Gob gas ventholes (GGVs) are used to control methane inflows into a longwall mining operation by capturing the gas within the overlying fractured strata before it enters the work environment. Using geostatistical co-simulation techniques, this paper maps the parameters of their rate decline behaviors across the study area, a longwall mine in the Northern Appalachian basin. Geostatistical gas-in-place (GIP) simulations were performed, using data from 64 exploration boreholes, and GIP data were mapped within the fractured zone of the study area. In addition, methane flowrates monitored from 10 GGVs were analyzed using decline curve analyses (DCA) techniques to determine parameters of decline rates. Surface elevation showed the most influence on methane production from GGVs and thus was used to investigate its relation with DCA parameters using correlation techniques on normal-scored data. Geostatistical analysis was pursued using sequential Gaussian co-simulation with surface elevation as the secondary variable and with DCA parameters as the primary variables. The primary DCA variables were effective percentage decline rate, rate at production start, rate at the beginning of forecast period, and production end duration. Co-simulation results were presented to visualize decline parameters at an area-wide scale. Wells located at lower elevations, i.e., at the bottom of valleys, tend to perform better in terms of their rate declines compared to those at higher elevations. These results were used to calculate drainage radii of GGVs using GIP realizations. The calculated drainage radii are close to ones predicted by pressure transient tests.

Drilling gob gas ventholes (GGVs) in longwall mining panels is a common technique to control methane emissions, allowing for the capture of methane within the overlying fractured strata before it enters the work environment during mining. The usual practice is to drill the GGVs prior to mining and locate a slotted casing in the zone that is expected to fracture (fractured zone). As mining advances under the venthole, the strata that surround the well deform and establish preferential pathways for the released methane, mostly from the coal seams within the fractured zone, to flow towards the ventholes [

GGVs are equipped with exhausters on the surface to provide negative pressure to produce methane from highly permeable fractured zones with a rate and concentration depending on various additional factors besides permeability [

It is difficult to predict production performance of GGVs due to the involvement of multiple factors [

Multiple factors studied in [

Despite the improvements for understanding the effects of various factors on GGV production and for predicting GGV performance, there are GGVs that perform much better or worse than expected in terms of methane production rate and production longevity. Although these unexpected production behaviors may be due to borehole stability issues, as mentioned before, they can also be related to spatial location of the borehole and how it interacts with other important production-influencing factors at that particular position. In other words, if there is a spatial correlation or stochastic dependency between borehole location, its rate transient, and other potentially influencing factors, the analyses should involve the geographical location of the boreholes, necessitating geostatistical methods.

Geostatistical methods, some of which are described in detail in [

The aim of this paper is to explore the possibility of modeling the attributes of decline curve analyses (DCA) conducted on gob gas ventholes by taking into account borehole locations and potential correlations between surface elevations at the wellheads. Geostatistical stochastic co-simulation methods were used to map the distribution of decline curve attributes. In addition, cell-based DCA parameters were interpreted with the GIP in the fractured zone to estimate radii of drainage area of GGVs.

The longwall mining site studied in this paper is in the Pittsburgh coal, Monongahela Group, southwestern Pennsylvania. The Monongahela Group includes sandstone, siltstone, shale and commercial coal beds and occurs from the base of the Pittsburgh coal bed to the base of the Waynesburg coal bed. Thickness within the general study area ranges from 270 to 400 ft. The Pittsburgh coal seam is unusually continuous and covers more than 5000 square miles [

Mining the Pittsburgh seam creates a gas emission zone that extends from the Pittsburgh Rider to Waynesburg coal beds (

The GGVs shown in red in

In southwest Pennsylvania, the topography consists of frequent hills and valleys, which control underground fracture networks, flow of groundwater, and the presence of gas. Fractures are usually within the valleys and are generally stress-relief fractures that were generated during erosional events [

Wyrick and Borchers [

Wells at higher elevations, and thus with greater overburden thickness for a nearly flat coal bed such as the Pittsburgh seam, usually cause lower hydraulic conductivities and potentially less effective GGVs as opposed to shallow overburden wells. Thus, less overburden and lower surface elevations correlate better with GGV production. These observations and monitoring results are in agreement with

Decline curve analysis is a rate transient test procedure used for analyzing declining production rates and forecasting future performance of wells. In this paper, Fekete’s rate transient analysis (RTA) [

In decline curve analysis, it is implicitly assumed that the factors causing the historical decline continue unchanged during the forecast period. These factors include both reservoir conditions and operating conditions of the borehole. As long as these conditions do not change, the trend in decline can be analyzed and extrapolated to forecast future well performance [

An example of traditional DCA with fitted data of GGV-1 shown in

The relationship of various parameters in exponential decline analysis are given below for decline coefficient and cumulative production between two time intervals, respectively, from the acronyms used in

Cumulative productions at different production times can be obtained by changing the FC to the desired time in

Ten observations for each DCA attribute are too few to establish a meaningful histogram for assessing the distributions of the DCA parameters across the study area and for selecting which ones could be used as primary variables.

The mining district modeled in this work (

Surface elevation of the study area was obtained from U.S. Geological Survey seamless data warehouse [

The data used in geostatistical modeling of gas-in-place (GIP) were obtained from 63 vertical exploration boreholes drilled over the mining area shown in

GIP simulations, whose modeling and computational procedure was developed and documented in detail for a different field in an earlier paper [

For sequential Gaussian simulation and co-simulation techniques to be applicable, the data should follow a Gaussian (normal) distribution. Therefore, the surface elevation and attributes of coals (depth and thickness) were transformed to normal scores by targeting a Gaussian distribution with a mean of

Sequential Gaussian simulation (SGSIM) is a semivariogram-based simulation technique that generates simulated results, or so-called realizations, of the attribute in question by extracting the spatial patterns from the input data and semivariograms. Realizations can be seen as numerical models of possible distributions of the simulated property in space. In practice, these realizations take the form of a finite number of simulated maps equally probable to represent the unknown true map. Therefore, each grid in each of these realizations, or simulated maps, generates a distribution of the particular attribute. These distributions can be used to analyze the data statistically for variances and to evaluate the uncertainty associated with various values in a probabilistic fashion. It should be mentioned that ordinary kriging and co-kriging could have been used instead of simulation for spatial modeling. However, kriging causes severe smoothing effect on the results and also simulation is more suited to evaluate uncertainty [

In this work, 100 realizations for each attribute of interest for GIP calculations were generated. For verification of the statistical accuracy of these realizations, the results of sequential Gaussian simulations of modeled attributes (thickness and overburden depth) were compared with the original data before proceeding with calculations of GIP and the associated uncertainties. These comparisons required

After the representativeness of these realizations for the raw attribute data were checked using

The simulation results distributed in each of the realizations can be used for statistical evaluations of uncertainty using the histograms. For instance, the values of GIP for the fractured zone can be calculated at 5%, 50%, and 95% quantiles (Q5, Q50, Q95). These quantiles represent the ranking of the estimated attribute, where each estimated value has the 5th, 50th, and 95th place in ranking analyses. In other words, the estimated values of 5%, 50%, and 95% have a probability to be lower than the actual unknown value. Among these, Q50 represent the median of the possible population distribution for the calculated variables.

The cell values within each of the 100 realizations and percentile analyses were conducted to extract the realizations that correspond to Q5, Q50, and Q95 of fractured zone GIP. The GIP results shows that cumulative GIP in this area ranges between 3550 MMscf (3.55 Bscf) and 4150 MMscf (4.15 Bscf). These values are important as they state that, assuming GGVs produce methane only from the GIP in the fractured zone, the cumulative production from all boreholes combined cannot exceed 4.15 Bscf.

In this paper, the potential of geostatistics to model decline curve attributes of a limited number of GGVs is sought by utilizing the location of wells and by considering the correlation potential of DCA attributes with surface elevation of wells. For this purpose, surface elevation data shown in

The next step was to identify which DCA parameters could be selected as primary variables of co-simulations. In order to determine these variables, a correlation analysis between all possible DCA parameters and surface elevation was conducted using the normal scores of all attributes. The results of this analysis are given in

Different implementations of sequential simulations in SGeMS can be used for different purposes [

Sequential Gaussian co-simulation allows for simulation of a Gaussian variable while accounting for the secondary information to which it correlates [

MM1 considers the following Markov-type screening hypothesis during simulations: the dependence of the secondary variable on the primary is limited to the co-located primary variable. The cross-covariance is then proportional to the auto-covariance of the primary variable [_{12} is the cross covariance between the two variables, and _{11} is the covariance of primary variable. Thus, solving the co-kriging algorithm with MM1 requires the knowledge of correlation between primary and secondary variables, as well as the semivariogram(s) of the primary variable(s). These requirements, as implemented in the face of limited amount of data for primary variables, were addressed by determining the range of correlation coefficients instead of using a single value. For this purpose, a Monte Carlo (MC) routine using multi-normal correlation based on Cholesky decomposition was implemented. The routine generated 1000 normal-score data for each of the primary DCA variables and the surface elevation by using their normal-score means and standard deviations. This procedure, implemented for each of the four primary-secondary variable pairs selected, generated a range of correlation coefficients that were normally distributed around the 10-data value. These 1000 values were reduced to 100 by random sampling and were used for running 100 realizations by varying the correlation coefficient in each co-simulation run. The correlation coefficient distributions for each primary-secondary variable pair are given in

Semivariogram of primary variable based on limited data locations was approximated by the semivariogram of the secondary variable in normal-score space as all attributes in normal-score space have sills of 1, regardless of the attribute being modeled. Therefore, the sill of the semivariogram for surface elevation is the same as the sill of the “unknown” semivariogram of the primary variable. This is especially true if the primary and the secondary variables are correlated. This implies that the semivariogram ranges and nuggets must be quite similar too. Of course, it can be argued that correlation coefficients based on 10 wells are in the order of ~0.7 and thus nugget and ranges may not be exactly the same. This argument is partly taken care of by generating a range of correlation coefficients around the mean that will reflect on results and is also supported by the influence of surface elevation on production and decline characteristics discussed in [

Co-simulations using the MM1 approach were performed to generate 100 realizations for each of the primary variables. The realizations of DCA parameters co-simulated with surface elevation shown in

The local probability maps were generated based on 100 values in each of the 5000 cells and, comparing these with the surface elevation map given in

The probability maps prove two important observations with regard to the decline properties of GGVs: (a) GGVs drilled at or close to hilltops have higher rates of decline and are shorter lived and (b) wells drilled at hilltops start producing methane at lower rates compared to their counterparts drilled in the valleys. They also have higher rates when the GGVs eventually enter the forecast period, which means that even though these GGVs may have rates sufficient to sustain production, they can cease production due to other problems that high overburden can create such as lower fracture permeabilities and larger strains on the wellbore that may promote casing failure. In fact, [

The histograms of co-simulation results for PD, END, QFC and QP were used to determine the realizations at Q5, median (Q50), and Q95 of simulated attributes using ranking analyses. Distribution of cell values of these realizations with corresponding quantiles are shown in

The spatial DCA data given as maps not only can be used to generate synthetic decline curve analysis test data for selected locations but can also be used to predict performance of any GGV that can be drilled at any random location on the terrain by use of decline functions. As an example of this application, the virtual GGVs shown in

GGVs, as with other boreholes in any reservoir, should be drilled with a well-planning protocol to determine where and how many wellbores should be drilled in a given region by considering surface and reservoir conditions. This includes paying attention to any possible interference between GGVs. The results presented in the previous section can be integrated with GIP maps (

In order to demonstrate the drainage radius estimation for GGVs, the same virtual GGVs shown in

Estimation of the drainage radii of GGVs starts with evaluating cumulative methane production of GGVs at any given time. For this purpose, cumulative production data for 30 days and 240 days at 50% quantile (Q50) given in

Radii values estimated in this section compare favorably with the ones predicted from pressure transient tests. Karacan [

The differences in production behaviors and rate transient (decline) behaviors of gob gas ventholes, along with their radii of investigations, can be attributed to various factors as discussed previously. Surface elevation of drill locations can have significant correlations with rate transient behaviors of these wells. Analyses reveal that the better performing wells are usually at lower elevations (and lower overburden depths) compared to poorly performing ones. Therefore, locations of the GGVs should be selected with care. This can be attributed to higher fracture permeability and shorter casing length for the exhauster to pull the methane, as opposed to tighter fractures below hilltops and longer casings. Therefore, if the GGVs have to be drilled at hilltops, it is advisable to drill them at closer spacings due to the smaller radius of drainage that was proven in this study and in earlier studies. The drainage radii can also be estimated using DCA and GIP predictions, which will give better design criteria when considered together. Along these lines, geostatistical simulation and co-simulation techniques can be used as advanced tools as part of the planning and to assess uncertainty in making the decisions related to drilling locations and prediction of rate declines of the GGVs.

Here we have simulated all four primary variables by correlating them to the same secondary variable. A challenge for the future that should yield additional improvements would be the simultaneous simulation of all five attributes. In addition, a rock fracture network model of gob and geostatistical implementation of fractures to compare and improve accuracy of the findings of simulation of DCA parameters will be highly valuable. Such models can show the paths of fluid flow through rock fractures [

In this paper, geostatistical analysis was pursued using sequential Gaussian co-simulation to characterize decline curve analyses (DCA) of gob gas ventholes in combination with GIP in fractured zone and surface elevation. Surface elevation was selected as the secondary variable, while various attributes of DCA were treated as primary variables. GIP was also simulated with sequential Gaussian technique, used in conjunction with decline curve results to determine the drainage radii and production quantities.

The results obtained from this study evaluated important attributes of methane capture from mining environments, such as gob gas venthole production rates, decline rates, production ending durations, and cumulative gas productions. Employing sequential Gaussian simulation and co-simulation enabled not only the estimation of important parameters of DCA that have correlations with surface elevations but also the assessment of their uncertainty and values at certain quantiles of statistical evaluation.

This study showed that GGVs can have very high decline rates for a majority of the modeled mining district. In addition, these high decline rates were associated with lower production rates at the start of production and consequently less cumulative production. Geostatistical simulation results were used to calculate drainage radii of GGVs using GIP realizations. This work showed that the calculated drainage radii were close to ones predicted by pressure transient tests. Therefore, geostatistical analyses along with co-simulations of DCA and GIP and surface elevation data could be used to estimate the rate transient parameters and drainage radii of the wellbores, thus aiding designers in both placement and spacing of the GGVs.

Although the general belief in the coal region of the Northern Appalachian Basin is that gas production is improved by drilling GGVs at the margins of the tailgate in the longwall panel, this study showed that surface elevation might be an important consideration as well. Therefore, it is important to select the locations of the GGVs with care. In general, wells located at lower elevations, i.e., at the bottom of valleys, tended to perform better in terms of their rate declines compared to those at higher elevations. Thus, it is advisable to drill GGVs with closer spacing at hilltops due to their smaller radii of investigations.

In conclusion, geostatistical simulation and co-simulation techniques can be used as advanced tools as part of the planning process and to assess uncertainty in making decisions related to drilling locations and prediction of rate declines of the GGVs.

Conversion table (English to SI units)

1 ft = 0.3048 m

1 ft^{2} = 22.957 × 10^{−6} acre

1 MMscf = 28316 m^{3}

1 scfm = 0.0004719 m^{3}/s

Disclaimer: The findings and conclusions in this paper are those of the authors and do not necessarily represent the views of the National Institute for Occupational Safety and Health. Mention of any company name, product, or software does not constitute endorsed by NIOSH or USGS.

Supplementary data associated with this article can be found in the online version at

We are grateful for the reviews as part of the internal approval process by our institutions: Gerrit Goodman on the NIOSH side, and Leslie F. Ruppert (USGS) and Michael Ed. Hohn (West Virginia Geological and Economic Survey) for the U.S. Geological Survey. We also thank Chris Garrity (U.S. Geological Survey) for providing the high-resolution surface elevation data.

Schematic representation of stratigraphy and completion of the gob gas ventholes (GGVs), as well as panels and locations of the GGVs, in the study area. The dimensions of the area shown in this figure are 8624 ft in the

Traditional DCS with exponential decline curve (red line) of methane production data (green circles) from GGV-1 (

Schematic representation of rate parameters and important times in exponential decline analysis. In this plot, QP, initial production rate; TP, production start time; FC, forecast start time; END, end of the potential production life of the well; PD, percentage decline (constant decline rate); QFC, rate at forecast start; CUM.P, cumulative production till forecast start; RR, recoverable reserves; EUR, expected ultimate recovery; Qab, abandonment rate.

Surface elevation map at 175 ft × 176 ft resolution after up scaling the high resolution map at 30 ft × 30 ft resolution.

Histograms of the surface elevation data shown in

Spatial locations of the exploration boreholes drilled over the area shown in

Omni-directional experimental semivariograms of normal scores of Sewickley seam depth (A) and surface elevation (B) (red crosses), and the spherical analytical semivariograms modeling them (black line). (For interpretation of the references to color in this figure caption, the reader is referred to the web version of this article.)

Distributions of fractured zone GIP in realizations corresponding to quantiles Q5, Q50 and Q95 (Real stands for realization in the legend).

Q5, Q50, and Q95 realizations of GIP in the fractured zone of the study area shown in

Range of correlation coefficients generated for each of the primary-secondary variable pairs to be used in co-simulations.

Maps that show the local probabilities for DCA parameters for values above their medians. The red line is the 1100-ft surface elevation contour. (For interpretation of the references to color in this figure caption, the reader is referred to the web version of this article.)

Histograms of cell values in realizations corresponding to Q5, Q50, and Q95 of DCA parameters (real stands for realization in the legends).

Q50 maps of percent decline (PD), production end time (END), methane rate at forecast start (QFC), and methane rate at production start (QP). The red line is the 1100-ft contour of surface elevation. (For interpretation of the references to color in this figure caption, the reader is referred to the web version of this article.)

Virtual GGV locations to predict their performances.

Cumulative production data (Q50) calculated using DCA maps and

GIP amounts determined from Q5, Q50 and Q95 realizations for GGV locations shown in

Drainage radius predictions as a function surface elevation using DCA and GIP results for GGVs drilled at virtual sample locations.

Descriptive statistics of the DCA results of methane production data of GGVs.

Variable | # of observations | Min. | Max. | Mean | Std. |
---|---|---|---|---|---|

PD (%/year) | 10 | 47.420 | 100.00 | 77.843 | 19.311 |

FC (days) | 10 | 23.000 | 348.300 | 213.300 | 130.426 |

QFC (MMscf/day) | 10 | 0.002 | 0.217 | 0.106 | 0.069 |

QP (MMscf/day) | 10 | 0.002 | 0.336 | 0.162 | 0.096 |

END (days) | 10 | 53.000 | 2517.000 | 793.350 | 772.359 |

CUM.P (Bscf) | 10 | 0.003 | 0.102 | 0.043 | 0.030 |

EUR (Bscf) | 10 | 0.005 | 0.172 | 0.068 | 0.051 |

RR (Bscf) | 10 | 0.000 | 0.095 | 0.025 | 0.032 |

Univariate statistical parameters of depth and thickness encountered by the exploration boreholes for Sewickley, Uniontown and Waynesburg coal seams.

Depth (ft) | Sewickley | Uniontown | Waynesburg |
---|---|---|---|

# of data | 62 | 30 | 63 |

Mean | 580.73 | 405.97 | 346.14 |

St. dev. | 130.62 | 139.44 | 127.47 |

Variance | 17,061.35 | 19,443.67 | 16,247.78 |

Minimum | 341.73 | 192.70 | 103.60 |

Maximum | 803.79 | 641.00 | 569.15 |

Thickness (ft) | |||

# of data | 62 | 30 | 63 |

Mean | 3.50 | 0.27 | 5.37 |

St. Dev. | 1.994 | 0.088 | 0.585 |

Variance | 3.979 | 0.008 | 0.343 |

Minimum | 0.33 | 0.10 | 3.60 |

Maximum | 6.90 | 0.50 | 6.99 |

Summary of parameters that describe analytical semivariograms for depth and thickness attributes of Sewickley, Uniontown and Waynesburg coal seams, which were used to calculate GIP, and surface elevation. All semivariograms were analyzed using normal-score data and described with one-nested structure (model).

Depth (ft) | Sewickley (SWC) | Uniontown coal (UNC) | Waynesburg (WBC) | Exploration boreholes |
---|---|---|---|---|

Model | Spherical | Exponential | Exponential | |

Nugget | 0.1 | 0.1 | 0.1 | |

Sill | 0.8 | 0.7 | 0.8 | |

Maximum range | 3528 | 5400 | 4080 | |

Medium range | 3384 | 5100 | 4020 | |

Minimum range | 3168 | 4950 | 3780 | |

Thickness (ft) | Sewickley (SWC) | Uniontown coal (UNC) | Waynesburg (WBC) | Surface elevation (ft) |

Model | Spherical | Gaussian | Spherical | Spherical |

Nugget | 0.1 | 0.07 | 0.3 | 0.1 |

Sill | 0.5 | 0.95 | 0.6 | 0.9 |

Maximum range | 5580 | 3850 | 3300 | 3872 |

Medium range | 5580 | 3700 | 3150 | 3630 |

Minimum range | 5580 | 3500 | 3075 | 3509 |

Basic statistics of the histograms shown in

Quantile | # of | Minimum | Maximum | Mean | Std. |
---|---|---|---|---|---|

GIP- Q5 | 5000 | 0.242 | 1.433 | 0.728 | 0.268 |

GIP- Q50 | 5000 | 0.255 | 1.474 | 0.761 | 0.282 |

GIP- Q95 | 5000 | 0.253 | 1.404 | 0.790 | 0.274 |

Correlations between normal-score values of the DCA parameters with surface elevation data (NS refers to normal-score values). Description of variables is in the caption of

Variable* | ELEV-NS | PD-NS | EUR-NS | END-NS | FC-NS | CUM.P-NS | RR-NS | QFC-NS | QP-NS |
---|---|---|---|---|---|---|---|---|---|

ELEV-NS | |||||||||

PD-NS | 0.581 | ||||||||

EUR-NS | −0.443 | −0.936 | |||||||

END-NS | −0.710 | −0.626 | 0.612 | ||||||

FC-NS | −0.226 | −0.521 | 0.696 | 0.754 | |||||

CUM.P-NS | −0.443 | −0.936 | 0.612 | 0.696 | |||||

RR-NS | −0.553 | −0.964 | 0.913 | 0.499 | 0.420 | 0.913 | |||

QFC-NS | −0.466 | −0.758 | 0.771 | 0.200 | 0.242 | 0.771 | 0.809 | ||

QP-NS | −0.449 | −0.820 | 0.868 | 0.362 | 0.474 | 0.868 | 0.884 | 0.929 |

Summary statistics of Q5, Q50, and Q95 realizations for DCA parameters. QP: initial production rate; END: end of the potential production life of the well; PD: percentage decline (constant decline rate); QFC: rate at forecast start (Real. stands for realization).

Variable/realization/quantile | # of cells | Min. | Max. | Mean | Std. Dev. |
---|---|---|---|---|---|

PD-Real96-Q5 (%/year) | 5000 | 59.66 | 94.07 | 77.62 | 5.48 |

PD-Real32-Q50 (%/year) | 5000 | 59.66 | 94.07 | 78.40 | 5.84 |

PD-Real63-Q95 (%/year) | 5000 | 59.66 | 94.07 | 79.03 | 5.90 |

END-Real90-Q5 (days) | 5000 | 132.72 | 1416.09 | 730.51 | 215.47 |

END-Real6-Q50 (days) | 5000 | 132.72 | 1416.09 | 759.38 | 212.32 |

END-Real18-Q95 (days) | 5000 | 132.90 | 1416.09 | 775.52 | 216.95 |

QFC-Real45-Q5 (MMscf/day) | 5000 | 0.007 | 0.184 | 0.096 | 0.032 |

QFC-Real21-Q50 (MMscf/day) | 5000 | 0.007 | 0.184 | 0.103 | 0.026 |

QFC-Real1-Q95 (MMscf/day) | 5000 | 0.007 | 0.184 | 0.109 | 0.028 |

QP-Real38-Q5 (MMscf/day) | 5000 | 0.075 | 0.260 | 0.153 | 0.027 |

QP-Real20-Q50 (MMscf/day) | 5000 | 0.075 | 0.260 | 0.158 | 0.023 |

QP-Real34-Q95 (MMscf/day) | 5000 | 0.075 | 0.260 | 0.162 | 0.027 |