A Geostatistical Approach to Finding Relationships Between Reservoir Properties and Estimated Ultimate Recovery in Shale Gas System

  • Qian Zhang
  • Shiyun Mi
  • Min Niu
Conference paper
Part of the Springer Series in Geomechanics and Geoengineering book series (SSGG)


Unconventional shale gas resources have become a major component of the energy mix in North America, with future growth projected globally. The nature of storage and the transport of hydrocarbon gas are not yet fully understood in these plays. However, prioritization of the key factors and measurement of the relevance between the reservoir attributes and the estimated ultimate recovery (EUR) are still poorly understood in practical studies. In this paper, spatial fuzzy ranking was proposed to prioritize the relevance of several reservoir properties on the EUR in shale gas system. The prioritization procedure includes four steps. The first step in the analysis was to determine a set of reservoir attributes to make description of the reservoir features through logging data analysis. Other than ordinary parameters, such as porosity, permeability, and thickness, three new attributes—mud rocks content, organic carbon content, and maturity index—are discussed. Secondly, the fuzzy ranking method is employed to prioritize the relevance between the identified reservoir attributes and the EUR. Finally, the geostatistical method was used to prioritize correlation between reservoir attribute variables and the EUR. Application of the spatial fuzzy ranking methods to the records from 1346 wells in the Barnett Field prioritized the key factors that impact the EUR. The result shows that the EUR performance of wells in the area could be spatially modeled and predicted by using the proposed spatial fuzzy ranking method.


Spatial fuzzy ranking Quantitative relation Estimated ultimate recovery 

145.1 Introduction

Shale gas is natural gas produced from shale rich in organic matter. The shale bearing the gas is fine-grained sedimentary rock with grain size less than 0.0039 mm in the USA [1].

Unconventional shale gas has developed into an significant resource play for the USA, providing more than 56.1% of produced gas in the USA by the end of 2015. PetroChina gets industrial gas flow from the Cambrian and Silurian shale in Wei-201 well in Sichuan Basin, realizing the first industrial breakthrough of Chinese shale gas.

Some studies [2] have been carried out to illustrate the factors influencing recovery for the shale gas. Most of them are based on reservoir simulation. Unconventional accumulations are found downdip from water-saturated rocks. They spread across lithological boundaries and representatively have large areal extent, low permeability, abnormally high or low pressure, and close association with source rocks. As a consequence, making volumetric assessments is difficult for the unconventional reservoir.

The estimated ultimate recovery (EUR) is the most important measurable source of information. Several methods are proposed to calculate EUR. The US Geological Survey has proposed a method of calculating EURs for wells in continuous-type plays, including shale gas plays. The EUR distribution of existing wells is employed as a guide for potential wells in areas of undiscovered resources. Decline curve analysis is also used to obtain the EUR.

With the existing estimation models, it is difficult to precisely evaluate and describe the factors affecting oil recovery for shale gas, due to the complex variation of geological conditions. Although raw data have been accumulated over the years, the challenge is often to marshal and interpret an overwhelming amount of raw data to discover the relationships between reservoir properties and oil production.

To achieve this goal, a different method is applied in this paper to solve the problem. We propose geostatistical methods to apply to large records from shale gas well to find correlations between the reservoir properties and oil production. The geostatistical method includes three steps, which are listed in the following:
  1. 1.

    Determine a set of reservoir attributes to make description of the reservoir features through logging data analysis. Other than ordinary parameters, such as porosity, permeability, and thickness, three new attributes—mud rocks content, organic carbon content, and maturity index—are discussed;

  2. 2.

    The fuzzy ranking method is employed to prioritize the relevance between the identified reservoir attributes and the EUR;

  3. 3.

    The geostatistical method was used to prioritize correlation between reservoir attributes variables and the EUR.


145.2 The Geostatistical Approach

In this section, we propose an integrated geostatistical approach for shale gas. The approach is explained by three steps, i.e., data preparation, variable ranking, and spatial analysis.

145.2.1 Manipulating and Organizing Data

Manipulating and organizing data is important for successful spacial analysis. It includes the extraction and calculation of parameters that describe reservoir properties and well production performance. A set of reservoir properties are established to describe reservoir characteristics through a log data analysis.

The basic log analysis includes the inferences for porosity, permeability, and gas saturation. Porosity was determined from combination analysis of sonic, density, and neutron logs. Permeability values were calculated using the porosity values, and mineral compositions were determined from well logs (including natural gamma ray and uranium gamma ray).

In addition, we also proposed three extra properties to reflect the production capacity of the reservoir. The three parameters are mudrock content, organic carbon content, and thermal maturity index [3].

The mineral compositions of shale gas are complex. Analysis of the mineral content is crucially important. The mudrock content is a very important index, in which the lateral sealing of fault can be judged. The production capacity of shale gas relied mostly on the artificial or natural fracture. Hence, the mudrock content is proposed to reflect the production capacity. Elemental capture spectroscopy (ECS) was used to identify the mudrock contents.

The organic carbon content can be calculated by using Eq. (145.1):
$$ V_{\text{TOC}} = 20.97{\text{e}}^{{\left( { - 14.05\rho_{\text{b}} } \right)}} $$
where \( V_{\text{TOC}} \) is the volume of TOC content, %; \( \rho_{\text{b}} \) is the value of density, \( \text{g}/{\text{m}}^{ 3} \).

The maturity index is an important index of the hydrocarbon-generating potential of source rocks of gas. Zhang [4] introduced an equation using neutron, density, and resistivity log. This equation is still in use nowadays.

145.2.2 Variable Ranking

Fuzzy ranking as a ranking tool is used to select the best correlating parameters. Some variables have greater influences on the EUR, while others have little or even no impact on the EUR. We use fuzzy curves to identify significant variables. To illustrate the fuzzy ranking method, an N data point array listed in Table 145.1 is envisioned. Our aim is to begin with the data in Table 145.1 and generate a significant analytical correlation between the inputs variables and the output variable. The use of fuzzy curves to prioritize important input is introduced in Zou [5]. Since this method is not widely known, it was reviewed here. Suppose the data in Table 145.1 represented correlations between N possible inputs variables \( {{x}}_{1} ,\,{{x}}_{2} , \ldots ,\,{{x}}_{M} \) and one output variable z. Fuzzy curves are generated by the following three procedures:
Table 145.1.

Inputs \( x_{1} ,x_{2} , \ldots,\, x_{N} \) and the output y table


\( x_{1} \)

\( x_{2} \)

\( x_{M} \)



\( x_{1,1} \)

\( x_{2,1} \)

\( x_{M,1} \)

\( z \)


\( x_{1,2} \)

\( x_{2,2} \)

\( x_{M,2} \)

\( z_{2} \)


\( x_{1,N } \)

\( x_{2,N} \)

\( x_{M,N} \)

\( z_{N} \)

  1. 1.

    Suppose the input candidate variables (the reservoir properties selected) were denoted by \( x_{1} ,\,x_{2} , \ldots ,\,x_{M} \). For M wells, each variable \( x_{i} \) had M data points, \( \left( {x_{ik} ,\,k = 1,2, \ldots ,\,N} \right) \). The output (EUR) was denoted by y, and \( \left( {z_{k} ,\,k = 1,2, \ldots ,\,N} \right) \) denoted the EUR of the kth well.

  2. 2.
    For each data point \( \left( {x_{i,k} ,\,z_{k} } \right) \) in each \( x_{i} - z \) space, we create a fuzzy membership function:
    $$ \mu_{i,k} \left( {x_{i} } \right) = { \exp }\left( { - \left( {\frac{{x_{i,k} - x_{i} }}{b}} \right)^{2} } \right)\quad k = 1,2,3, \ldots ,\,N, $$
where b represents a factor for controlling the size of the local neighborhood.
  1. 3.
    These fuzzy membership functions are defuzzified to generate a fuzzy curve \( c_{i} \) for each input variable \( x_{i} \) using
    $$ c_{i} \left( {x_{i} } \right) = \frac{{\sum\nolimits_{k = 1}^{N} {z_{k} \times \mu_{i,k} \left( {x_{i} } \right)} }}{{\sum\nolimits_{k = 1}^{N} {\mu_{i,k} \left( {x_{i} } \right)} }} $$
  2. 4.
    Finally, the mean square error
    $$ {\text{MSE}}_{{c_{i} }} = \frac{1}{N}\sum\limits_{k = 1}^{N} {\left( {c_{i} \left( {x_{i,k} } \right) - z_{k} } \right)^{2} } $$

between each fuzzy curve \( c_{i} \) and the primary records was used to select important input variables. The large \( {\text{MSE}}_{c} \) indicates that the fuzzy curve c represented the output with respect to the input poorly; in other words, the fuzzy curve c cannot act as an optimum fitting line of the input variable (x, z). For instance, if there is a thoroughly random correlation between the input and the output, then the fuzzy curve is a straight line, and the \( {\text{MSE}}_{c} \) is large. If the \( {\text{MSE}}_{c} \) is small, then we evaluate the correlation to be more important. Hence, we calculated the fuzzy curves \( c_{i} \) for all input variables \( x_{i} , \) and also the mean square error \( {\text{MSE}}_{c} \) was calculated for each fuzzy curve. The input variables can be ranked according to the MSE size, and these variables were rearranged in order. The input variables with the smallest \( {\text{MSE}}_{c} \) are most significant, and the input variables with the largest \( {\text{MSE}}_{c} \) are least significant.

145.2.3 Spatial Modeling

Spatial analysis plays an important role in quantifying geographic variation patterns. In this study, the results of fuzzy ranking were used to fuse the six parameters into a confidence map. It is commonly used in disease surveillance, spatial epidemiology, population genetics, landscape ecology, crime analysis, and many other fields, but the underlying principles are the same. With the result from fuzzy ranking, the confidence map is created by following two steps:
  1. 1.

    Let \( I = \{ I_{1} , \ldots ,I_{N} \} \) denoted the importance index of the inputs \( x_{1} ,x_{2} , \ldots ,x_{N} \) to the output y, and \( L = \{ L_{1} , \ldots ,L_{N} \} \) denoted the kriging interpolation map of the inputs \( x_{1} ,x_{2} , \ldots ,x_{N} \).

  2. 2.
    The confidence map was created by
    $$ L = \sum\limits_{i = 1}^{N} {w(I_{i} )L_{i} } $$

where \( \sum\nolimits_{i = 1}^{N} {w(I_{i} ) = 1}. \)

145.3 Case Study

In this study, data from shale gas wells in the Barnett shale area were collected from IHS data, as shown in Fig. 145.1. However, accounting for the lack of availability of other datasets for the area, only the relationships between reservoir properties and EURs were studied as a realization of the approach.

The Barnett Shale is a hydrocarbon-producing geological formation of great economic significance to Texas. It consists of sedimentary rocks, and the productive part of the formation is estimated to stretch from the city of Dallas west and south, covering 5000 square miles (13,000 km2) and at least 18 counties (Fig. 145.1).
Fig. 145.1.

Location of the study area

By 2012, the study area had more than 6000 wells. The wells for this study were selected by the constraint that the conventional logs of the wells are available. According to this constraint, 1346 wells were selected.

In the variable ranking step, the fuzzy curves are plotted and the MSE is calculated. Taking the relationship between mean porosity and EUR for example, it can be seen that the cross-plots indicated little conventional correlation. Then, we constructed the fuzzy curve which showed as declining curve in Fig. 145.2. From this curve, the correlation between mean porosity and EUR can be seen. The fuzzy curves of other variables are also constructed. The MSE result for each variable was listed in Table 145.2.
Fig. 145.2.

Fuzzy curve showed the relationship between the mean porosity and the EUR abundance

Table 145.2.

MSE values of the six variables





Porosity (%)



Permeability (%)



Thickness (m)



Mudrock content (%)



TOC (%)



Maturity index (%)


With the significance of the six variables identified by the fuzzy curves, kriging interpolation maps are constructed (Fig. 145.3), and the confidence map was calculated and constructed (Fig. 145.5).
Fig. 145.3.

Kriging interpolation map of thickness

Fig. 145.4.

Kriging interpolation map of EUR

The EUR kriging interpolation maps are constructed for comparison. From the confidence map (Fig. 145.5) and the EUR map (Fig. 145.4), it can be seen that the EUR performance of wells in the area could be described and predicted and the red area indicated good confidence of exploration. In the west of this area, the wells are not included in this study; hence, the approach showed high confidence in this area.
Fig. 145.5.

Confidence map of EUR prediction

145.4 Conclusion

In this paper, we analyzed a set of reservoir properties that are identified to describe reservoir characteristics, which included six variables. The importance of the identified reservoir properties in terms of EUR is ranked by the fuzzy ranking method. The result was Porosity > Permeability > TOC > Mudrock content > Thickness.

With this ranked result, the confidence map is constructed. The result shows that the EUR performance of wells in the area could be described and predicted by using the found quantitative relations. The confidence map performs well in the area where the wells of this study located, but in the no well area, optimistic prediction is given and showed the weakness of this approach.


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Copyright information

© Springer Nature Singapore Pte Ltd. 2019

Authors and Affiliations

  1. 1.Research Institute of Petroleum, Exploration and DevelopmentBeijingChina

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