reservoir. The resulting AHP structure is shown in Fig. 1. Fig. 1—The structure of the AHP method.

All of the subfactors can be expressed with numbers except for reservoir type, facies type, and lithology. These three subfactors, however, cannot be absent because they have great influence on the development of carbonate reservoirs. Therefore, a set of methods using natural numbers was built to quantify these three parameters. The difference between two numbers is relative to the similarity of representative geological characteristics.

Standardization of Reservoirs Data: TOPSIS/MLS Method. Because the range of subfactors is different, their level of effect on the results is different in the fitting process. For example, if formation thickness is 40 and 20 m and oil saturation is 0.6 and 0.3, respectively, and their weights are equal, then the difference in thickness will have a greater effect on the results. Therefore, standardizing the reservoir geological data (subfactors) is necessary.

The development of a reservoir is a reflection of its geological characteristics. The MLS method is a scientific way to analyze the development data on the basis of geological data.

Discussion and Conclusions

• A new economic prediction method is proposed for carbonate reservoirs. The DATMF method can predict a reservoir’s economy from the scale of a whole reservoir instead of from a few cores or wells. It also takes into consideration influencing factors from the development process, further reducing the risk that comes with conventional economic prediction for carbonate reservoirs.
• On the basis of big-data analysis, the DATMF method improves the professionalism and accuracy of the prediction. The method emphasizes the value of expert experience and uses professional knowledge to constrain the data. Compared with conventional big-data analysis, the results from the DATMF method reflect more-professional characteristics rather than relying solely on mathematical methods. Further, with the help of the AHP/TOPSIS/MLS method, fitting precision is improved and the results become more reasonable and accurate.
• The FNPV method takes into account the influence of various economic factors in the process of oilfield development. The economic factors are divided into disposable investment, continuous investment, and oil earning, for example, and their formulas are derived respectively. The whole operation process requires only 1.3 seconds. Results from a case study show that the selected reservoir will start to make a profit in 2.28 years and can be developed for approximately 7 years before adjustment is necessary, resulting in a profit of \$110.32 million at that time.
• In the field of petroleum exploration and development, the DATMF method can be applied more widely than is discussed here.

This article, written by Special Publications Editor Adam Wilson, contains highlights of paper SPE 190868, “A New Method for Economic Prediction of Carbonate Reservoirs Based on Expert Library and Small Database,” by Wenbin Chen, SPE, Hanqiao Jiang, and Junjian Li, China University of Petroleum; Shan Jiang, PetroChina; and Hanxu Yang, SPE, and Yan Qiao, China University of Petroleum, prepared for the 2018 EAGE Annual Conference and Exhibition/SPE Europec, Copenhagen, Denmark, 11–14 June. The paper has not been peer reviewed.

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