1. This document offers practice to the author
to estimate the reserves present for a real
reservoir. The project was provided by Dr.
Matthew Pranter of the Petroleum Geology
Department at CU, and will be critiqued by
Dr. Peter Hamlington of the Mechanical
Engineering Department at CU.
Reserves
Estimation
Project
Reservoir Engineering
Independent Study – 5/8/13
Mark Hinaman
Mechanical Engineering
University of Colorado at Boulder
2. 1
Introduction
This project was provided as supplemental practice estimating the amount of recoverable reserves for a
given reservoir with minimal development data. The premise follows:
The Chester 18 Field is located in Ostego County, Michigan. The field was discovered in 1971
and produces from a Silurian-age reef reservoir (Niagaran pinnacle reefs). Assume that you can
go back in time and the date is January 1, 1977. You are to estimate, among other things, the
remaining (primary) reserves (ERR) for the field effective January 1, 1977.
As of January 1977, 14 exploratory wells had been drilled. Of the 14, 12 were producing from the
Niagaran formation and two (The 1-7 and 2-19) were dry holes (no oil or gas present to well below the
known formation). Four methods were used to estimate either the original oil in place (OOIP) or the
estimated remaining reserves (ERR) for the field: volumetric approach to OOIP using the tabular
method, volumetric approach to OOIP using Petrel, Material Balance approach to OOIP, and a decline
curve analysis. Each method is outlined below with its respective data and analysis. The results of all
methods are discussed afterward along with a brief discussion on what other technical information
would be necessary to make an educated proposal to purchase the wells and continue development.
A note on units: Within the oil and gas industry, it is common practice to refer to the thousand
abbreviations as “M” and the million abbreviation as “MM” rather than “k” and “M” as is common in the
conventional scientific community. It is believed the abbreviation is derived from roman numerals,
where M is standard for a thousand, and therefore MM would be a thousand thousands. This is, of
course, inaccurate for roman-numeral notation where MM would conventionally be two thousands.
Regardless, for the duration of this report, MMRB is denotes million reservoir barrels, and MMSTB
denotes million standard surface barrels.
OOIP and EUR Calculations
Tabulated Volumetric
The equation used to calculate the original oil in place was:
𝑂𝑂𝐼𝑃 =
7758𝐴𝜙ℎ(1 − 𝑆 𝑤𝑖)
𝐵 𝑜𝑖
It was necessary to map the porosity height (𝜙ℎ) of the reservoir to estimate the pore volume. A “hand-
drawn” structure contour map and phi-h (𝜙ℎ) map were created using the provided well data and blank
maps for the Chester 18 field. The relevant 𝜙ℎ map is shown below in Figure 1. This map illustrates the
height of pore space present during well logs within the reservoir rock. The more porous the rock is, the
larger the 𝜙ℎ value. The well data used to draw the maps and the structure contour map may be found
in the Appendix.
Reservoir water saturation (𝑆 𝑤) and original oil formation volume factor (𝐵 𝑜𝑖) were given below in Table
1. Traditionally, these data would need to be acquired from core sampling and lab measurements.
3. 2
Table 1 - Known Constants for Volumetric Calculation
Known
Variable Symbol Value Units
Int Water Sat S_wi 0.1 Fraction
Int FVF B_oi 1.4515 RB/STB
bbl/acre-ft Conv 7758 bbl/acre-ft
Figure 1 - Phi-H Map of Niagaran Reef (Compare to Petrel Generated Below)
4. 3
The area encapsulated within each contour line was measured using Adobe’s Area Measurement tool
and recorded in square inches. Then, using the conversion of 1in = 1,000ft, the area was converted to
feet and then to acres. This was performed for each contour line on the 𝜙ℎ map and tabulated in Table
2. Once an area for each contour was confirmed, the ratio of successive areas was used to determine
which volumetric approximation equation to use – the pyramidal equation or the trapezoidal. The logic
for which one to use was:
𝐼𝑓
𝐴 𝑛+1
𝐴 𝑛
> 0.5, 𝑇𝑟𝑎𝑝𝑒𝑧𝑜𝑖𝑑𝑎𝑙 → Δ𝑉𝑏 =
ℎ
2
(𝐴 𝑛 + 𝐴 𝑛+1)
𝐼𝑓
𝐴 𝑛+1
𝐴 𝑛
< 0.5, 𝑃𝑦𝑟𝑎𝑚𝑖𝑑𝑎𝑙 → Δ𝑉𝑏 =
ℎ
3
(𝐴 𝑛 + 𝐴 𝑛+1 + √𝐴 𝑛 𝐴 𝑛+1)
Table 2 - Tabulated Volumetric Calculation
Productive
Area
(Contour
Value)
Color
PhiH
Value
Area
(sqin)
Area
(sqft)
Area Inside
contour
(acres)
Ratio of
Areas
Equation Used
(pyr. or trap.)
ΔV
(acre-ft)
A0 Black 19.31 33.55 3.36E+07 770.20 - - -
A1 Grey 19.31 31.15 3.12E+07 715.10 0.92846 Trapezoidal 624.6785
A2 Purple 19.31 29.04 2.90E+07 666.67 0.93226 Trapezoidal 581.1345
A3 Blue 19.31 25.59 2.56E+07 587.46 0.8812 Trapezoidal 527.4527
A4 Green 19.31 22.45 2.25E+07 515.38 0.8773 Trapezoidal 463.8262
A5 Yellow 19.31 16.00 1.60E+07 367.31 0.71269 Trapezoidal 371.2348
A6 Orange 19.31 7.20 7.20E+06 165.29 0.45 Pyramidal 218.4162
A7 Red 19.31 2.86 2.86E+06 65.66 0.39722 Pyramidal 93.96144
A8 Pink 19.31 1.24 1.24E+06 28.47 0.43357 Pyramidal 38.51179
A9
None
(Point) 19.31 0 0 0 0 Pyramidal 7.981467
TOTAL (Acre-ft) 2927.197
Hand
Pore Volume
(MMRB) 22.7092
OOIP (MMRB) 20.43828
OOIP (MMSTB) 14.0808
Petrel
Pore Volume
(MMRB) 41.5618
OOIP (MMRB) 37.40562
OOIP (MMSTB) 25.77032
Finally, all the volumes from each contour were summed together to calculate the total pore volume
present with the reservoir.
𝑃𝑜𝑟𝑒 𝑉𝑜𝑙𝑢𝑚𝑒 = 𝑉𝑝 = 𝐴𝜙ℎ
5. 4
With the pore volume known and the initial water saturation and formation volume factor assumed, the
original oil in place could be calculated as
𝑂𝑂𝐼𝑃 =
𝑉𝑝(1 − 𝑆 𝑤𝑖)
𝐵 𝑜𝑖
Table 2 demonstrates the tabulated volumetric approach to calculating the OOIP, but a similar approach
was used to calculate the OOIP from the maps generated in Petrel. The Petrel results are listed as well
for convenience.
Petrel Mapping Volumetric
Petrel is a mapping program available in Benson Earth Sciences used to create 2D and 3D contour maps
of the subsurface with limited available data. It was used to compute the pore volume present and
OOIP (results listed in Table 2). In order to accurately complete the volume calculations, several maps
were created. First, a top Nagaran reef reservoir surface constrained by the oil-water contact at -4642ft
was created. This is similar to the structure contour map created for the tabulated volumetric approach
which may be found in the Appendix. The top Niagaran surface is shown below in Figure 2.
Figure 2 - Top Niagaran Reservoir Structure Contour Map
Next, a base Niagaran map was created to demonstrate the oil-water contact present at -4642ft (Figure
3).
6. 5
Figure 3 - Base Niagaran (Oil-Water Contact) -4642ft
Next, a porosity and 𝜙ℎ map were created (Figure 4 and Figure 5).
Figure 4 - Porosity Map
7. 6
Figure 5 - Phi-H Map (Compare to Hand-Drawn Above)
The pore volume and OOIP were calculated two in two separate ways, primarily because the results of
the first calculation were seemingly inconsistent with other volume calculations.
Gridding System and Porosity Overlay
The first attempt at pore volume and OOIP calculation involved creating a 3D grid within Petrel and
overlaying the respective porosity values within the grid. Petrel has a function which may be utilized
then to calculate the pore volume and OOIP given the appropriate inputs. Because the author is
borderline illiterate in speaking the vast and complex language of Petrel, it was difficult to generate
outputs. Furthermore, even once outputs from the volumetric calculation were complete, it was
8. 7
anyone’s guess about whether or not they were accurate. This is a cautionary tale for future endeavors
within industry to not trust model’s results unless one can be absolutely sure of their accuracy and cross
checked with competent peers.
The grid generated grid with the porosity overlay is shown below in Figure 6.
Figure 6 - 3D Grid with Porosity Overlay
The pore volume calculation and OOIP function outputs values of 44.03 MMRB and 31.45 MMRB,
respectively. These results are reasonably close to what could be expected for the standard values. It
should be noted that these estimates were converted from million cubic meters and were of a much
smaller resolution (7 and 5 million cubic meters, respectively). Therefore, it could be possible the pore
volume and OOIP calculation using the grid function matches the volumetric approach described below,
and the only discrepancies exist because of significant figure truncation from the program. Because this
is likely the case, the volumetric approach results are the only ones reported when summarizing the
Petrel results at the end of the report.
9. 8
𝝓𝒉 Volumetric Approach
To validate the results from the tabulated volumetric approach, a second method was used to calculate
the pore volume and OOIP. The 𝜙ℎ map shown in Figure 5 was used to directly calculate the pore
volume present. This value was then converted to an OOIP value using the initial given constants for
water saturation and oil formation volume factor. This method returned a pore volume and OOIP of
41.56 MMRB and 25.77MMSTB, respectively.
Material Balance
The Material Balance equation was used to estimate the original oil-in-place (OOIP) with the Havlena
and Odeh method (1963):
𝑃𝑟𝑜𝑑𝑢𝑐𝑡𝑖𝑜𝑛 = 𝐸𝑥𝑝𝑎𝑛𝑠𝑖𝑜𝑛
Production Term:
𝐹 = 𝑁𝑝(𝐵𝑜 + 𝑅 𝑝 − 𝑅 𝑠)𝐵𝑔) + 𝑊𝑝 𝐵 𝑤
Expansion Term:
Expansion of oil and originally dissolved gas
𝐸 𝑜 = (𝐵𝑜 − 𝐵 𝑜𝑖) + (𝑅 𝑠𝑖 − 𝑅 𝑠)𝐵𝑔
Expansion of gas cap
𝐸𝑔 = 𝐵 𝑜𝑖 (
𝐵𝑔
𝐵𝑔𝑖
− 1)
Expansion of connate water and reduction in pore volume
𝐸𝑓,𝑤 = (1 + 𝑚)𝐵 𝑜𝑖 (
𝑐 𝑤 𝑆 𝑤𝑖 + 𝑐𝑓
1 − 𝑆 𝑤𝑖
) Δ𝑝
Combining equations, the material balance equation becomes
𝐹 = 𝑁(𝐸 𝑜 + 𝑚𝐸𝑔 + 𝐸𝑓,𝑤) + 𝑊𝑒 𝐵 𝑤
Where F represents the net production from the reservoir, and 𝐸 𝑜, 𝐸𝑔, and 𝐸𝑓,𝑤 represent the
expansion of oil, gas, and formation water (and reduction in pore volume). 𝑁 represents the OOIP
within the reservoir.
Assuming no water influx and no gas cap (valid assumptions based on production data), then the
material balance equation becomes:
𝐹 = 𝑁(𝐸 𝑜 + 𝐸𝑓,𝑤)
The relevant terminology for the data provided is listed below in Table 3.
10. 9
Table 3 - Material Balance Variable Descriptions
Variable Description Units
𝐵𝑔 Gas formation volume factor bbl/SCF
𝐵𝑔𝑖 Initial Gas formation volume factor bbl/SCF
𝐵𝑜 Oil formation volume factor bbl/STB
𝐵 𝑜𝑖 Initial oil formation volume factor bbl/STB
𝐵 𝑤 Water formation volume factor bbl/STB
𝑐𝑓 Formation isothermal compressibility psi^-1
𝑐 𝑤 Water isothermal compressibility psi^-1
𝐸𝑓,𝑤 Expansion of Formation Water bbl/STB
𝐸𝑔 Expansion of Gas bbl/STB
𝐸 𝑜 Expansion of Oil bbl/STB
𝐹 Production STB
𝑁 Initial reservoir oil STB
𝑁𝑝 Cumulative produced oil STB
Δ𝑝 Change in average reservoir pressure psia
𝑅 𝑝 Cumulative Produced GOR SCF/STB
𝑅 𝑠 Solution GOR SCF/STB
𝑅 𝑠𝑖 Initial Solution GOR SCF/STB
𝑊𝑒 Water influx into reservoir bbl
𝑊𝑝 Cumulative Produced Water STB
Data was provided at three different pressures to calculate the expansion oil and formation water
terms. With this, 𝐹 could be plotted as a function of (𝐸 𝑜 + 𝐸𝑓,𝑤), which allowed the OOIP (𝑁) to be
calculated utilizing a simple regression tool. That is to say,
𝑑𝐹
𝑑(𝐸 𝑜 + 𝐸𝑓,𝑤)
= 𝑁 = 𝑂𝑂𝐼𝑃
The data used to calculate 𝐸 𝑜, 𝐸𝑓,𝑤, and 𝐹 may be found in the appendix. Charts demonstrating the
relationship between the formation volume factor and pressure and the gas-oil ratio (GOR) and pressure
may also be found in the appendix. The results are summarized below in Table 4.
11. 10
Table 4 - Production Summary for Three Different Pressures
F (MMSTB) Eo Ef,w El = Eo + Ef,w
1,026,404 0.01410 0.007630 0.021730
5,021,684 0.10166 0.011411 0.113071
6,276,970 0.16418 0.012209 0.176389
A simple linear regression forced through the origin was used to calculate the slope, 𝑁, and
subsequently determine OOIP.
Thus, the original oil in place using the material balance approach was 38.25MMSTB.
Decline Curve
The decline curve analysis attempts to fit an exponential function to the preliminary data in order to
extrapolate and predict the future production of the field. Oil fields produce at a declining exponential
rate, and if the decline rate can be accurately predicted, then the production rate can be modeled
accurately. For this example, fast forward two years and suppose two years of production data is
available from the producing wells. With these data, the time to abandonment and estimated
remaining reserves can be calculated. The production rate formula may be described as
𝑞𝑡 = 𝑞𝑖 𝑒−𝐷𝑡
Where 𝑞𝑡 is the production flow rate at time 𝑡, 𝑞𝑖 is the initial production flow rate, and 𝐷 is the decline
constant.
Known (given) data include:
y = 38253064.773x
R² = 0.950
-
1,000,000
2,000,000
3,000,000
4,000,000
5,000,000
6,000,000
7,000,000
8,000,000
0.000000 0.050000 0.100000 0.150000 0.200000
Production(F,STB)
Expansion Terms (EI = Eo + Ef,w)
OOIP Calculation
El = Eo + Ef,w
Linear (El = Eo + Ef,w)
12. 11
Table 5 - Decline Curve Inputs
Variable Value Units Description
q_t Variable STB/month rate of production at time t
q_i 69,000 STB/month rate of initial production (12/31/76)
D 0.45 yr^-1 decline rate
N_p 3,939,881 STBO Cumulative Production (12/31/76)
q_ec 3,000 STB/month Economic Limit for Profitable Production
In order to determine the time to abandonment, the production exponential formula is rearranged and
solved for 𝑡:
𝑡 =
ln (
𝑞𝑖
𝑞 𝑒𝑐
)
𝐷
In the above equation, 𝑞𝑡 = 𝑞 𝑒𝑐 which represents the economic limit of production at time 𝑡. That is,
once production drops below that rate, it will then cost more to produce the hydrocarbons than value
provided from producing them. An economic limit of 3,000 STB/month was provided. The time to
abandomnet was calculated to be 6.97 years.
The remaining reserves may be calculated as the difference between initial and final production rates
divided by the decline rate:
𝑁𝑝 =
𝑞𝑖 − 𝑞𝑡
𝐷
From this model, the number of hydrocarbons remaining to be produced (estimated remaining reserves,
or ERR) are 146,667 STB. Because a number of hydrocarbons have already been produced, the
estimated ultimate recovery (EUR) may be calculated as
𝐸𝑈𝑅 = 𝐸𝑅𝑅 + 𝐶𝑢𝑚𝑢𝑙𝑎𝑡𝑖𝑣𝑒 𝑃𝑟𝑜𝑑𝑢𝑐𝑡𝑖𝑜𝑛
→ 𝐸𝑈𝑅 = 146,667𝑆𝑇𝐵 + 3,939,881𝑆𝑇𝐵 = 4,086,548𝑆𝑇𝐵
Finally, the recovery factor (RF) may be calculated as the ratio of reserves over resources. Another way
of describing it is as the number of hydrocarbons which can be extracted from the subsurface (EUR)
divided by the number of hydrocarbons originally there (OOIP).
→ 𝑅𝐹 =
𝐸𝑈𝑅
𝑂𝑂𝐼𝑃
=
4,086,548
14,080,798
= 0.29
The outputs from the decline curve analysis are summarized in Table 6.
13. 12
Table 6 - Decline Curve Outputs
t 6.97 yr Time to reach economic limit
ERR 146,667 STB Estimated Remaining Reserves
EUR 4,086,548 STB Estimated Ultimate Recovery
RF 0.29 Fraction Recovery Factor (EUR/OOIP)
Summary of Results and Discussion
The results for each relevant calculation is summarized below in Table 7. While there was variation over
the volumetric calculation for OOIP, it was not an unreasonable amount of variation. The smallest
estimate (the hand drawn tabulated method) is believed to be the smallest since very few contour lines
were used to estimate the volume of the reservoir. The decline curve analysis was beneficial for
practicing the decline of value over the following years, but it painted a very dismal future for the
development the remainder of the field. For most fields, a recovery factor of 29% is not uncommon for
primary recovery. However, this may be increased with additional wells drilled and enhanced oil
recovery techniques. Some fields may have recovery factors of upwards of 75% utilizing enhanced oil
recovery (EOR) techniques.
Table 7 - Summary of Results
Result Value Units
Original Oil-in-Place (OOIP)
Volume Calculation (OOIP) 14.08 MMSTB
Petrel Volume (OOIP) 25.77 MMSTB
Material Balance (OOIP) 38.25 MMSTB
Decline Curve Analysis
Time to Abandonment 6.97 Years
Estimated Remaining Reserves (ERR) 146.67 MSTB
Estimated Ultimate Recovery (EUR) 4.09 MMSTB
Estimated Recovery Factor (RF) 29% -
Answers to Posed Questions
Several questions were posed at the end of the project and will be answered here.
If you were asked to bid on this property, list and describe (as many as you can think of) the key
factors that you believe are most important to consider in establishing your bid from a technical
standpoint. There are obviously significant financial factors to consider (too many to list here),
but focus on the scientific aspects about the reservoir that are significant (e.g. secondary
potential, etc.).
14. 13
If I were asked to bid on this property, I would want to acquire as much data as possible. Since the initial
wells were drilled in the beginning of 1971 and it is now 1977, it is likely there is data available to the
public. In most states, companies will have the luxury of keeping all their data “tight hole” (confidential)
for a given period of time – usually six months to a year. However, after that point, the data becomes
part of the public domain and can be accessed by anyone. I would start my bidding estimate by
reviewing all of the available public data, which typically includes monthly production rates, core
samples, and completion type information.
Since the reservoir seems to be declining rapidly (based on the decline curve analysis), I would want to
understand what could be done to improve (decrease) the decline rate. Recall the decline rate was
variable D in the above decline curve analysis. It was currently sitting at a large 0.45/year. What work
could be completed to reduce that and potentially improve the production of the field?
As I understand it, the field is currently only undergoing primary oil recovery. That is, they simply drilled
holes in the ground and allowed oil to flow to the surface. Some of the wells may have pumps, but I
want to know what kind of pumps they have and how fast/variable the flow rates are. If they can be
turned up to increase production, how quickly might it reduce reservoir pressure? Furthermore, what
are the opportunities available for secondary and tertiary recovery? Secondary or tertiary recovery
methods could include performing a gas or water flood, by which the operating company begins
injecting CO2 or water into the reservoir to simultaneously maintain the reservoir pressure and free
hydrocarbons from sand grains which may be strongly absorbed into the rock. If such a recovery effort
were to commence, how difficult would it be to acquire the resource? Are some of the wells producing
so little that they could be immediately converted to injection wells, or would new wells need to be
drilled to be the injection wells for the water flood?
Finally, and possibly most importantly, I would want to know the rock and reservoir characteristics.
What are the average porosity and permeability of the reservoir? Are well logs available to interpret
and map the porosity of the reservoir? Are there porous zones present which haven’t been drilled into
yet and could be isolated from the currently producing reservoir? From the well logs, are there other
reservoirs present which could be completed to increase production?
Explain where you believe the greatest uncertainty is in your estimate of remaining reserves
(ERR).
The greatest uncertainty in my estimate of remaining reserves (ERR) lies in two places: the decline rate
and the economic limit. To refresh, the ERR is calculated as:
𝐸𝑅𝑅 =
𝑞𝑖 − 𝑞 𝑒𝑐
𝐷
The decline rate, 𝐷, is a variable which was given during the project. I’m unsure of where it originated
from, so it have been calculated from previous production data. However, as is mentioned above, it
could be altered if the reservoir were allowed to produce more or increase production from methods
such as a water flood or additional drilling.
15. 14
The economic limit is a huge uncertainty and can almost certainly not be predicted further than 24
months out without room for enormous error. The reason for this is the primary driving force is the
price at which oil and gas are selling for, which is tremendously volatile. Even a marginal price change
may have monumental effects on some companies – enough to push them out of business. The industry
has been fortunate to witness more stable oil prices over the past decade, but natural gas prices have
plummeted as the availability of natural gas skyrocketed in the late 2000’s. Regardless, it is merely the
nature of the industry and will likely continue to experience booms and busts for the remainder of its
life.
What data would you acquire or purchase to resolve this uncertainty? Explain how the data
would be useful.
I would acquire production data (probably free) and well logs (probably need to purchase) in an attempt
to resolve the decline rate uncertainty. Production data would allow me to see exactly how the wells
have been producing over the life of the field, which will give me a better estimate for how they will
continue to produce in the future and potentially could be improved. The well logs, as mentioned
above, will provide insight into the availability for additional zones and if it might be possible to either
complete additional formations/reservoirs or drill additional wells on the acquired acreage.
16. 15
Appendix
Well Data
X Y Well Top Base Isopach Porosity Phi-H)
(feet) (feet) Name (tvdss) (feet) (fraction) (feet)
4290 7960 1.7 -4841 NR NR NR NR
4400 7900 1-7A -4841 NR NR NR NR
360 2070 2-19 -4850 NR NR NR NR
490 2040 2-19A -4850 NR NR NR NR
1810 4310 6-18 -4542 -4642 100.0 0.0523 5.23
1770 2720 5-18 -4526 -4642 116.0 0.0652 7.56
5160 3400 2-17 -4491 -4642 151.0 0.0597 9.02
1820 2140 1-19 -4560 -4642 82.0 0.1182 9.69
4060 4080 1-18 -4501 -4642 141.0 0.0726 10.24
3150 5360 4-18 -4498 -4642 144.0 0.0747 10.75
2760 3100 2-18 -4555 -4642 87.0 0.1331 11.58
5120 6600 1-17 -4471 -4642 171.0 0.0725 12.39
5560 8120 1-8 -4552 -4642 90.0 0.1603 14.43
4290 6940 3-18 -4482 -4642 160.0 0.0933 14.92
5030 4020 3-17 -4490 -4642 152.0 0.1012 15.38
5690 5930 4-17 -4506 -4642 136.0 0.1420 19.31
