# Production Patterns of Eagle Ford Shale Gas: Decline Curve Analysis Using 1084 Wells

^{1}

^{2}

^{*}

## Abstract

**:**

## 1. Introduction

## 2. Methodology

#### 2.1. Decline Curve Models

#### 2.2. Goodness of Fit

^{2}) and the normalized root mean square error (N-RMSE) are used as measures for the goodness of fit [21,22]. R

^{2}ranges from 0 to 1, and the goodness of fit will become better closer to 1. N-RMSE also ranges from 0 to 1, but here the goodness of fit will become weaker closer to 1. The boundaries that are introduced to exclude the poorest fits are R

^{2}≥ 0.8 and N-RMSE ≤ 0.2 at the same time.

#### 2.3. Data

## 3. Results

#### 3.1. Aggregate Decline Curves

^{2}and N-RMSE. For the Hyperbolic model, the R

^{2}value is 0.9987 and the N-RMSE value is 0.0073. In comparison, the Stretched Exponential model has an R

^{2}value of 0.9985 and an N-RMSE value of 0.0080. The parameter values of the curves are also shown in the text box in Figure 5.

#### 3.2. Individual Well Decline Curves

#### 3.2.1. Hyperbolic Decline Curve

#### 3.2.2. Stretched Exponential Decline Curve

#### 3.2.3. Summary of Decline Curves

^{2}and for about 76% of all wells using N-RMSE. However, the result maybe only represents the Eagle Ford case. Longer data series and larger databases are needed to find out which model is better on a greater scale.

#### 3.3. Initial Production and Decline Rate

#### 3.3.1. Initial Production

#### 3.3.2. Decline Rates in Different Time Phases

#### 3.4. Estimated Cumulative Production

## 4. Conclusions

^{2}and N-RMSE), both the Hyperbolic model and the Stretched Exponential model fits well to aggregated well data and to individual wells. The Hyperbolic model is slightly better than the Stretched Exponential model based on the Eagle Ford case in this study, there are about 37% of the β-parameter values of Hyperbolic larger than 1. However, further research is needed to find out which model is better on a greater scale. On average, shale gas wells were estimated to yield an URR of 1.41 to 2.03 Bcf based on the two decline curve models when 20 years was set as well life span, which is in line with some other studies. As mentioned in the methodology Section 2.1, the traditional Arps model (Hyperbolic) was supposed to be used only for describing and predicting production in conventional oil and gas wells. While this study indicates that it is still effective for a shale gas well if the life span is set reasonably (20 years, for example). Deeper analysis of the economic aspects, such as the cut-off-rate for continued production and further research with more accuracy, are still needed to be able to estimate the future production and resources.

## Acknowledgments

## Author Contributions

## Conflicts of Interest

## Abbreviations

SE | Stretched Exponential |

Tcf | Trillion cubic feet |

Bcf | Billion cubic feet |

Mcf | Mil cubic feet = Thousand cubic feet |

URR | Ultimate recoverable resource |

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**Figure 1.**US natural gas production by sources, 1990–2040; Source: EIA 2014 [7].

**Figure 5.**The Hyperbolic and the Stretched Exponential decline curves fitted to average normalized production data on logarithmic scale. Only after 40 months do the two models start to diverge.

**Figure 6.**(

**a**) Distributions of β values. β values are on the x-axis and the probability on the y-axis, the Weibull parameters are α = 2.13, β = 1.11, γ = −0.13; (

**b**) Distributions of λ values. λ values are on the x-axis and the probability on the y-axis, the Weibull parameters are α = 1.15, β = 0.23, γ = 0.04.

**Figure 8.**Distributions for the monthly IP. Production is on the x-axis and the probability is on the y-axis; production unit is Mcf per month, the Weibull parameters are α = 2.63, β = 1.17 × 10

^{5}, γ = −5.29 × 10

^{4}.

**Figure 9.**(

**a**) Distributions for the first year decline rates. Rates are on the x-axis and the probability is on the y-axis, the Weibull parameters are α = 14.27, β = 1.68, γ = −0.93; (

**b**) Distribution for the first two years decline rate. Rates are on the x-axis and the probability is on the y-axis, the Weibull parameters are α = 8.16 × 10

^{7}, β = 6.52 × 10

^{6}, γ = −6.52 × 10

^{6}.

Properties | Hyperbolic | SE |
---|---|---|

$q(t)$ | ${q}_{0}{\left[1+\lambda \beta (t-{t}_{0})\right]}^{-1/\beta}$ | ${q}_{i}\text{exp}\left(-{D}_{i}{t}^{n}\right)$ |

$Q(t)$ | ${Q}_{0}+\frac{{q}_{0}}{\lambda (1-\beta )}\left\{1-\left[1+\lambda \beta {(t-{t}_{0})}^{1-\frac{1}{\beta}}\right]\right\}$ | ${Q}_{0}+\frac{{q}_{i}\tau}{n}\left\{\Gamma \left[\frac{1}{n}\right]-\Gamma \left[\frac{1}{n},{\left(\frac{t}{\tau}\right)}^{n}\right]\right\}$ |

URR | ${Q}_{0}+\left[{q}_{0}/\lambda (1-\beta )\right]$ | ${Q}_{0}+\frac{{q}_{i}\tau}{n}\Gamma \left[\frac{1}{n}\right]$ |

${\mathit{q}}_{\mathit{i}}$ | ${\mathit{D}}_{\mathit{i}}$ | n | |
---|---|---|---|

Mean | 138.95 | 1.39 | 0.49 |

Std. Deviation | 589.07 | 1.95 | 0.30 |

Min | 0.86 | <0.01 | 0.06 |

25% (Q_{1}) | 1.34 | 0.27 | 0.28 |

50% (Median) | 1.84 | 0.58 | 0.45 |

75% (Q_{3}) | 4.26 | 1.45 | 0.63 |

Max | 4608.88 | 8.46 | 2.78 |

**Table 3.**Average value of the first year and the first two years decline rates for new wells annually.

2010 | 2011 | 2012 | 2010–2012 | |
---|---|---|---|---|

First year | 70.58% | 70.40% | 66.76% | 68.54% |

First two years | 83.72% | 83.74% | 80.57% | 82.09% |

10-Year | 15-Year | 20-Year | 30-Year | |||
---|---|---|---|---|---|---|

Hyperbolic | Median | q(t) | 85 | 53 | 38 | 23 |

Q(t) | 1.49 | 1.61 | 1.69 | 1.80 | ||

Mean | q(t) | 68 | 43 | 31 | 19 | |

Q(t) | 1.25 | 1.35 | 1.41 | 1.50 | ||

Aggregate | q(t) | 132 | 90 | 68 | 46 | |

Q(t) | 1.40 | 1.89 | 2.03 | 2.24 | ||

SE | Median | q(t) | 41 | 15 | 7 | 2 |

Q(t) | 1.44 | 1.49 | 1.51 | 1.52 | ||

Aggregate | q(t) | 76 | 36 | 20 | 8 | |

Q(t) | 1.58 | 1.68 | 1.73 | 1.78 |

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**MDPI and ACS Style**

Guo, K.; Zhang, B.; Aleklett, K.; Höök, M.
Production Patterns of Eagle Ford Shale Gas: Decline Curve Analysis Using 1084 Wells. *Sustainability* **2016**, *8*, 973.
https://doi.org/10.3390/su8100973

**AMA Style**

Guo K, Zhang B, Aleklett K, Höök M.
Production Patterns of Eagle Ford Shale Gas: Decline Curve Analysis Using 1084 Wells. *Sustainability*. 2016; 8(10):973.
https://doi.org/10.3390/su8100973

**Chicago/Turabian Style**

Guo, Keqiang, Baosheng Zhang, Kjell Aleklett, and Mikael Höök.
2016. "Production Patterns of Eagle Ford Shale Gas: Decline Curve Analysis Using 1084 Wells" *Sustainability* 8, no. 10: 973.
https://doi.org/10.3390/su8100973