Modeling Shale Well Declines

Traditionally natural gas (UNG) producers use the classical Arps formula to model a conventional oil or gas well's production decline.

As I discovered, and as many people pointed out, the classical Arps formula is not suitable for projecting shale well's decline patterns, as shale wells decline much faster than the formula projects in the long term. Specifically the terminal decline of Arps formula approaches zero, and the cumulative production it projects approaches infinity with a b-factor larger than 1.0. That's problematic, as in the long term, shale wells should decline a terminal decline rate above zero.

Let's re-cap about the classical Arps formula and how I modified it:

(click to enlarge)

I am happy to find out that even though most producers insist on using the classical Arps formula, QEP does use the SAME modified Arps formula with a terminal decline term introduced. In that sense they agree with my own modeling method. I congratulate management of QEP for being a little bit more honest than Chesapeake (CHK) and Cabot Oil & Gas (COG).

But even QEP used the same correct modified Arps formula as I do, and admitted a reasonable terminal decline rate, they still pushed for a set of parameters that gave a higher EUR (Estimated Ultimate Recovery) than what is realistically possible.

Modeling Bakken Well No. 16637

I extracted monthly production data from ND DMR web site. I did the calculation on a spreadsheet. Here are the comparisons. Note that both QEP and I used the same formula with four parameters: IP, D, b-factor and terminal decline rate Beta. I just disagree with QEP on what parameters provide the best fit. Here is QEP's model:

(click to enlarge)

According to the chart, here are QEP's parameters, versus mine:

• QEP adopts IP = 724 BPD, D = 0.0035/day, B = 1.80 and Terminal decline rate Beta = 0.000228/day
• I adopt IP = 1250 BPD, D = 0.020/day, B = 1.80 and Terminal decline rate Beta = 0.000280/day.

Both QEP and I use the same b-factor of 1.80. I use slightly higher IP, slightly higher terminal decline rate beta. But the biggest difference is that QEP uses an extremely low initial decline rate, by the shale industry's standard. I think there is no justification for using such a low value of D. Shale wells decline extremely fast in the first few weeks. Other producer use a D ten times as higher.

As I said, I agree with QEP in the formula used, I disagree with them in the specific fitting parameters. Let's see who fit the data better:

(click to enlarge)

It appears to me that my curve fit the actual production data much better. The QEP curve does not fit the well data very well.

My speculation is that they know that they need a flat curve to obtain a higher EUR value. The more flat the curve is, the higher EUR it will calculate. Thus they probably deliberately pull the IP down to a much lower starting point.

To compensate for a lower starting IP, they adopt a much smaller initial decline rate D, which makes the curve flatter.

Finally, to further flatten the curve, they tried to fit the artificial local peak of production, at April and May of 2008, which resulted from re-fracing operation (re-stimulation). I believe the cur should follow the non-disturbed natural decline trend, instead of following the artificial temporary boost of production, to be realistic.

The chart above shows that my curve following the real production down closely, while the QEP curve deviate on the higher side.

(click to enlarge)

The above chart, plotted in much longer time scale, and using logarithm scale, shows the deviation much better. Once again, my curve tracks the actual production data very closely. But the QEP curve clearly deviates from the real data and projects too high.

As a result, when you integrate the cumulative production over time, QEP's curve would over-estimate while my curve gives the accurate projection. See below:

(click to enlarge)

As shown above, my parameters leads to accurate projection of the actual production. The QEP curve clearly deviates on the high side.

I projected that the EIR of well No. 16637 will likely be 500 MBOE. The QEP projection is 750 MBOE. The chart clearly agrees with me.

Calculation and Discussion

As of now, the well 16637 is a bit more than five years old, and has produced an accumulative 355.280 MBOE. Current production rate is 80 BOE/day. Current annual decline rate is -16% to -22%. Using -18% annual decline, and using 10 BPD as cut off, the well will produce another 145 MBOE, bring the total EUR to 500 MBOE.

This well is NOT a typical or average Bakken shale well. If it is, even if the EUR is only at 500 MBOE, producers would make an incredible profit at $100/barrel oil price. Unfortunately that is not the case. The average Bakken shale well has a much lower IP and much lower EUR, even if they are equally cost to drill.

As of October 2012, there are 6349 producing Bakken shale wells. They collectively produced 821.30 MBOE/day. There are 6077 wells which were also producing in September, and 272 new wells which first show up in October. The 6077 wells producing in both months collectively declined from 790.33 MBOE/day to 715.820 MBOE/day from September to October, or -9.5%/month. That is a daily decline rate of /month, or -0.33%/day. At this decline rate, these well's future production will be equivalent to 1/0.33% = 303 days worth of production at current rate of 716 MBOE/day, or 217 million BOE. Divided by well numbers, each well has an average of 35.7 MBOE remaining production. That does not look like a lot of value to me. At $90/barrel, that's a remaining production value of $3.2M each.

Good luck drilling every well as productive as No. 16636, producers!

I repeatedly pointed out that shale oil and gas producers tend to over-exaggerate productivity of their wells, under-estimate the well declines, and under-calculate the fair capital amortization cost, in order to pitch their investment case to banks and investors, so they can keep borrowing more money to keep drilling shale wells.

In reality, even Bakken shale oil wells are hardly profitable at current oil prices and current development costs. My advice to investors is to do your own due diligence research and scrutinize the data. Avoid the hyped shale oil and gas sector. The sector you should get into, is the US coal mining sector. The meme that natural gas is replacing coal, is completely wrong. Natural gas will always be an important part of America's energy supply. But at fair cost, shale gas can not compete with the cheap king coal.

The investment case in coal is made better as nearly 99% of investors made the wrong bet, as there is 75 times more market capital invested in the NG sector than in the US coal sector, while both sectors contribute about equal energy to the US economy.

Imagine what happens when the looming debt crisis in the NG sector unfold, and shale gas production collapses, sending prices of both NG and coal much higher, and 75 more market capital in the NG sector now moves to coal sector instead. This is not an opportunity you get to see every year. Now is the best time to get into coal.

Disclosure: I am long [[JRCC]], [[ANR]], [[ACI]], [[BTU]].

I decided to survey a group of shale gas developer to sum their financial data together into one collective financial statement, including cash flow, income statement and balance sheet. The data comes from Yahoo Finance. I wrote a computer program so that I can retrieve and tabulate tens of thousands of data items at a click of a computer button, without spending hundreds of hours.

The Collective Financial Statement of 30 Shale Gas Developers

Here is the result I got after tallying everything together into three tables: cash flow, income statement and balance sheet:

(click to enlarge)

I picked the companies from NGSA's top 40 NG producers list, with big oil and foreign names removed. The 30 companies surveyed are:

1. Chesapeake Energy (CHK)
2. Anadarko (APC)
3. Devon Energy (DVN)
4. Southwestern Energy Co. (SWN)
5. WPX Energy Inc. (WPX)
6. EOG Resources (EOG)
7. Occidental (OXY)
8. Apache (APA)
9. Ultra Petroleum (UPL)
10. QEP Resources (QEP)
11. Cabot Oil & Gas (COG)
12. EQT Resources (EQT)
13. Exco Resources (XCO)
14. Range Resources (RRC)
15. Newfield Exploration (NFX)
16. Noble Energy, Inc. (NBL)
17. Pioneer Natural (PXD)
18. Marathon (MRO)
19. Cimarex Energy (XEC)
20. SM Energy Company (SM)
21. Plains Exploration & Production Co. (PXP)
22. Quicksilver Resources (KWK)
23. Forest Oil (FST)
24. Linn Energy (LINE)
25. Energen Resources Corp. (EGN)
26. SandRidge Energy (SD)
27. W&T Offshore, Inc. (WTI)
28. Unit Corporation (UNT)
29. MDU Resources (MDU)
30. Stone Energy (SGY)

Further, the production data is not shown in the above table. The total NG production rates of these 30 companies are listed below:

(click to enlarge)

Let's have a look at the numbers.

What kind of Numbers Can We Trust?

I repeatedly warned people that NG producers routinely over-estimate EURs (Estimated Ultimate Recovery) of their shale wells and grossly under-calculated the fair amortization of their capital expenditures in developing shale wells. Productions from shale wells fall far below projections in the long term, as wells decline faster than projected by the classical Arps formula. Drilling shale wells is very capital intensive. Producers love to pitch rosy pictures in order to attract investment money and bank loans so they can continue to drill wells. How do we know if the industry is realistic or not in making those long term production projections?

We cannot look at just the models. Any one can propose a model and cherry pick good wells to show how legitimate these models are. We cannot look at just the shale wells that producers pitched in their press releases. Out of tens of thousands of wells drilled, there are always some wells with exceptional performance.

What numbers told by producers can we trust?

We need to look at the totals with little room for fuzzy math. If you look at just a subset of the data, those numbers could be carefully selected and tailored to make them look good. But the company-wide or industry-wide numbers, the totals that the producers file in their SEC reports, are more reliable.

If a producer says that one rig drills one will in 6.5 days and costs only $3.2M per well, and that the wells have an initial production of 750 BOE/Day, I will hold these numbers with skepticism. There are too much fuzzy room in how they come up with such averages. The "average" numbers can not stand up when they are checked against the total figures. Ask them: If one well costs $3.2M and they spent $500M in capital spending, shouldn't there be 156 new wells? Why there were only 80 completed? If 80 new wells each brings in 750/Day, production should gain 60 MBOE/Day. Why it gained only 4 MBOE/Day quarter-over-quarter? And so on.

If they say that they have 22 rigs in operation; completed 80 wells in the quarter; and incurred capital spending of $500M; and that production grew from 66 MBOE/day to 70 MBOE/day. Such numbers are more likely accurate. These totals have no room of manipulation. They must be reported as they are. If they spent $500M, they cannot claim they spent $400M or $600M. If they completed 80 wells, they cannot say 79 or 81. If production was 66 MBOE/Day, they cannot say it was 67 MBOE/day.

So I spent time to get the total figures in the two tables above.

Data Analysis and Discussion

The 30 companies listed produced gas at 20.874 BCF/day in Q2 2012, versus the US total of 68.9 BCF/day. So they represent 30% of the US NG production sector. But these 30 companies represent almost the entire US shale gas industry, as they are picked from the top 40 US producers, with only a few big oil companies removed. The total gas production from these producers was 20.874 BCF/day. That roughly equals to total US shale gas production, 26 BCF/day, minus royalty payments of about 20%, or 5.2 BCF/day.

Total capital spending averaged $225.866M/day in 2011, and increased to $243.253M/day in first half of 2012. How much production gain did they achieve after such heavy spending?

In one year from Q1 of 2011 to 2012, production increased from 18.997 BCF/day to 20.413 BCF/day, a gain of 1.416 BCF/day. The average daily gain is 3.88 MMCF/day. That is a rather modest production gain for an average of $226M/day capital spending.

In first half of 2012, production went from 20.345 BCF/day in Q4 2011 to 20.874 BCF/day in Q2 2012, gaining 0.529 BCF/day in 182 days. The average daily gain is 2.91 MMCF/day, thanks to the $243M per day capital spending.

That's $83.50 spent to gain just one CF per day production. You read it right, one cubic feet per day. At $3.35 per thousand cubic feet today, $83.50 can buy 24925 cubic feet of gas, or 68 years worth of production at 1 CF/day. The new production of any shale well hardly last 2 years, let alone 68 years. As I summarized before, a shale well likely will produce about 500 days worth of production at its IP (initial daily production) rate.

Of course, the bulk of $243M spent per day does not contribute to production gain. It was spent merely to bring in new production to counter the decline from existing wells. Let's calculate how much is spent maintaining the production, and how much is spent growing it.

Using my 500 days rule of thumb, or -0.20%/day collective decline, the existing 20.6 BCF/day (average of H1 2012) production rate will lose 0.20% per day, or 41.2 MMCF/day. Net production gain is 2.91 MMCF/day. So new production must have brought in 44.11 MMCF/day capacity, with 41.2 MMBCF/day lost to the declines, resulting in a net gain of 2.91 MMBCF/day. But $243M/day spent to gain 44.11 MMCF/day new production capacity is still expensive. Since the new capacity will bring in a lifetime production worth 500 days of initial production rate, 44.11 MMCF/day is worth 22 BCF.

The capital cost of the gas is $243M/22BCF = $11.05/mmBtu!!! The shale gas industry loses money at gas price below double digits!

Conventional Gas Wells vs Shale Gas Wells

How did the US NG Industry fund the shale gas development if it is such a huge money losing adventure? The answer begins to emerge once you look at the US conventional gas production:

(click to enlarge)

For years, the US NG industry has maintained flat conventional gas production at roughly 1500 BCF/month. But it started to decline in 2007 at a rate of losing 7% per year. The NG industry was able to maintain flat conventional production by continuous conventional gas well drillings, as shown in the chart below:

(click to enlarge)

From 2000 to 2008, the industry was adding an average of 15,280 conventional wells per year to maintain conventional gas production at a flat 1500 BCF/month. That averaged 42/day new wells to maintain 50 BCF/day production. Based on fair replacement, each conventional well has a lifetime production of about 50/42 = 1.25 BCF. The decline rate of conventional wells after 2007, was 7%/year, or -0.02%/day. On each day existing conventional wells lost 0.02%*50 BCF/day = 0.01 BCF/day. The lost production is replaced by 42 new wells. So the well IP (initial production) was (1/42)*0.01 BCF/day = 0.238 MMCF/day:

• Conventional wells have an effective IP of 0.238 MMCF/day.
• The initial decline is much less steep than shale wells.
• They settle to the long term slow decline much faster.
• Collective decline of all conventional wells is -0.02%/day.
• The well has an EUR=1.25BCF, or 5000 days worth of IP.
• Drilling cost is much cheaper. You only need to drill a hold straight down. No horizontal laterals to drill. No fracking.

Let's compare those metrics with the shale gas wells:

• Shale wells have a typical IP of 3.0 MCF/day.
• They start with very steep decline for a year or so.
• After the initial decline, the decline rate slowly drops.
• Collection decline rate of all shale wells is -0.2%/day.
• The well has a typical EUR = 1.5 BCF, or 500 days of IP.
• Drilling cost is much higher than conventional wells. You have to drill the horizontal laterals. You have to do multi-stage fracking.

Here are the differences. Shale wells have remarkably high IPs ten times higher than a conventional gas well. But they also decline ten times faster. So by the end of their life cycles, shale wells do not deliver much higher EURs than conventional gas wells.

Capital Destruction in the US NG Industry

It puzzles me how the US NG industry manage to fund development of shale gas for these years, if the adventure is deeply unprofitable?

Let me return to the collective financial statements of the top 30 USNG producers as presented above. Let's look at the cash flows from beginning of 2009 to end of Q3, 2012, or for 3.75 years:

• Capital expenditures were $265.539B, or $194M/day.
• Cash flow from operations $224.590B, or $164M/day.
• Cash flow from financing was $47.441B, or $35M/day.
• Cash and cash equivalent change $6.79B, or $5M/day.

So the Cash flow from operations were short $30M/day to fund the well drillings and developments. The deficiency was funded by net borrowing and stock selling to the tune of $35M/day.

But that is not the entire picture. The $224.590B net cash from operations, or $164M/day, sounds like too high to me. These 30 producer produced an average of less than 20 BCF of gas per day. According to EIA, well head gas price during those 45 months averaged $3.72/mmBtu. So producers took home no more than $74.4M/day from gas sells, not including operation costs and SG&A. How did they report a net positive cash flow of $164M/day?

The operating cash flow is much higher than gas sells revenue as producers have revenues from oil and from foreign businesses. Take Apache for example. APA received only 45% of its revenue from N. America operations. The other 55% comes from overseas. Yet APA spent 62% of its capital expenditure in NA, only 38% overseas.

Here is the problem, the conventional oil and gas, and foreign operations are profitable. But the profits they generate is not spent to grow the profitable business. Instead they are spent to grow the unprofitable US shale projects.

The profitable portion of business does not receive the capital it needs to maintain and grow business. So the profitable business is shrinking. Instead, money is spend to grow the non-profitable US shale projects. Good money is thrown after bad money. This can be seen from APA's Q3 2012 result compared with one year ago:

• Total oil production dropped from 343.4 to 341 MBOE/day.
• Foreign oil production dropped from 210 to 192.9 MBOE/day.
• Domestic oil production grew from 120.4 to 133.0 MBOE/day.
• Most of the growth happens at Bakken (7.9 to 17.0 MBOEPD) and Permian (51.4 to 60.8 MBOEPD).
• The really profitable part of APA's domestic oil play, GOM shelf, dropped from 45.1 to 38.6 MBOE/day.

What did APA gain in allowing its profitable part of business to decline, for lack of capital investment, as they spend the capital instead to grow the non-profitable Bakken and Permian plays?

The same problem exists in the entire US NG industry. Conventional gas is still the bulk of US gas production, contributing 40 BCF/day. Shale gas contributes 26 BCF/day. But my previous chart show that in 2007, the industry completely abandoned its decade long efforts of drilling conventional gas wells to maintain flat production. They turned their entire effort to drill shale gas wells, leaving conventional wells to decline at 7%/year.

Mean while, as conventional gas wells continue to decline as they receive no capital spending, they still generate a lot of revenue. That revenue is spent to subsidize the shale developments.

This is throwing good money at bad money. This is capital and value destruction. How much good money do they throw away? When the industry stopped investing in conventional gas (CG in brief) plays in 2007, the CG sector produced 50 BCF/day and declined at 7% annual rate, or -0.02%/day. At that decline rate, the existing CG wells can produce 50/0.02% = 250 TCF of gas before they are depleted. At $4/mmBtu of gas price, those CG assets are worth one trillion dollars of future revenue, at only little cost of maintenance. Today, CG production dropped to 40 BCF/day, with 200 TCF of gas remaining, or worth $800B. The CG sector already generated $200B of revenue which was wasted in the shale plays with no profits.

The NG industry is on an unsustainable path of capital destruction.

Investment Implications

There is an ongoing capital destruction in the shale industry. It will lead to production collapse in the near future, which will send gas price much higher. But what kind of gas price will allow the shale industry to generate $243M cash flow a day, net of costs, from 20 BCF/day worth of shale gas production, in order to maintain current capital spending at $243M/day? The gas price need to be in the double digits. Will such gas price be sustainable? I doubt it.

Investors are better off staying away from the NG sector. Do not be lured back into the NG sector just because gas price is going higher. The sector that will benefit most from the capital destruction in the NG sector, and from rising gas price, is the US coal mining sector.

I have urged people to buy coal stocks for a long time now. The current setup for a big coal rally is much better than the conditions existed at the onset of the 2007-2008 coal rally. This time it will bring more profit to people willing to hold their coal positions firm.

Based on the first 11 months data, China will import 265M tons of coal in 2012, up 45% from last year's 182.4M tons. The naysayers still call it a China demand slow down when China coal import grows at 45%? For the first 11 month, China generated 707.8 billion TWH of hydro-electricity, a gain of 149.2 TWH versus last year, saving China 82M tons of coal demands. This one time weather anomaly will not repeat in 2013. China will need 82M tons more coal just to compensate for hydro-electricity falling back to normal, on top of demand grow. At 4B tons per year demand, any demand grow is huge to the international coal trade market of 800M tons a year.

I am sticking to my coal stocks, and I look for opportunity to short NG players when the time is right, when we reach a high gas price.

Disclosure: I am long [[JRCC]], [[ANR]], [[ACI]], [[BTU]].

When the capital costs are fairly amortized, most shale oil and gas development projects are deeply non-profitable. Even the Bakken shale oil, regarded as the most profitable shale play under current pricing environment, is not profitable. Let me use real data from Whiting Petroleum (WLL), the second largest Bakken shale oil developer, to demonstrate the real economy in Bakken shale.

Let the Real Numbers Tell The Real Story

Putting aside the shenanigans of how to properly model a shale well's production decline over time, I think the actual numbers that are indisputable will tell the true story:

• How much does a producer spend on capital spending.
• How much is the daily production volume.
• How much the production gained due to capital spending.
• What's the cost without considering the capital spending.

While any one can say anything about models, the above items are very specific real numbers that producers must report to SEC as they are, with little room for manipulation or speculation.

My idea is that the well drilling and development capital spending can be considered to serve two things:

1. To compensate for the lost production due to depletion.
2. To expand business and grow the daily production rate.

I think the portion of capital spending that counters the shale well declines and maintains the production at the current level, replaces the loss of value due to depletion and amortization. This portion of capital spending should be the fair amount of amortization costs.

What portion of the capital spending compensates for depletion? What portion is for growth of production? We know new wells drilled should be roughly proportional to the capital spending. Thus the production rate gained is proportional to capital spending. Part of the production rate gained merely compensate for the decline and does not show up in total production growth. The remaining part of new production rate gained shows up as growth. If we know the generate decline rate of existing production wells, we can calculate the percentage of these two portions.

Case Study on Whiting Petroleum

I choose to do a case study on WLL as they are the second largest Bakken shale developer with a long history in Bakken, and a previous case study on their Federal 14-24H well gave me a good idea how fast their wells decline.

Here are the financial numbers of recent four quarters of WLL:

Note that I removed items not directly related to well drilling and production, like gains or losses of asset sell, gains and losses from financial hedge contracts etc.

For each BOE that WLL produced, it brought home $71.88. Subtracting $23.62 operating costs and $21.71 amortization of capital cost, the net gain from the barrel is $26.55/Barrel. Sound like a very profitable performance, right?

But is it fair that they spend $174.98/barrel on capital spending but amortized only $21.71/barrel of that cost? Where does the bulk of capital spending go? How much production growth did WLL gain from that capital spending?

In one year from Q3 2011 to Q3 2012, the daily production grew from 70670 BPD to 82620 BPD, or 16.91%. The daily production growth was +0.0428%/day.

As I discussed before, Bakken shale wells collectively decline about -0.2% each day, or that newly added production rate may bring in roughly 1/0.2% = 500 days worth of current production rate in the future. So I use the -0.2%/day natural decline rate to calculate.

To go from -0.2% decline below 0.0% to +0.0428% growth above 0%, the difference is 0.2428%. The portion of growth equals to 0.0428%/0.2428% = 17.628%. The portion that counters the well decline is 82.372%.

Thus, 82.372% of the daily capital spending, or $11.342M, was spend merely to maintain production at average level of 78692 BPD. That should be the fair amortization amount. It averages to $11.342M/78692BOE = $144.12/Barrel amortization cost.

The remaining 17.628% of daily capital spending, or $2.427M/day, was spend to boost average production by 0.0428% in a day. That's a production gain of 78692 BPD * 0.0428% = 33.68 BPD. The cost to grow each Barrel per day production, is $2.427M/33.68 = $72061.

As I explained, each 1 BPD of initial production gain can be expected to bring in 500 days worth of production, or 500 barrels. So capital spending to gain one future barrel is $72061/500 = $144.12/barrel.

Notice that both the amortization cost of current barrels and the capital spending on future barrels both comes to the same number, $144.12/barrel. Those are very expensive barrels of oil.

This is not all the cost of the Bakken shale oil. It is only the capital cost portion. The operating cost was $23.62/barrel. So the real total cost is $23.62 + $144.12 = $167.74/barrel.

But WLL takes home only $71.88/barrel in revenue. That leaves WLL in $96 in loss per barrel. That is the true economy of the Bakken shale oil play.

Discussions and Investor Implications

I have written many articles to point out that there are mounting evidences to suggest that the US shale oil & gas industry has systematically exaggerated EURs and under-calculated the fair amortization of the capital costs as the wells deplete much faster than their projections. Thus you can not take the profit or loss number reported by these companies at face value, because they have not fairly accounted for the reasonable amortization costs.

There has been a widely spread and mistaken meme that the so called shale gas revolution brings cheap and abundant natural gas to the USA, thus it brings about the demise of the US coal industry. I keep hearing people singing the song that:

"Coal is dead. Cheap and abundant natural gas is replacing coal"

Nothing is further from the truth! I hope that by looking at the true capital and armortization costs, by looking at the rapidly growing debts in the shale industry, people should finally realize that shale gas and shale oil is not cheap at all, nor are they abundant. In the long term, coal is still the king of fossil energy. Calling coal dead is way premature. This presents an excellent opportunity for investors to jump into the coal sector to reap huge profits in a coal rebound. The profit potential is huge, because there is now a disparity of 75 times more money invested in the shale oil and gas industry versus that invested in the coal sector. When every one bets on the other side, you'd better on the other side of the market. I am holding my coal stocks firm, I advice you to do the same.

Disclosure: I am long [[JRCC]], [[ANR]], [[ACI]], [[BTU]].

I want to demonstrate that the classical Arps formula, which the shale industry loves to use to project the EURs (Estimated Ultimate Recovery), tend to result in unrealistically high EURs, and that the long term productivity of the shale wells generally fall way below the industry's projections. A well that wasn't re-stimulated during its history will adequately reflect how the well's productivity declines naturally over time.

The classical Arps Type Curve vs. Modified Arps Type Curve

Let's re-cap about the classical Arps formula and how I modified it:

(click to enlarge)

Geologists Arthur Berman often criticized the industry for using the classical Arps formula which exhibit a hyperbolic decline with the long term decline rate approaching zero. In reality, shale wells exhibit a non-zero terminal decline, so they fall far behind the projections of the Arps formula in the long term. I agree with Berman. I proposed to add a exponential decaying factor to account for the terminal decline. See the chart above.

This decay rate beta is small, so in the short term it makes little difference, but in the long term, it makes a huge difference. Let me use real production data to find out which one is right.

The Whiting Federal 14-24H Bakken Shale Well

The Bakken well I study is Federal 14-24H, well No. 15776. The link contains data on that well. The well was developed by Whiting Petroleum Corp. (WLL). Production started on Sep. 22, 2005. So it has seven years of production. That's longer than the XTO Energy operated Sveen 34X-14 that I discussed in my last article. XTO is now part of Exxon Mobil (XOM).

See the monthly production data below. All the monthly days of production are full months, suggesting that production was never interrupted by any re-fracing operations or shut-downs.

click to enlarge)

This well is the kind of best performing shale wells that the industry would love to pitch to investors. When it started, it was one of the highest producing well at the time. The well decline was also one of the slowest. First year production decline was only 55%. Compare that to the 80%-85% first year decline in the latest Bakken wells!

Modeling The Production Using Arps and Modified Arps Formula

I found the following parameters to fit the actual production using both the classical and modified Arps formula:

• IP = 400 BOE/Day for both formulas
• B-Factor = 1.50 for both formulas
• D = 0.00467/Day for the classical Arps formula
• D = 0.00333/Day for my modified Arps formula
• Decay factor Beta = 0.000333/Day for modified Arps
• EUR from classical Arps is 640 MBOE (in 500 months)
• EUR from modified Arps is 288 MBOE (<20 BPD in 110 months)

Note that the long term decay factor Beta=0.000333/day is higher than the 0.0002/day I found for the Sveen 34X-14 well. So although the initial decline of the older wells flatten out faster, its longer term decline is actually steeper. The shale producers just can not gain.

Here are projections from each formula compared to actual data:

click to enlarge)

Although both the classical Arps and my modified Arps fit the data nicely for the first three years, I can not find the right parameters to make the classical Arps curve fit the data in longer term. The Arps curve continues to flatten out while the actual production continued to decline beyond three years. On the other hand, my modified Arps curve still fits perfectly in the long term.

This deviation is what Arthur Berman has been criticizing about. The data agrees with Arthur Berman and me in exhibiting continued decline beyond three years. The industry's classical Arps formula fails to follow the long trend.

We can see the deviation more clearly when we plot the graph in logarithm scale, as shown below:

click to enlarge)

The logarithm scale plot above shows that the real production data continued to decline following almost a straight line, as suggested by my modified Arps curve. The classical Arps curve continued to flatten out to a horizontal line. Once again, the data clearly agrees with the modified Arps curve I proposed, not with the classical Arps.

As a result, the cumulative production also follows the projection of the modified Arps. It deviates from the classical Arps curve:

click to enlarge)

The deviation of cumulative production is more clear when we plot the longer term trend as below:

click to enlarge)

As shown in the above graph. The classical Arps formula projects an EUR of 640 MBOE in 500 months (41.67 years). But modified Arps projects an EUR of not much more than 300 MBOE. If we cut off the well as it falls to below 20 BOE/day production level, which happens after 110 months (9.17 years) then the EUR will be 288 MBOE.

The Well Data Disagrees with EUR from Classical Arps Formula

As of today, the well has produced for 7 years. The accumulative production is 257 MBOE. How much more can it produce?

According to North Dakota DMR data, well No. 15776, the well we discuss here, produced 569 barrels of oil and 1626 MCF of gas in 30 days in September 2012, or total of 849.3 BOE, or 28.3 BOE/day.

This is not much higher than the 20 BOE/day cut off threshold.

My modified Arps formula projects a production rate of 30.84 BOE/Day here. It seems to agree with the data pretty well. The model projects a current decline of roughly 0.000583/Day, or 19% decline annually!

If this decline rate continues and we continue to produce until the production rate is almost zero, the remaining production will be 30.84 BPD / 0.000583 = 53 MBOE. If we cut off at a threshold:

• If we cut off at 20 BPD, then 18.6 MBOE remains.
• If we cut off at 15 BPD, then 27.2 MBOE remains.
• If we cut off at 10 BPD, then 35.8 MBOE remains.

I think the ultimate production of this well will be 280 MBOE, or roughly 44% of the EUR calculated from classical Arps formula.

Investment Implications

There are mounting indisputable evidences that critics like Arthur Berman are right. The shale industry has systematically exaggerated EUR projects of shale wells by more than a double. More over, they systematically under-calculated the armortization of the capital expenditures as the wells deplete much faster than they expected.

Is there a Ponzi Scheme going on in the shale oil and gas industry? I will let others do the finger pointing. But as an independent investor, I have repeatedly warned people that they should NOT take the rosy pitches from shale development companies at face value. They should always take the projections with a grain of salt, and do their one data analysis to find out the truth. I encourage people to follow my math analysis to find out the reality.

I keep urging people to get out the shale oil and gas sector, and get into the coal sector. People wrongly believe this meme that:

"Coal is dead. Cheap and abundant natural gas is replacing coal"

Just think about how big an investment opportunity it will be when people find out the truth, and shift their investment money from shale gas to coal. Currently there is a huge disparity that for every $75 people spend investing in the shale oil and gas sector, only $1 is invested in the US coal sector. I expect the ratio to be reversed to the other way, for every $1 people invest in the shale sector, there will be $10 invested in coal instead.

Disclosure: I am long [[JRCC]], [[ANR]], [[ACI]], [[BTU]].

How to Calculate a Reasonable EUR Estimate

To re-cap, I proposed to modify the Arps Type Curve formula by introducing a decay factor of roughly 7% annually, or 0.0002/Day, so as to reflect a reasonable terminal decline of the wells. I also proposed a rule of thumb to estimate the EUR quickly:

Wait 60 days or 90 days after production started, so that the production rate PR stabilizes. Take that production rate PR and multiply by 500 days to estimate how much more will be produce, add the volume already produced to get the EUR.

How accurate does my method project? To find out, I need to test my method on a well with long production history to study. I found one such well to study. It started production on Sep 19, 2006.

The Sveen 34x-14 Bakken Well Owned By XTO Energy

The Sveen 34X-14 well was developed by XTO Energy Inc., which is now part of Exxon Mobil (XOM). Here is a link to data on that well. There is a 230 pages comprehensive document on that well. The production started on Sep. 20, 2006. So there's six years of history.

Here are the monthly productions of that well, in BOEs:

(click to enlarge)

Cumulative production of the well is 280 MBOE after six years.

Modeling the Production of the Sveen 34X-14 Well

I selected these parameters to model the well's historic production:

• IP = 900 BPD (Same as in my last article)
• D = 0.02/Day (a bit less than 0.027/Day in my last article)
• B-Factor = 1.55 (a bit higher than 1.465 in my last article)
• Decay factor Beta = 0.0002/Day (Same as last article)

Here is how my projection compares with the actual production:

(click to enlarge)

My projection seems to match pretty well. XTO conducted a re-fracing operation on the well in August 2009, which seems to have boosted the production rate for a while. But the production rate has since then fallen back to my projection curve.

I used the same IP = 900 BPD and same long term decay factor of Beta = 0.0002/Day as used in my last article. But I had to make two adjustments to make the curve fit:

1. The initial decline D is reduced from 0.027/Day to 0.020/Day. This means the wells six years ago probably declined a bit slower. The newer wells today, due to closer fracing stages, may decline faster.

2. The B-factor is increased a bit from 1.465 to 1.550. This means the decline flatten out a little bit sooner in the old wells. The newer wells takes a little bit longer for the decline to flatten out.

Both of the above changes would result in a slightly higher EURs. So I am not surprised that the EUR will be higher than 200 MBOE. The accumulated production so far is 280 MBOE.

Since the initial decline D is slower, the production rate stabilize quicker in the old wells. So I will use 60 days after the production start, instead of 90 days, to use my rule of thumb to estimate EUR:

• At 60 days, the projected IP is 451.4 BPD, the projected cumulative production is 36.78 MBOE.
• EUR = 451.4 BPD * 500 days + 36.78 MBOE = 263 MBOE.

My result of EUR = 263 MBOE is close to cumulative production of 280 MBOE, but is still a bit lower than the actual production. This is mainly due to the re-fracing done in August 2009 which did boosted the production rate. But it appears to me that the EUR gain from re-fracing is very limited.

How much more will this well produce?

As of Sep. 2012, the well produces 40 BPD. The projected decline rate is 0.0005/Day. Assuming this decline rate holds, the remaining production volume is approximately 40 BPD / 0.0005 = 80 MBOE. If we cut the well off at 20 BPD level, then 40 MBOE will be produced.

So this well's ultimate production will likely be 280 MBOE + 40 MBOE, or 320 MBOE. Compared with my estimate of 263 MBOE, the well has gained 60 MBOE of extra production due to re-fracing treatment.

How Much Does Re-Fracing Help?

Producers pitch re-fracturing the wells as being effective in boosting EURs and extend a well's life span. I am skeptical to the claim. As shown in the above chart, the re-fracing done in August 2009 only marginally boosted the production rate. However the production boosting effect diminished quickly. In three years, it's almost gone.

In SPE 154669, Mark Craig of Devon Energy (DVN) claimed that a cash study of 13 re-stimulated (re-fracing) Barnett wells show that re-fracing, at a cost of $0.9M per well, can boost EUR by 0.8 BCF.

Such claim is ridiculous. The average accumulative production of all Barnett shale wells is no more than 0.67 BCF per well. It is absurd to claim that re-fracing can more than double a well's EUR. As a matter of fact, paying $0.9M cost to gain 0.8 BCF extra production. That's a production cost of only $1.13/mmBtu. If it is a such a great deal, producers should rush back to Barnett to re-stimulate all the wells. But they don't. So the claim cannot stand the test of water.

Craig Cooper estimated that re-fracing costs $0.095M per stage. If a well contains 25 stages, one re-fracing operation will cost $2.4M. As the re-fracing only boost production marginally and it lasts less than three years, it seems to me that re-fracing is wasting money.

In a presentation (page 16), XTO showed the production rate before and after the Sveen 34x-14 was re-stimulated:

(click to enlarge)

It looks to me they did manage to boost water production a lot, as all the injected water comes right back out. But the oil and gas production gain was much less impressive.

Based on my calculation, re-fracing contributed to 60 MBOE extra production. At $65/BOE value, it contributed to $3.90M revenue. As XTO carried out multiple re-fracing operations on the well's six year history so far, I believe the economic benefit of re-fracing is zero.

Discussions and Investment Implications

Geologist Arthur Berman and others have been sounding the alarm for a long time that the US NG industry is engaged in efforts to pitch overly-optimistic projections in the shale well revolution. The money spent on shale development far out-weight the economic return. The capital spending of shale producers routinely out-pace revenue stream by several times. Despite of the gloomy reality, producers continue reckless money spending in aggressive well drillings, thanks to generous money from banks and investors.

This is an non-sustainable bubble. I see a looming debt crisis in the shale industry, which has accumulated more than half a trillion dollars in debts thanks to their shale revolution adventure. The NG industry will collapse once bank lending is cut off, leading to collapse of US natural gas supply. As a result it will send natural gas and coal price skyrocketing. It will happen soon.

The biggest beneficiary to the looming crisis in the NG sector, is the US coal sector. That's where I put my money in. You should, too!

The coal sector was wrongfully punished by the wide-spread meme:

"Coal is dead. Cheap and abundant natural gas is replacing coal"

Nothing is further from the truth!

I made the efforts to do the calculation and modeling to find the truth behind the rosy pitches of NG companies. I am convinced that the real data says I was right and the industry experts were wrong.

I ask you to follow my math and do your own analysis. If you agree with me, pull your money out of the shale industry and into the US coal sector. The coal story is the biggest investment opportunity in more than a decade. I am holding my coal stocks firm.

Disclosure: I am long [[JRCC]], [[ANR]], [[ACI]], [[BTU]].

The Charlotte 2-22H Well of the Continental Resources

Let me do a case study on one particular Bakken shale well owned by Continental Resources Inc (CLR), the Charlotte 2-22H well. CLR pitched this well in its 10/09/2012 investor presentation (page 63). It must be one of the best performing CLR wells.

Fellow SA writer Richard Zeits quoted CLR describing this well:

The Charlotte 2-22H tested at an initial one-day rate of 1,396 Boe/d and is assigned a EUR of 561 MBoe; the well had cumulative production of 87 MBoe in the first 9.8 months, or just under 300 Boe/d average.

The well might had a peak 24 hours production of 1396 BOE. But it was an unstable and non-representative production volume to be used for EUR projection. I find a reference of the production in the first 35 days. During the first 5 days, oil produced was 3434 barrels and gas produced was 3449 MCF. Using 5.8 MCF of gas equivalent to one barrel of oil, the total production in 5 days was 4029 BOE. That's averaging roughly 806 BOE per day.

Modeling Shale Well Decline Using Modified Arps Formula

I discussed the Arps Empirical Formula in the past. The industry uses the Arps Type Curve formula to project a well's future productions. The problems with using the original Arps formula are:

• For the initial few months of production, almost any parameter will be able to fit with the production data. So the industry tends to fit the curves using a very high b-factor, in order to project a lower long term decline rate and a higher EUR.
• The Arps formula itself is divergent when a b-factor higher than 1.0 is used, resulting in a cumulative production that approaches infinity when integrated over long time.
• The Arps formula has a long term decline rate that approaches zero. In reality, terminal decline rate is roughly 7% or higher. The terminal decline rate does not approach zero in long term.
• The long term productivity of shale wells routinely come up far short of what's being projected using the Arps formula, as the production declines faster than the formula predicts.

To adjust for problems above, I adopt a modified Arps formula to model shale well declines. The adjustment is simply multiply the original formula by an additional slow decaying factor Exp(-Beta*T).

(click to enlarge)

The original Arps formula, and my modification is explained above.

Modeling the Charlotte 2-22H Bakken Shale Well

Using proper parameters, I can model the well's actual production with a perfect match, see my modeling curve as superimposed on the original chart taken from CLR's presentation:

(click to enlarge)

My model used the following parameters:

• IP = 903 BOE per day.
• D = 0.027 / Day.
• B-Factor = 1.465 (typical value used)
• The decay factor Beta = 0.0002 / Day.

Note that the IP I used is pretty close to the first 5 day average of 806 BOE per day, as mentioned above. My model is validated by matching the actual production in the first 10 months.

Based on my calculation, my spread sheet gave these projections:

• First year cum. production is 96.949 MBOE. PR=129.62 BPD
• Two year cum. production is 132.88 MBOE. PR=76.78 BPD
• Five year cum. production is 187.45 MBOE. PR=33.46 BPD
• Ten year cum. production is 227.787 MBOE. PR=14.54 BPD
• First year production rate decline is -85.65%.

The EUR estimate can be estimated in two ways:

1. Use 20 BPD daily production rate as the cut-off. I project that the well drops to below the cut-off production in 2880 days or 7.89 years. The cumulative production will be 214.5 MBOE.
2. Use my 500 days of IP production rule. But since the initial production drops too fast, let's apply this rule after the first 90 days. By the end of 60 days, the cumulative production is 44.166 MBOE and the production rate is 314.8 BPD. So 500 days at 314.8 BPD will produce another 157.4 MBOE. The total is an EUR = 202 MBOE. Only 5.8% lower than above estimate.

CLR projected a much higher EUR of 561 MBOE. I do not think their projection is supported by actual data. The original Arps formula would project EUR = 474 MBOE in 15000 days or 41 years.

The Economy of This Bakken Shale Well

What's the profitability outlook of this Bakken shale well?

Based on most recent CLR quarterly report, I estimate that direct well drilling cost is $11.65 per well. Figuring in overhead and production maintenance costs, I think a lifetime cost of $13M per well is a very conservative estimate. Let me do the calculation using $13M and $15M cost per well. Realized revenue was $65 per BOE.

Just for comparison, let's say CLR borrows $13M from millionaire Joe at a moderate 5% interest. Joe will be earning 5% interest from day one. CLR will be paying the interest and principal from the oil and gas revenue. Let's see how they perform over time.

(click to enlarge)

The above chart shows the relative financial performances. The two thick lines represent the accumulative production, with the scale on the right side. The thin lines represents the financial performances.

I did the calculation using both the original Arps formula, and the modifies formula. The blue lines represent the original Arps formula, which tend to over-estimate. The pink lines use modified formula.

The red line shows interest and principal accumulated if the money is lent out at 5% interest rate. The horizontal axis is in days.

As can be seen, CLR would pay off the loan after 3280 days. That's the break even point after a full NINE years. After that point, any revenue earned less the production and maintenance cost would be the profit that gets into CLR's pocket. However, by then, there is not much profit to be made at all: The well will be producing 16.9 BOE per day. That's already below the 20 BPD production threshold I used above for the end of the well's useful lifespan.

CLR is definitely not making a profit if my calculation is right. I said $13M per well lifetime cost was conservative. Let's see what happens if the cost is $15M per well instead:

(click to enlarge)

The above is the same calculation, but done assuming the lifetime well cost is $15M instead of $13M.

The result is even gloomier for CLR. They are still under water at the far right edge of the chart, which is for 5000 days or 13.69 years.

By the end of 5000 days, CLR still owes the bank $2.837M debt. Mean while the millionaire Joe who loaned out the $15M have happily earned compounded interest of $14.264M during the same time.

Discussion and Investment Implication

After the above discussions, if you have $13M or $15M of cash, do you think you get a better deal simply saving the money in a bank account earning 5% interest, or is it a better deal to invest the money in a shale company to drill a Bakken oil shale well?

I think the answer is obvious. Bakken shale wells are simply non-economical at current oil price and at current well productivity.

Why do investors continue to pile on Bakken shale companies like CLR and EOG Resources (EOG)? Why the investment community dedicates 75 times more capital money in the shale development sector, than in the US coal mining sector? I believe this is the biggest investment mistake in the history of energy investment! It creates an excellent investment opportunity in the coal sector.

I stated that the US natural gas industry and coal industry each produces an equal amount of fossil energy. There is no reason why the coal sector deserves only 1/75th of the investment capital of the NG sector, especially when current coal price is at or nearly the profitable level, while the NG price is deeply non-profitable.

My statement is based on that:

• US produces roughly 1 billion tons of coal per year. Each ton contains 20 MMBTU of energy. Total is 20 quadrillion BTU.
• US produces roughly 24 TCF of natural gas per year. Each MCF contains 1 MMBTU of energy. Total is 24 quadrillion BTU.

But since most of the NG industry has given up on conventional gas and concentrated their effort on shale development, it is fair to compare coal with just the shale gas industry:

• US produces 9.25 TCF of shale gas and 360M barrels of shale oil, which is equivalent to 5.8 MCF per barrel. The total is 11.34 TCFE of gas. Total energy is 11.34 quadrillion BTU.

So the disparity is even more extreme. The entire US coal industry produces TWICE as much energy as the shale oil and gas industry. Yet the investment community dedicates only 1/75th of capital in the US coal sector while wasting 75 times money in shale players.

My advice: Get out of shale plays and get into the coal plays.

Disclosure: I am long [[JRCC]], [[ANR]], [[ACI]], [[BTU]].