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Impacts of Completion and Production Decisions for Vertical versus Horizontal Technologies on Shale Gas Well Cumulative Productivity1

Janie M. Chermaka James W. Craftonb Robert H. Patrickc

University of New Mexico Performance Sciences, Inc. 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 Please do not quote or cite without permission of the authors.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: jchermak@unm.edu 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: rpatrick@rutgers.edu.

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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.

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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

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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.

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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.

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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 A production choke is a flow control device that limits the flow of natural gas. 6 Petrohawk Q3 2010 Results: Earnings Call Transcript (11/02/2010).

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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( ),...,ZM 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+( ), K0( ) . 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 ,

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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

+ ,τj+1

− ], j = 0,...k , τ k+1 = T . The firm chooses both Kj and

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

Rj (t) = s[A, K j , R,q,t], R 0+( ) = R0 A 0+( ), K0( ), 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

R(t) = s[A, K j , R,q,t]= −q(t) , (so that

sq = −1and sqq = 0) , an assumption traditionally

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

∂2s(R(t),q(t),t) / ∂q2 ≤ 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.

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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 (shut-

down) 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− ), Kk ,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

π = e−rt

0

T

∫ P(t)q(t)− w t( )Z t( )⎡⎣ ⎤⎦dt − e−rτ j v(R(τ j− ), K j ,τ j )

j=1

k

∑ , (4)

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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,

R(t), Z(t),τ 0 ,...,τ k ,T , K0 ,..., Kk( ) ,

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⎡

⎣⎤⎦+λs 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

−HR = λ = −λsR , (6)

HZi

= e−rt PhZi− w⎡

⎣⎤⎦ + λshhZi

≤ 0 = 0, if q > 0( ), ∀i = 1,..., M , (7)

λ(t) uK j

( R(t),0,t)− vK j( R(t),0,t)⎡

⎣⎤⎦K j ≤ 0 ∀ K j ∈κ (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 j

and vK j are the marginal value of the

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

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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, T , satisfies

H (T ) = e−rT P(T )q(T )−C(q(T ), R(T ),T )⎡⎣ ⎤⎦ + λ(T )s( R(T ), q(T ),T ) = 0. (9)

The transversality condition is

λ(T ) ≥ 0 = 0 if R(T ) > 0( ) . (10)

The optimal completion investments occur at discrete points in time. At all jump points

τ j , j=1,…,k, we have the following conditions:

λ(τ j

+ )− λ(τ j− ) = −vR( R(τ j ), K j ,τ j )− λ(τ j

+ ) uR( R(τ j ), K j ,τ j ) , (11)

λ(τ j

+ ) uK j( R(τ j ), K j ,τ j )− vK j

( R(τ j ), K j ,τ j )⎡⎣

⎤⎦(K j − K j ) ≥ 0 ∀ K j ∈κ , (12)

and

H ( R(τ j+ ), q(τ j

+ ), K j ,τ j )− H ( R(τ j− ), q(τ j

− ), K j ,τ j )

− vτ j( R(τ j

− ), K j ,τ j)− λ(τ j

+ )uτ j( R(τ j

− ), K j ,τ j)

≥ 0 if τ j = 0

= 0 if τ j ∈(0,T )

≤ 0 if τ j = T

⎧

⎨⎪⎪

⎩⎪⎪

(13)

(11) provides the jump condition on the in situ resource price at the optimal jump times τ j ,

j=1,…,k. (12) implies that the optimal capital increment K j at time

τ 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 τ j , j=1,…,k, i.e., the timing for the discrete periodic

capital investments (fracturing and completion). The number times completion takes place over

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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

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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,

Ai0 = A1i0,...,Ani0( ), i = 1,..., I , which can also impact reserves; completion production functions,

Fj and

C j ; and production q t( ) through the choices Ki0 = K1i0,...,KMi0( ), 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 ,Kij ,Fij ,Cij( ) (14)

Cumulative production at time t is then given by

Qi t( ) = qi x( )0

t

∫ dx = h Ai0,Ki0,Fi0,Ci0, x( )0

t

∫ 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

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Fi0 = f Ai0 , Ki0( ), (16)

and the fracture conductivity production function

Ci0 = g Ai0 , Ki0( ) . (17)

(16) and (17) are both expressed as functions of Ki0 for notational ease, note that each of these

equations will contain both common and mutually exclusive elements of the vector Ki0 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.,

∂Qi t( ) ∂Kim0 =

0

t

∫ ∂hit ∂Kim0

direct + ∂ fit ∂Fim0 ∂Fim0 ∂Kim0

indirect + ∂git ∂Cim0 ∂Cim0 ∂Kim0

indirect dx (18)

The system of equations as described above, the specified econometric model is of the

form:

lnQit = β0 + β jj=1

M

∑ lnKij0 + β j lnj⊂ A[ ]∑ Aij0 + βF lnFit0 + βC lnCit0 + β j

j⊂ D[ ]∑ Dijt + e1it (19)

lnFi0 = β0 + β jj⊂ K[ ]∑ lnKij0 + β j ln

j⊂ A[ ]∑ Aij0 + β j

j⊂ D[ ]∑ Dij0 + e2it (20)

lnCi0 = β0 + β jj⊂ K[ ]∑ lnKij0 + β j ln

j⊂ A[ ]∑ Aij0 + β j

j⊂D∑ Dij0 + e3it , (21)

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.,

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Qit = exp β0 + β jj=1

M

∑ lnKij0 + β j lnj⊂ A[ ]∑ Aij0 + βF ln Fi0 + βC lnCi0 + β j

j⊂ D[ ]∑ Dijt + eit

⎛

⎝⎜⎞

⎠⎟. (22)

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 The product of reservoir permeability times thickness of the reservoir. 9 The hydrostatic pressure of the formation prior to first production.

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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.

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TABLE 1: Variable Names, Descriptions, and Units Variable Description Units Cumulative Production i (i =10, 30, 60, 90, 180, 260, 720 days)

Cumulative Production to a point in time MCF

Final Fracture Half-length Effective final fracture from wellbore Feet Dimensionless Fracture Conductivity

Product of fracture permeability and propped fracture width divided by the product of fracture half-length and formation permeability

Initial Reservoir Pressure Pressure prior to completion and production Pounds per square inch (PSIG)

Permeability thickness Reservoir permeability * reservoir thickness millidarcy feet Perforated Interval Range of reservoir perforated Feet Early Fracture Half-length Effective early period fracture length from wellbore Feet Proppant Concentration Pounds of proppant divided by gallons of hydraulic

fracturing fluid Pounds per gallon

Average Pounds of Proppant per stage

Pounds of proppant used in completion divided by the number of stages

Pounds

Surfactant Concentration (horizontals) or CnF Concentration (verticals)

Percentage fluid that is a surface active agent additive (scaled by 100)

Percent*100

Stages Number of stages used for the completion Numeric (1,2,3) Average Injection Rate Rate at which fluids are injected Barrels per minute Average Treatment Pressure Average pressure used for injection Pounds per

square inch Difference Difference in Days between beginning of

completion job and day of first production Days

Ratioi (i =10, 30, 60, 90, 180, 260, 720 days)

Ratio of total days of production to total calendar days necessary to achieve the days of production

Percent

Cumulative Production i (i =10, 30, 60, 90, 180, 260, 720 days)

Cumulative days of production 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.

18

TABLE 2: Descriptive Statistics

Variable Vertical Horizontal Mean s.d. Min Max Wells Mean s.d. Min Max Wells

Well Characteristics Permeability Thickness 0.82 0.93 0.14 6.77 72 3.08 4.44 0.04 18.68 39 Initial Reservoir Pressure 4703.86 268.48 2609.50 5015.80 72 5071.60 843.93 2892.58 8073.99 39 Perforated Interval 72.86 21.04 40.00 129.00 72 na na na na na

Completion Outcome Final Fracture Half-length 48.32 18.12 15.96 109.55 72 122.47 96.71 3.54 419.54 39 Early Fracture Half-length 40.29 18.78 2.67 80.12 72 163.72 135.12 3.54 655.03 39 Dimensionless Fracture Conductivity 1790.28 1415.14 150.00 6038.00 72 2808.57 5759.69 36.99 29400.40 39

Completion Choices Average Pounds Proppant per Stage 945592 233178 369000 1256600 72 597728 243522 59600 1018010 39 Proppant Concentration 0.85 0.18 0.50 1.32 72 1.18 0.52 0.17 3.21 39 Surfactant Concentration na na na na na 0.09 0.07 0.00 0.37 39 CnF Concentration 0.12 0.06 0.02 0.22 72 na na na na na Average Injection Rate 109.11 19.52 44.70 134.20 72 71.82 14.88 15.65 89.71 39 Average Treatment Pressure 5903.83 552.55 3868.00 7307.00 72 5867.71 1140.82 3486.00 8170.07 39 Stages na na na na na 6.44 3.73 1.00 15.00 39 Winter Fracture 0.29 0.46 0.00 1.00 72 0.33 0.48 0.00 1.00 39 Difference 7.67 8.05 2.00 36.00 72 6.92 23.63 0.00 150.00 39

Production Cumulative Production 10 6096 5595 174 30330 72 18029 11395 1290 43820 39 Ratio 10 Days 98.29 8.42 43.48 100.00 72 58.38 39.41 2.87 100.00 39 Cumulative Production 30 15113 12825 855 78598 72 63526 42755 7069 181871 35 Ratio 30 Days 97.28 10.77 35.29 100.00 72 42.14 30.26 7.87 100.00 35 Cumulative Production 60 25123 20668 1342 131111 72 126762 91813 15437 428638 32 Ratio 60 Days 98.02 7.95 51.28 100.00 72 52.25 27.87 14.47 100.00 32 Cumulative Production 90 33183 27540 1736 174876 72 182450 118871 19635 379801 27 Ratio 90 Days 98.48 6.32 60.40 100.00 72 60.01 24.28 20.19 99.68 27 Cumulative Production 180 51730 44357 2794 296232 70 292418 229082 30251 764838 20 Ratio 180 Days 98.74 5.55 59.02 100.00 70 68.57 21.98 32.33 99.84 20 Cumulative Production 360 78478 47821 24929 172550 20 384113 432480 47738 1426010 11 Ratio 360 Days 99.02 2.75 87.80 100.00 20 80.24 17.05 51.37 99.92 11 Cumulative Production 720 na na na na na 262897 320541 76980 633025 3 Ratio 720 Days na na na na na 85.43 12.09 72.23 95.96 3

19

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.

20

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 Mean of X Ln Initial Reservoir Pressure 3.0431 0.4142 0.00 8.45 Ln Permeability Thickness 0.9554 0.2150 0.00 -0.56 Ln Perforated Interval 0.0748 0.0682 0.27 4.25 Ln Fracture Half Length 0.5087 0.0884 0.00 3.82 Ln Dimensionless Fracture Conductivity 0.4326 0.2188 0.05 7.16 Ln CnF Concentration 0.0624 0.0274 0.02 -2.25 Ln Difference -0.2205 0.0346 0.00 1.73 Ln Ratio 0.5411 0.2177 0.01 4.58 Winter Fracture 0.0413 0.0424 0.33 0.31 30 Days 1.0372 0.0492 0.00 0.19 60 Days 1.5764 0.0491 0.00 0.19 90 Days 1.8613 0.0491 0.00 0.19 180 Days 2.3229 0.0495 0.00 0.19 360 Days 2.7141 0.0765 0.00 0.05 Constant -24.2175 4.6091 0.00

Equation 2: ln(Final Fracture Half-length)= Variable Coefficient s.e. Probability Mean of X Ln Initial Reservoir Pressure -0.1825 0.1855 0.33 8.45 Ln Permeability Thickness 0.1057 0.0186 0.00 -0.56 Ln Average Treating Pressure -0.2898 0.1628 0.08 8.68 Ln Early Fracture Half-length 0.3472 0.0269 0.00 3.55 Ln Injection Rate 0.0526 0.0820 0.52 4.66 Ln Proppant 0.0033 0.0565 0.95 13.72 Ln CnF Concentration 0.0061 0.0205 0.77 -2.25 Winter Fracture 0.0323 0.0285 0.26 0.31 Constant 6.4118 1.9080 0.00

Equation 3: ln(Dimensionless Fracture Conductivity)= Variable Coefficient s.e. Probability Mean of X Ln Initial Reservoir Pressure -1.4234 0.0933 0.00 8.45 Ln Permeability Thickness -1.0296 0.0079 0.00 -0.56 Ln Average Treating Pressure -0.3847 0.0749 0.00 8.68 Ln Proppant Concentration 0.2536 0.0363 0.00 -0.17 Ln CnF Concentration -0.0071 0.0105 0.50 -2.25 Winter Fracture -0.1485 0.0142 0.00 0.31 Constant 22.0255 0.8700 0.00 Based on 378 observations Equation 1: RMSE=.295, "R2"≅ .93, and χ

2 = 5240.70

Equation 2: RMSE=.235, "R2"≅ .61, and χ2 = 562.43

Equation 3: RMSE=.120, "R2"≅ .98, and χ2 = 18431.78

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TABLE 4: Horizontal Well Results Equation 1: Ln(Cumulative Production)=

Variable Coefficient s.e. Probability Mean of X Ln Initial Reservoir Pressure 0.0311 0.2280 0.89 8.51 Ln Permeability Thickness 0.6459 0.1377 0.00 -0.06 Ln Fracture Half Length 0.3540 0.0459 0.00 4.58 Ln Dimensionless Fracture Conductivity 0.2134 0.1347 0.11 6.43 Ln Surfactant Concentration -0.0540 0.0161 0.00 -6.12 CnF Intercept 15.5696 3.2559 0.00 0.12 Ln CnF Interaction 2.3360 0.4795 0.00 -0.81 Ln Difference -0.1240 0.0339 0.00 0.93 Ln Ratio -0.0009 0.0414 0.98 3.80 Winter Fracture -0.1079 0.0775 0.16 0.34 30 Days 1.2483 0.0881 0.00 0.21 60 Days 1.8456 0.0908 0.00 0.19 90 Days 2.1760 0.0965 0.00 0.16 180 Days 2.7238 0.1083 0.00 0.12 360 Days 3.2311 0.1352 0.00 0.07 720 Days 3.4582 0.2390 0.00 0.02 Constant 6.1013 2.4231 0.01

Equation 2: Ln(Final Fracture Half-length)= Variable Coefficient s.e. Probability Mean of X Ln Initial Reservoir Pressure 1.3838 0.2104 0.00 8.51 Ln Permeability Thickness 0.0227 0.0603 0.71 -0.06 Ln Early Fracture Half-length 0.7568 0.0439 0.00 4.80 Ln Stages 0.5373 0.1162 0.00 1.57 Ln Average Injection Rate 0.6683 0.1331 0.00 4.24 Ln Avgerage Proppant per Stage -0.5129 0.2802 0.07 5.73 Ln Surfactant Concentration 0.0769 0.0161 0.00 -6.12 CnF Intercept -0.6211 3.2125 0.85 0.12 Ln CnF Interaction -0.1650 0.4744 0.73 -0.81 Winter Fracture 0.0743 0.0781 0.34 0.34 Constant -11.1769 2.0457 0.00

Equation 3: ln(Dimensionless Fracture Conductivity)= Variable Coefficient s.e. Probability Mean of X Ln Initial Reservoir Pressure 0.0007 0.0007 0.35 8.51 Ln Permeability Thickness -1.0003 0.0001 0.00 -0.06 Ln Stages 0.0007 0.0003 0.01 1.57 Ln Proppant Concentration 0.9987 0.0004 0.00 6.38 Ln Surfactant Concentration 0.00004 0.0001 0.43 -6.12 CnF Intercept 0.0072 0.0097 0.46 0.12 Ln CnF Interaction 0.0011 0.0014 0.46 -0.81 Winter Fracture 0.0008 0.0002 0.00 0.34 Constant 0.0017 0.0074 0.82 Based on 167 observations Equation 1: RMSE=.3852, "R2"≅ .92, and χ

2 = 2023.53

Equation 2: RMSE=.3787, "R2"≅ .84, and χ2 = 889.67

Equation 3: RMSE=.0012, "R2"≅ .99, and χ2 = 3.77E+08

22

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.

23

TABLE 5: Cumulative Production Elasticities* VERTICAL HORIZONTAL Variable Marginal SE Prob>0 Marginal SE Prob>0

Reservoir Characteristics Initial Reservoir Pressure 2.335 0.330 1.000 0.521 0.234 0.987 Permeability Thickness 0.564 0.027 1.000 0.440 0.029 1.000 Perforated Interval 0.075 0.068 0.863 n.a. n.a. n.a.

Completion Outcomes Final Fracture Half-length 0.509 0.088 1.000 0.354 0.046 1.000 Early Fracture Half-length 0.177 0.034 1.000 0.268 0.037 1.000 Dimensionless Fracture Conductivity 0.433 0.219 0.976 0.213 0.135 0.943

Completion Choices CnF 0.062 0.029 0.984 2.251 .486 1.000 Surfactant n.a. n.a. n.a. -0.027 0.016 0.055 Average Proppant per Stage 0.0017 0.029 0.523 -0.182 0.102 0.037 Proppant Concentration 0.11 0.057 0.972 0.213 0.135 0.943 Average Injection Rate 0.027 0.042 0.738 0.237 0.056 1.000 Average Treatment Pressure -0.314 0.124 0.006 n.a. n.a. n.a. Difference -0.221 0.035 0.000 -0.124 0.034 0.000 Stages n.a. n.a. n.a. 0.190 0.047 1.00

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

24

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

25

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.

26

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.

27

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.

28

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

29

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.

30

• 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 better-

informed 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.

31

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