Department of Economics Discussion Paper 2002-08

The Cost of Lifting Natural Gas in Alberta: A Well Level Study

Matthew Foss, Daniel Gordon and Alan MacFadyen May 2002

Department of Economics University of Calgary

Calgary, Alberta, Canada T2N 1N4

This paper can be downloaded without charge from http://www.econ.ucalgary.ca/research/research.htm

The Cost of Lifting Natural Gas in Alberta: A Well Level Study

by

Matthew Fossa) Daniel V. Gordonb) Alan MacFadyenb)

Abstract The economics literature on natural resource depletion and petroleum/gas extraction is extensive. Much less research has been devoted to empirical modeling and measurement of the cost characteristics of lifting natural gas at the well level. The contribution of this paper is to add to empirical understanding of the cost characteristics in lifting natural gas at the well level using data for wells in Alberta, Canada. We are particularly interested in measuring for common factors affecting production costs across reservoirs and also for individual well effects. Information on extraction cost at the well level can be used in calculating projected cost in gas production and combined with expected drilling and infrastructure cost allow a total cost forecast for the project. Keywords: Natural Gas, Cost Characteristics, Well Level JEL classification: Q4 a) CERI, Canadian Energy Research Institute, Calgary, Alberta Canada T2L 2A6

b) Department of Economics, University of Calgary, Calgary, Alberta Canada T2N 1N4

The Cost of Lifting Natural Gas in Alberta: A Well Level Study

I. Purpose

The economics literature on natural resource depletion and petroleum/gas

extraction is extensive. Sweeney (1993) describes the basic model for resource depletion

based on maximization of present value of profits subject to a time path of extraction.

This model makes clear that in resource depletion marginal cost has two components, the

marginal extraction cost and the marginal user cost. The marginal extraction cost is the

cost of lifting the next unit of gas from the well. The marginal user cost is the opportunity

cost of producing now rather than waiting to produce at some point in the future. In

extracting natural gas, production now reduces pressure in the well increasing the cost of

extraction in the future. Current extraction reduces future profits.i Kuller and Cummings

(1974) provide a detailed characterization of the many facets of marginal cost in a

petroleum production model. The basic Sweeney model has been generalized by

Krautkraemer (1998) to incorporate reserve additions and thus, explicitly account for

exploration in the stock formulation of the model.

Some research has been devoted to empirical modeling and measurement of the

cost of lifting natural gas at the well level. Chermak and Patrick (1995) using data for gas

wells in Wyoming and Texas found that operating costs are determined by the quantity of

gas lifted and by reserves remaining in the well. In this paper, our contribution is to add

to empirical understanding of the cost characteristics in lifting natural gas at the well

level using data for wells in Alberta, Canada. We are particularly interested in measuring

for common factors affecting production costs across reservoirs and also for individual

well effects. Using well-level data allows us to avoid the problems of aggregation

common in regional gas analysis.ii Information on extraction costs at the well level can be

used in calculating projected costs in gas production and combined with expected drilling

and infrastructure costs to allow a total cost forecast for the project. Knowledge of the

cost function is also important for measuring costs associated with different output levels

and for determining when production is no longer economically viable and the well

should be abandoned.iii

The paper is organized as follows. In Section II, a brief

survey of the characteristics and nature of natural gas is

presented. Section III describes the basic economic model of

gas extraction and the cost estimation model. In Section IV, the

data and empirical cost estimates are reported. Section V is a

conclusion.

II. Nature of Natural Gas

Conventional natural gas is a depletable resource found in underground

reservoirs. To accumulate in a reservoir an original source of carbon and hydrogen,

buried by porous rock, must have undergone sustained heat and pressure and eventually

natural gas formed that migrated through the porous rock until entrapped in reservoir

rock. The larger the pores in the rock the greater the porosity (i.e., the greater the amount

of fluids that the rock could contain) and permeability (i.e., the easier it is for the gas to

flow). Natural gas is primarily composed of methane with lesser concentrations of ethane,

propane and butane.iv

Hydrocarbons within a reservoir are driven by pressure. Pressure increases with

the depth of the reservoir due to gravity. Gas has a tendency to expand and being trapped

in the reservoir adds to the pressure. When water is present it moves into pores in the

rock vacated by gas further enhancing pressure. Pressure is the key to gas production.

The difference in pressure between the well bore and the reservoir acts to lift or push the

gas to the surface. The flow of petroleum into the well bore and up to the surface reduces

the pressure differential between the reservoir and the well bore and eventually the flow

decreases and production slows.v

Porosity and permeability differ across reservoirs and within the reservoir itself.

As well, the volume of the reservoir rock, the depth at which natural gas is found, the

sulphur content, the amount of associated water, the presence of other hydrocarbons and

the pressure of the gas are all variable factors that differ across reservoirs. These variable

factors affect the value of the natural gas and the cost of production.

Often it is necessary to assist the flow of gas by fracturing the reservoir rock

around the well bore (Berger and Anderson, 1992). Injecting acid or other fluids

containing a propping agent into the reservoir does this. The acid dissolves part of the

formation around the well bore, making existing pores larger. Injecting fluids causes the

formation to crack. The propping agent prevents the formation from collapsing back.vi In

some cases, if the reservoir size is large, compressed gas is added to the reservoir to

enhance pressure levels.

The fact that deposits of petroleum are underground implies that natural gas

stocks are not known with certainty. Exploration to locate deposits is a fundamental

activity in this industry. Once a reservoir of petroleum has been found estimates of the

size can be made and potential production determined. Investment in development of the

formation is based on expected profits. Importantly, development of the reservoir

improves estimates of stock size and production potential. After the well has been

developed, changing price expectations can impact production and may warrant well

abandonment. But with government regulation requiring special sealing of abandoned

wells (and thus costly for the firm to reopen the well) it is not uncommon to observe

producing wells with operating costs exceeding revenue (Brennan and Schwartz, 1985).

The nature and characteristics of the reservoir determines the rate of flow of gas

from a well. Lifting gas too rapidly can pull excess water into the reservoir as gas is

extracted. Excess water can impede the flow and reduce the amount of total gas

recoverable from a reservoir. The efficient rate of gas flow is set by engineering

standards and allows for the greatest rate of flow without damaging the reservoir. The

spacing of wells is also important for gas production and is set by regulation.vii The rate

of gas flow is subject to external factors such as government regulations and pipeline and

processing plant capacity. After lifting to the surface gas is processed to remove foreign

components (e.g., sulphur, water and other hydrocarbons) and shipped by pipeline to

markets.

III. Modelling Depleteable Resources

Economic models of depleteable natural resources start from the proposition that

there exists a fixed stock of the resource. Production overtime reduces the amount of

stock. Depleting the resource today generates an opportunity or user cost because there

would be less resource available in the future. A profit maximising firm will account for

user cost in decision making. The user cost of not extracting the resource is measured as

the increase in the present value of future profits. Sweeney (1993) represents the user cost

of production in a resource model to maximise the present value of profits by choosing a

time path of extraction. Let the cost equation at time t be a function of the extraction

rate q and the stock remaining at the end of the period , or . Also, let the

interest rate be defined as r and the price of the resource at time t as . The firm is

assumed to be a price taker and extraction takes place over a known time period with

terminal time denoted as T. The resource owners problem is to maximise discounted

profits subject to the resource constraint or

)( tC

1−tRt )R,q(C ttt 1−

tp

(1) ∑=

−−−=

T

t

rttttt e)]R,q(Cqp[

01Π

subject to , for all t. The solution to the problem is a straightforward

application of Lagrangian multipliers (

ttt qRR −= −1

)tλ with first order conditions

11

0

−

−− ∂

∂+=

>+∂∂

=

t

trtt

ttt

tt

RC

e

,qifqC

p

λλ

λ (2)

The terminal conditions 0=TT Rλ must also be satisfied. The first expression in

Equation (2) makes clear that price is equal to the sum of marginal extraction cost and the

marginal user cost. In natural gas extraction, marginal user cost is associated with the

decline in pressure as gas is lifted, which makes production in the future more costly.

Krautkraemer (1998) generalizes the model by incorporating reserve additions

(RA) into the stock equation and explicitly accounting for the cost of reserve additions

in the maximization problem. The profit-maximizing problem is now written as )C( RA

(3) ∑=

−− −−=

T

t

rtt

RAtttttt e)]RA(C)R,q(Cqp[

01Π

subject to , for all t. Nothing fundamental has changed with the

addition of reserve additions but solving the first order conditions provides a rule for

exploration or

tttt qRARR −+= −1

t

RAt

t

tt RA

CqC

p∂∂

=∂∂

− (4)

Equation (4) states that a resource firm will incur the cost of exploration until the stated

marginal conditions are satisfied. Importantly for this study, Equation (4) makes clear

that extraction costs are an important determining factor for the levels of both current

production and exploration and shows the importance of empirically measuring costs of

extraction.

A number of empirical studies have been formulated based on this fundamental

economic model of resource depletion (Livernois, 1987; Livernois and Uhler, 1987;

Griffin and Jones, 1989; Helliwell, et. al., 1989). However, Chermak and Patrick (1995)

appear to be the first to model and estimate a cost function for natural gas extraction at

the individual well level. Chermak and Patrick argued that cost (C) of lifting natural gas

is influenced by quantity (q) of gas extracted, the reserves (R) remaining, a time (t) trend

to capture macro (e.g., inflationary) effects and the number of months since

commencement of production (pm), which is a measure of the age of the well. Although a

variety of functional forms where tested they argued that the basic log-log model was

preferred on statistical grounds and written as

ttpmttRtqot pmlntlnRlnqlnCln εβββββ +++++= (5)

where ln is the logarithmic transform and tε is a random error term. The log-log model

has the advantage that the estimated beta coefficients can be interpreted as elasticities

measuring the partial influence of each independent variable on costs

Chermak and Patrick extended the model somewhat to include variables defining

ownership, geographic location, rock formation and specific well characteristics. They

argued that well ownership impacts costs through differing levels of efficiency; that

locationviii is important because cost factors can be specific to each region; and that

different geological formations may be more costly to produce from than others.

Chermak and Patrick also postulated that it is possible for individual wells to be quite

unique in their production costs as would be the case, for example, if reservoirs differ

significantly in characteristics. Two wells within the same reservoir could have quite

different costs if well spacing in the pool is not even, or if the pool has heterogeneous

reservoir characteristics.

The data they used in estimation represented 451 monthly time series

observations covering twenty-nine tight gas wells. They report results showing operating

cost inversely related to reserves, and directly related to quantity, with marginal cost of

production decreasing in quantity of gas extracted. The month of production variable

showed inconsistent results over the different models estimated. The ownership variable

proved statistically important and this was explained by different accounting and business

practises for the different firms.

The Chermak- Patrick approach to cost modelling is followed in this paper and

applied to a cross-section, time-series panel data set for natural gas wells in Alberta. The

panel nature of the data lends itself to econometric estimation to account for both

individual fixed well effects as well as common factors across wells impacting cost of

production

IV. An Empirical Cost Model for Alberta Gas Wells

The model developed in this paper is premised on the position that natural gas

firms attempt to minimize the cost of lifting natural gas. In the very short run or

immediate run period, the firm must operate within a fixed input setting i.e., the cost of

lifting gas depends on the economic and physical input factors in place during the period

of production. A longer run approach to cost modelling would allow for variable input

relationships. The data available for our analyses would not allow for this longer run

approach and, consequently, the focus of the study is on the immediate cost period.

The data used in measurement represents monthly observations on operating

costs, reserves, production month, depth of well, geological zone and reservoir pool for

twenty-two natural gas wells in Alberta over the period 1/96 to 12/98. Some wells report

no gas extraction in some months and these observations have been deleted from the data

set. The panel data set represents a total of 608 observations. Table 1 provides a

description of the variables showing mean and range of the data on an annual basis. There

is substantial variation in all variables defined as indicated by the range of standard

errors. Of particular note is the large variation in reserve size and depth of well. To

provide some information on the statistical relationship across variables Table 2 shows a

matrix of pair-wise correlations between variables. Note the strong positive correlation

between quantity of gas extracted and the remaining reserves reflecting the fact that

higher reserves support higher production levels. Operating cost is the sum of many

different types of expenditures related to gas operation and this aggregate sum is

described in an appendix.

The estimating equation is a regression of operating costs on variables defined in

Table 1, written in general form as,

),,.,( εdmrqfC = , (6)

where C is operating cost, q is gas extracted, r is reserves, t is a time variable, m is

monthly age of well, d is depth of well and ε is a random error term. We start the

empirical analysis by testing for functional form of the cost equation using a Box-Cox

transformation and then testing for fixed versus random-effects in the panel data set.

A non-linear Box-Cox transformation is applied to each variable used in the

regression equation, where the transformation takes the form λ

λ 1−ix (Greene, 2000). The

non-linear transformation requires a maximum likelihood estimation procedure where λ

and the vector of regression coefficients are measured based on maximising the log of the

likelihood function. The Box-Cox transformation allows testing the functional form of

the cost equation by measuring the value of the parameter, λ. If λ equals 1 the data

support a model linear in the variables and if λ equals 0 the data support a model where

the variables are linear in logarithmic form. A Wald test procedure is used in testing the

alternative null-hypotheses. The results of the testing procedure are reported in Table 3.

A null-hypothesis that λ = 0 (calculated ) can not be rejected at the 5% level

whereas a null-hypothesis that λ = 1 (calculated ) is easily rejected. (The

critical value of with one degree of freedom.) Consequently, the test results

support a cost equation where the variables are linear in logarithmic form. This result is

consistent with results reported by Patrick and Chermak.

39.02 =χ

χ 70.5632 =

84.32 =χ

iitC βα +=

The panel nature of the data set allows investigation of well-specific effects. One

procedure for measuring this effect assumes that the cost differences across wells can be

captured in differences in the constant term. The fixed effects model introduces a specific

dummy variable for each well. The fixed effects model is written as:

, ititT X ε+

where the vector X includes all variables defined in Equation 6 and iα is an intercept

term specific to each well but constant over time. The fixed effects model allows

variations in X to affect costs in the same way across wells but for each well the level of

costs can vary. The random effects model captures cost differences across wells by

assuming that constant effects for each well are randomly distributed across wells. The

general random effects model is written as:

,iititT

it XC µεβα +++=

where it is assumed that the random effects term iµ has zero mean and is not correlated

with the random error term itε . Greene (2000) describes a Hausman procedure to test the

data to find statistical support for either the fixed or random effects model. The procedure

is a test for correlation of the errors specific to a given well. In the fixed effects model,

the constant term models differences across wells whereas the random effects model

includes a well specific error term. The null hypothesis is that the random effects model

is the correct specification and is distributed as with k degrees of freedom. The

Hausman statistic generates a =629.12 and compared to a critical value of 9.49 at the

5% level we reject the random effects model and conclude that the panel data support a

log-log fixed effects cost representation.

2χ

t +ln

24χ

t +

To fix ideas, the basic cost equation will take the following form:

ttti

itt epmRqC +++= ∑=

lnlnlnln 4321

22

1ββββα . (7)

where the fixed effects are captured by itα . The model is essentially that of Patrick &

Chermak except for the fixed effects modification. Different forms of the cost equation

are estimated to capture nonlinearity in output, the importance of depth of well and

constant effects caused by ownership, geological zones and reservoir pools. The results of

the estimation are reported in Table 4. The individual fixed effects dummy variables are

not reported, however, an F-statistic is reported at the bottom of the table testing the null

that all fixed effects coefficients are equal to zero. The first column of Table 4 shows

results reported by Patrick & Chermak, Model 1 is our corresponding fixed effects

model. Model 2 adds the variable depth which is not included in Patrick & Chermak.

Model 3 allows for non-linear output in the basic cost equation. Model 4 includes a

dummy variable to account for the fact that the 22 wells in the study are divided up in

ownership between two companies. Model 5 accounts for the five different geological

zones that define the area where the wells are located.ix Finally, Model 6 includes

constant effects resulting from different reservoir pools as defined by Alberta Energy and

Utilities Board.

The estimated equations seem to provide reasonable good fit to the data with

pseudo R2 of between 0.73 and 0.80x. All coefficients are of the expected direction, costs

are increasing in both quantity produced and age of the well, and decreasing in remaining

reserves. The estimated coefficients are reasonably consistent across models. This is

especially true of the estimated coefficients on remaining reserves (ln r), with a range

-0.84 to -0.98, (all of which are statistically significant at the 95 percent level). Except for

Model 3, which includes a non-linear output variable the coefficients on quantity

produced (ln q) ranged from 0.07 to 0.10. Introducing the square of the output variable

(Model 3) changes the sign and magnitude of the linear output variable however, the R2

statistic indicates that no real advantage in explanatory power of the model is obtained. A

range of -0.03 to -0.04 is observed for the coefficients on the time trend. The time trend

indicates that operating costs have a tendency to fall. The age of the well had a

coefficient that ranged from 0.05 to 0.16. In some of the models, the coefficients on time,

well age, and quantity do not hold their statistical significance at the 95 percent

confidence level however, all, but well age in Model 3 and Model 6, remain significant at

the 90 percent confidence level. Compared to the results obtained by Chermak and

Patrick (column 1), our results imply that the wells in this sample have a larger elasticity

of cost with respect to remaining reserves, and smaller elasticity of costs with respect to

quantity produced.

Models 5, 6 and 7 account for the fixed effect of ownership, geological zone and

reservoir pool, respectively; however, these factors are measured not to have a significant

effect on the cost equation. The fit, as measured by the R2, stays in a narrow range of 0.76

to 0.78. Moreover, the coefficients on production, reserves, time, and age, are altered

little with the addition of other variables.

The depth of well is found to be statistically significant (Model 2), and suggests,

as expected, that operating costs increase with the depth of the well. The addition of

depth has little influence on the coefficient on quantity, and decreases the coefficient on

reserves slightly. Both time and age of the well lose their significance at the 95 percent

level with the addition of depth. However, the fit of the model, as measured by the R2, is

not improved.

Model 4 includes a company dummy variable that is found to be significant,

implying that one company has higher operating costs than the other. This might be

explained by differences in accounting practices. The addition of this dummy variable

has little impact on the coefficients for quantity, reserves, or well age. The coefficient on

time again loses its significance with the addition of a company variable. Again the fit is

not improved with the addition of a company dummy variable.

Dummy variables for the different zones (Model 5) did not prove to add

explanatory power of the model. Only one of the four variables is significant at the 95

percent level, and only the coefficient on reserves remained significant at this level. The

results tend to suggests that operating costs are higher for zones other than the Belly

River zone. It is possible that this captures some of the same relationship that depth of

well does. In this sample, the Belly River zone (the reference zone) is the shallowest zone

and the Bow Island zone (Zone 1) (which is the only zone dummy variable that is

significant at the 95 percent level) is the deepest.

Dummy variables for the individual reservoirs were all significant at the 95

percent level (Model 6). This implies that different reservoir characteristics are important

in determining operating costs at the well level and that some reservoirs may have

characteristics that are more or less amiable to production. The addition of these dummy

variables lowers the statistical confidence on the variables quantity, time, depth and gas

extracted below the 95 percent level.

The fixed effects regression includes an F test with the null hypothesis that the

fixed effects are all equal to zero. The critical value for this test at the 99 percent level is

roughly 1.9. All of the tests are rejected soundly at the 99 percent level, with test values

ranging from 60.8 to 85.2. This implies that there exists some residual unexplained

variance in well operating costs that arises because of individual well differences.

V. Conclusions The primary focus of this work was an empirical estimate of operating cost for a

natural gas well. The results suggest that operating costs are increasing in quantity

produced, decreasing in the remaining reserves, and increasing with the age of the well.

These results confirm both what depletable natural resource theory has generally assumed

about operating costs, as well as the results obtained by Chermak and Patrick.

The results further found support for the notion that operating cost functions for

natural gas should be modeled at the individual well level. Using a panel data series, the

individual well effects were found to be non-zero across all models tested. This suggests

that ignoring the impacts at the individual well by aggregating up to the pool or the

region may not model costs effectively. Important differences in reservoir characteristics

and costs make aggregation difficult.

References

Berger, Bill D. and Kenneth E. Anderson, Modern Petroleum: A Basic Primer of the

Industry, (Tulsa: PennWell Books, 1992).

Brennan, Michael J., and Eduardo S. Schwartz, "Evaluating Natural Resource

Investments", Journal of Business, Volume 58, Number 2 (1985): 135-157.

Chermak, J.M., and R.H. Patrick, "A Well-Based Cost Function and the Economics of

Exhaustible Resources: The Case of Natural Gas", Journal of Environmental

Economics and Management, Volume 28, (1995): 174-189.

Chermak, J. M., J. Crafton, S.M. Norquist, and R.H. Patrick, "A hybrid economic-

engineering model for natural gas production", Energy Economics 21, (1999):

67-94

Cullen, Susan. Natural Gas From Wellhead to Burnertip (Calgary: Canadian Energy

Research Institute, 1993)

Greene, William H. Econometric Analysis: Forth Edition, (Prentice Hall: New Jersey,

2000).

Griffin, James M., and Clifton T. Jones., 'Economies of Scale in a Multiplant

Technology: Evidence from the Oilpatch,' Economic Inquiry, Volume 26, (1998):

107-122.

Helliwell, J.F., M.E. MacGregor, R.N. McRae, and A. Plourde, Oil and Gas in Canada:

The Effects of Domestic Policies and World Events, Canadian Tax Paper Number

83 (Canadian Tax Foundation, 1989).

Hobson, G.D., and E.N. Tiratsoo, Introduction to Petroleum Geology: Second Edition,

(Beaconsfield: Scientific Press, 1981).

Krautkraemer, Jeffery A., 'Nonrenewable Resource Scarcity', Journal of Economic

Literature 36, (December 1998): 2065-2107.

Kuller, Robert G. and Ronald G. Cummings, 'An Economic Model of Production and

Investment for Petroleum Reservoirs', The American Economic Review 64,

(March 1974): 66-79.

Livernois, John R. 'Empirical Evidence on the Characteristics of Extractive

Technologies: The Case of Oil', Journal of Environmental Economics and

Management 14, (1987): 72-86.

Livernois, John R., and Russell S. Uhler 'Extraction Costs and the Economics of

Nonrenewable Resources', Journal of Political Economy 95, (1987): 195-202.

Nind, T.E.W. Principles of Oil Well Production: Second Edition, (New York:

McGraw-Hill, 1981).

Sweeney, James L., 'Economic Theory of Depletable Resources: An Introduction,' in

Handbook of Natural Resource and Energy Economics, vol.III, Allen V. Knese

and James L. Sweeney, eds., (Amsterdam: Elsevier Science Publishers, 1993):

759-854.

Appendix

In this appendix, a description of operating cost is reported. Operating cost for

the well is made up of numerous categories within the company's records. Some

categories report expenditures sporadically throughout the year whereas others are

incurred annually or monthly. In Table A1, we present for descriptive purposes a

breakdown of expenditure by variable and quasi-fixed groupings. A variable expenditure

is defined as changing in response to the level of gas production and a quasi-fixed

expenditure is necessary for production to take place but independent of the level of

production. In building up a monthly aggregate expenditure index, the following

procedure is used. Monthly expenditure is reported directly in the index. For expenditure

that occurs sporadically throughout the year, the procedure is to apply the expenditure

equally to all future months until the expenditure occurs again, and the process repeated.

For annual expenditure, the total value is applied in each month. Of course, the actual

monthly expenditure index is not meaningful but nevertheless, the variation in the index

will capture fully expenditure changes that occur monthly and throughout the year.

Endnotes

i This is known in the literature as a ‘stock effect’ or a ‘degradation effect’. ii Aggregation is a problem because reservoirs are not homogenous. Different reservoirs have differing levels of porosity, permeability, pressure, and viscosity, among other factors. Even within the same reservoir differences may exist. Studies such as Livernois (1985) and Livernois and Uhler (1987) have shown that models that are built around individual reservoirs rather then regions are preferred. Chermak et al (1999) outlined four conditions for aggregatability from well to reservoir level (i.e. conditions under which a reservoir could be treated as if it operated like a single well). These are: homogeneity of a reservoir, identical production paths of the wells, identical time horizons of all wells, and identical production technology. iii Knowing the production function would make it possible to investigate characteristics such as economies of scale in gas pools. This may be useful in determining whether reservoirs should be operated in a unitized fashion, with one firm making production decisions for the entire reservoir. Griffin and Jones (1988) undertook such a study at the lease level and found evidence for unitization. iv Methane typically makes up 84 to 96 percent of the natural gas in a deposit, Hobson and Tiratsoo, 1981. More complex molecules are less common, though ‘wet’ gas reservoirs include heavier liquid hydrocarbons. Other gases also can be found in natural gas including carbon dioxide, hydrogen sulfide and helium.

v Production decline in petroleum reservoirs typically exhibits hyperbolic decline. In this case, using Nind (1981), the relationship between the rate of change in current production and time is:

)(

)()(btatq

ttq

+−

=∂

∂

where: q (t) is production at time t, a is the hyperbolic constant, b is the natural log of initial production (ln q0). Integrating to get the production at any time t as:

at

eqtq−

= 0)( if b = 0 (in this case a is the constant production decline rate), and

b

btaaqtq

1

0)(

+= if b ≠ 0

vi Silica sand, glass beads, and epoxy are often used as propping agents.

vii Well spacing requirements set the minimum distance between wells, and between a well and the lease boundary or property line. This promotes an optimal rate of production and limits damage from overproduction. In Southern Alberta well spacing requirements are such that there can be only one well in a legal subdivision (sixteen hectares), unless it can be shown that more are needed to drain the reservoir. This is in contrast to the 258 hectares, or one section, that is the norm in the rest of the province for well spacing. Cullen (1993) argues that this is because pools are generally "tighter", or less permeable in Southern Alberta. More wells are needed to drain reservoirs in a way that allows producers to generate sufficient revenues to make the ventures worthwhile. viii The wells are in three different regions (West Texas, East Texas, and Wyoming), ix The five different geological zones include Belly River (the reference case), Bow Island (zone 1), Medicine Hat/Milk River (zone 2), Medicine Hat (zone 3), and Basal Colorado (zone 4). x The fixed effects model does not provide a true R2 and is not bounded by 0 and 1.

Table 1 Annual Summary Statistics

Variable Name

Variable Symbol Mean Standard Deviation

Operating Costs, dollars

C 7465.5 9912.7

Gas Extracted, thousand cubic

meters

q 1687.3 2453.5

Reserves, thousand cubic meters

R 11967.6 20084.8

Well Age, months

m 86.0 111.0

Depth, feet

d 795.7 267.8

Table 2 Correlation Matrix: Annual Data

C Q r m d C

1

q

0.668 1

r

0.527 0.844 1

m

0.211 -0.078 0.099 1

d

0.508 0.319 0.381 0.477 1

Table 3

Test for Functional Form: Box-Cox Transform Number of Observations

608

λ

0.02

Log Likelihood at 0

-5560.86

Log Likelihood at 1

-6114.47

Maximized Log Likelihood

-5550.47

Wald Test λ =0a

0.39

Wald Test λ=1a

563.70

a The critical value for at the 5% level with one degree of freedom is 3.84 2χ

Table 4

Fixed Effects Cost Equation: various specifications Variable

Patrick & Chermak

Model 1 Model 2 Model 3 Model 4 Model 5 Model 6

ln q

0.48 (14.83)a)

0.09 (2.32)

0.09 (2.31)

-0.44 (-2.66)

0.10 (2.54)

0.07 (1.74)

0.07 (1.67)

ln r

-0.35 (-12.45)

-0.90 (-8.86)

-0.96 (-9.67)

-0.84 (-8.16)

-0.93 (-9.33)

-0.91 (-9.25)

-0.98 (-9.81)

l n t

-0.50 (-6.83)

-0.04 (-2.31)

-0.03 (-1.71)

-0.04 (-2.21)

-0.03 (-1.78)

-0.03 (-1.76)

-0.03 (-1.88)

ln m

0.13 (6.78)

0.11 (2.67)

0.06 (1.40)

0.16 (3.65)

0.09 (2.09)

0.07 (1.65)

0.05 (1.24)

ln d

- - 0.34 (5.87)

- - - -

ln q2

- - - 0.06

(3.30) - - -

Company

- - - - 0.18 (4.16)

- -

Zone 1

- - - - - 0.35 (5.68)

-

Zone 2

- - - - - 0.08 (1.39)

-

Zone 3

- - - - - 0.45 (0.55)

-

Zone 4

- - - - - 0.09 (1.36)

-

Pool 1

- - - - - - 0.61 (5.51)

Pool 2

- - - - - - 0.34 (2.97)

Pool 3

- - - - - - 0.25 (2.31)

Pool 4

- - - - - - 0.32 (3.44)

Pool 5

-

-

-

-

-

-

0.30 (2.55)

Adjusted R2 0.42 0.79 0.76 0.76 0.76 0.77 0.78 Fixed Effectsb) - 85.24 69.21 75.56 60.80 78.08 78.42 Model 1: Fixed Effects Log-Log equation comparable to Patrick & Chermak. Model 2: Fixed Effects plus depth. Model 3: Fixed Effects plus output squared. Model 4: Fixed Effects plus company dummy. Model 5: Fixed Effects plus geological zone. Model 6: Fixed Effects plus reservoir pool.

a) t-statistics in parentheses b) F-test that all Fixed Effects Dummy variables equal zero.

Table A1 Summary of Expenditure Categories

Variable Operating Costs Share of Costs

Quasi-fixed Operating Costs

Share of Costs

contract operator 19.6% lease and road* 2.8% Chemicals* 2.5% municipal property

tax* 6.7%

repair and maintenance* 1.9% freehold surface lease* 14.3% salt water disposal* 0.4% freehold lease* 0.6% trucking* 1.0% testing-pressure

survey* 2%

small tools and supplies* 0.3% analysis* 0.2% chart reading 0.6% production and Alberta mineral tax*

42.7%

AEUB administration fee* 3.2% * indicates expenditure that occurs annually or sporadically throughout the year