©2017, Vesmir Inc.

TECHNICAL WHITE PAPER

Instantly Generate Accurate Projections from Large Datasets

Dynamic Geospatial Intelligence

©2017, Vesmir Inc. TWP_PetroDE_Statistical Decline Curves_201704025.docx 2

Introduction

This paper shows how the PetroDE application calculates accurate decline projection curves to quickly

provide performance projections for producing wells.

Traditional methods for calculating decline curves require engineers to evaluate producing wells

individually and then perform a statistical analysis for each group of wells, or to take a simple average

on a per month basis and fit that average dataset to a curve. PetroDE can accurately analyze an area

of interest while honoring all of the available data at the click of a button, saving the user invaluable

time. PetroDE also provides insight into the variance in performance by calculating multiple curves

that illustrate the range of production performance.

Decline Curve Logic Explained

PetroDE calculates projected production for any given set of wells. There are four Decline Projection

curves generated 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: . The method is selected by the user.

The mean projection is 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.

where

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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.

where is the desired quantile (P10 = 90th percentile = 0.9 quantile, P50

= 50th percentile = 0.5 quantile, P90 = 10th percentile = 0.1 quantile),

is the y value of the estimated curve and is the y-axis value of the

observed data. For example, for a P10 projection, = 0.9, so the points

above the line are weighted by 0.9 and the points below the line are

weighted by 0.1. This results in a curve with approximately 90% of

points below and 10% of points above.

©2017, Vesmir Inc. TWP_PetroDE_Statistical Decline Curves_201704025.docx 4

Mine, Extract and Build Entire Data Set

Generate Accurate Statistical Decline Curve(s)

Share Results

Mine Data Source(s)

Extract Data

Build/Assemble for Application

Generate Several Decline Curves

Share Results

Traditional Method vs PetroDE

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 can produce 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 an area of interest. PetroDE can analyze more data and return more

information for any area of interest in a fraction of the time previously required.

Traditional Approach PetroDE Approach

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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. The comparison shows that PetroDE’s QR method P90

curve will generally be a little less than the individual well data curve and PetroDE's P10 curve will

generally be a little 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.

Figure 1. Cumulative Comparison for 101 Wells

©2017, Vesmir Inc. TWP_PetroDE_Statistical Decline Curves_201704025.docx 6

For Example

PetroDE's liquid production decline chart is illustrated in the example below. It provides four curves:

Mean, P10, P50 and P90. The liquid production rate for individual wells is shown in grey. The analysis

is for Reeves county in the Wolfcamp formation and includes horizontal wells with a First Production

Date of 1/01/2011 - 12/31/2016. PetroDE generated this curve from IHS Production Data in 11

seconds.

The curve fit results are reported in PetroDE's statistics box (circled), together with the resulting

decline projection curves. The curve fit parameters are defined as follows:

q0 = initial flow rate

b = degree of curvature of the line

D = initial decline rate

In the chart below, the well highlighted in red exemplifies the erratic behavior of individual curves due

to operational problems. By using PetroDE’s statistical approach, outliers are not discounted, and yet

the curves are not unreasonably skewed.

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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,

thus eliminating the need to calculate the EUR for each individual well. The chart below shows the

combined mean cumulative production for gas, liquid, and water for the same Wolfcamp area of

interest in the above example. The 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.

Conclusion

PetroDE provides engineers 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 can be 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 can analyze

production for an entire area of interest at the click of a button.

©2017, Vesmir Inc. TWP_PetroDE_Statistical Decline Curves_201704025.docx 8

About us

Vesmir Inc. is a software development company that produces and markets cloud-based mapping and

asset management solutions. We believe the effectiveness of information depends on its analytical

quality, accessibility, and clarity of presentation.

Our team has an extensive background in the geosciences, software development, and economics.

Together our goal is to give you a tremendous edge in the quest for resources by making your most

important information available to your entire team anywhere, anytime.

Alan Lindsey is a co-founder and CEO. He is a geoscientist with more than 30 years of experience in

the petroleum industry. Most recently, he has developed resource plays on three continents using key

metrics & scoring methods for identifying core shale play acreage. He has applied the method to the

Eagle Ford, Marcellus, Utica, and Barnett shale systems, greatly simplifying acreage evaluation. Prior

to focusing on resource plays, Alan explored for conventional resources for Shell Exploration &

Production from California to the Deepwater Gulf of Mexico. Alan received a B.S. in Geophysical

Engineering from the Colorado School of Mines.

Contact Us

Vesmir Inc. 2150 W. 6th Avenue, Suite H Broomfield, CO 80020 USA Website: www.PetroDE.com

Email: sales@PetroDE.com

________________________

©2017, Vesmir Inc. The document can be distributed only in its integral form and acknowledging the source. No selection of this material

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Inc. While the document is based upon information that we consider accurate and reliable, Vesmir Inc. makes no warranty, express or

implied, as to the accuracy of the information in this document. Vesmir Inc. assumes no liability for any damage or loss arising from reliance

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