Have you ever wondered why everyone comes up with a slightly different EUR or reserves estimate in a given area?

PetroDE has greatly simplified EUR estimation, reserves estimation, completion evaluation, and production efficiency. Our new approach uses quantile regression to calculate statistical decline curves. We supply geoscientists and engineers with statistically valid and consistent estimates of production to then compare with geologic controls in an area of interest. An additional benefit of this method is an index of production and completion efficiency.

**Statistical Decline Curve Logic Explained**

Traditional methods for calculating decline curves require you to evaluate producing wells individually and then perform a statistical analysis for each group of wells. Another method takes a simple average on a per month basis and fits that average dataset to a curve. PetroDE can quickly and accurately analyze an area of interest while honoring *all* of the available data, saving you invaluable time. We also provide insight into the variance of performance by calculating multiple curves that illustrate the range of production performance.

PetroDE uses statistical decline curves to calculate projected production for any given set of wells. We generate four Statistical Decline Projection curves to illustrate the result:

- Mean – the average daily production rate for each month
- P10 – the value where 10 percent of the outcomes (or values) are greater than this value
- P50 – the median of a distribution, such that 50 percent of the outcomes are greater, and 50 percent of the outcomes are less than this value
- P90 – the value where 90 percent of the outcomes are greater than this value.

First, PetroDE generates the decline projection curves using either the Arps equation:

or the Stretched Exponential equation:

as specified by the user.

The mean projection is then estimated using the least squares fit method, which minimizes the sum of the squared residuals. The residual is the difference between the observed data point and the value on the estimated curve.

The P10, P50, and P90 projections are estimated using the **quantile regression method**, which minimizes the sum of residuals with a weight determined by the desired quantile:

Next, PetroDE uses the Nelder-Mead method to optimize the parameters and find the best fit line for the P10, P50, P90, and Mean curves. The best fit curves generated by PetroDE for the Bakken formation are shown below.

**Traditional Method vs PetroDE for Performance Projection**

Traditional approaches for determining liquid production projections evaluate each well separately using the Arps or SE equations, and then perform an analysis for each small group of wells to generate a decline curve based on that small group of wells. The PetroDE approach uses a repeatable process of aggregating all wells at once instead of one well at a time, and generates an accurate statistical decline curve for an entire area of interest in seconds.

The traditional method produces decent curve fits, but because different assumptions are used for the curve fit parameters, results tend to be inconsistent, especially between different people performing the analysis. PetroDE’s simplified process calculates consistent, accurate, and repeatable statistical curves for all wells in your area of interest. We analyze more data and return more information for any area of interest in a fraction of the time previously required.

To further illustrate the difference between using traditional methods and PetroDE’s Quantile Regression (QR) Method, let’s compare cumulative results for 101 horizontal wells in Reeves county in the Wolfcamp formation. For the individual wells, we determined the cumulative production for the first 35 months, then generated P10, P50, and P90 for that dataset. We then used PetroDE’s much faster QR method to directly generate P10, P50, and P90 aggregate curves and calculated 35-month cumulative data for those curves.

The chart in Figure 1 compares P90, P50, and P10 cumulative at 35 months for the individual well data curve values and the PetroDE QR method curve values. The orange line is a line with slope 1 (y=x), where the cumulative data are identical. PetroDE is very close to matching the individual well data curve; with PetroDE’s QR method P90 curve being slightly less than the individual well data curve and PetroDE’s P10 curve being slightly more. This reflects cases where operational issues create noise in the monthly production dataset. The two approaches would yield the same results if the input data was smooth and noise-free.

**Example of Liquid Production Decline Curves**

The chart below illustrates PetroDE’s liquid production decline chart for Reeves county in the Wolfcamp formation. It provides four curves: Mean, P10, P50 and P90. The liquid production rate for individual wells is shown in grey and includes horizontal wells with a First Production Date of 1/01/2011 – 12/31/2016. We generated this statistical decline curve from IHS Production Data in 11 seconds.

Curve fit results are reported in PetroDE’s statistics box (circled), together with the resulting decline projection curves, and are defined as follows:

- q0 = initial flow rate
- b = degree of curvature of the line
- D = initial decline rate

Erratic behavior of individual wells due to operational problems is highlighted in red in the following figure. By using PetroDE’s statistical decline curve approach, outliers are not discounted, and yet the curves are not unreasonably skewed.

**Example of Easy EUR Calculation**

PetroDE also calculates the average Estimated Ultimate Recovery (EUR) in an area of interest. Instead of calculating the EUR for each individual well, PetroDE approximates the P10, P50 and P90 values for all wells in an area of interest. The chart below shows the combined mean cumulative production for gas, liquid, and water for the same Wolfcamp area of interest in the previous example. Projected 30-year EUR values are shown in the list on the right side of the chart.

This chart was generated from IHS Production Data in 24 seconds, further illustrating how PetroDE saves valuable time in the risk analysis process.

**Quick Method for Obtaining an Index of Production and Completion Efficiency **

The traditional approach to understanding completion efficiency requires determining EURs on individual wells, followed by comparing completion parameters like proppant load and fluid volume to those EURs. There are two key challenges to this approach: (1) It is very time consuming to determine EURs for individual wells; (2) The EUR fits for individual wells are very difficult to reproduce due to the fact that no two individuals will come up with the same estimates for production.

The QR method offers an alternative approach by analyzing wells in aggregate sets. To determine the ideal proppant load per foot, first choose a reasonable range of gross perforated length intervals for an area. In this example we used a range surrounding the mode for the area of interest (8,200 ft to 11,100 ft).

Next, find the range of proppant load, and divide that range into uniform intervals to determine the aggregate set of wells within each interval. The following figure illustrates the concept. Ideally each aggregate set has 21 or more wells for improved statistics.

Once you have wells for the aggregate sets, determine the P50 proppant load using quantile regression on the monthly production from wells in each set. This determines the P50 QR EUR for each set. The P50 proppant load can now be related to the P50 QR EUR for each aggregate set, and the mathematical relationship determined, as shown below.

**Statistical Decline Curves for Understanding Geologic Controls**

A similar approach can be used to understand how geologic controls are impacting EUR. The concept is to aggregate the data by similar parameters, then compare to QR EUR computed for all wells in the aggregate set.

For example, the formation in which to complete a horizontal well is picked by comparing EURs generated from up to five years of production in a nearby or analogous area. If we look at parallel wellbores in the northern DJ Basin,

We see that Codell completions, shown in the first graph are projected to have higher EURs than the Niobrara completions, shown in the second graph.

This analysis generated in a few minutes, thus supporting a time-sensitive acquisition decision.

**Conclusion**

PetroDE provides you with a tool that can instantly and accurately calculate decline projection curves for an area of interest or an entire formation. By using a set of wells together in an appropriate statistical way, a better estimate is made by aggregating all the pertinent wells together. This highly repeatable process of aggregating all wells at once instead of one well at a time lessens the effect of outliers, while not completely discounting their contribution.

It is no longer necessary to identify a specific group of producing wells to analyze individually and then perform a statistical analysis of each group of wells using Arps or SE equations. PetroDE analyzes production for an entire area of interest at the click of a button.

This blog post is based on a white paper written by Alan Lindsey, the CEO of PetroDE, titled * Statistical Decline Curves for Performance Projection Modeling*. You can request to download the white paper here.