This is part 2 of a 2-part article. Part 1 is available here.
Example 1: Woodford Shale Gas Well
Rate-time data for a Woodford shale gas well is used to illustrate the methodology. The Woodford shale is located primarily in the state of Oklahoma, USA. The rate-time data for the well covers 22 months. The DCA models are the stretched exponential decline model (SEDM) and the logarithm model (RLNT). Model input parameters are selected from a triangle distribution. The optimum value is the value calculated by the program for the linear regression case. The user specifies the range of uncertainty. Figure 2 shows a sample of the range of trials generated from a set of 1000 trials using the RLNT model.
The value of the objective function depends on the number of rate-time points and the quality of the data. Figure 3 shows the 10th, 50th and 90th percentile trials for the subset of trials obtained by imposing an objective function constraint.
Example 2: Barnett Shale Gas Well
Figure 4 shows the deterministic best fit of rate-time data for a Barnett shale gas well. The Barnett shale is located in the northern part of the state of Texas, USA. The best-fit for the RLNT model is a better match of the data than the best-fit for the SEDM model. Figure 5 shows that 10th, 50th and 90th percentile trials for the probabilistic analysis using the RLNT model. The subset of trials was constrained using the objective function.
Example 3: Barnett Shale Gas Well with Multiple Peak Rates
A shale gas well can exhibit multiple peak rates when modes of operation change. For example, the peak rate for a vertical well will not be the same as the peak rate for a lateral drilled from the vertical well. Rate-time data for a Barnett shale gas well with multiple peak rates is shown in Figure 6. The DCA model can be applied to one or more peaks. Figure 6 shows the deterministic best fit of all data for both the SEDM model and RLNT model. Key percentile results for the RLNT model applied to the entire data set are shown in Figure 7. A subset of 470 trials is used to determine percentiles using only the objective function constraint.
Suppose we apply the DCA model to the data that begins with the last (fifth) peak rate. Figure 8 shows key percentile results for the RLNT model beginning with the fifth peak rate. The figure also shows a rate forecast for key percentile trials. Figure 9 shows that the range of forecasts narrows substantially when we apply the cumulative gas production constraint in addition to the objective function constraint. In this case, we require cumulative gas production for each trial to be within 1% of the historical cumulative gas production for data beginning with the fifth peak rate. Table 1 presents a comparison of actual and model calculated cumulative gas production, and expected recovery for the cases shown in Figure 9.
We have presented a systematic methodology in the form of a software program that is designed to identify the distribution of Estimated Ultimate Recovery (EUR) for production of gas from unconventional gas shale. The methodology quantifies uncertainty using minimal input data and Monte Carlo analysis of suitable rate-time decline curves. The workflow described here is repeatable, can quantify uncertainty, and uses decline curve models that have finite EUR values for production from shale gas reservoirs.
About the Author
John R. Fanchi is holder of the Matthews Chair of Petroleum Engineering at TCU. Recent books include Energy in the 21st Century, 2nd Edition (with C.J. Fanchi, World Scientific, 2011) and Integrated Reservoir Asset Management (Elsevier, 2010). He co-edited Volume 1 of the SPE Petroleum Engineering Handbook (L.W. Lake edition, SPE, 2006). More of Fanchi's work can be found here.
Arps, J.J., 1945. Analysis of Decline Curves. Paper SPE 945228-G. Trans. AIME, Volume 160, 228-247.
Fanchi, J.R., 2010. Integrated Reservoir Asset Management. Elsevier-Gulf Professional Publishing, Burlington, Massachusetts.
Fanchi, J.R., 2011a. Flow Modeling Workflow: I. Green Fields, Journal of Petroleum Science and Engineering Volume 79, 54–57.
Fanchi, J.R., 2011b. Flow Modeling Workflow: II. Brown Fields, Journal of Petroleum Science and Engineering Volume 79, 58–63.
Johnston, D.C., 2006. Stretched Exponential Relaxation Arising from a Continuous Sum of Exponential Decays. Physical Review B 74: 184430.
Lee, W.J., 2009. Reserves in Nontraditional Reservoirs: How Can We Account for Them? SPE Economics and Management (October) 11-18.
Phillips, J.C., 1996. Stretched Exponential Relaxation in Molecular and Electronic Glasses. Reports of Progress in Physics 59, 1133 – 1207.
Valkó, P.P. and W.J. Lee, 2010. A Better Way to Forecast Production from Unconventional Gas Wells. Paper SPE 134231. Society of Petroleum Engineers, Richardson, Texas.