Forecasts of gas production from shale are complicated by our inability to correctly account for all of the mechanisms that affect production, and by the lack of wells with enough production history to validate models. Consequently, shale gas production forecasts are inherently uncertain. We have developed a methodology that quantifies uncertainty using minimal input data and Monte Carlo analysis of suitable rate-time decline curves. The methodology is automated in the form of a software program that calculates the distribution of Estimated Ultimate Recovery (EUR) for production of gas from unconventional gas shale. It is based on workflows for green fields (Fanchi, 2010 and 2011a) and brown fields (Fanchi, 2010 and 2011b) that use reservoir flow models to generate a distribution of recovery forecasts.

We begin by describing rate-time decline curve models that are applicable to shale gas production. The Monte Carlo based decline curve analysis (DCA) is then described and illustrated using production from two shale gas plays.

**Decline Curve Models for Unconventional Resources**

Decline curve models used here must have finite, bounded values of EUR. Not all decline curve models satisfy this criterion. For example, Arps (1945) presented the following empirical decline curve model for flow rate q as a function of time t and parameters a, n:

(1)

The Arps models are harmonic decline (n = 1), exponential decline (n = 0), and hyperbolic decline with other positive values of n. The hyperbolic model typically has n < 1 for conventional reservoir production. The Arps harmonic model (n = 1) and hyperbolic model with n > 1 are not always applicable to unconventional reservoir production forecasts because extrapolation of the decline curve can lead to unbounded values of EUR and corresponding overestimates of EUR.

The Arps exponential model does not always adequately model the decline rate of unconventional reservoir production. Valkó and Lee (2010) introduced the Stretched Exponential Decline Model (SEDM) into decline curve analysis as a generalization of the Arps exponential model. The SEDM is based on the idea that several decaying systems comprise a single decaying system (Phillips, 1996; and Johnston, 2006). If we think of production from a reservoir as a collection of decaying systems in a single decaying system, then SEDM can be viewed as a model of the decline in flow rate. The SEDM has three parameters qi, τ, n (or a, b, c):

(2)

Parameter qi is flow rate at initial time t. The Arps exponential decline model is the special case of SEDM with n = 1.

A second decline curve model is based on the logarithmic relationship between pressure and time in a radial flow system. The logarithmic decline model is referred to as the RLNT model.

**Probabilistic DCA Workflow**

Reserves estimates may be either deterministic or probabilistic (Lee, 2009). A deterministic estimate of reserves is a single best estimate of reserves based on geological, engineering, and economic data. Linear regression is used in the software to obtain a deterministic estimate of reserves.

A probabilistic estimate of reserves uses geological, engineering, and economic data to generate a range of estimates and their associated probabilities. The probabilistic estimate of reserves is obtained using the workflow outlined in Figure 1 (below). It is a Monte Carlo method because it incorporates the following procedure:

1. Define a set of input parameter distributions.

2. Generate a set of input parameter values by randomly sampling from the associated probability distributions.

3. Use the input parameter values in a deterministic model to calculate a trial result.

4. Gather the results for a set of trials.

Each step of the probabilistic decline curve analysis method in Figure 1 (below) is briefly described below.

**Step DCA1: Gather Rate-Time Data**

Acquire gas production rate as a function of time. Remove significant shut-in periods so rate-time data represents continuous production.

**Step DCA2: Select a DCA Model and Specify Input Parameter Distributions**

The number of input parameters depends on the DCA model chosen. The SEDM model requires three parameters, and the RLNT model requires two parameters. Model input parameters are determined from sampling a distribution of parameters. Parameter distributions may be either uniform or triangle distributions.

**Step DCA3: Specify Constraints**

Available rate-time production history is used to decide which DCA trials are acceptable. Every DCA model run that uses a complete set of model input parameters constitutes a trial. The results of each trial are then compared to user-specified criteria. One key criterion is the objective function. The objective function quantifies the quality of the match by comparing the difference between model rates and observed rates. Objective functions with smaller values are considered better matches than objective functions with larger values.

**Step DCA4: Generate Forecast of Performance Results**

We obtain forecasts by running the DCA model. The number of trials is specified by the analyst.

**Step DCA5: Determine Subset of Acceptable Trials**

The trials generated in Step DCA4 are compared to the criteria specified in Step DCA3. Each trial that satisfies the user-specified criteria is included in a subset of acceptable trials.

**Step DCA6: Generate Distribution of Performance Results**

The distribution of EUR values for the subset of acceptable trials is analyzed and the 10th (PC10), 50th (PC50), and 90th (PC90) percentiles are determined.

**Illustrative Applications**

The workflow in Figure 1 (below) is illustrated using rate-time date for gas production from a Woodford shale gas well, and two Barnett shale gas wells.

End of Part 1

*Part 2 of John Fanchi’s Forecasting Shale Gas Recovery Using Monte Carlo Analysis is available here.*

**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.

**References**

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.