An Improved Method for Resource Evaluation of Shale Gas Reservoir

An Improved Method for Resource Evaluation of Shale Gas Reservoir Bao Xing MOE Key Laboratory of Oil & Gas Resources and Exploration Technique, Yangtze University, Wuhan 430100, China; School of Geosciences, Yangtze University, Wuhan 430100, China e-mail: 258485036@qq.com Li Shao-hua* MOE Key Laboratory of Oil & Gas Resources and Exploration Technique, Yangtze University, Wuhan 430100, China; School of Geosciences, Yangtze University, Wuhan 430100, China * Corresponding author e-mail: jpishli@163.com Zhang Chang-min MOE Key Laboratory of Oil & Gas Resources and Exploration Technique, Yangtze University, Wuhan 430100, China; School of Geosciences, Yangtze University, Wuhan 430100, China e-mail: zcm@yangtzeu.edu.cn Li Jun Research Institute of Explopment,Tarim Oilfield Company, CNPC, Korla 841000, China e-mail: ljkzf@126.com Yu Si-yu` MOE Key Laboratory of Oil & Gas Resources and Exploration Technique, Yangtze University, Wuhan 430100, China; School of Geosciences, Yangtze University, Wuhan 430100, China e-mail: feiyuno2@163.com ABSTRACT At present, China is at the initial stage in shale gas exploration and development. Generally speaking, shale gas has no clear physical boundaries and it is hard to accurately control relevant parameters in reserve calculation. Therefore, probability volume method is a relatively ideal reserve estimation method at present. By taking Upper Ordovician Wufeng Formation Lower Silurian Series Longmaxi Formation in X Well Area of Fuling Shale Gas Field as an example, the geological models are established to analyze five uncertain parameters influencing the shale gas reserve. Moreover, according to the principle of probability volume method, three levels covering Pessimistic, Possible and Optimistic are set for various parameters. A quantitative evaluation is conducted on various parameters via orthogonal experimental design method, and 18 groups of simulation schemes are designed for separate calculation. The simulation results are analyzed via intuitive and variance analysis method; a quantitative evaluation is conducted on uncertain parameters influencing the shale gas reserve. This method has reduced the test number and greatly improved the evaluation efficiency. KEYWORDS: shale gas; orthogonal experimental design; stochastic modeling; reserves calculation - 4821 -

Vol. 21 [2016], Bund. 15 4822 INTRODUCTION Shale gas refers to the subject that can occur as mud rock with gas generating ability or natural gas in shale formation in adsorption and unbound states at the same time [1-3]. Shale gas possesses a relatively special accumulation mechanism, and it is an important type of unconventional natural gas in the reservoir stratum. In China, the recoverable resource of 26 10 12 m 3 marks its huge exploration and development potential [4-5]. However, shale gas resource quantity evaluation and research work conducted in China is still at the exploration stage. In order to improve its output, resource quantity evaluation and estimation should be conducted via appropriate methods by directing at different characteristics of shale gas. At present, domestic and overseas shale gas reserve calculation methods not only include common volume method and resource abundance analogy method, but also cover FORSPAN method, single well reserve estimation method, material balance method, decline curve method, and numerical simulation method [6-7]. At present, China is at the initial stage in shale gas exploration and development. Comparatively speaking, volume method is a relatively suitable reserve calculation method. Besides, shale gas has no clear physical boundaries and it is hard to accurately control relevant parameters in reserve calculation. Therefore, probability volume method [8] is a relatively ideal reserve estimation method at present. Through screening and assignment, analysis and calculation, and result characterization for various parameters of reserve calculation by applying the principle of probability method, the uncertainty in calculation will be reflected and meanwhile the veracity of calculation can be guaranteed within a certain risk scope. Therefore, a foundation is laid for the implementation of exploration and development. Based on previous geological researches, the author reasonably predicts key parameters in reserve calculation by adopting multi-parameter co-simulation method under geological constraint. Meanwhile, the simulation scheme for geological model of shale gas is determined by utilizing Experimental Design method, and the evaluation model of shale gas reserve is established via random modeling technology. Moreover, a quantitative evaluation is conducted on key geological parameters influencing reserve calculation.

Vol. 21 [2016], Bund. 15 4823 CALCULATION STEPS AND PRINCIPLE OF PROBABILITY VOLUME METHOD According to the principle of volume method [9-11], the reserve of shale gas is equal to the sum of free gas, adsorbed gas and solution gas. Generally speaking, the content of solution gas is quite low [12], so it is often ignored in gas content analysis and resource quantity calculation. Geological reserve calculation of free gas According to the estimation method of conventional natural gas, volume method can be used to calculate the reserve of free gas. See the following formula: G sf = 0.01A H φ ( 1 - S w ) / B gi (1) In the formula, G sf means the geological reserve of free gas, 10 8 m 3 ; A refers to the gas bearing area, km 2 ; H indicates the average effective thickness, m; φ denotes the effective porosity of gasbearing shale, %; S w represents the average original water saturation, %; B gi signifies the original natural gas volume factor. Geological reserve calculation of adsorbed gas Shale gas is similar to coal bed gas in the adsorption and desorption mechanisms, so there is a need to refer to the evaluation method of adsorbed gas in coal bed gas to some extent. At present, the major calculation method for the adsorption rate of shale gas in China is Langmuir isothermal adsorption experiment method [13]. This method requires the storage environment of experiment samples to approach the subsurface temperature. Then the maximum adsorption capacity of samples under different pressures is calculated, and the corresponding relation model is established by applying the adsorbed gas content and pressure values. This model can be applied to the follow-up calculation in practical situations. Langmuir isothermal adsorption abides by the following relation: V = V L * P / ( P L + P ) (2) In the formula, V refers to the volume of adsorbed gas in the reservoir stratum of unit volume under the pressure P, m3/t; V L represents Langmuir volume which means the maximum adsorption volume in the experiment, m3/t; P indicates the gas pressure, MPa; P L denotes Langmuir pressure, MPa. The reserve of adsorbed gas is equal to the product of multiplying the gas volume V in the shale of unit mass with the total mass m, i.e. the product of the adsorption rate of shale and its mass. The following formula is adopted:

Vol. 21 [2016], Bund. 15 4824 G ad = 0.01A H ρ G sd (3) In the formula, G ad means the geological reserve of adsorbed gas, 10 8 m 3 ; A refers to the gas bearing area, km 2 ; H indicates the average effective thickness, m; ρ denotes the rock density of shale, g/cm 3 ; G sd represents the adsorbed gas of unit mass gained in the isothermal adsorption test, m 3 /t. Total geological reserve calculation of shale gas The geological reserve of free gas G sf and geological reserve of adsorbed gas G ad are calculated respectively via the above methods, and the total reserve G is the sum of the above two values, i.e. G = G sf + G ad (4) Shale gas involves a complex forming process and accumulation mechanism, so it is hard to accurately and exclusively determine many parameters of reserve calculation under the existing material conditions. Therefore, various required parameters with typical and representative characteristics should be obtained through methods like statistical analysis and calculation and geological analogy test by combining with the existing materials. They need to meet the requirements of statistics. Moreover, research and evaluation should be conducted by applying probabilistic method according to the changing law of shale gas. Three levels covering pessimistic, possible and optimistic are selected for each parameter type influencing the reserve of shale gas. Meanwhile, the corresponding reserves are calculated respectively and a quantitative evaluation is conducted on various parameters. GEOLOGICAL OUTLINE OF THE RESEARCH AREA The work area of this study is located in X Well Area of Fuling Shale Gas Field in Jiaoshiba Town of Chongqing. In the tectonic aspect, it is situated in Chuandong wide spaced anticlines in the east of Sichuan Basin as well as the west of the basin boundary faults and Qiyueshan fault; it is the special positive tectonics in Wanzhou Synclinorium. The overall terrain of the work area is gentle, the fault is not developed, and the area is 9.25 square kilometers (Figure 1). Target stratum of the work area is located in the lower part of Upper Ordovician Wufeng Formation - Lower Silurian Series Longmaxi Formation, and it belongs to shelf sediments. Ash black organic shale is developed, and the organic carbon content increases gradually from up to down. Rich in organic shale, it possesses a good reservoir performance.

Vol. 21 [2016], Bund. 15 4825 Figure 1: Location of the work area and structure outline map of Jiaoshiba (According to Guo Xu-sheng, 2014) The work area includes 5 parameter wells, and the reserve of shale gas is gained via the random geological model established on the basis of various parameters in the coring segments (2,330-2,415.5m) of the 5 wells in this paper. Firstly, the geological model of shale in the work area is established, so as to provide an elaborate geological data volume for the follow-up reserve calculation (Figure 2). Petrel software is utilized to establish tectonic model, density model, volume model, total organic carbon content (TOC) model and adsorption rate model of shale required to calculate the reserve of adsorbed gas as well as porosity model, gas saturation model and net-to-gross ratio (NTG) model required to calculate the reserve of free gas. Figure 2: Random geological model of adsorbed gas in the work area

Vol. 21 [2016], Bund. 15 4826 KEY PARAMETERS OF SHALE GAS RESERVE EVALUATION AND THEIR VALUES By combining with the data collection situations and geological features of this work area, according to the reserve calculation formula of shale gas, the adsorbed gas reserve of shale is mainly controlled by shale volume, density and adsorption rate. The target stratum belongs to dessert area of shale gas. Moreover, different from conventional natural gas, shale gas is generated and reserved by itself in the stratum. Generally speaking, stratum contains gas, so the effective gas volume of shale is treated as a constant value, i.e. the volume of geological model. In this study, 8 shale cores in the lower part of Wufeng Formation Longmaxi Formation in the target stratum are collected for Langmuir isothermal adsorption experiment. After fitting for the measured data, it is discovered that the adsorbed gas content rises with the increase of pressure; when a certain pressure is reached, the adsorbed gas enters a saturation state. It has a relatively good adsorption performance, and the adsorption rate of shale is gained through calculation. According to the analysis, total organic carbon content (TOC) and adsorption rate of shale have a relatively close relation, and they present a good positive correlation (Figure 3). The correlation coefficient between them is R 2 =0.868. The richer TOC is, the higher the adsorption rate will be. Therefore, co-simulation is conducted for adsorption rate model in the work area through TOC model, so as to increase the precision of adsorption rate model. The value of TOC directly influences the adsorption rate, and finally TOC is selected to replace adsorption rate as a parameter of influencing the reserve. The free gas reserve is mainly controlled by shale volume, porosity, gas saturation and original volume factor of shale gas in the work area. Therefore, its calculation is the same with that of adsorbed gas. The model volume participates in reserve calculation as the effective gas volume of shale.

Vol. 21 [2016], Bund. 15 4827 Figure 3: Relational graph of TOC and adsorbed gas content in shale of the lower part of Wufeng Formation Longmaxi Formation In this way, major parameters influencing the total reserve of shale gas in this work area are determined: shale density (ρ), total organic carbon content (TOC), porosity (φ), gas saturation (S g ) and original natural gas volume factor (B gi ). Quantitative analysis and evaluation are conducted on the pessimistic value, possible value and optimistic value of the above five parameters. As for the density value of shale, according to statistical analysis of the model, the minimum value of density is 2.44g/cm 3, the maximum value is 2.82g/cm 3, and the average value is 2.58g/cm 3. The density is mainly distributed between 2.55g/cm 3 and 2.65g/cm 3. After comprehensively considering factors like uncertainty of stratum, three equal percent levels are taken. In another word, values floating up or down by 1% around the average value under the reference density model are selected as three levels of the test: the model of -1% is the pessimistic value; the reference model is the possible value; the model of +1% is the optimistic value. Similarly, three levels with equal interval are taken for the three parameters covering total organic carbon content (TOC), porosity and original natural gas volume factor. Values floating up or down by 5% around the average value of the three attribute parameters are selected as three levels of the test: the model of -5% is the pessimistic value; the reference model is the possible value; the model of +5% is the optimistic value. As for the value of gas saturation, relevant analysis data are missing, and factors with relatively great gas saturation changes in shale gas pool are comprehensively considered. Values floating up or down by 10% around the average value are selected as three levels of the test: the model of -10% is the

Vol. 21 [2016], Bund. 15 4828 pessimistic value; the reference model is the possible value; the model of +10% is the optimistic value. PROBABILITY VOLUME METHOD OF SHALE GAS BASED ON ORTHOGONAL EXPERIMENTAL DESIGN Problem posing and Experimental Design The British statistician Fischer designed the basic idea and method of Experimental Design at the beginning of the 20 th century. As a branch of mathematical statistics, it gains sufficient and accurate practical information by scientifically designing the test scheme and objectively and accurately analyzing the test results on the basis of methods including mathematical statistics, probability theory and linear algebra [14]. By adopting orthogonal Experimental Design method, this paper designs and analyzes the multifactor test by referring to the orthogonal table. Some representative combinations are selected from all level combinations of test factors via scientific and reasonable methods, some test results are observed, and the situation of overall test is analyzed. Then factors with an obvious influence on the test indexes among all test factors are analyzed [15]. According to the principle of probability volume method, three levels covering optimistic, possible and pessimistic are often selected for each parameter type influencing the reserve of shale gas. Firstly, the table of factor level is established. As for the values of different levels, -1 means the pessimistic value, 0 represents the possible value, and 1 stands for the optimistic value (Table 1). Table 1: Table of factor level Level Shale TOC Porosity Gas volume factor density saturation 1-1 -1-1 -1-1 2 0 0 0 0 0 3 1 1 1 1 1 According to parameter statistics in this test, in order to conduct a comprehensive evaluation on the five factors and three levels, calculation should be conducted for 243 times, which will waste time and energy. When the simulation scheme is designed by adopting orthogonal Experimental Design method, uncertain parameters influencing the reserve can be reasonably reflected by conducting calculation for only 18 times. Moreover, an evaluation can also be carried out. Therefore, the efficiency will be increased greatly.

Vol. 21 [2016], Bund. 15 4829 Table 2: Table of intuitive analysis Number ρ TOC φ S g B gi Adsorbed gas ( 10 8 m 3 ) Free gas ( 10 8 m 3 ) Total reserve ( 10 8 m 3 ) Test 1 1 1 1 1 1 55.37 81.74 137.11 Test 2 1 0 0 0 0 54.63 71.52 126.15 Test 3 1-1 -1-1 -1 54.39 61.30 115.69 Test 4 0 1 1 0 0 54.83 75.10 130.93 Test 5 0 0 0-1 -1 54.09 64.53 118.62 Test 6 0-1 -1 1 1 53.85 73.95 127.8 Test 7-1 1 0 1-1 54.28 86.04 140.32 Test 8-1 0-1 0 1 53.55 64.71 118.26 Test 9-1 -1 1-1 0 53.30 64.37 117.67 Test 10 1 1-1 -1 0 55.37 58.24 113.61 Test 11 1 0 1 1-1 54.63 90.34 144.97 Test 12 1-1 0 0 1 54.39 68.12 122.51 Test 13 0 1 0-1 1 54.83 58.39 113.22 Test 14 0 0-1 1 0 54.09 77.65 131.74 Test 15 0-1 1 0-1 53.85 79.05 132.90 Test 16-1 1-1 0-1 54.28 71.52 125.80 Test 17-1 0 1-1 1 53.55 61.30 114.85 Test 18-1 -1 0 1 0 53.30 81.74 135.04 Average value 1 126.67 126.83 129.74 136.16 122.29 Average value 2 125.87 125.77 125.98 126.09 125.86 Average value 3 125.32 125.27 122.15 115.61 129.72 Range 1.350 1.564 7.588 20.553 7.425 Analysis of test results The reserve of shale gas is the sum of adsorbed gas reserve and free gas reserve. Therefore, when the table is designed, they should be calculated separately and then the total reserve can be gained (Table 2). By determining primary and secondary factors according to the range calculation result in the table of intuitive analysis (the greater the range is, the more important the influence will be), factors influencing the shale gas reserve in this work area can be gained (from large to small): gas saturation, porosity, shale gas volume factor, TOC, and shale density. Intuitive analysis is simple, practicable, intuitional and pellucid. However, range analysis cannot distinguish the data fluctuation caused by the changes of factor levels in the test process. Meanwhile, it cannot conduct accurate quantitative estimation for the importance degree (significance) of factor influence. In order to make up the disadvantages of intuitive analysis, variance analysis is carried out for the test results. The table of variance analysis (Table 3) is gained through orthogonal design analysis software. F- test is adopted to conduct a quantitative evaluation on the significance degree of various factors. * means that this factor is significant; no mark means that this factor has a weak influence. According to the value of F ratio, gas saturation has the most significant influence on the reserve in this

Vol. 21 [2016], Bund. 15 4830 Experimental Design. By combining with the value of F ratio and range analysis results, factors influencing the shale gas reserve are gained (from large to small): gas saturation, porosity, shale gas volume factor, TOC, and shale density. Table 3: Table of variance analysis Factor DEVSQ Degree of freedom F ratio F 0.10 F 0.05 F 0.01 Significance ρ 5.735 2 0.017 2.92 4.10 7.56 TOC 7.357 2 0.024 2.92 4.10 7.56 φ 173.753 2 0.534 2.92 4.10 7.56 S g 1267.587 2 3.815 2.92 4.10 7.56 * B gi 165.489 2 0.511 2.92 4.10 7.56 Error 1618.81 10 CONCLUSIONS (1) In reserve calculation of shale gas based on two-dimensional graph, the average values are taken for key parameters like shale density, volume, adsorption rate in adsorbed gas, porosity, and gas saturation. In this way, the influence of anisotropy in the reservoir stratum on the calculation result is covered. In reserve calculation based on three-dimensional model, calculation is conducted according to various grids in the model. In this way, the accuracy can be greatly increased. (2) By combining with data collection situations of this work area, the values of various parameters influencing the shale gas reserve are selected by applying the method of Experimental Design. Three levels covering pessimistic, possible and optimistic are selected for each parameter type. If overall test is conducted for these parameters, 243 models should be established and corresponding reserves need to be calculated. By adopting the method of orthogonal Experimental Design, probability distribution of shale gas reserves can be gained by conducting 18 tests. Thus the calculation efficiency is improved. (3) Through intuitive and variance analysis, important parameters influencing the shale gas reserve in this work area are gained: gas saturation, porosity, shale gas volume factor, TOC, and shale density.

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