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©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
©2017, Vesmir Inc. TWP_PetroDE_Statistical Decline Curves_201704025.docx 3
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
©2017, Vesmir Inc. TWP_PetroDE_Statistical Decline Curves_201704025.docx 5
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.
©2017, Vesmir Inc. TWP_PetroDE_Statistical Decline Curves_201704025.docx 7
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: [email protected]
________________________
©2017, Vesmir Inc. The document can be distributed only in its integral form and acknowledging the source. No selection of this material
may be copied, photocopied, or duplicated in any form or by any means, or redistributed without express written permission from Vesmir
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
on this information. Trademarks mentioned in this document are property of their respective owners.