There is an important controversy on shale gas boom and burst. The controversy focuses on whether the shale gas is economical to produce or not. Critics say the shale industry exaggerated the EUR (estimated ultimate recovery) of shale wells and painted a rosy picture while the productions come out far short of expectations.

Whether a shale gas well is economical or not relies on these things:

- The life cycle total cost of exploration and production.
- The EUR, estimated ultimate recovery from each well.
- How fast can the gas be recovered and revenue realized.
- What is the market price of natural gas produced.

I will discuss how the industry models shale well declines. Why they often over-estimate the EUR, and why the industry faces gloomy reality when it comes to the profitability of shale gas wells.

**To B Or Not to B - That is The Question**

If you have read Arthur Berman, the outspoken critic of the shale gas industry, you might have wondered what was the **b** parameter. Berman often referred to the **b** parameter when he criticized the hyperbolic decline models that shale gas experts use to calculate EUR. Berman believes that such models lead to EUR over-estimates.

All natural gas wells, whether conventional or shale gas, have their highest daily production rate on day one. They continue to decline throughout their life cycles. The declines of shale gas wells are very steep. Thus correctly modeling the decline is the key to correctly project the EURs. Since few shale wells have gone through a whole life cycle, it leaves plenty of wigging rooms for experts to come up with all sorts of decline models and push for more optimistic results.

I have developed my own shale gas decline model. The gas industry uses a formula first developed by Arps. They call it type curve. It is an empirical formula. Empirical means it is not supported by physics, but merely by the experience that it seems to give good results.

My decline model and the Arps type curve model is compared below:

As you can see, 0<b<1 is the reasonable range for the parameter. But the industry prefers to use b>1. This often leads to much higher EUR estimates. But it is problematic as it leads to infinity. Nature does not allow infinity.

Do experts deliberately use a parameter that looks ridiculous from basic physics, in order to intentionally over-estimate EUR? I think I have a more reasonable explanation without pointing fingers. The Arps formula is inadequate that it has only three freely adjustable parameters. When you remove the IP (initial production rate), which is a trivial parameter confined by the total production, you are left with two parameters, initial decline rate D and parameter b. The D can be removed by scaling the time. Thus b is the only adjustable parameter. When b=0, it is just exponential decay. When when a wells decline does not follow simple exponentially decay, which is mostly the case, you have to push b away from 0 for a better data fitting. This often leads to b being pushed too high and b>1.

But the shale gas industry experts should know better! They should know that the Arps formula has its limit and can no describe the long term trend beyond the first few years, as it has only three freely adjustable parameters. They should have learned from school that the b>1 should not be allowed in the Arps formula as it leads to divergence and infinity.

I think my own model, with one more parameter than Arps', can better describe the shale gas declines. To verify, I used Berman's chart on Haynesville shale. I super-imposed my own model and CHK's type curve onto the chart, to see how good they match:

My model seems to match the data better than the CHK model did. There is no long term Marcellus well data yet. But in long term, the CHK model is problematic as it has virtually no terminal decline:

Arthur Berman pointed out that during early well productions; models with vastly different b values all look similar. The differences only show up in the long term, leading to vastly different EUR values.

Since there is insufficient long term data to tell which model works better, let me run both models to analyze some data.

**Profitability Case Study on Marcellus Shale Wells**

I have studied an EIA document and obtained a type curve chart for Marcellus shale wells. I could use the parameters to construct the same Arps type curve for calculation comparison with my model:

The D and b parameters were not given. But given one year, five year and ten year cumulative production and a 3.75 BCF EUR, I could easily found out the D and b used, and verify that I had the correct values:

- D =
**1/3**per month;**b = 1.461**(b>1!); IP = 4.11 MCF/day. I obtained the same 1 year, 5 year and 10 year productions.

It comes out that the claimed EUR of 3.75 BCF is the cumulative production after exactly 500 month, or 40 years and 20 months. The daily production will drop to 0.095 MCF a day. It could fetch $228 at $2.40/mmBtu gas price, enough to pay one day's minimum wage.

Does Chesapeake Energy (**CHK**) honestly believe a shale gas well can be produced for that long. at such a low yield? As a matter of fact, since the function is divergent for b = 1.461 > 1, they could let the well run a thousand year and brag about any arbitrarily high EUR number they like. In 1000 years the EUR would be 11.56 BCF:-)

My calculation results:

As can be seen, my model can match the early stage of decline behavior nicely. But my model can also reflect the terminal decline correctly, but CHK's Marcellus type curve can not. The Marcellus type curve is no longer useful after the first 10 years, as it does not reflect the terminal decline phase correctly.

The above is the same chart like last one, but with a different time scale to have a closer look at short term pattern of the curves.

Once the production decline is known, I can proceed to calculate the profitability of Marcellus shale wells. I assume the following for calculations:

- Based on numbers contains in CHK's Marcellus type curve chart, they have a drilling cost of $3.6M, finding cost of $1.12/mmBtu * 3.75 BCF. Total $7.8M per well. They excluded many costs. The numbers are several years old so when you add real inflation the numbers are much higher. I assume $15M per well cost for the calculation.
- I assume the per month production maintenance cost is $30K.
- I start with a debt of $15M for completing the well. The debt carries a 5% annual interest cost.
- I assume the principal of the debt is paid off as fast as possible. I tally the number for each month. When there is a debt I subtract interest cost. When there is cash, I add 5% interest income from teh cash.

Here are the results.

I will explain later.

Further reading: Hamilton. Read Arthur Berman on Marcellus. Stay tuned on my main SA article which has been submitted. Cheers!

**Disclosure: **I am long JRCC, PCX, ACI, ANR, BTU.