Prediction of coalbed methane content based on uncertainty clustering method

Abstract

An analysis of factors that influence coalbed methane content showed that seven factors had a major influence: coal thickness, methane concentration, vitrinite reflectance, permeability, cracks, and sealing conditions hydrodynamic conditions were selected as criterion indexes. The prediction model of coalbed methane content was built based on the uncertainty measure theory. Data from six regions in the central and southern Qinshui Basin were used as the training sample. The sample mean was set as the cluster centers, and the index weight was determined by information entropy theory. Calculation of the multi-index comprehensive measure of the sample showed that the sample was classified according to the minimum uncertainty measure distance principle, which was used to predict coalbed methane content. The research results show that: the obtained level by the prediction method is consistent with the practical level, the predictive value is basically consistent with the actual value, coalbed methane content prediction method based on uncertainty measure theory is reliable and practical, as well as showing a new way for the prediction and evaluation of coalbed methane content in the future.

Keywords

Coalbed methane uncertainty clustering gas content prediction

Introduction

Coalbed methane is a type of unconventional natural gas storage, which exists in the coal seam and its adjacent rocks in reservoir type. Coalbed methane is not only one of the important disasters factors in coal mine production, but also is a prerequisite for commercial exploration and development of coalbed methane resources in a region (Cai et al., 2014; Lee et al., 2014). Therefore, whether it is for coal mine production safety, or for accurate evaluation and prediction of coalbed methane development prospects, coalbed methane content is one of the most important parameters (Lian et al., 2008).

At present, domestic and foreign scholars have done a lot of research work in coalbed methane content prediction. The research mainly includes: the statistical method of coalbed methane content and the effective depth (Li et al., 1998), the temperature and stress method (Wang et al., 2002), the multivariate regression method of coalbed methane content, coal quality, logging, and other parameters integrated (Li et al., 2005; Pan and Huang, 1998), the desorption rate-isothermal adsorption curve based on Lang Mueller equation(Chen and Lin, 2005), the method based on support vector machine (Lian et al., 2008), the method based on fractal and Autoregressive Integrated Moving Average Model (ARIMA) (Wang et al., 2011), Back Propagation (BP) neural network method (Lian et al., 2005; Meng et al., 2008; Pan and Liu, 1997), and grey system theory (Tian, 2008; Tian et al., 2008). Because coalbed methane is a kind of complex and uncertain phenomenon, the research of coalbed methane content prediction did not reach a consensus, so far there is no mature theory and accurate calculation method recognized.

Uncertainty information put forward by Wang (1990) of Harbin Institute of Architecture and Engineering is new and different from fuzzy information, random information, and gray information. Wan (2004) proposed uncertainty clustering forecasting method, and used the method to predict the spaceflight material loss which gained satisfactory prediction results. The class discrimination of coalbed methane content exploration has many uncertainty factors and is very complicated work; therefore, uncertainty mathematics theory provides a good basis. This paper applied the uncertainty clustering method in order to study the class discrimination of coalbed methane content exploration, selected the main factors of coalbed methane content and built an uncertainty measurement model. This provides a new idea for coalbed methane resource evaluation.

Uncertainty clustering forecasting optimization method

Uncertainty clustering forecasting optimization method is based on uncertainty measure clustering theory (Chen et al., 2014; Dong et al., 2008; He et al., 2012, 2013; Zhao and Wu, 2013). Each discrimination index uses the mean value of sample measurement data as a classification center. First, based on the classification model, single index measure function was built up and then the weight of indexes was determined by the information entropy theory. After that, the multi-index comprehensive measure of the objects was calculated. The object category was determined by the multi-index comprehensive measure of objects and the classification model of uncertainty measure distance. At last the predictive value of objects was obtained by sum of products of the multi-index measurement by the mean value of object sample. Specific methods are as follows:

Construction of the criterion index system of research object. After analysis of influential factors of the research object, the discriminant index of research object samples is established. To make research object space for D, if any sample $D_{i} (i = 1, 2, \dots, n)$ in D is related with m influencing factors W₁, W₂, … , W_m, then $W = {W_{1}, W_{2}, \dots, W_{m}}$ is named for an index set.

Carrying through the classification of samples. The sample set $D = {D_{1}, D_{2}, \dots, D_{n}}$ is divided into k categories according to the research object characteristics, compose classification set $C = {C_{1}, C_{2}, \dots, C_{k}}$ .

Determination of the single index measure. $p_{ijk} = r (r_{ij} \in C_{k})$ is set for W_j measurement valued $x_{ij}$ of the j index of sample D_i value, $x_{ij}$ belongs to the k category degree, $p_{ijk}$ is the single index measure, also meet the following conditions:

0 \leq p (x_{ij} \in C_{k}) \leq 1 (i = 1, 2, \dots, n; = j = 1, 2, \dots, m; = k = 1, 2, \dots, p)

(1)

p (x_{ij} \in C) = 1 (i = 1, 2, \dots, n; = j = 1, 2, \dots, m)

(2)

p | x_{ij} \in ⋃_{t = 1}^{k} C_{t} | = \sum_{t = 1}^{k} p (x_{i} \in C_{t}) (k = 1, 2, \dots, p)

(3)

Determination of the index weight. Because the influence of each discrimination index to the research object is not the same, the weight coefficients u_j indicate the influence degree of W_j influencing factors in sample D_i. There are many methods to determine the index weight. This research calculates the index weight based on the information entropy theory.

v_{j} = 1 + \frac{1}{\lg k} \sum_{i = 1}^{k} p_{ijk} \lg p_{ijk}

(4)

u_{j} = v_{j} / \sum_{i = 1}^{m} v_{j}

(5)

where v_j is the amount of information provided by the j factors, m is the criterion index number.

Calculation of multi-index measure. $P_{ik} = p (p_{i} \in C_{k})$ is set for C_k probability of the k category of sample D_i, $P_{ik}$ is multi-index measure,

P_{ik} = \sum_{j = 1}^{m} u_{j} P_{ijk}

(6)

Determination of the category of the measured object. The measured object category is determined by the minimum uncertainty measure distance principle. The uncertainty measure distance d_k is set for multi-index measuring p_i and p_k distance:

d_{k} = [(p_{i 1} - 0)^{2} + (p_{i 2} - 0)^{2} + (p_{ik} - 1)^{2} + \dots (p_{iK} - 0)^{2}]^{0.5}

(7)

By comparing each uncertainty measure distance value, the minimum distance classification is selected based in the category of the measured object.

Calculation of the predictive value. The sample mean of classification model is written as ${\bar{x}}_{k}$ , the predictive value Z of the measured object can be expressed as:

Z = p_{i 1} {\bar{x}}_{1} + p_{i 2} {\bar{x}}_{2} + \dots p_{iK} {\bar{x}}_{K} = \sum_{k = 1}^{K} p_{iK} {\bar{x}}_{K}

(8)

Application in prediction of coalbed methane content

Classification samples set

In this paper, six locations in the central and southern of Qinshui Basin provided by Min Tian (2008) were taken as the research object (Table 1). The values of the quantitative parameters such as coal thickness, permeability, gas content, etc. in the research area were gained by the collection, collation, and comprehensive analysis. The qualitative parameters such as the development condition of fissures, sealing condition, and water dynamic condition are valued by the following methods: the qualitative parameters are divided into three levels according to the degree that they benefit coalbed methane preservation. The most favorable to coalbed methane preservation is 3; somewhat favorable is 2, while unfavorable is 1. According to the evaluation principle of coalbed methane exploration selection area, and combined with the specific characteristics of coalbed methane geological conditions in Qinshui Basin, the range of coalbed methane content is from 8.5 to 18.8 by comparison. The content can then be divided into three categories, namely C₁, C₂, and C₃, which, respectively, represent the unfavorable area of coalbed methane, the somewhat favorable area of coalbed methane and the favorable area of coalbed methane. Table 2 shows the maximum coalbed methane content range of each sample, the average value of each classification system, and the average value

{\bar{x}}_{1}

{\bar{x}}_{2}

{\bar{x}}_{3}

{\bar{x}}_{4}

{\bar{x}}_{5}

{\bar{x}}_{6}

and

{\bar{x}}_{7}

for seven influence factors, which were used to establish uncertainty measure function.

Table 1.

Prediction sample data.

Regions	Discriminant index							The measured gas content (m³/t)
Regions	Coal thickness (m)	Methane concentration (%)	Ro (%)	Permeability (10⁻³µm²)	Sealing condition	The development condition of fissures	Water dynamic condition	The measured gas content (m³/t)
Fanzhuang	8.9	94	3.39	1.3	3	3	3	18.8
Panzhuang	8.4	95	4.11	1.1	3	3	3	18.3
Tunliu	7.1	75	1.68	0.03	2	2	2	12.2
Changzhi	7.9	72	1.72	0.05	2	2	2	8.5
Qinyuan	5.6	49	1.55	0.4	1	2	2	11.2
Zhengzhuang	6.5	89	2.75	0.6	3	2	3	15.3

Table 2.

The sample classification data of coalbed methane.

Classification	No.	Gas content range (m³/t)	Mean of measured gas content (m³·t⁻¹)	Coal thickness (m)	Methane concentration (%)	Ro (%)	Permeability (10⁻³µm²)	sealing condition	The development condition of fissures	water dynamic condition
C ₁	4	<8	8.5	7.9	72	1.72	0.05	2	2	2
C ₂	3,5	8–15	11.7	6.35	62	1.62	0.22	1.5	2	2
C ₃	1,2,6	>15	17.47	7.93	92.67	3.42	1	3	2.67	3

Uncertainty measure function of influencing factors

According to the constructing method of linear uncertainty measure function, combined with the classification standard in Table 2, the establishment of uncertainty measure functions such as coal thickness, methane concentration, vitrinite reflectance, permeability, the development condition of fissures, sealing conditions, and water dynamic condition are shown in Figures 1 –7.

Figure 1.

Uncertainty measure function of coal thickness.

Uncertainty clustering forecasting method of coalbed methane content

Fanzhuang exploration region is used as an example for prediction. According to uncertainty measure function of each impact factor in Table 1, the single index measure evaluation matrix can be obtained:

(p_{ijk})_{7 \times 3} = [001001 0.02 0 0.98 001001001001]

(9)

Formulae (4) and (5) determine the weight of each evaluation index. Each evaluation index weights of Fanzhuang exploration region were

{w_{1}, w_{2}, w_{3}, w_{4}, w_{5}, \dots w_{7}} = {0.145, 0.145, 0.13, 0.145, 0.145, 0.145, 0.145}

. Using formula (6), weighted uncertainty measure was {0, 0, 1}. Uncertainty distance

d_{1} = 1.4142

d_{2} = 1.4142

, and

d_{3} = 0

were obtained by formula (7). According to the uncertainty clustering forecasting criteria, gas content region was predicted level C₃. This was completely consistent with the measured level. Finally, according to formula (8), the predictive value was calculated for 17.47 m³/t, and is very close to the actual value 18.8 m³/t. Similarly, the prediction level and value of the remaining six exploration regions could be obtained. In order to test optimization effect of the discrimination method and analyze the feasibility and reliability of clustering optimization method, grey clustering evaluation results were also listed in Table 3. The results show that this method’s results are most consistent with the actual results: judgment error rate is 0, six samples coalbed methane’s forecast value is very close with the actual value, the average relative error is 5.55%, and control is less than 10%. The results indicate that the uncertainty clustering optimization method is superior for predicting and evaluating the content of coalbed methane.

Table 3.

Determination results comparing comprehensive uncertainty measure and uncertainty measure analysis method.

Regions	Weighted uncertainty measure	Uncertainty distance			Determination results			Predictive value	Measured value
	Weighted uncertainty measure	d ₁	d ₂	d ₃	This paper method	Grey clustering analysis method	Measured result	Predictive value	Measured value
Fanzhuang	(0,0,1)	1.4142	1.4142	0	C ₃	C ₃	C ₃	17.47	18.8
Panzhuang	(0,0,1)	1.4142	1.4142	0	C ₃	C ₃	C ₃	17.47	18.3
Tunliu	(0.3676,0.6344,0.018)	0.8908	0.5232	1.2385	C ₂	C ₂	C ₂	10.8615	12.2
Changzhi	(1,0,0)	0	1.4142	1.4142	C ₁	C ₂	C ₁	8.5	8.5
Qinyuan	(0.45,0.527,0.023)	0.5809	0.4268	1.4348	C ₂	C ₁	C ₂	10.3927	11.2
Zhengzhuang	(0.07,0.36,0.57)	1.1487	0.8599	0.5652	C ₃	C ₃	C ₃	14.7649	15.3

Conclusions

Coalbed methane content is affected by many factors. Each factor has non dimension, quantitative, and non quantitative characteristics, which were influenced by uncertainty and concealment. Considering the importance of each factor, based on uncertainty measure theory, the uncertainty measure model of coalbed methane content was established.

The weight of each index was calculated based on information entropy, in accordance with the minimum uncertainty measure distance principle, coalbed methane content exploration region level is evaluated, which makes evaluation results more scientific, objective and reasonable, thus providing a new way for coalbed methane content prediction and evaluation.

Six typical regions in the central and southern areas of Qinshui Basin were used as examples of coalbed methane content prediction evaluation method and model of uncertainty clustering theory. Through calculation, coalbed methane contains grade in six target regions, which are consistent with those obtained by the measured method.