Download Impacts of Completion and Production Decisions for

Impacts of Completion and Production Decisions for Vertical versus Horizontal
Technologies on Shale Gas Well Cumulative Productivity1
Janie M. Chermaka
University of New Mexico
James W. Craftonb
Performance Sciences, Inc.
Robert H. Patrickc
Rutgers University
July 2012
Preliminary Draft. Please do not quote or cite without permission of the authors.
Abstract
We develop a theoretical model for optimal discrete capital investment, discrete completion, and
dynamic production of shale gas wells. We then econometrically estimate early period
cumulative production functions for vertical and horizontal shale gas wells that require an initial
capital investment for production. Results indicate reservoir and completion outcomes have
significant impacts that are consistent in sign across the two technologies, but the magnitudes
and probabilities of these impacts vary, sometimes substantially so. The impact of completion
decisions on cumulative production is highly variable, with differences in early period
production declines across the two well technologies. These results may, in part, explain the
downward trend in reserve estimates for shale gas, as there is uncertainty in the impact of
completion choices early period production.
1.0 INTRODUCTION
Shale gas production is a recent entrant into the natural gas industry. While the potential
of shale gas had been known for some time, advancements in technology allowed the use of
hydraulic fracturing, directional and horizontal drilling, and reservoir evaluation methodologies
resulted in the ability to exploit these reserves. This was once a phenomenon largely confined to
the US energy industry, but is increasingly important throughout the world. For example, Great
1
We’d like to thank Alan Krupnick and other participants at the 2011 IAEE meetings in Washington DC,
and David Lamont and other participants at the Rutgers University CRRI Advanced Workshop and
Regulation and Competition, 31st Annual Eastern Conference, PA, for helpful comments on previous
versions of this paper. Chermak and Patrick would like to thank PSI for partial financial support.
a
Department of Economics, University of New Mexico, MSC05 3060, 1UNM, Albuquerque, NM 87131:
[email protected]
b
Performance Sciences, Inc., Evergreen, CO 80439
c
Finance and Economics, Rutgers Business School–Newark and New Brunswick, Rutgers University, 1
Washington Park 1148, Newark, New Jersey 07102. Email: [email protected].
1
Britain, Poland, Argentina and the Ukraine are now focusing on potential shale gas reserves
within their borders.
But shale gas is not without controversy. In addition to the well-publicized debate over
potential environmental effects of hydraulic fracturing, there is significant uncertainty
concerning the quantity of actual reserves. For example, the US Energy Information
Administration (EIA) reduced its estimate of unproved technically recoverable resource for the
US from 847 trillion cubic feet (TCF) in its 2011 Annual Energy Outlook (AEO) to 482 TCF in
the early release of the 2012 AEO.2 In part this is due to early period production decline (which
impacts ultimate recovery) that is far greater than originally expected.
Ultimately, the impact of shale gas on the natural gas industry and its contribution to the
long-term viability of the industry will depend on actual production meeting forecasts and
estimated ultimate recovery (EUR). As with any natural gas resource, well performance depends
not only on the characteristics of the well and the reservoir, but also on choices made by the
producer; completion, production, and recompletion choices can all impact EUR. In the case of
shale gas wells, this may be even more important as recent work suggests early production
management decisions and can significantly impact EUR (Crafton 2008). Consequently, a better
understanding of the impact of reservoir and completion characteristics on early period
production, and the impact on economic vitality is of importance. Included in this is the
consideration of vertical versus horizontal well performance. While horizontal wells can have
substantially larger initial production levels than vertical wells, this is a newer technology with
greater uncertainty of ultimate recovery.
2
Unproved technically recoverable reserves are defined as reserves estimated to be commercially
recoverable in the future from known reservoirs and under current economic conditions, operating
methods, and government regulations, but have not been proven to exist based on accepted geologic
information.
2
This paper focuses on factors affecting early period production, including the
characteristics of the well, completion and production choices made by the producer, production
impacts, and well technology (vertical versus horizontal). We begin with the development of a
theoretical model of capital investment for well fracturing, completion, and subsequent
production, followed by an empirical analysis of early period production technologies.
Employing data from 111 (39 horizontal and 72 vertical) shale gas wells, we econometrically
estimate a system of equations for early period cumulative production conditional on discrete
inputs into fracturing and completion of the well. We find reservoir characteristics and
completion outcomes are statistically significant but vary substantially in magnitude across the
vertical versus horizontal well technologies. Further, we find the marginal impacts of
completion choices on well cumulative production are variable both in sign and magnitude
across the two technologies.
2.0 BACKGROUND
While natural gas was first produced commercially in the US in 1821 and the existence of
deep shale gas resources was known by the 1980’s, it wasn’t until the early 1990’s that
technology advanced enough to result in wider spread shale gas production (although production
from the Niobrara began almost a decade earlier). In 2000, less than 0.4 TCF of natural gas
production in the U.S. was from shale gas reserves. By 2010 more than 4.8 TCF of natural gas
production (almost 23%) was from shale gas. This is projected to increase to more than 45% of
U.S. production by 2035 (EIA 2011).
Shale gas reserves are an unconventional resource where the gas is deposited in a very
low permeability geologic formation such as the Devonian age shale, generally referred to as the
Marcellus. Low permeability makes movement of the gas difficult, which precipitates the need
3
for appropriate technology to be able to move the gas through the reservoir to the well, and
finally to the earth’s surface. The combination of technologies that makes production possible is
hydraulic fracturing, which provides a conduit from the reservoir to the wellbore, and drilling
technology enabling directional and horizontal drilling. Coupled with the drilling and
completion technology, reservoir evaluation is a necessary component of shale gas production.
The US Securities and Exchange Commission (SEC) recognized this need by publishing Release
33-8995 (SEC, Jan, 2009), in which they identify the requirements for improved evaluation
procedures. This has been further documented in technical papers (e.g., Lee 2010). In this
study, one of the evaluation tools satisfying the SEC requirements was employed for the
evaluation of reservoir quality and stimulation effectiveness (Crafton, 1997).
After a well is drilled and it is determined that the presence of hydrocarbons justifies the
completion of the well, a completion plan is made. The plan will include, among other things,
the interval to be perforated, the amount and type of hydraulic fracturing fluid and proppant to be
injected into the reservoir, the speed with which the hydraulic fracturing fluid is introduced and
the number of stages (the number of completion intervals) – all of which will result in a conduit
being formed through the reservoir, providing a path for the gas to move from the reservoir to the
wellbore and finally to the surface.
Perforations are holes shot through the well casing in order to make a connection between
the wellbore and the reservoir rock. Hydraulic fracturing fluid is injected into the reservoir at
pressure to propagate fractures or fissures through the reservoir rock to the wellbore. The
proppant is a material that keeps the fracture open and provides a conduit for the flow of gas to
the wellbore.
4
The decision to include various additives in the completion job is also made. The
additives can include, for example, corrosion and scale inhibitors, biocides, and surface active
agents. The surface active agents, which help reduce the surface tension, can include surfactants
or a Complex nano-Fluid (CnF). The composition of these additives varies and is often
proprietary - historically many of them have not been environmentally benign. With the
negative publicity from hydraulic fracturing fluid, there has been a push by industry to reduce the
environmental footprint of these various additives. This can, in itself, become a completion
choice.3 For example, CnF is relatively environmentally benign and has the distinction thatwhen
used in the North Sea, in the case of a spill, it is classified as a non-environmental event.4
These completion decisions made by the company are, in part, based on the
characteristics of the reservoir, but also may depend on a company’s management styles and
policies, as well as on those of the completion company.
While shale gas reservoirs are substantially different from other unconventional natural
gas reservoirs, initially the conventional wisdom in their production followed that of other
reservoirs; mainly high flowback (production of the fracturing fluid) and production rates. More
recently, discussions have emerged about what constitutes the optimal completion and
production plan for a shale gas well (Crafton 2008). Fracture length, number of stages, fracture
conductivity, and production pressure chokes have all come into play (Crafton 2011). While the
initial capital investment may be increased and the time to payout extended due to lower initial
production rates, the overall profitability of a well can be improved if total revenues are
increased over the life of the well due to increased production and/or total capital costs are
3
For example, the US Environmental Protection Agency held a workshop in February 2011, in which
industry representatives presented the changes that are being made to reduce potential environmental
degradation.
4
Certified by the Center for Environment Fisheries and Aquatic Science, Department of Energy and
Climate Change, State Supervision of Mines, Ministry of Economic Affairs, UK.
5
decreased over the life of the well due to lower initial expense and fewer work-overs of the well.
For example, Petrohawk Energy is employing a more conservative production plan in the
Haynesville producing wells on more restrictive chokes (15/64 or 16/64 inch choke) and reports
decreases in decline rates.5,6
Specific to economic analyses, Caputo (2010) considers, among other things, continuous
capital investment in production of exhaustible resources. See his paper for a review of the
capital literature in this regard. In this paper we consider discrete capital investment (e.g.,
fracturing) in pressure driven exhaustible resources such as natural gas and oil. Existing
economic studies have focused on the optimal completion and production of other
unconventional gas resources. Chermak et al. (1999) and Patrick and Chermak (1992) develop
hybrid economic-engineering models for optimal tight-sand natural gas well fracturing,
completion, and production. Chermak and Patrick (2012) further develop such modeling in a
numerical simulation to determine optimal fracturing, completion and production of such natural
gas resources, finding, among other things, that larger fractures are suboptimal relative to shorter
fractures. Specific to shale gas, Gray, et al. (2007) recognize the uncertainty associated with
shale gas and develop a probabilistic approach to shale play evaluations. Adamson and Parker
(2011) develop a time series analysis of horizontal wells producing from the Haynesville shale in
Louisiana focusing on improved efficiency. They find increased productivity and response to
price changes. Overall, the economics literature is in its infancy with respect to shale gas well
production and efficiency.
3.0 THEORETICAL MODEL
5
6
A production choke is a flow control device that limits the flow of natural gas.
Petrohawk Q3 2010 Results: Earnings Call Transcript (11/02/2010).
6
In this section we develop an economic model for optimal completion and production of
a shale gas well. This model considers the interdependence of the discrete completion
investment, i.e., fracturing and completing the well so that it can produce, and subsequent
production path of the well. In many natural gas resources (from shale or tight sands) the initial
recoverable stock would in fact be zero, or near zero, without the capital investment for
completion, so that the natural gas resource can be extracted. This investment is not only made
initially, but for some resource deposits, periodically over the life of the deposit (Emrich, et al.,
2001). The model developed in this section is general in the context of any number of discrete
periodic investments over the life of the well.
Given the vector of physical characteristics of a well, A( t ) , some of which may be
(
)
constant over time, a vector of s discrete inputs at time j, K j = K j1 ,..., K jN , is required so that
production can take place. The physically recoverable stock of the resource, R, is impacted by
the physical well characteristics and these completion decisions, as is the quantity, q, of natural
gas that can be produced at any time after the well has been completed. This periodic production
occurs according to the production function
(
)
q ( t ) = h A( t ) ,Z ( t ) , K j ,
(
(1)
)
where Z ( t ) = Z1 ( t ) ,...,Z M ( t ) represents a vector of inputs used in producing the well.
Next we consider how the production function, (1), impacts the physically recoverable
stock of the resource. Conditional on the initial completion of the well, the initial recoverable
( )
( ( ) )
physical stock is given by R 0+ = R0 A 0+ , K 0 . In general, remaining physically recoverable
reserves, R ( t ) , will be impacted indirectly by the input choices, Kj, at time τ j ∈[0,T ], j = 0,...k ,
7
(
)
and amount of the resource produced, q(t), at each time over t ∈[0,T ]. K j = K j1 ,..., K jN is
constant for all t ∈[τ +j ,τ − ], j = 0,...k , τ k+1 = T . The firm chooses both Kj and
j+1
τ j ∈[0,T ], j = 0,..., k , which allows the possibility that τ 0 = 0 and τ k = T . Once production
begins at the initial time τ 0+ = 0 , the remaining stock at any t changes according to
( )
( ( ) )
R j (t) = s[ A, K j , R,q,t], R 0+ = R0 A 0+ , K 0 , and R(T + ) ≥ 0,
(2)
until another jump in capital occurs or the optimal terminal time T arrives.
It is assumed that q is a piecewise continuous control vector, R is piecewise continuous
and piecewise continuously differentiable state variable, and both are left-continuous. The stock
of the resource will not regenerate so s[ A, K j , R,q,t] ≤ 0 and T will generally be finite. This
decline in the stock may be due directly to production only, with the limiting case being
 = s[ A, K , R,q,t] = −q(t) , (so that s = −1 and s = 0) , an assumption traditionally
R(t)
j
q
qq
maintained in nonrenewable resource models (e.g., Caputo 2010). Pressure driven resources,
such as oil and natural gas, are subject to the physically recoverable stock of the resource being
reduced by an amount greater than the production rate. That is, the natural decline in pressure
may imply s[ A, K j , R,q,t] > q(t) , ∂ s[ A, K j , R,q,t] / ∂ q < −1 (the effect of production on the
recoverable stock may reduce the stock by more than the amount extracted, q), and
∂ 2 s(R(t),q(t),t) / ∂ q 2 ≤ 0 .7
7
Patrick and Chermak (1992) and Chermak, et al., (1999) develop the reservoir engineering to capture the
important physical characteristics of the production process and provide additional references in this
regard.
8
The magnitude of the capital induced jump in the resource stock is dependent on the
stock of the resource prior to the investment, the capital input, and the timing of the capital input.
It is given by
R(τ +j ) − R(τ −j ) = u(R(τ −j ), K j ,τ j ), j = 1,...,k
(3)
where R(τ +j ) denotes the right-hand limit of R(τ j ) at τ j , R(τ −j ) the left-hand limit, τ j is the
time of the jth jump and k is the number of jump points. Both the timing of the discrete
increments as well as the number are chosen endogenously by the producer. The discrete inputs,
K j ∈κ , κ is convex, 0 ∈κ , j = 1,...,k, are control parameters which influence the magnitude of
the jump in the resource stock, u(R(τ −j ), K j ,τ j ) , at τ j , j = 1,..., k . The cost of the discrete input
at each τ j is given by v(R(τ −j ), K j ,τ j ) , where v(R,0,t) = 0 for all R and t. That is, the capital
cost depends on the resource stock immediately before the jump occurs, the capital input at the
jump, and the timing of this input. The initial and terminal times may also be jump points.
Production cannot occur without the capital investment, which, if it occurs initially, then a jump
takes place initially. Either a negative cost (i.e., a scrap value) or possibly a positive cost (shutdown) may be associated with the terminal time if τ k = T . Thus, v(R(τ −j ), K j ,τ j ) > 0 for
j=1,…,k-1, and possibly for j=k, although v(R(τ k− ), K k ,τ k ) < 0 if τ k = T and there is a terminal
(scrap) value which exceeds any shut-down costs. Otherwise, if τ k < T , there are no terminal
time costs (i.e., v(R,0,T ) = 0 ).
The value of the resource is then given by
k
− rτ
π = ∫ e− rt ⎡⎣ P(t)q(t) − w ( t ) Z ( t ) ⎤⎦ dt − ∑ e j v(R(τ −j ), K j ,τ j ),
0
T
j=1
9
(4)
where the output price P and input prices w, are assumed exogenous and may vary over time.
The firm’s optimization problem is to search for an admissible collection,
( R̂(t), Ẑ(t),τˆ ,...,τˆ ,Tˆ , K ,..., K ) ,
0
k
0
k
which maximizes (4) subject to the production function (1), the resource stock transition
equation (2), and the jump in the resource stock condition (3).
The Hamiltonian is defined by
(
)
(
)
H (R,q, λ ,t) = e− rt ⎡ P(t)h A,Z, K j − wZ ⎤ +λ s ⎡ R,h A,Z, K j ,t ⎤
⎣
⎦
⎣
⎦
(5)
where λ is the in situ price (option value) of the resource.
For all t ∈(τ +j −1 ,τ −j ) , j = 1,..., k , i.e., for all t at which there is no jump in capital,
necessary conditions include
− H R = λ = − λ sR ,
H Z = e− rt ⎡ PhZ − w ⎤ + λ sh hZ ≤ 0
⎣
⎦
i
i
i
(6)
( = 0, if q > 0) , ∀i = 1,..., M ,
⎡ λ (t) u ( R̂(t),0,t) − v ( R̂(t),0,t) ⎤ K ≤ 0 ∀ K ∈κ
Kj
Kj
j
⎣
⎦ j
(7)
(8)
The dynamic optimality condition, (6), is complicated, relative to traditional resource models, by
the fact that the change in the in situ resource price over time is determined by the in situ value
of the rate of change in the remaining stock as the remaining stock changes. (7) is the condition
on optimal variable inputs between jumps in capital. λuK and v K are the marginal value of the
j
j
increase in the stock of the resource as a result of the capital investment and marginal cost of
capital, respectively. Equation (8) states that the marginal cost of capital is greater than the
marginal value of the increase in the stock of the resource from the capital investment for all
10
t ∈(τ +j−1 ,τ −j ) . That is, no investment takes place between jump points in capital since the cost of
increasing capital exceeds any benefit of such.
The optimal terminal time, Tˆ , satisfies
H (Tˆ ) = e− rT ⎡⎣ P(Tˆ )q̂(Tˆ ) − C( q̂(Tˆ ), R̂(Tˆ ), Tˆ ) ⎤⎦ + λ (Tˆ )s( R̂(Tˆ ), q̂(Tˆ ), Tˆ ) = 0.
(9)
The transversality condition is
(
)
λ (Tˆ ) ≥ 0 = 0 if R̂(Tˆ ) > 0 .
(10)
The optimal completion investments occur at discrete points in time. At all jump points
τˆ j , j=1,…,k, we have the following conditions:
λ (τˆ +j ) − λ (τˆ −j ) = −v R ( R̂(τˆ j ), K j ,τˆ j ) − λ (τˆ +j ) uR ( R̂(τˆ j ), K j ,τˆ j ) ,
(11)
⎡ λ (τˆ + ) u ( R̂(τˆ ), K ,τˆ ) − v ( R̂(τˆ ), K ,τˆ ) ⎤ (K − K ) ≥ 0 ∀ K ∈κ ,
j
Kj
j
j
j
Kj
j
j
j ⎦
j
j
j
⎣
(12)
and
H ( R̂(τˆ +j ), q̂(τˆ +j ), K j ,τˆ j ) − H ( R̂(τˆ −j ), q̂(τˆ −j ), K j ,τˆ j )
⎧ ≥ 0 if τˆ = 0
j
⎪
⎪
−
+
−
− vτ ( R̂(τˆ j ), K j ,τˆ ) − λ (τˆ j )uτ ( R̂(τˆ j ), K j ,τˆ ) ⎨ = 0 if τˆ j ∈(0, Tˆ )
j
j
j
j
⎪
ˆ
⎪⎩ ≤ 0 if τˆ j = T
(13)
(11) provides the jump condition on the in situ resource price at the optimal jump times τˆ j ,
j=1,…,k. (12) implies that the optimal capital increment K j at time τˆ j , where K j is the jth
jump in capital, is determined such that the value (in terms of the in situ resource price) of the
increment in the stock of the resource is equal to the marginal cost of capital. (13) provides
candidates for the optimal jump times τˆ j , j=1,…,k, i.e., the timing for the discrete periodic
capital investments (fracturing and completion). The number times completion takes place over
11
the life of the well, i.e., the number of jumps, k, is determined endogenously in simultaneously
solving conditions (6) through (13).
This model developed above theoretically links the physical science implications to the
economics of completing and producing shale gas wells. We can’t approach making optimal
decisions for these types of resources treating economics as an accounting add-on to physical
science modeling or as treating the physical world as exogenous to the economics. The above
optimization model specifically demonstrates how completion decisions impact production, and
how current production and previous completion decisions influence future completion
requirements and subsequent production, as well as how much of the potential resource stock is
ultimately recoverable. In the next section we turn to the development of our econometric
model, which will provide the basis for estimating the production function relationships that are
required to empirically implement the above model.
4. 0 THE ECONOMETRIC MODEL
Based on the above model for the completion and production of a well, we develop an
econometric model of cumulative production, conditional on the initial fracture and completion,
and subsequent production over a limited time horizon. This limited time horizon is relative to
the expected productive life of the wells, since this is the time horizon of available data. So we
are considering how decisions on the initial capital investment affect cumulative production over
the initial production periods of the life of the well. Specifically, we consider the factors
impacting production, as well as those factors impacting the capital investment (the fracture and
conductivity in this case). While the above conditions are solved simultaneously for the
optimum, in this paper we are interested in the developing the empirical representations of the
components of the model related to completion and production geology and technology, i.e., how
12
decision variables affect the fracture and conductivity (capital investments) and how these affect
cumulative production. The completion and production of a well involve a number of
interdependent decisions. We model the physical interdependency through a series of
interdependent production functions representing the completion and production of the well.
These interdependent physical relationships are required to determine the economically optimal
completion and production of the natural gas well (i.e., to maximize the value of the resource).
Specifically, for completion, we consider the fracture and conductivity of the well, F and
C respectively, as endogenous. F and C each require discrete inputs and such completion
investment must take place before the well can produce natural gas. Empirically, we specify and
simultaneously estimate specifications of the production functions for each technology, vertical
and horizontal. Factors impacting production will include physical attributes of the reservoir,
A i 0 = ( A1i 0 ,..., Ani 0 ) , i = 1,..., I, which can also impact reserves; completion production functions,
Fj and C j ; and production q ( t ) through the choices Ki 0 = ( K1i 0 ,..., K Mi 0 ) , i = 1,..., I; that impact
productivity either through reserves or feedback. That is, the production function from the
previous section for well i, i = 1,..., I, at any t is given by
(
qi ( t ) = h Aij , K ij , Fij ,Cij
)
(14)
Cumulative production at time t is then given by
t
t
0
0
Qi ( t ) = ∫ qi ( x )dx = ∫ h ( Ai 0 , K i 0 , Fi 0 ,Ci 0 , x )dx.
(15)
For notational ease, we abstract at this point from the fact that not all characteristics or inputs are
of relevance in each of the discrete production functions represented. Since cumulative
production is dependent on the endogenous variables Fj and C j , we estimate (15)
simultaneously with specifications of the fracture production function
13
Fi0 = f ( Ai0 , K i0 ) ,
(16)
and the fracture conductivity production function
Ci0 = g ( Ai0 , K i0 ) .
(17)
(16) and (17) are both expressed as functions of K i 0 for notational ease, note that each of these
equations will contain both common and mutually exclusive elements of the vector K i 0 as
explanatory variables in our empirical application below.
Explanatory variables that are in (15) and (16) and/or (17) will have both direct and
indirect effects on cumulative production, Qit , e.g.,
t
∂Qi ( t ) ∂K im 0 = ∫ ∂hit ∂K im 0 + ∂ fit ∂Fim 0 ∂Fim 0 ∂K im 0 + ∂git ∂Cim 0 ∂Cim 0 ∂K im 0 dx
  


0
direct
indirect
(18)
indirect
The system of equations as described above, the specified econometric model is of the
form:
M
lnQit = β 0 + ∑ β j ln K ij 0 +
j=1
ln Fi 0 = β 0 +
lnCi 0 = β 0 +
∑β
j⊂[ A ]
∑β
j
lnAij 0 + β F ln Fit 0 + βC lnCit 0 +
j
ln K ij 0 +
∑β
ln K ij 0 +
j⊂[ K ]
j⊂[ K ]
j
∑β
j⊂[ A ]
j
∑β
j⊂[ A ]
j
lnAij 0 +
∑βD
∑βD
j⊂[ D ]
j
ijt
+ e1it
(19)
+ e2it
(20)
lnAij 0 + ∑ β j Dij 0 + e3it ,
(21)
j⊂[ D ]
j
ij 0
j⊂D
where the β ' s in each equation are the parameters to be estimated, and only subsets of the A, K,
and D variables are in each equation, with some of the subset elements mutually exclusive (the
equations are completely specified with the estimates below). Equations (19), (20), and (21)
comprise the empirical system of equations we estimate. Expected cumulative production is then
given by the exponent of (19), i.e.,
14
M
⎛
⎞
Q̂it = exp ⎜ β 0 + ∑ β j ln K ij 0 + ∑ β j lnAij 0 + β F ln F̂i 0 + βC ln Ĉi 0 + ∑ β j Dijt + eit ⎟ . (22)
⎝
⎠
j=1
j⊂[ A ]
j⊂[ D ]
5.0 DATA
The data are from 111 shale gas wells located in the US. Due to producer confidentiality,
the locations and the plays are not revealed. There are 39 horizontal wells and 72 vertical wells
in our sample. All of the wells have been completed and production initiated since 2007. We
categorize the vertical and horizontal technologies sample data by production, reservoir or well
characteristics, completion choices, and completion outcomes. Naturally, some, but not all,
variables are applicable across the technologies.
Well characteristics include permeability thickness8, initial reservoir pressure9, and the
perforated interval (to proxy for reservoir thickness – included for vertical wells, but not for
horizontal due to the lack of variation in the data for horizontal).
Completion choices include the quantity of hydraulic fracturing fluid, proppant quantity
per stage and proppant concentration (pounds per barrel of hydraulic fracturing fluid), and the
concentration of the surface active agent (gallons of additive relative to total gallons of fluid).
In the case of the vertical wells, all wells were treated with CnF at varying
concentrations. For horizontal wells, three were treated with CnF and the remaining 36 wells
were treated with a variety of traditional surfactants. We test the statistical significance of
traditional surfactants versus CnF in the horizontal wells, distinguishing the CnF wells using
intercept and interactions terms. The interest in comparing impacts of the traditional surfactants
versus CnF is due to the environmental aspects of CnF.
8
9
The product of reservoir permeability times thickness of the reservoir.
The hydrostatic pressure of the formation prior to first production.
15
We also consider the choice of the number of stages for the horizontal wells (all vertical
wells have only a single stage). Because summer versus winter temperature differentials may
impact the completion outcome, we include a binary dummy for winter completion jobs as a
completion choice variable.
In addition, the injection rate and resulting average treatment pressure is included for
vertical wells, while only the injection rate is included for horizontal wells (lack of variation in
treatment pressure precludes its inclusion for the horizontal wells). Because the speed with
which a completion job in finished may impact production, we include the time between the
beginning of the completion job and first production.
Completion outcomes include final and early fracture half-lengths and normalized
fracture conductivity.10 Finally we consider the impact of time on cumulative production
through two variables. First, we include a ratio of production days to total calendar days to
produce those production days.11 Second we consider seven production periods; first ten days
(D10), then 30, 60, 90, 180, 360, and up to 720 days. The 720 days of production are only
applicable to horizontal wells in our sample. Thus we have incremental production for up to 12
months for our vertical well data set and up to 24 months for our horizontal well data set. Table
1 provides a dictionary for our sample data.
10
Fracture conductivity, which measures how easily fluids move through a fracture, is the product of
fracture permeability and fracture width. We utilize a more common dimensionless fracture
conductivity, equal to fracture conductivity divided by the product of final fracture half-length and
formation permeability, which accounts for differences in reservoir characteristics.
11
For example, if we were interested in one day (24 hours of production) and a well was produced for 12
hours each day for two consecutive days, the ratio would be ½. We include the ratio to test for the impact
of inactivity on cumulative production.
16
TABLE 1: Variable Names, Descriptions, and Units
Variable
Description
Cumulative Production i (i
=10, 30, 60, 90, 180, 260, 720
days)
Final Fracture Half-length
Dimensionless Fracture
Conductivity
Initial Reservoir Pressure
Permeability thickness
Perforated Interval
Early Fracture Half-length
Proppant Concentration
Average Pounds of Proppant
per stage
Surfactant Concentration
(horizontals) or
CnF Concentration (verticals)
Stages
Average Injection Rate
Average Treatment Pressure
Difference
Ratioi (i =10, 30, 60, 90, 180,
260, 720 days)
Cumulative Production i (i
=10, 30, 60, 90, 180, 260, 720
days)
Units
Cumulative Production to a point in time
MCF
Effective final fracture from wellbore
Product of fracture permeability and propped
fracture width divided by the product of fracture
half-length and formation permeability
Pressure prior to completion and production
Feet
Reservoir permeability * reservoir thickness
Range of reservoir perforated
Effective early period fracture length from wellbore
Pounds of proppant divided by gallons of hydraulic
fracturing fluid
Pounds of proppant used in completion divided by
the number of stages
Percentage fluid that is a surface active agent
additive (scaled by 100)
Number of stages used for the completion
Rate at which fluids are injected
Average pressure used for injection
Difference in Days between beginning of
completion job and day of first production
Ratio of total days of production to total calendar
days necessary to achieve the days of production
Cumulative days of production
Pounds per
square inch
(PSIG)
millidarcy feet
Feet
Feet
Pounds per gallon
Pounds
Percent*100
Numeric (1,2,3)
Barrels per minute
Pounds per
square inch
Days
Percent
Days
Descriptive statistics for the data are provided in Table 2.12 Based on the above
discussion, the specified variables across the models are not identical. Of note are the
differences in the average cumulative production between the vertical and horizontal wells. The
first ten days production for the horizontal average is almost three times that of the vertical
average cumulative production. This relatively large production is a reason for the immense
interest in the horizontal technology.
12
Wells refers to the number of wells on which the statistic is based. Note later production periods have
smaller numbers of wells as all wells do not have the same production periods.
17
TABLE 2: Descriptive Statistics
Variable
Mean
s.d.
Permeability Thickness
Initial Reservoir Pressure
Perforated Interval
0.82
4703.86
72.86
0.93
268.48
21.04
Final Fracture Half-length
Early Fracture Half-length
Dimensionless Fracture Conductivity
48.32
40.29
1790.28
18.12
18.78
1415.14
Average Pounds Proppant per Stage
Proppant Concentration
Surfactant Concentration
CnF Concentration
Average Injection Rate
Average Treatment Pressure
Stages
Winter Fracture
Difference
945592
0.85
na
0.12
109.11
5903.83
na
0.29
7.67
233178
0.18
na
0.06
19.52
552.55
na
0.46
8.05
6096
98.29
15113
97.28
25123
98.02
33183
98.48
51730
98.74
78478
99.02
na
na
5595
8.42
12825
10.77
20668
7.95
27540
6.32
44357
5.55
47821
2.75
na
na
Vertical
Min
Max
Wells
Well Characteristics
0.14
2609.50
40.00
6.77
5015.80
129.00
Horizontal
Min
Mean
s.d.
Max
Wells
72
72
72
3.08
5071.60
na
4.44
843.93
na
0.04
2892.58
na
18.68
8073.99
na
39
39
na
72
72
72
122.47
163.72
2808.57
96.71
135.12
5759.69
3.54
3.54
36.99
419.54
655.03
29400.40
39
39
39
72
72
na
72
72
72
na
72
72
597728
1.18
0.09
na
71.82
5867.71
6.44
0.33
6.92
243522
0.52
0.07
na
14.88
1140.82
3.73
0.48
23.63
59600
0.17
0.00
na
15.65
3486.00
1.00
0.00
0.00
1018010
3.21
0.37
na
89.71
8170.07
15.00
1.00
150.00
39
39
39
na
39
39
39
39
39
72
72
72
72
72
72
72
72
70
70
20
20
na
na
18029
58.38
63526
42.14
126762
52.25
182450
60.01
292418
68.57
384113
80.24
262897
85.43
11395
39.41
42755
30.26
91813
27.87
118871
24.28
229082
21.98
432480
17.05
320541
12.09
1290
2.87
7069
7.87
15437
14.47
19635
20.19
30251
32.33
47738
51.37
76980
72.23
43820
100.00
181871
100.00
428638
100.00
379801
99.68
764838
99.84
1426010
99.92
633025
95.96
39
39
35
35
32
32
27
27
20
20
11
11
3
3
Completion Outcome
15.96
2.67
150.00
109.55
80.12
6038.00
Completion Choices
369000
0.50
na
0.02
44.70
3868.00
na
0.00
2.00
1256600
1.32
na
0.22
134.20
7307.00
na
1.00
36.00
Production
Cumulative Production 10
Ratio 10 Days
Cumulative Production 30
Ratio 30 Days
Cumulative Production 60
Ratio 60 Days
Cumulative Production 90
Ratio 90 Days
Cumulative Production 180
Ratio 180 Days
Cumulative Production 360
Ratio 360 Days
Cumulative Production 720
Ratio 720 Days
174
43.48
855
35.29
1342
51.28
1736
60.40
2794
59.02
24929
87.80
na
na
18
30330
100.00
78598
100.00
131111
100.00
174876
100.00
296232
100.00
172550
100.00
na
na
6.0 RESULTS
We consider cumulative production within the first two years of production for a sample
of shale gas wells from the US. Existing work indicates early production impacts ultimate
recovery from a well. Thus a better understanding of early period production is of paramount
importance. Our systems of equations for vertical and horizontal wells consist of three equations
each:
EQ1: Cumulative Production (Q) is a function of:
− Well Characteristics (A; initial reservoir pressure, permeability thickness, perforated
interval for the vertical wells).13
− Completion choices (K; difference between start of completion job and first production,
and winter fracture)
o Specific to vertical wells (CnF concentration)
o Specific to horizontal wells (Surfactant concentration, CnF intercept and
interaction)
− Completion outcomes (F, fracture half-length (late) and C, dimensionless fracture
conductivity)
− Time (D; ratio of production days to calendar days and intervals (30 days, 60 days, etc.)
EQ2: Final Fracture Half-length (F) is a function of:
− Well Characteristics (A; initial reservoir pressure and permeability thickness).
− Completion outcome (F, early fracture half-length)
− Completion Choices (K; average pounds of proppant per stage, average injection rate and
winter fracture).
o Specific to the vertical wells (average treating pressure and CnF concentration).
o Specific to horizontal wells (number of stages, surfactant concentration, CnF
intercept and interaction)
EQ3: Dimensionless fracture (C) conductivity is a function of:
− Well Characteristics (A; initial reservoir pressure and permeability thickness).
− Completion choices (K; proppant concentration)
o Specific to the vertical wells (average treating pressure, CnF concentration).
o Specific to horizontal wells (number of stages, surfactant concentration, CnF,
intercept and interaction).
We estimate the system of equations for vertical wells and for horizontal wells separately.
3SLS is used to simultaneously estimate the systems of equations for each technology. With the
exception of the binary variables for winter fracture, the CnF intercept for the horizontal wells,
13
Although perforated interval could be classified as a production choice, we specify it as a proxy for
reservoir thickness because it is based on the thickness of the productive interval. Regardless, the
classification will not impact our econometric results.
19
and the time effects for days of production, all variables are transformed by taking the natural
logarithm. Table 3 presents the estimated parameters, and their standard errors, probabilities,
and means for vertical wells. Table 4 contains the estimated model for horizontal wells.
TABLE 3: Vertical Well Results
Equation 1: ln(Cumulative Production)=
Variable
Coefficient
s.e.
Probability
Ln Initial Reservoir Pressure
Ln Permeability Thickness
Ln Perforated Interval
Ln Fracture Half Length
Ln Dimensionless Fracture Conductivity
Ln CnF Concentration
Ln Difference
Ln Ratio
Winter Fracture
30 Days
60 Days
90 Days
180 Days
360 Days
Constant
Variable
0.4142
0.2150
0.0682
0.0884
0.2188
0.0274
0.0346
0.2177
0.0424
0.0492
0.0491
0.0491
0.0495
0.0765
4.6091
0.00
0.00
0.27
0.00
0.05
0.02
0.00
0.01
0.33
0.00
0.00
0.00
0.00
0.00
0.00
Equation 2: ln(Final Fracture Half-length)=
Coefficient
s.e.
Probability
Ln Initial Reservoir Pressure
Ln Permeability Thickness
Ln Average Treating Pressure
Ln Early Fracture Half-length
Ln Injection Rate
Ln Proppant
Ln CnF Concentration
Winter Fracture
Constant
Variable
3.0431
0.9554
0.0748
0.5087
0.4326
0.0624
-0.2205
0.5411
0.0413
1.0372
1.5764
1.8613
2.3229
2.7141
-24.2175
-0.1825
0.1057
-0.2898
0.3472
0.0526
0.0033
0.0061
0.0323
6.4118
0.1855
0.0186
0.1628
0.0269
0.0820
0.0565
0.0205
0.0285
1.9080
0.33
0.00
0.08
0.00
0.52
0.95
0.77
0.26
0.00
Equation 3: ln(Dimensionless Fracture Conductivity)=
Coefficient
s.e.
Probability
Ln Initial Reservoir Pressure
Ln Permeability Thickness
Ln Average Treating Pressure
Ln Proppant Concentration
Ln CnF Concentration
Winter Fracture
Constant
Based on 378 observations
-1.4234
-1.0296
-0.3847
0.2536
-0.0071
-0.1485
22.0255
0.0933
0.0079
0.0749
0.0363
0.0105
0.0142
0.8700
Equation 1:
RMSE=.295,
"R 2" ≅ .93, and
χ 2 = 5240.70
Equation 2:
RMSE=.235,
"R 2" ≅ .61, and
χ 2 = 562.43
Equation 3:
RMSE=.120,
"R 2" ≅ .98, and
χ 2 = 18431.78
20
0.00
0.00
0.00
0.00
0.50
0.00
0.00
Mean of X
8.45
-0.56
4.25
3.82
7.16
-2.25
1.73
4.58
0.31
0.19
0.19
0.19
0.19
0.05
Mean of X
8.45
-0.56
8.68
3.55
4.66
13.72
-2.25
0.31
Mean of X
8.45
-0.56
8.68
-0.17
-2.25
0.31
TABLE 4: Horizontal Well Results
Equation 1: Ln(Cumulative Production)=
Variable
Coefficient
s.e.
Probability
Ln Initial Reservoir Pressure
Ln Permeability Thickness
Ln Fracture Half Length
Ln Dimensionless Fracture Conductivity
Ln Surfactant Concentration
CnF Intercept
Ln CnF Interaction
Ln Difference
Ln Ratio
Winter Fracture
30 Days
60 Days
90 Days
180 Days
360 Days
720 Days
Constant
Variable
0.2280
0.1377
0.0459
0.1347
0.0161
3.2559
0.4795
0.0339
0.0414
0.0775
0.0881
0.0908
0.0965
0.1083
0.1352
0.2390
2.4231
0.89
0.00
0.00
0.11
0.00
0.00
0.00
0.00
0.98
0.16
0.00
0.00
0.00
0.00
0.00
0.00
0.01
Equation 2: Ln(Final Fracture Half-length)=
Coefficient s.e.
Probability
Ln Initial Reservoir Pressure
Ln Permeability Thickness
Ln Early Fracture Half-length
Ln Stages
Ln Average Injection Rate
Ln Avgerage Proppant per Stage
Ln Surfactant Concentration
CnF Intercept
Ln CnF Interaction
Winter Fracture
Constant
Variable
0.0311
0.6459
0.3540
0.2134
-0.0540
15.5696
2.3360
-0.1240
-0.0009
-0.1079
1.2483
1.8456
2.1760
2.7238
3.2311
3.4582
6.1013
1.3838
0.0227
0.7568
0.5373
0.6683
-0.5129
0.0769
-0.6211
-0.1650
0.0743
-11.1769
0.2104
0.0603
0.0439
0.1162
0.1331
0.2802
0.0161
3.2125
0.4744
0.0781
2.0457
0.00
0.71
0.00
0.00
0.00
0.07
0.00
0.85
0.73
0.34
0.00
Equation 3: ln(Dimensionless Fracture Conductivity)=
Coefficient s.e.
Probability
Ln Initial Reservoir Pressure
Ln Permeability Thickness
Ln Stages
Ln Proppant Concentration
Ln Surfactant Concentration
CnF Intercept
Ln CnF Interaction
Winter Fracture
Constant
Based on 167 observations
0.0007
-1.0003
0.0007
0.9987
0.00004
0.0072
0.0011
0.0008
0.0017
0.0007
0.0001
0.0003
0.0004
0.0001
0.0097
0.0014
0.0002
0.0074
Equation 1:
RMSE=.3852,
"R 2" ≅ .92, and
χ 2 = 2023.53
Equation 2:
RMSE=.3787,
"R 2" ≅ .84, and
χ 2 = 889.67
Equation 3:
RMSE=.0012,
"R 2" ≅ .99, and
χ 2 = 3.77E+08
21
0.35
0.00
0.01
0.00
0.43
0.46
0.46
0.00
0.82
Mean of X
8.51
-0.06
4.58
6.43
-6.12
0.12
-0.81
0.93
3.80
0.34
0.21
0.19
0.16
0.12
0.07
0.02
Mean of X
8.51
-0.06
4.80
1.57
4.24
5.73
-6.12
0.12
-0.81
0.34
Mean of X
8.51
-0.06
1.57
6.38
-6.12
0.12
-0.81
0.34
We find statistically significant direct impacts for both models across each of the three
equations in the system. For example, consistent (same sign) statistically significant (at 90% or
better) direct impacts for both the vertical and horizontal results on cumulative production
(Equation 1) include Initial Reservoir Pressure, Permeability Thickness (+), Fracture Half Length
(+), Dimensionless Fracture Conductivity (+) and Difference (-). In the case of vertical wells,
the CnF concentration is positive and significant. In the case of the horizontal wells, while the
surfactant concentration is negative and significant, the CnF intercept and interaction terms are
positive and significant. Thus, CnF has a statistically different impact on early period
cumulative production relative to traditional surfactants. In addition, as expected, the parameter
estimates for all time dummies are significant and positive. Similarly, there are variables in each
of the systems for equations 2 and 3 that are statistically significant and of the same sign across
the two models.
However, the vertical versus the horizontal technology results diverge for some variables.
There are a number of cases in which a parameter estimate is significant for one technology and
not in the other (e.g., Initial Reservoir Pressure in Equations 2 and 3); or the signs of the
parameter estimates vary (e.g., Winter Fracture in Equations 3); and/or the magnitudes of the
parameter estimates are different (e.g., Initial Reservoir Pressure or Fracture Half Length in
Equations 1).
We next consider the estimated direct and indirect cumulative production impacts of the
variables specified in the models. Table 5 provides cumulative production elasticities with
respect to the continuous variables in the models. These elasticities include both direct and,
where applicable, indirect impacts of the variables on cumulative production.
22
TABLE 5: Cumulative Production Elasticities*
VERTICAL
Variable
Marginal
SE
HORIZONTAL
Prob>0
Marginal
SE
Prob>0
0.521
0.440
n.a.
0.234
0.029
n.a.
0.987
1.000
n.a.
0.354
0.268
0.213
0.046
0.037
0.135
1.000
1.000
0.943
2.251
-0.027
-0.182
0.213
0.237
n.a.
-0.124
0.190
.486
0.016
0.102
0.135
0.056
n.a.
0.034
0.047
1.000
0.055
0.037
0.943
1.000
n.a.
0.000
1.00
Reservoir Characteristics
Initial Reservoir Pressure
Permeability Thickness
Perforated Interval
2.335
0.564
0.075
0.330
0.027
0.068
1.000
1.000
0.863
Completion Outcomes
Final Fracture Half-length
Early Fracture Half-length
Dimensionless Fracture Conductivity
0.509
0.177
0.433
0.088
0.034
0.219
1.000
1.000
0.976
Completion Choices
CnF
Surfactant
Average Proppant per Stage
Proppant Concentration
Average Injection Rate
Average Treatment Pressure
Difference
Stages
0.062
n.a.
0.0017
0.11
0.027
-0.314
-0.221
n.a.
0.029
n.a.
0.029
0.057
0.042
0.124
0.035
n.a.
0.984
n.a.
0.523
0.972
0.738
0.006
0.000
n.a.
Production
Ratio
0.541
0.218
0.994
-0.00088 0.0414
0.491
*
The Delta method is used for standard error (SE) calculations. n.a. implies the variable is not applicable in the
indicated model.
In the case of reservoir characteristics, the signs of the cumulative production elasticities
are consistent across the vertical and horizontal technologies. The reservoir characteristics that
determine final fracture half-length and dimensionless fracture conductivity indirectly impact
cumulative production, and also directly impact cumulative production if they are variables in
equation 1. Initial reservoir pressure and permeability thickness are positively related to
cumulative production, as expected. These elasticities are precisely estimated. The magnitudes,
however, are substantially different - both initial reservoir pressure and permeability thickness
have relatively greater impacts on cumulative production with the vertical technology than with
the horizontal, all else equal. Perforated interval is also positively related to cumulative
production for the vertical wells, with the estimated probability of a positive impact of 86.3%.
Returns to the reservoir characteristics are decreasing except in the case of initial reservoir
23
pressure in vertical wells, where there is an estimated 2.335% increase in cumulative production
for every percentage increase in initial reservoir pressure.
Completion outcomes are also consistent in sign across the two well types - the
probability of a positive cumulative production elasticities is 94.3% or greater in all cases. In
addition, we find that completion outcomes exhibit diminishing returns. The cumulative
production elasticities with respect to final fracture half-length and dimensionless fracture
conductivity indicate the percentage change in cumulative production given a percentage change
in the respective variable, regardless of the source of the change in the variable. For example,
consider the cumulative production elasticity of 0.509 for final fracture half-length for the
vertical technology. Given a percentage increase in final fracture half-length, this indicates that
cumulative production increases .509%, irrespective of the source of the percentage increase in
the final fracture half-length. Note that this expected increase is only over the relatively short
time horizon, compared to the expected life of the well, represented in our sample. In contrast,
the elasticity is .354 for the horizontal technology, and can be interpreted analogously. Both
elasticities are large relative to their respective standard errors, so they are precisely estimated.
Variation in the cumulative production elasticities is more pronounced with respect to the
completion choice variables. The completion choices that determine final fracture half-length
and dimensionless fracture conductivity will at least indirectly impact cumulative production.
They will also directly impact cumulative production if they are explanatory variables in the
cumulative production equation. For example, consider the central tendency of the impact of
proppant on cumulative production for the vertical versus horizontal technologies. For vertical
wells, a one percent increase in proppant implies an expected 0.0017% increase in cumulative
production, but the probability of this elasticity being positive is only 52.3%, so it is not very
24
precisely estimated. In contrast, for horizontal wells, a percentage increase in average proppant
per stage indicates an expected decrease in cumulative production of 0.182%, with probability of
96.3% that the elasticity is negative. As in all of these estimated elasticities, these are the central
tendencies for the ranges of the variables in our data. While we do not expect proppant in
horizontal wells to be counterproductive at all levels of proppant use, our results indicate that it
is highly likely to be negative for the levels of proppant used across wells in our horizontal
technology sample. This suggests that for the horizontal wells, the conventional wisdom of
larger completion jobs (i.e., more pounds of proppant) does not necessarily result in higher
cumulative production.
Proppant concentration (pounds of proppant to gallons of fluid) impacts cumulative
production indirectly through Equation 3). The cumulative production elasticities with respect to
proppant concentration are positive for both vertical and horizontal technologies, with
probabilities of 97.2% and 94.3% respectively.
The elasticities for average injection rates are positive for both technologies, but this
probability for the vertical wells is only 73.8%. For the vertical wells we also include the
average treatment pressure, which has a negative elasticity with probability 99.4%. As discussed
previously, there was too little variation in the treatment pressure for the horizontal wells in our
sample, so it was not included in the econometric specification.
The cumulative production elasticities with respect to the differences between the
beginning of the completion job and the first day of production are negative for both
technologies and very precisely estimated. That is, the longer it takes to complete the well, the
lower cumulative production. This impact is relatively larger for the vertical wells.
25
The cumulative production elasticity with respect to the number of completion stages for
the horizontal wells is positive, with a high probability. As with the other completion outcomes,
except for CnF with the horizontal technology, this elasticity indicates that marginal returns to
completion stages are diminishing. As explained above, the multi-stage completion processes
are not relevant for the vertical technology.
All of the vertical technology wells used CnF, which is highly likely to provide a positive
impact on cumulative production from these wells (with 98.4% probability). The point estimate
of the cumulative production elasticity for this impact is .062, i.e., a one percent increase in CnF
in a vertical well is expected to yield a .062% increase in cumulative production. Again, note
that this impact is only measured over the limited time horizon represented in the data so actual
cumulative production increases over the life of the well may be significantly larger (as is the
case with other impacts).
The cumulative production elasticity with respect to CnF in horizontal wells is 2.251,
which is calculated from the cumulative production elasticities with respect to surfactants and the
CnF interactions throughout the estimated equations in the horizontal system. This implies that
cumulative production is expected to increase by approximately 2.251% for every 1% increase in
CnF for horizontal wells, indicating that CnF use in horizontal wells provides increasing returns.
Given it is economic to use CnF at all in horizontal wells, this result implies that higher levels of
CnF would be economically efficient. The standard error for the 2.251% is approximately
0.486%, so this elasticity is precisely estimated. In addition to this marginal impact of CnF use,
there is also a fixed shift in cumulative production with the use of CnF in the horizontal
technology, as discussed below.
26
As discussed above, traditional surfactants and CnF are substitutes in well completion.
The cumulative production elasticity with respect to traditional surfactants is estimated to be .027, with a probability of 94.5% that it is negative. That is, for the ranges of traditional
surfactants used in our horizontal sample, we find negative returns to traditional surfactants.
Analogous caveats to those in our above discussion of propprant use apply here as well.
Finally in terms of estimated elasticities, as in the theoretical development above, not
only how the well is completed but also how it is produced will impact cumulative production.
The ratio (days of production to total days required for that production) is highly likely to have a
positive impact on vertical well cumulative production. The cumulative production elasticity
with respect to this ratio for vertical wells is .541, with a probability of 99.4% of a positive
elasticity. The likely impact for the horizontal wells is less certain. The analogous elasticity for
horizontal wells is much less precisely estimated to be -.00088, with a probability of 50.9% of
being positive.
Table 6 provides semi-elasticities for completion choice variables that are binary and
have both direct and indirect impacts on cumulative production. The time effects are not
reproduced here, as they are already provided in the estimated cumulative production equations
in Tables 3 and 4. The winter fracture indicator is relevant for both the vertical and horizontal
technologies. Although not highly significant, the central tendency for the vertical technology is
that a winter fracture reduces cumulative production by approximately .64%, and cumulative
production for the horizontal technology decreases approximately 8.14%. However, given the
wide probability bounds around these point estimates, particularly for the vertical wells,
relatively little confidence can be placed in them.
27
TABLE 6: Discrete Effects Impacts on Cumulative Production*
VERTICAL
HORIZONTAL
Variable
Marginal
S.E.
Prob>0
Marginal
S.E.
Prob>0
Completion Choices
Winter Fracture -0.0064
0.040
0.436
-0.081
0.079
0.151
CnF Intercept
n.a.
n.a.
n.a.
15.351
3.300
1.000
*
Delta method standard errors. n.a. implies the variable is not applicable in the indicated model.
Next, consider the indicator variable for CnF, which is only applicable to the horizontal
technology model. The implication of using CnF versus a traditional surfactant, i.e., the fixed
impact of CnF in completion, all else equal, is on average an increase of 15.35 times the MCF in
cumulative production of a horizontal well completed with traditional surfactants. This seems a
rather large impact and we must caution that our results are sample specific, the horizontal
sample is relatively small and contains only three CnF wells, comprising 11.976% of the
horizontal technology observations. Regardless, considering both this discrete result and the
marginal CnF impact above, i.e., the CnF elasticity presented in Table 5, the CnF wells in the
horizontal sample are significantly more productive than the wells that use traditional
surfactants.
So, for these data sets, using CnF (an environmentally benign additive and a substitute for
traditional surfactants) results in a positive impact on early period production, but the use of the
general category of surfactant (for the horizontal wells) has a negative marginal impact on early
period cumulative production. These results naturally lead to more questions, for example:
“What is the optimal level of a surfactant or CnF?” and “Are there statistically significant
differences to production across different additives and, if so, how do the more benign additives
fare relative to toxic additives?” Unfortunately, given that most additive ingredients are
proprietary information, the latter question may be one that goes unanswered. But it is clear
28
from our results for this sample, CnF enhances productivity relative to traditional surfactants.
Naturally, analogous questions could be asked in the case of other production choices as well.
The physical production implications of these results are that the manner in which a well
is completed matters, as do the characteristics of the well. And, while some factors impact
vertical and horizontal wells in a similar fashion, this is not true in all cases. The economic
implications of these results are that the marginal benefits gained from changing a completion or
production choice can be measured through the change in marginal production and the
cumulative benefits of that production can be weighed against the marginal costs of that action.
Further, there is an optimal completion choice for a given well or type of well and that choice
may very well differ between vertical and horizontal wells.
7.0 CONCLUSIONS AND FUTURE RESEARCH
Technological advancement has made economic production from shale gas plays viable.
However, the cumulative benefits and ultimate recovery from a shale gas well can be impacted
by the completion and production strategies utilized. We find a substantial difference in the
marginal impacts for a vertical and horizontal shale gas wells that could ultimately impact the
total recoverable reserves of the wells. Our findings include:
•
Reservoir characteristics, as well as completion outcomes, impact horizontal and
vertical wells in the same direction, but not necessarily at the same magnitude or
probability.
•
Completion choices are more variable in the impact on cumulative production and
are not necessarily consistent in either sign, magnitude, or significance for the
vertical versus horizontal technology.
•
Different additives have different impacts. That is, the CnF wells are relatively
more productive than the non-CnF wells in the horizontal well set and the level of
CnF in the vertical wells is positively correlated with production.
29
•
The size of the completion job matters and “more” is not necessarily better, when
it comes to proppant.
These factors result in heterogeneous production functions for vertical and horizontal
wells and the recognition that a “one-size-fits-all” mentality can lead to a sub-optimal outcome.
Early production could be improved through a number of controls or control parameters, but the
value of this change has to be compared to the incremental costs of that change. Further, given
that discrete capital investments impact initial completion and early period production, there are
additional costs/benefits to understand over the longer term, hence longer-term analysis is
important - we only consider the initial in this study. For example, the marginal product (in
terms of cumulative production) exhibits diminishing returns to fracture length as well as for
other choice variables in well completion and production. This includes stages in the case of
horizontal wells, or pounds of proppant used per stage. This is consistent with the notion that a
bigger may not always be better. Larger fractures and larger completion jobs may not always be
optimal, and, for the ranges in the wells analyzed here, larger completion jobs may be
counterproductive. However, the value and costs of obtaining the product must be considered to
determine the optimal fracture length (or number of stages or amount of proppant). See
Chermak and Patrick (2012) for an example of such an analysis for tight sand gas wells.
Integrated analysis that simultaneously considers the economic and engineering aspects
of the problem can provide information that can be used by firms and investors to make betterinformed completion, production, and risk mitigation decisions. This work provides a first step
in integrating economic and engineering analysis and allows us to consider the impact of
alternative completion strategies. On-going work will extend this to consider a larger suite of
wells and a wider array of factors. Included in this is the development of multiple periodic
capital investments and optimal completion and production over the life of a well.
30
REFERENCES
Adamson, S. and G. Parker (2011). “Productivity and Technological Change in Shale Gas
Production: An Econometric Analysis of Well Data from he Haynesville Shale.” Proceedings
of the 34th IAEE International Conference, Stockholm, June 19-23, 2011.
Boyce, John R., and Linda Nøstbakken (2011). “Exploration and Development of U.S. Oil and
Gas Fields, 1955-2002.” Journal of Economic Dynamics and Control 35(6):891-908.
Caputo, M.R. (2010). “The Testable Implications of a Capital Accumulating, Price-Taking,
Vertically Integrated, Nonrenewable Resource Extracting Model of the Firm.” Optimal
Control Applications and Methods 31, 5–27.
Chermak, J.M., and R.H. Patrick (2012). “Irreversible Discrete Capital Investments in
Exhaustible Resource Production,” working paper available from the authors.
Chermak, J.M., J. Crafton, S. Norquist, and R.H. Patrick (1999). "A Hybrid EconomicEngineering Model for Optimal Natural Gas Production," Energy Economics 21(1):67-94.
Chermak, J.M. (1996) “The Economic Possibilities of Natural Gas Conservation: Antithetical
Results of Prorationing Regulation,” Journal of Regulatory Economics; 10:147-163.
Chermak, J.M., and R.H. Patrick (1995). "A Well-Based Cost Function and the Economics of
Exhaustible Resources: the Case of Natural Gas," Journal of Environmental Economics and
Management 28(2):174-189.
Chermak, J.M., and R.H. Patrick (1995). "Technological Investment and the Recovery of Natural
Gas: The Value of Information," The Energy Journal 16(1):113-135.
Crafton, J.W. (2011). “Completion Geology: A Geologist’s Role in a Successful Shale Well,”
AAPG US Shale Plays Geo-Technology Workshop. Fort Worth, TX: August, 2011.
Crafton, J.W. (2008). “Modeling Flowback Behavior or Flowback Equals Slowback,” SPE
Shale Gas Production Conference, Conference Paper SPE 119894.
Crafton, J.W. (1997). “Oil and Gas Well Evaluation Using the Reciprocal Productivity Index
Method,” SPE Production Operations Symposium, Conference Paper SPE 37409.
Coleman, J.L., Milici, R.C., Cook, T.A., Charpentier, R.R., Kirshbaum, Mark, Klett, T.R.,
Pollastro, R.M., and Schenk, C.J., (2011) “Assessment of undiscovered oil and gas
resources of the Devonian Marcellus Shale of the Appalachian Basin Province,” U.S.
Geological Survey Fact Sheet 2011–3092, 2 p., (Available at
http://pubs.usgs.gov/fs/2011/3092/. Last accessed 10/02/2011).
Emrich, C., Shaw, D., Reasoner, S., Ponto, D. (2001) “Codell Restimulations Evolve to 200%
Rate of Return” SPE Production and Operations Symposium, Conference Paper SPE
67211-MS.
31
Gray, W.M., T.A. Hoefer, A. Chiappe, and V.H. Koosh (2007) “A Probabilistic Approach to
Shale Gas Economics.” SPE Hydrocarbon Economics and Evaluation Symposium.
Conference Paper SPE 108053.
Kuller, Robert G., and Ronald G. Cummings (1974), "An Economic Model of Production and
Investment for Petroleum Reservoirs," The American Economic Review, 64(1):66-79.
Lee, W. J., and Sidle, R. E. (2010) “Gas Reserves Estimation in Resource Plays”, SPE
Unconventional Gas Conference, Conference Paper SPE 130102.
Levinsohn, J., and A. Petrin (2003), “Estimating Production Functions Using Inputs to Control
for Unobservables,” Review of Economic Studies 70(2):317-341.
Olley, G.S., and A. Pakes (1996), “The Dyanmics of Productivity in the Telecommunications
Equipment Industry,” Econometrica 64(6):1263-1297.
Patrick, R.H., and J.M. Chermak (1992). The Economics of Technology Research and
Development: Recovery of Natural Gas from Tight Sands. Gas Research Institute Report No.
GRI-92/0267, Washington, D.C.: National Technical Information Services.
Pursley, J. T., Holcomb, D. L., Penny, G. S. (2008) “Composition and process for well cleaning”
U.S. Patent Number 7,380,606, Canadian Patent Number 2,478,433.
----. “Modernization of Oil and Gas Reporting”, Securities and Exchange Commission, Federal
Register, Vol. 74, No. 9 (Wednesday, January 14, 2009), pg. 2158.
US Energy Information Administration (2012). Annual Energy Outlook 2012: Early Release.
US Department of Energy, Washington, DC. (Available at:
http://www.eia.gov/forecasts/aeo/er/. Last accessed 04/15/2012).
US Energy Information Administration (2011). Annual Energy Review 2011: US Department of
Energy, Washington, DC.
32