Impacts of Hydraulic Fracturing and Completion Technology on Shale Gas Well Production 1

Transcription

1 Impacts of Hydraulic Fracturing and Completion Technology on Shale Gas Well Production 1 Janie M. Chermak a James W. Crafton b Robert H. Patrick c University of New Mexico Performance Sciences, Inc. Rutgers University Revised August 2015 May 2013 Abstract We estimate early period shale gas cumulative production functions and output elasticities for vertical and horizontal well technologies. Results indicate reservoir characteristics 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 impacts of completion decisions on cumulative production are highly variable, with differences in early period production declines across the two 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 on early period production. KEYWORDS Production function, technology, shale gas, hydraulic fracturing, output elasticities CLASSIFICATION CODES Q4 (energy), Y8 (Related Disciplines), L7 (Industry Studies: Primary Products), L71 (Mining, Extraction, and Refining: Hydrocarbon Fuels), D (Microeconomics), D24 (Production) C3 (Simultaneous Equations), C33 (Models with Panel Data) 1 We d like to thank Alan Krupnick, Tim Fitzgerald, and other participants at the 2011 and 2012 USAEE/IAEE North American Conferences, David Lamont and other participants at the Rutgers University CRRI Advanced Workshop and Regulation and Competition, 31 st Annual Eastern Conference for helpful comments on previous versions of this paper. Chermak and Patrick thank PSI for partial financial support. a Department of Economics, University of New Mexico, MSC , 1UNM, Albuquerque, NM 87131: jchermak@unm.edu b Performance Sciences, Inc., Evergreen, CO c CORRESPONDING AUTHOR; Finance and Economics, Rutgers Business School Newark and New Brunswick, Rutgers University, 1 Washington Park 1148, Newark, New Jersey rpatrick@rutgers.edu. 1

2 1.0 INTRODUCTION Shale gas production is a relatively recent entrant into the natural gas industry. While the potential of shale gas had been known for some time, advancements in technology have 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 gaining interest throughout the world. For example, China and Canada are now producing shale gas as wellit should be noted, however, that other countries are proceeding more slowly. Shale gas is not without controversy, which may be one of the reasons for the caution shown. In addition to the well-publicized debate over potential environmental effects of hydraulic fracturing and the amount of water needed to complete a well, 2 there is significant uncertainty concerning the quantity of actual reserves. For example, between 2011 and 2012, the US Energy Information Administration (EIA) reduced its estimate of unproved technically recoverable resource for the US by almost half in its Annual Energy Outlook (AEO).. 3 In part this was due to early period production decline (which impacts ultimate recovery) that was far greater than originally expected (EIA 2012, 2011). 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 2 Although the US Environmental Protection Agency (2015) issued a draft assessment of the potential impacts of hydraulic fracturing and found no evidence of widespread systematic impacts on drinking water resources in the United States, the debate appears far from over. 3 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

3 not only on the characteristics of the well and the reservoir, but also on choices made by the producer; completion, production, and recompletion choices. In the case of shale gas wells, this may be even more important as some 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 may have substantially larger initial production levels than vertical wells, this is a newer technology with greater uncertainty of ultimate recovery. This paper provides estimates of the impacts of shale well completion and production decisions on early-period natural gas production, controlling for well characteristics, for vertical and horizontal well 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 cumulative production elasticities are variable both in sign and magnitude across the two technologies. 2.0 BACKGROUND Natural gas was first produced commercially in the US in Initially production was from conventional reservoirs. That is, onshore, sandstone reservoirs which are characterized by high porosity and permeability, allowing gas in the reservoir and conduits to flow through the reservoir. Over time, improved technology allowed economic production from increasingly 3

4 challenging plays, including offshore reservoirs, tight formations (low porosity and permeability), coalbed methane, and more recently, shale. Shale gas production is unique in that the gas is in situ in the source rock and has not migrated to a reservoir. While the existence of deep shale gas resources was known by at least the 1980 s, the economic conditions didn't exist to pursue the technology and/or the plays. In the early 1990 s, Mitchell Energy began utilizing hydraulic fracturing in the Barnett shale in Texas to stimulate production and then incorporated horizontal drilling to potentially increase the yield from a well. Shale gas reserves are an unconventional resource where the gas is located in very low permeability geologic formations. Large estimated reserves in the US are located in the Devonian-age Marcellus shale in the northeast, the Jurassic-age Haynesville shale in the south, the Cretaceous-age Eagle Ford shale in the south, and the Missipian-age Barnet in Texas. Low permeability makes movement of the gas difficult, which precipitates the need 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 pioneered by Mitchell Energy enabled the production of this resource. 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 (SEC 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). 4

5 The impact of shale production on the natural gas industry is substantial. In 2000, less than 0.4 TCF of natural gas production in the U.S. was from shale gas reserves. By 2013 more than 11.8 TCF of natural gas production was from shale gas. While the total production contribution from shale is forecast to increase in the long run, the EIA (2015) is projecting a short-term decline in shale production for the first time since its been tracked due to production declines in existing wells not being offset by new wells coming on line. This illustrates the importance of improving efficiency, especially in times when natural gas prices are low. After a well is drilled, a completion plan is made. The plan can 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 then injected at pressure to propagate fractures or fissures through the reservoir rock to the wellbore. Proppant is a material that keeps the fracture open and provides a conduit for the flow of gas to the wellbore. Figure 1 illustrates the vertical and horizontal technologies. In both cases, the wells have the same shale zone of interest and the fractures are propagated out from the casing. Given the position of the casing, the vertical well results in fractures relatively parallel to the length of the formation, while the horizontal well results in fractures perpendicular to the thickness of the formation. The length of a fracture is dependent on a number of factors, including the characteristics of the host rock and, as discussed earlier, the completion job chosen. A 5

6 characteristic of the horizontal technology is that the horizontal portion of the well is drilled parallel to the zone of interest, resulting in the potential for a number of stages, while the vertical technology is limited by the thickness of the zone. FIGURE 1: Vertical versus horizontal wells The completion decisions include the volume of fluids, the pressure under which the fluids are delivered, the characteristics of the proppant, as well as the additives to include in the fluid. 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 historically were often proprietary and may not have been environmentally benign. 4 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 4 As of 2015, 29 states now require some type of hydraulic fracturing chemical disclosure (fracfocus.org: Last accessed 08//30/2015). 6

7 choice. 5 For example, CnF is relatively environmentally benign and has the distinction that when used in the North Sea, in the case of a spill, it is classified as a non-environmental event. 6 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 than other unconventional natural gas reservoirs, initially the standard industry practices were used in their production, i.e., they followed that of other reservoirs - mainly high flowback (production of the fracturing fluid) and production rates. 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 reduced capital costs over the life of the well due to lower initial expense and fewer work-overs of the well. 7 For example, Petrohawk Energy has employed more conservative production plans in the Haynesville, producing wells on more restrictive chokes (15/64 or 16/64 inch choke) and reported decreases in decline rates. 8,9 5 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. 6 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. 7 This is consistent with Patrick and Chermak (1992) and Chermak et al. (1999) on producing other alternative natural gas sources, discussed further below. 8 A production choke is a flow control device that limits the flow of natural gas. 9 Petrohawk Q Results: Earnings Call Transcript (11/02/2010). 7

8 In terms of the economics literature addressing shale gas, Fitzgerald (2013) discusses economic factors in hydraulic fracturing, including environmental impacts. Lake, et al., (2013) provide a case study of a single well, developing a model to evaluate the economic viability of a shale gas well. They conclude that most shale gas wells are profitable (under their modeling assumptions). Hefley and Wang (2014) provide additional details and shale gas case studies. Fitzgerald (2015), discussed further below, analyzes hydraulic fracturing data for wells in North Dakota and Montana, and finds, among other things, that producers benefit from experience. Otherwise, previous economic studies have focused on the optimal completion and production of other types of unconventional gas resources, in particular, vertical technology, tight sand resources. Chermak and Patrick (1995a), among other things, estimate well-level cost functions for tight sand natural gas wells. Chermak and Patrick (1995b) estimate the value of information technology in tight sand gas production. Patrick and Chermak (1992) and Chermak et al. (1999) develop hybrid economic-engineering models for optimal tight sand natural gas well fracturing, completion, and production. They show how fracture length affects well profitability, among other things, and find that larger fractures are not necessarily the most profitable. In this paper we contribute to this literature by analyzing a unique sample of shale natural gas wells, including the relatively new horizontal drilling technology, as well as traditional vertical technology wells. The completion and production of a well involve a number of interdependent decisions. We are interested in the developing the empirical representations of the interdependencies between the components of completion and production geology and technology, i.e., how decision variables affect the fracture and conductivity (capital investments) and how these in turn affect cumulative production. We model the physical interdependency through a series of interdependent production functions representing the completion and production of the well. 8

9 These interdependent physical relationships are a necessary input to determine the economically optimal completion and production of the natural gas well (i.e., to maximize the value of the resource) MODELING FRAMEWORK We adopt a relatively simple representation of a shale gas production function. 10 The natural gas production function for well i = 1,..., I, at time t is given by q it = h( A i0,k i0,f i0,c i0 )θ it (1) where θ it = Be η i +u t +v it with η i and u t, unobserved well and time specific effects, and v it is a random component. Factors impacting production include physical attributes of the reservoir, A i0 = ( A 1i0,..., A ni0 ), i = 1,..., I, which can also impact reserves; completion (input) production functions, F i and C i ; and production q it through the choices K i0 = ( K 1i0,...,K Mi0 ), i = 1,..., I; that impact productivity either through reserves or feedback. The logarithmic specification of the production function is q q q lnq it = β A ln A i0 + ( ε K ) it ln K i0 + ( ε F ) it ln F i0 + ( ε C ) it lnc i0 + lnθ it (2) q where ( ε j ) is the output elasticity for factor j = K, F,C it ( ) and β A is a parameter (elasticity) associated with the logarithm of exogenously fixed variables A. Analogous to Solow (1957), firms are assumed to maximize profits given input and output prices, i.e., they are price takers in input and product markets. At time t = 0, all factors that the firm controls in terms of fracturing and completing the well are variable, so profit maximization implies the first-order conditions 10 Caputo (2010) considers, among other things, continuous capital investment in production of exhaustible natural resources. See his paper for a review of the capital literature in this regard. In this paper we consider a simple model of discrete capital investment (e.g., fracturing) in pressure driven exhaustible resources such as natural gas. 9

10 q ( ε j ) it = ( β j ) it, for all j (3) where ( β j ) = w jit j it, the share of factor j costs in total revenue, and j it P it q i0 and q it are at their profit it maximizing levels. 11 This implies that factors are paid the value of their marginal product. Since firms are producing an exhaustible resource, profit maximization implies q it is determined so that the sum of marginal cost, c qit, and the shadow (option) value of the exhaustible resource, λ it, will equal the contemporaneous product price. 12 So the ratio P it c qit + λ it = 1. Substituting conditions (3) into (2), we have the form of the relationship we estimate, lnq it = ( β A ) it ln A i0 + ( β K ) it ln K i0 + ( β F ) it ln F i0 + ( β C ) it lnc i0 + lnθ it (4) F and C, the fracture and conductivity of the well, respectively, are not directly observed, so they are estimated. F and C each require discrete inputs initially so that natural gas can be produced from the well. Therefore we estimate a system of equations that includes sub-production functions for F and C. Cumulative production at time t is then given by integrating (1), t Q it = q i ( x) dx = h( A i0,k i0,f i0,c i0 )θ ix dx. (5) 0 t 0 From the perspective of estimating cumulative production, the discrete factors are fixed as they are chosen initially. 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. Since 11 We directly estimate the production function to obtain the factor output elasticities reported below. Mairesse and Jaumandreu (2005) find very little difference in results from estimating the production function (using a real output) versus a revenue function (using price index weighted output). 12 This follows from Hotelling (1931). Chermak and Patrick (2001, 2002) summarize tests of Hotelling and, analyzing a panel data set for 29 tight-sand gas wells, find that producer behavior is consistent with Hotelling s exhaustible resource theory. 10

11 cumulative production is dependent on the endogenous variables F i and C i, we estimate cumulative production simultaneously with specifications of the fracture production function and the fracture conductivity production function. Explanatory variables that are in Q it and F i and/or C i will have both direct and indirect effects on cumulative production, Q it, e.g., t Q it K im0 = ( h it K + h im0 it F im0 F im0 K + h im0 it C im0 C im0 K im0 ) dx (6) 0 direct indirect The specified average production functions comprising the system of equations that we estimate are then given by M indirect lnq it = β 0 + β j ln K ij 0 + β j lna ij 0 + β F ln F it 0 + β C lnc it 0 + β j D ijt + e 1it (7) j=1 n j=1 j and ln F i0 = δ 0 + δ j ln K ij 0 + δ j lna ij 0 + δ j D ij 0 + e 2it (8) j j j lnc i0 = γ 0 + γ j ln K ij 0 + γ j lna ij 0 + γ j D ij 0 + e 3it, (9) j j j where the β, δ and γ ' s in each equation are the parameters to be estimated, the D variables are binary variables and time fixed effects, and only subsets of the A, K, and D variables are in each equation, with some of the subset of elements mutually exclusive (the equations are completely specified with the estimates below). Time fixed effects are used to capture unobserved heterogeneity over time. We expect these effects to approximate the impact of unobservable production decisions and pressure declines on cumulative production. Equations (7), (8), and (9) comprise the empirical system of average production and subproduction functions we estimate. The expected cumulative production for well i at time t can 11

12 then calculated as follows. Denote the expectations of (8) and (9), conditional on all information available at time t, E( ln F i0 ) = ln F i0 and E( lnc i0 ) = lnc i0, respectively. Substitute these conditional expectations into the expected value of (7), conditional on all information available at time t, and apply the exponential operator to obtain the predicted average cumulative production for well i at time t, i.e., ˆQ it = exp ˆβ M 0 + ˆβ j ln K ij 0 + ˆβ j lna ij 0 + ˆβ F ln F i0 + ˆβC lnc i0 + ˆβ j D ijt (10) j=1 j j 4.0 DATA The data are from 111 shale gas wells located in the US. Due to producer confidentiality, the locations are not revealed. However, the data are all from a single basin and a single geologic setting. Thus heterogeneity across basins is not a consideration in the study. There are 39 horizontal wells and 72 vertical wells in our sample. All of the wells have been completed and production initiated since 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 both the vertical and horizontal technologies. Well characteristics include permeability thickness 13, initial reservoir pressure 14, 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). 13 The product of reservoir permeability times thickness of the reservoir. 14 The hydrostatic pressure of the formation prior to first production. 12

13 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. One interest in comparing the impacts of the traditional surfactants versus CnF is due to the environmental aspects of CnF. 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. 15 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 15 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. 13

14 produce those production days. 16 Second, there are at most seven cumulative production periods for each well; the first ten days, then 30, 60, 90, 180, 360, and 720 days. The 720 days of production are only applicable to some of the 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 for each well. 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 Thousand cubic feet (MCF) Final Fracture Half-length Effective final fracture from wellbore Feet Dimensionless Fracture Product of fracture permeability and propped Unitless Conductivity 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 of proppant used in completion divided by the number of stages Percentage fluid that is a surface active agent additive (scaled by 100) Pounds per gallon Average Pounds of Proppant Pounds per stage Surfactant Concentration Percent*100 (horizontals) or CnF Concentration (verticals) 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 Ratio i (i =10, 30, 60, 90, 180, 260, 720 days) Days i (i =10, 30, 60, 90, 180, 260, 720 days) 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 (scaled by 100) Cumulative days of production Days Percent*100 Days 16 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. 14

15 Descriptive statistics for the data are provided in Table 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. 17 Wells refers to the number of wells on which the statistic is based. Note later production periods have smaller numbers of wells because all wells do not have the same production periods. 15

16 TABLE 2: Descriptive Statistics Variable Vertical Horizontal Mean s.d. Min Max Wells Mean s.d. Min Max Wells Well Characteristics Permeability Thickness Initial Reservoir Pressure Perforated Interval n.a. n.a. n.a. n.a. n.a. Completion Outcome Final Fracture Half-length Early Fracture Half-length Dimensionless Fracture Conductivity Completion Choices Average Pounds Proppant per Stage Proppant Concentration Surfactant Concentration n.a. n.a. n.a. n.a. n.a CnF Concentration n.a. n.a. n.a. n.a. n.a. Average Injection Rate Average Treatment Pressure Stages n.a. n.a. n.a. n.a. n.a Winter Fracture Difference Production Cumulative Production Ratio 10 Days Cumulative Production Ratio 30 Days Cumulative Production Ratio 60 Days Cumulative Production Ratio 90 Days Cumulative Production Ratio 180 Days Cumulative Production Ratio 360 Days Cumulative Production 720 n.a. n.a. n.a. n.a. n.a Ratio 720 Days n.a. n.a. n.a. n.a. n.a

17 5.0 RESULTS Based on (7), (8) and (9), we consider cumulative production within the first two years of production for our sample of shale gas wells from the US. 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). 18 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). With the exception of the binary variables for winter fracture, the CnF intercept for the horizontal wells, and the time effects for days of production, all variables are transformed by taking the natural logarithm. 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. Table 3 18 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. 17

18 presents the estimated parameters, and their standard errors, probabilities, means for vertical wells, and specification tests for each equation in the system. Table 4 contains the analogous estimated model for horizontal wells. TABLE 3: Vertical Well Results Equation 1: ln(cumulative Production)= Variable Coefficient SE Probability Mean of X Ln Initial Reservoir Pressure Ln Permeability Thickness Ln Perforated Interval Ln Final Fracture Half Length Ln Dimensionless Fracture Conductivity Ln CnF Concentration Ln Difference Ln Ratio Winter Fracture Days Days Days Days Days Constant Equation 2: ln(final Fracture Half-length)= Variable Coefficient SE Probability Mean of X 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 Equation 3: ln(dimensionless Fracture Conductivity)= Variable Coefficient SE Probability Mean of X Ln Initial Reservoir Pressure Ln Permeability Thickness Ln Average Treating Pressure Ln Proppant Concentration Ln CnF Concentration Winter Fracture Constant observations RMSE "R 2 " χ 2 (df) Hausman (df) Equation 1: , (14) (2) 7.11 (7) 3.79 (5) Equation 2: (8) 3.72 (8) Equation 3: , (6) (6) χ 2 degrees of freedom (in parentheses). Hausman specification tests for 1 st equation restrictions are the endogenous variables, the exogenous variables, and the time effects, respectively. 18

19 TABLE 4: Horizontal Well Results Equation 1: Ln(Cumulative Production)= Variable Coefficient SE Probability Mean of X Ln Initial Reservoir Pressure Ln Permeability Thickness Ln Final Fracture Half Length Ln Dimensionless Fracture Conductivity Ln Surfactant Concentration CnF Intercept Ln CnF Interaction Ln Difference Ln Ratio Winter Fracture Days Days Days Days Days Days Constant Equation 2: Ln(Final Fracture Half-length)= Variable Coefficient SE Probability Mean of X Ln Initial Reservoir Pressure Ln Permeability Thickness Ln Early Fracture Half-length Ln Stages Ln Average Injection Rate Ln Average Proppant per Stage Ln Surfactant Concentration CnF Intercept Ln CnF Interaction Winter Fracture Constant Equation 3: ln(dimensionless Fracture Conductivity)= Variable Coefficient SE Probability Mean of X Ln Initial Reservoir Pressure Ln Permeability Thickness Ln Stages Ln Proppant Concentration Ln Surfactant Concentration CnF Intercept Ln CnF Interaction Winter Fracture Constant observations RMSE "R 2 " χ 2 (df) Hausman (df) Equation 1: , (16) 7.83 (2) 6.35 (8) 4.72 (6) Equation 2: (10) 6.77 (10) Equation 3: E+08 (8) 2.81 (8) χ 2 df=degrees of freedom (in parentheses). Hausman specification tests for 1 st equation restrictions are for the endogenous variables, the exogenous variables, and the time effects, respectively. 19

20 As in most empirical analyses, we d like to have more data through time, cross-section and the range of explanatory variables available. Nonetheless, we want to understand what we can from the data available. Recognizing that there may be omitted variables or other problems that can affect the consistency of our estimated parameters, we provide a number of Hausman specification tests as checks. 19 For horizontal cumulative production, equation 1, the test statistic is 7.83 with 2 degrees of freedom (for the specified endogenous variables on the right hand side of 1), so the null hypothesis (of model misspecification) is rejected at the usual levels of significance. This specific application of the Hausman test supports the model specification with final fracture half-length and the dimensionless fracture conductivity variables as endogenous. Analogous results hold for the vertical technology specification. For both technology models, we also test the exogeneity of the variables specified as exogenous in each equation. This provides two additional tests for the first equation in each of the systems; a test of the subgroups of the explanatory variables and a test of the subgroup of time effects. All of these tests support the consistency of the estimated parameters in our specified models. Regarding the estimated parameters, we find statistically significant direct impacts for both models across each of the three equations in the system. For example, statistically significant (at 90% or better) direct impacts, consistent in sign, for both the vertical and horizontal results on cumulative production (Equation 1) include Initial Reservoir Pressure, Permeability Thickness (+), Fracture Half Length (+), Dimensionless Fracture Conductivity (+), Difference (-), and i Days (i = 30, 60, 90, 180, 360, 720). As would be expected, cumulative 19 To carry out the tests, the paired bootstrap was used to estimate the variances of the two estimators being contrasted (see Cameron and Trivedi 2005). Instruments in addition to those specified in the system are used in order to carry out some the specification tests. However, we do not have sufficient valid instruments to carry out the 2 nd and 3 rd Hausman tests for the first equations in each system simultaneously. Therefore two tests are carried out, the first for the set of exogenous explanatory variables specified conditional on the time effects, the second for the set of time effects, conditional on the specified exogenous X variables. 20

21 production increases over time, but at a decreasing rate. 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. The probability that the estimated elasticity is greater than zero is also provided in the table. 21

22 TABLE 5: Cumulative Production Elasticities * VERTICAL HORIZONTAL Variable Elasticity SE Prob>0 Elasticity SE Prob>0 Reservoir Characteristics Initial Reservoir Pressure Permeability Thickness Perforated Interval n.a. n.a. n.a. Completion Outcomes Final Fracture Half-length Early Fracture Half-length Dimensionless Fracture Conductivity Completion Choices CnF Surfactant n.a. n.a. n.a Average Proppant per Stage Proppant Concentration Average Injection Rate Average Treatment Pressure n.a. n.a. n.a. Difference Stages n.a. n.a. n.a Production Ratio * 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 22

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 technologies - the probability of a positive cumulative production elasticities is 94.3% or greater in all cases. 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 for final fracture half-length for the vertical technology. Given a percentage increase in final fracture half-length, this indicates that cumulative production increases 0.509%, 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 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 % increase in cumulative production, but the probability of this elasticity being positive is only 52.3%, so it is not very 23

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 this 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, on average, for the levels of proppant used across wells in our horizontal technology sample. 20 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. Further research in determining optimal proppant use is warranted. 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 20 Fitzgerald (2015), discussed above, finds that proprietary additives are not significantly correlated with higher production by most firms. 24

25 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. The cumulative production elasticity with respect to the number of completion stages for the horizontal wells is positive, with a high probability. 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 0.062, i.e., a one percent increase in CnF in a vertical well is expected to yield a 0.062% 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 provides increasing returns in horizontal wells. 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. While these are rather dramatic results, a caveat is in order, our results are sample specific, the horizontal sample is relatively small and contains only three CnF wells, providing 20 of the 167 horizontal technology observations in the sample. 25