Journal of Petroleum Enineerin Volume 13, Article ID 81793, 1 paes http://dx.doi.or/1.1155/13/81793 Research Article Well Screen and Optimal Time of Refracturin: A Barnett Shale Well Shayan Tavassoli, 1 Wei Yu, 1 Farzam Javadpour, and Kamy Sepehrnoori 1 1 Department of Petroleum and Geosystems Enineerin, The University of Texas at Austin, Austin, TX 7871, USA Bureau of Economic Geoloy, Jackson School of Geosciences, The University of Texas at Austin, Austin, TX 78713, USA Correspondence should be addressed to Farzam Javadpour; farzam.javadpour@be.utexas.edu Received 3 January 13; Accepted 1 April 13 Academic Editor: Jore Ancheyta Copyriht 13 Shayan Tavassoli et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the oriinal work is properly cited. Gas-production decline in hydraulically fractured wells inshale formations necessitates refracturin. However, the vast number of wells in a field makes selection of the riht well challenin. Additionally, the success of a refracturin job depends on the time to refracture a shale-as well durin its production life. In this paper we present a numerical simulation approach to development of a methodoloy for screenin a well and to determine the optimal time of refracturin. We implemented our methodoloy for a well in the Barnett Shale, where we had access to data. The success of a refracturin job depends on reservoir characteristics and the initial induced fracture network. Systematic sensitivity analyses were performed so that the characteristics of a shale-as horizontal well could be specified as to the possibility of its candidacy for a successful refracturin job. Different refracturin scenarios must be studied in detail so that the optimal desin miht be determined. Given the studied trends and implications for a production indicator, the optimal time for refracturin can then be suested for the studied well. Numerical-simulation results indicate sinificant improvement (on the order of 3%) in estimated ultimate recovery (EUR) after refracturin, iven presented screen criteria and optimal-time selection. 1. Introduction Shale-as resources, predominantly lithified clays with low permeability [1], are considered unconventional as reservoirs and important resources for the United States. However, as production from these low-permeability resources is much reater than what is anticipated owin to non-darcy flows and different sources of as in their formations []. Gas flowissourcedfromstoredasinnanoporenetworksand adsorbed as on oranic materials in the shale formations. However,newtechniquesarerequiredforaccesstoand economical production from these resources. Recent advances in hydraulic-fracturin techniques have resulted in economic production from shale-as reservoirs. Effective fracturin techniques make for successful economic production from extremely low (on the order of nanodarcies) permeability formations because they create a lare, stimulated reservoir volume [3, ]. Such a success would be attributed to the potential for developin complex fracture networks, which could sinificantly improve reservoirwellbore connectivity. Refracturin is a process of improvin production rates and ultimate recovery, which is an economicalalternativetoinfilldrillin.althouhrefracturin seems an excellent method of sinificantly increasin as production, only 15% to % of refractured wells achieve any desired improvement in practice [5 7]. Therefore, a reliable andsystematicapproachiscriticaltoanincreaseinthe success of refracturin jobs. Several published works [8 11] have suested a selection of methodoloies for findin ood shale-as-well candidates for refracturin. However, application of these methods is limited, and results are unsatisfactory in horizontal-well or complex-fracture-network cases or when adequate completion and reservoir/eoloy data sets are lackin. With the aid of numerical-simulation methods,
Journal of Petroleum Enineerin however, we are now able to study well performance properly by considerin the presence of a complex fracture network, a tiht matrix, and initial hydraulic fractures. Field results demonstrate that refracturin success can be attributed to different parameters, such as the existin fracture network and reservoir properties, and a successful refracturin job should increase reservoir-wellbore connectivity, which is associated with further openin, extension, and reorientation of existin fractures. Reorientation is enerally perpendicular to an initial hydraulic fracture as the result of minimum and maximum stress reversal, which occurs if induced stress chanes are lare enouh to overcome the effect of initial horizontal stress [1]. Such a reversal could betheresultofthestresscreatedbytheopeninofanadjacent fracture or pore-pressure alteration due to previous production periods [13 15].Insuchcases,thefracturenetworkpropaates,and,asaresult,alarerportionofthereservoirisstimulated, subsequently increasin as production and ultimate recovery. Owin to the complexity of fracture rowth in many shale-as reservoirs, accurate prediction of fracture propaation is impossible; therefore, conductivity of the fracture network and the effectiveness of stimulation treatment are difficult to predict [16, 17]. Detailed numerical reservoir modelin is thus needed for us to better understand the mechanisms that control production in shale-as reservoirs and to improve completion strateies and stimulation desins. First, we needed to validate our simulation model by modelin initial fractures and the refracturin process in a horizontal well in the Barnett Shale formation. Second, on the basis of our simulation model, we performed a sensitivity study on the effect of different parameters on refracturin performance. Sensitivity analyses provide insihts into the dependency of the refracturin-process performance on correspondin parameters. The result would be helpful for selectin candidates for successful refracturin. We also compared results of the refracturin performance with closely spaced initial fracturin as an alternative to increasin as recovery from the early staes of production. Note that specifyin the optimal time of refracturin is crucial to maximizin performance of the process. Simulation results of refracturin at different staes of production suest calculation of the optimaltimeonthebasisofasflowrateorcumulativeasproduction recovery. networks should therefore be considered in the simulation of the refracturin process, even thouh their initial network fracture conductivity may be relatively low (e.., in the BarnettShale,itranesfrom.5to5md-ft)[18, ]. Development of numerical simulation approaches that can properly model fluid flow in tiht formations and that are capable of capturin complex fracture networks and initial hydraulic fractures is important in an evaluation of well performance and an explanation of properties that affect as recovery. Gas flow from ultralow-permeability rock throuh complex fracture networks must be modeled so that stimulation desins and completion strateies can be properly evaluated. Therefore, the complex fracture network and initial hydraulic fractures must be discretely characterized in these reservoir-simulation models. We validated our simulation methodoloy usin field data from a refractured horizontal well in the Barnett Shale formation.weselectedthebarnettshalebecauseoftheavailability of production data and because, so that economically viable production rates miht be attained, hydraulic-fracture stimulation is a necessity in this formation. The simulation model is based on a dual permeability model for two-phase (as-water) fluid flow. Such a model considers the communication between the interranular void spaces in contrast to the dual porosity model, which nelects this communication. The dual permeability model considers flow in the two domains of matrix and fracture, whereasthedualporosityapproachassumestwodomains with different hydraulic and transport properties [1]. The dual permeability model allows for simulations involvin as and water transfer between the fracture and matrix domains. Gas flow velocities in matrix and fracture are calculated on the basis of (1)and(), respectively, V m = (Km p μ + D m C m ), (1) C m V f = (Kf p μ + D f C f ), () C f. Methodoloy Numerical simulation is a promisin method in any desin or well-performance evaluation and is commonly used to predict as production. Specifically this approach has increased in importance for shale-as reservoirs owin to the complexity of fracture networks and the low permeability of the formations because numerical simulations are capable of modelin fracture networks. Note that fracture-network complexity and conductivity control well productivity in shale-as reservoirs the more complex the fracture networks (i.e., the smaller the blocks or the denser the fracture spacin), the hiher the production rates [18, 19]. Fracture where V is as velocity, K is as permeability, D is as diffusivity, P is as pressure, C is as concentration, and μ is as viscosity. Superscripts m and f represent matrix and fracture, respectively. Water-flow velocities in matrix and fracturearecalculatedonthebasisof(3)and(), respectively, V m w = Km w μ w p m w, (3) V f w = Kf w μ w p f w, ()
Journal of Petroleum Enineerin 3 where V w is water velocity, K w is water permeability, P w is water pressure, and μ w is water viscosity. The equations are thus simplified to represent as flux in matrix: m Pm t (C Z m )= (P K m P m Z μ m +Dm P m C m Z + D P m Z Cm ) RT M (qmf +q m ), (5) where Z is the as compressibility factor, R is the as constant, T is temperature, M is as molecular weiht, and q is as mass-flow rate per unit matrix-block volume. Superscript mf represents the exchane between matrix and fracture. We can alsowritethisequationfortheaqueousphaseinmatrixas t (φ ms m w B w )= ( Km w P m w B w μ ) RT w M (qmf w +qm w ), (6) where φ m is matrix porosity, s w is water saturation, and B w is the water compressibility factor. As a result of simplification oftheequations,asfluxinfracturebecomes f Pf t (C Z f )= (P K f Z andalsoforwaterinfracture: B w f P f μ +Df P Z + D f C f P f Z Cf ) + RT M (qmf q f ), (7) t (φ fs f w ) = ( Kf w P f w B w μ ) + RT w M (qmf w qf w ) (8) with auxiliary equations 3. History Matchin C m =φ ms m, C f =φ fs f, s m +sm w =1, s f +sf w =1. The simulation results presented in this work are obtained mainly by usin the Computer Modelin Group (CMG) model []. Our modifications and methodoloy of usin this model are presented in Section. In order to validate our simulation model, we modeled initial fractures and the refracturin process in a horizontal well in the Barnett Shale formation. The Barnett Shale is a Mississippian-ae marine shelf deposit havin a formation thickness that varies from to 8 ft throuh the reservoir and ultralow permeability in the rane of 7 5 nanodarcies [3]. The selected well is a cased, uncemented well in the formation. (9) Gas flow rate (Mscf/day) 3 5 15 1 5 5 1 15 5 3 Field data Gas rate refracturin Gas rate no refracturin 1 3 5 35 3 5 15 1 5 Cumulative as production (Mscf) Production refracturin Production no refracturin Fiure 1: Comparison between simulation results and field data. The well is located in the lower Barnett Shale and drilled northwest to maximize fracture-network formation. It has five equally spaced initial fractures coverin a depth interval from 7,9 to 1,16ft [3]. The well was refractured after more than years in four staes in the middle of the initial fractures. Gas production from the well was monitored and plotted for its 6 years of production (.5 years before and 1.5 years after refracturin) (Fiure 1). Inputdatausedinthesimulationmodeltopredictas production from the well appear in Table 1. Refracturin after years of production sinificantly increased productivity of the horizontal well (Fiure 1), and comparison of the simulation-model results and field data verifies that our model is capable of modelin initial fractures and refracturin. Fractures postclosure occurs durin production and depletion of any shale well, closure stress, and lon-term deradation of proppants controllin the extent of fracture postclosure. Gas production may decrease owin to fractureconductivity impairments, especially durin later as production. Yu and Sepehrnoori [] recently studied the effect of reservoir depletion on fracture conductivity in the Barnett Shale. They showed that fracture conductivity reduces to about % of oriinal conductivity at a limitin bottom-hole pressure of 5 psi. However, because of the reat contrast between matrix permeability and fracture permeability in shale, fracture postclosure has a neliible effect (<%) on as production,evenafter3years[].thisisespeciallytrueof formations with a hih Youn s modulus (6 1 6 psi to 1 1 6 psi), such as the Barnett Shale.. Results and Discussion In this section we use our verified numerical model and the present as production rate and cumulative as production of the studied well. In our sensitivity analyses we present the effects of formation permeability and porosity, as well
Journal of Petroleum Enineerin Table 1: Input data used in simulation model. Parameter Value(s) Unit: field (SI) Model dimensions 5 5 3 (15 15 91) ft(m) Initial reservoir pressure 38 (.6 1 7 ) psi(pa) BHP 11 (7.58 1 6 ) psi(pa) Production time 3 year Reservoir temperature 15 (66) F( C) Gas viscosity.1 (.1 1 5 ) cp(pa.s) Initial as saturation.7 fraction Total compressibility 3 1 6 (.35 1 1 ) Psi 1 (pa 1 ) Matrix permeability 5 1 (.93 1 19 ) md(m ) Matrix porosity.18 fraction Fracture conductivity 1 (3 1 16 ) md-ft (m -m) Fracture half-lenth Varied: Min = 7 (13), Max = 187 (57) ft (m) Fracture spacin 55 (168) ft (m) Refracture half-lenth 97 (96) ft (m) Refracture spacin 75 (8) ft (m) Fracture heiht 3 (91) ft (m) Horizontal well lenth 8 (853) ft (m) Number of fractures 5 number Number of refractures number as initial induced hydraulic-fracture conductivity on well performance. These analyses are followed by a discussion on well-screenin criteria and time optimization of refracturin. We used base data (Table 1) to create simulation cases by varyin individual parameters for sensitivity analyses. Gasproduction rate and cumulative as production were plotted aainst time for all parameters to show the performance of the well. Each plot included well performance with and without refracturin to hihliht refracturin effectiveness on asproduction performance. Gas flow rate (MMSCF/day) 3 1.1. Effects of Permeability. We created two plots to show the effects of formation permeability on as flow rate and cumulative as production rate (Fiures and 3). In each plot we considered two scenarios performance of the well without refracturin and a case of refracturin after years. Intuitivelyweknewthatbothasflowrateandcumulative as production would improve if permeability increased. The refractured wells showed better as flow rates and 3% to 7% improvement in cumulative as production for the hihest (.5 md) and lowest (.5 md) permeabilities, respectively... Effects of Porosity. We created two plots to show the effects of formation porosity on as flow rate and cumulative as production rate (Fiures and 5). In each plot we considered two scenarios performance of the well without refracturin and a case of refracturin after years. The refractured wells showed better as flow rates and 5% to 7% improvement in cumulative as production for the lowest (.) and hihest (.8) porosities, respectively. 5 1 15 5 3 Refracturin permeability.5 md No refracturin permeability.5 md Refracturin permeability.1 md No refracturin permeability.1 md Refracturin permeability.5 md No refracturin permeability.5 md Fiure : Effects of formation permeability on as flow rate. Two scenarios: no refracturin and refracturin after years of production..3. Effects of Initial Fracture Conductivity. We created two plots to show the effects of initial fracture conductivity on as flow rate and cumulative as production rate (Fiures 6 and 7). In each plot we considered two scenarios performance of thewellwithoutrefracturinandacaseofrefracturinafter
Journal of Petroleum Enineerin 5 Cumulative as production (MMSCF) 1 3 1 8 6 5 1 15 5 3 Refracturin permeability.5 md No refracturin permeability.5 md Refracturin permeability.1 md No refracturin permeability.1 md Refracturin permeability.5 md No refracturin permeability.5 md Fiure 3: Effects of formation permeability on cumulative as production. Two scenarios: no refracturin and refracturin after years of production. Cumulative as production (MMSCF) 1 3 1 8 6 5 1 15 5 3 Refracturin porosity.8 No refracturin porosity.8 Refracturin porosity.6 No refracturin porosity.6 Refracturin porosity. No refracturin porosity. Fiure 5: Effects of formation porosity on cumulative as production. Two scenarios: no refracturin and refracturin after years of production. Gas flow rate (MMSCF/day) 3 1 5 1 15 5 3 Refracturin porosity.8 No refracturin porosity.8 Refracturin porosity.6 No refracturin porosity.6 Refracturin porosity. No refracturin porosity. Fiure : Effects of formation porosity on as flow rate. Two scenarios: no refracturin and refracturin after years of production. years. Both as-flow rate and cumulative as production improved when initial fracture conductivity was increased. The refractured well showed better as flow rates and 5% to 8% improvement in cumulative as production for the hihest (1 md-ft) and the lowest (.1 md-ft) initial fracture conductivities, respectively... Well Screen Criteria. Cumulative as production and as flow rate increase as reservoir permeability, porosity, and initial fracture conductivity increase (Fiures 7). Because increase in the trends of as production in these cases is sinificant in contrast to the increase in trends of as flow rate, we are unable to refine our selection on the basis of these trends. We therefore compared our results on the basis of production indicators to select candidate shale-as wells for refracturin. Given the correlation between monthly incremental and 5-year cumulative as production, wells fallin off the trend line indicate wells that had ood initial production but for which loner-term recovery was poor [9] (Fiure 8).Becauseallofourcasesarelocatedonthe trend line, this method adds no information about rane of selection. To determine and compare production enhancement in each case study, we introduce a production indicator, known as lon-term refracturin efficiency and defined as the ratio of cumulative as production after refracturin to its value before refracturin in 3 years of production: Lon-term refracturin efficiency = Total cumulative as production after refracturin Total cumulative as production with no refracturin. (1) We calculated and plotted lon-term refracturin efficiency for each case and found that refracturin efficiency increases as reservoir permeability reduces to its lower limits (Fiure 9). Efficiency enhancement is not that sinificant,
6 Journal of Petroleum Enineerin Gas flow rate (MMSCF/day) 6 5 1 15 5 3 Refracturin fracture conductivity 1 md-ft No refracturin fracture conductivity 1 md-ft Refracturin fracture conductivity 1 md-ft No refracturin fracture conductivity 1 md-ft Refracturin fracture conductivity.1 md-ft No refracturin fracture conductivity.1 md-ft Fiure 6: Effects of initial fracture conductivity on as flow rate. Two scenarios: no refracturin and refracturin after years of production. Cumulative as production (MMSCF) 1 3 1 8 6 5 1 15 5 3 Refracturin fracture conductivity 1 md-ft No refracturin fracture conductivity 1 md-ft Refracturin fracture conductivity 1 md-ft No refracturin fracture conductivity 1 md-ft Refracturin fracture conductivity.1 md-ft No refracturin fracture conductivity.1 md-ft Fiure 7: Effects of initial fracture conductivity on cumulative as production. Two scenarios: no refracturin and refracturin after years of production. however, at permeability values reater than.1 millidarcy. Refracturin efficiency increases as porosity increases (Fiure 1). Efficiency enhancement due to refracturin is sinificant when porosity values are reater than 6%. The difference in as-production enhancement with respect to permeabilitymihtseemtobeincontradictiontoitstrend with respect to porosity because of the correlation between permeability and porosity. However, note that refracturin enhances as production from low-permeability reservoirs by formin a more complex fracture network that has been depleted from a larer stimulated reservoir volume (SRV). On the other hand, larer porosity corresponds to a larer amount of initial as in place. Hence, refracturin enhancement cannot be responsible for an increase in as production in cases with hih-porosity values. We also studied the effect of initial fracture conductivity on the performance of refracturin. Refracturin efficiency increases as fracture conductivity decreases (Fiure 11), efficiency enhancement increasin in sinificance for values lower than 1 md-ft. Results of these simulations reveal that lon-term refracturin efficiency can provide insiht into the effect of each parameter and its importance. On the basis of this sensitivity study we have proposed a screenin method for existin fractured horizontal wells that is based on reservoir and initial hydraulic-fracture properties (Table )..5. Initial Fracture Spacin. Here we compare results of refracturin performance with that of closely spaced initial fracturin,whichcanbeanalternativetoincreasinas recovery beinnin in the early staes of production. Different values of fracture spacin (5, 1,, 35, and 5 ft) are considered here. Refracturin in the middle of initial 5-year cumulative production (Mcf) 1 5 35 3 5 15 1 5 5-year cumulative production (Mcf) 1 3 35 3 5 15 1 5 1 3 6 8 1 1 Averae production durin the best year (Mcf/month) 6 8 1 1 Averae production durin the best year (Mcf/month) 1 3 Fiure 8: Correlation between short-term and lon-term production [9], alon with our simulation results. fracturesisalsoperformedinallthecasesafteryearsof production, except in cases where initial fractures are close to one another (5 ft). The total number of fractures for each case is 57 (57 initial fractures), 57 (9 initial fractures and 8 refractures), 9 (15 initial fractures and 1 refractures), 17 (9 initial fractures and 8 refractures), and 13 (7 initial fractures and 6 refractures). Cumulative as production from refractured wells havin hiher initial values of fracture spacin is similar to that of closely spaced initial fractures if the ultimate fracture spacin remains the same (Fiure 1). In other words, we expect the same performance in the two cases havin the same value of total fracture lenth, includin
Journal of Petroleum Enineerin 7 Table:Wellscreenincriteria. Property Perfect selection Fair selection Poor selection Unit: field (SI) Permeability <.1 (9.8 1 ) <.5 (.9 1 19 ) >.5 (.9 1 19 ) md(m ) Porosity >.6 >. <. fraction Fracture conductivity >1(3 1 16 ) <1 (3 1 15 ) >1 (3 1 15 ) md-ft (m -m) Lon-term refracturin efficiency factor 1.8 1.6 1. 1. 1...6 Permeability (md) Fiure 9: Lon-term refracturin efficiency versus different permeabilities. Lon-term refracturin efficiency factor 1.7 1.6 1.5 1....6.8.1 Porosity Fiure 1: Lon-term refracturin efficiency versus different porosities. refractured lenths. Hence, refracturin at the proper time of production appears to be an attractive restimulation method for wells havin lare initial fracture spacin..6. The Optimal Time to Refracture a Well. Findin the optimal time to refracture so as to maximize the performance of the refracturin job is crucial. On the basis of available field-production data of successful refracturin processes in Barnett Shale formations and the simulation results of different refracturin scenarios, we proposed an indicator for findin the proper time for refracturin. To find the optimal time, we considered different times of refracturin. Cumulative as production and as flow rate Lon-term refracturin efficiency factor 1.9 1.8 1.7 1.6 1.5 1. 6 8 1 1 Fracture conductivity (md-ft) Fiure 11: Lon-term refracturin efficiency versus different fracture conductivities. for these different cases are obtained from simulation results (Fiures 13 and 1, resp.). Because of the difficulty involved in such a task, however, we studied trends in detail and proposed an indicator for comparison between various production trends. The proposed indicator suests that if the decline rate of as production falls below 1% to 15%, the refracturin processshouldbeapplied.thecumulativeasproduction result of refracturin after or 3 years of production is hiher than that of a well refractured after years of production (Fiure 13). However, the incline rate of the cumulative as production result of refracturin after or 3 years of production is still sinificant (more than %) (Fiure 15). Hence, the decline rate of as production is pronounced early in the stimulation process, but only until it reduces below 15%, at which point the initial stimulation effect has vanished and as production levels off. Under these conditions, refracturin should be considered as a way to increase as production from the well. Incline-decline rates can be defined as Declinerateofasproduction= qn 1 r q n 1 r q n r Incline rate of cumulative as production = Qn+1 Q n Q n, (11) where n is refracturin time in years, q r is as flow rate, and Q is cumulative as production. Both decline rate of as production and incline rate of cumulative as production durinthefirst6yearsofaproject slifereduceoverthat time and level off (Fiure 15). Accordin to the introduced,
8 Journal of Petroleum Enineerin Cumulative as production (MMSCF) 1 5 5 35 3 5 15 1 5 5 1 15 5 3 No refracturin fracture spacin 5 ft Refracturin fracture spacin 1 ft No refracturin fracture spacin 1 ft Refracturin fracture spacin ft No refracturin fracture spacin ft Refracturin fracture spacin 35 ft No refracturin fracture spacin 35 ft Refracturin fracture spacin 5 ft No refracturin fracture spacin 5 ft Fiure 1: Cumulative as production for different fracture-spacin values. indicator, the proper time for refracturin occurs after years of production because the decline rate of as production drops to less than 15% durin that fourth year. 5. Conclusions We used numerical simulation to study refracturin of wells in shale formations by selectin a well in the Barnett Shale formation and simulatin as production from this well. We used the verified model to perform sensitivity studies on formation properties and initial-fracture conductivity on as-production performance. We found that refracturin is an effective restimulation technique if it is performed for a proper candidate well and at the optimal time. Numericalsimulation results indicate sinificant improvements on the order of 3% in estimated ultimate recovery (EUR) after refracturin. Some specific conclusions are as follows. (1) Our simulation model results suest that refracturin is more effective in low-permeability reservoirs. Refracturin enhances as production by formin a more complex fracture network and producin larer stimulated reservoir volume (SRV) in these low-permeability reservoirs. Larer porosities result in hiher as production owin to an increase in the amount of as in place. () Results show that hiher values of initial fracture conductivity eliminate the need for refracturin owin Cumulative as production (MMSCF) 5 35 3 5 15 1 5 5 1 15 5 3 Refracturin after years Refracturin after 3 years Refracturin after years Refracturin after 5 years Refracturin after 6 years No refracturin Fiure 13: Cumulative as production for different times of refracturin. Gas flow rate (MMSCF/day) 3 1 5 1 15 5 3 Refracturin after years Refracturin after 3 years Refracturin after years Refracturin after 5 years Refracturin after 6 years No refracturin Fiure 1: Gas flow rate for different times of refracturin. to the presence of conductive paths between wellbore and reservoir. (3) Refracturin performance was compared with that of closely spaced initial fractures. Results show that cumulative as production correlates with total fracture lenth, includin refracture lenths. () We developed a screenin method for existin wells in a formation that was based on reservoir characteristics and initial hydraulic-fracture properties. The screenin method provides perfect, fair, and poor selection cateories that are based on ranes of the studied variables.
Journal of Petroleum Enineerin 9 Incline rate of cumulative as production 1.8.6.. 15% 1 3 5 6 7.7.6.5..3..1 Incline rate of cumulative as production Fiure 15: Decline rate of as flow rate and incline rate of cumulative asproductionversustime. (5) Findin the optimal time for refracturin so as to maximize its performance is crucial. On the basis of detailed study of as flow rate and cumulative as production in the first 6 years of a project s life, we suest performin refracturin at the point in the life of the project when decline of the as flow rate falls below 1% to 15%. Nomenclature V: Flowvelocity,m/s μ: Viscosity, Pa s p: Pressure, Pa K: Phasepermeability,m C: Concentration, m 3 /m 3 D: Diffusivity,m /s Z: Gas-compressibility factor φ: Porosity B: Compressibility factor, Pa 1 R: Gasconstant,Pa m 3 /(mol K) M: Molar mass, k/mol T: Temperature,K q: Massflowrateperunitmatrix-blockvolume, k/(m 3 s) q r : Gas flow rate, MMSCF/D Q: Cumulative as production, MMSCF s: Phasesaturation. Superscripts m: Matrix f: Fracture mf: Exchane between matrix and fracture. Subscripts : Gas w: Water. Acknowledments The authors would like to thank Computer Modelin Group Ltd. for use of the CMG-IMEX software. They would also like to express their ratitude for financial support from the Hilcorp Enery Company and NanoGeosciences lab at the Bureau of Economic Geoloy (UT-Austin) and to thank Ms. L. Dieterich for editin the paper. References [1] F. Javadpour, D. Fisher, and M. Unsworth, Nanoscale as flow in shale sediments, JournalofCanadianPetroleumTechnoloy, vol. 6, no. 1, pp. 55 561, 7. [] F. Javadpour, Nanopores and apparent permeability of as flow in mudrocks (shales and siltstone), Journal of Canadian Petroleum Technoloy,vol.8,no.8,pp.16 1,9. [3] N. R. Warpinski, M. J. Mayerhofer, M. C. Vincent, C. L. Cipolla, and E. R. Lolon, Stimulatin unconventional reservoirs: maximizin network rowth while optimizin fracture conductivity, JournalofCanadianPetroleumTechnoloy,vol.8,no.1,pp. 39 51, 9. [] M. Y. Soliman and C. S. Kabir, Testin unconventional formations, Journal of Petroleum Science and Enineerin,vol.9-93, pp. 1 119, 1. [5] S.R.Reeves, Restimulationtechnoloyfortihtassandwells, in Proceedins of the SPE Annual Technical Conference, SPE- 568, Houston, Tex, USA, 1999. [6] D.G.HillandS.R.Reeves, Restimulationresearchtotaret low cost, incremental as reserves, Gas Tips, vol., no. 3, 1998. [7] T. Lantz, Refracture treatments provin successful in horizontal Bakken wells, SPE Production & Operations, vol.3,no.3, pp. 373 378, 8. [8] L. P. Moore and H. Ramakrishnan, Restimulation: candidate selection methodoloies and treatment optimization, in Proceedins of the SPE Annual Technical Conference, SPE-1681, SanAntonio,Tex,USA,6. [9] S. Sinha and H. Ramakrishnan, A novel screenin method for selection of horizontal refracturin candidates in shale as reservoirs, in Proceedins of the North American Unconventional Gas Conference, SPE-13, The Woodlands, Tex, USA, 11. [1] N. P. Roussel and M. M. Sharma, Selectin candidate wells for refracturin usin production data, in Proocedins of the SPE Annual Technical Conference, SPE-1613, Denver, Colo, USA, 11. [11] A. A. Ketter, J. L. Daniels, J. R. Heinze, and G. Waters, A field study optimizin completion strateies for fracture initiation in barnett shale horizontal wells, in Proocedins of the SPE Annual Technical Conference and Exhibition (ATCE 6),Focus on the Future, SPE-133, pp. 531 536, San Antonio, Tex, USA, September 6. [1] E.Siebrits,J.L.Elbel,R.S.Hooveretal., Refracturereorientation enhances as production in Barnett Shale tiht as wells, in Proceedins of the SPE Annual Technical Conference, SPE-633, Dallas,Tex,USA,October. [13] M. C. Vincent, Refracs why do they work, and why do they fail in 1 published field studies? in Proceedins of the SPE Annual Technical Conference, SPE-1333, Florence, Italy, 1. [1] M. C. Vincent, Restimulation of unconventional reservoirs: when are refracs beneficial? in Proceedins of the Canadian
1 Journal of Petroleum Enineerin Unconventional Resources and International Petroleum Conference, SPE-136757, pp. 7 3, Alberta, Canada, October 1. [15] M.K.Fisher,J.R.Heinze,C.D.Harris,B.M.Davidson,C.A. Wriht, and K. P. Dunn, Optimizin horizontal completion techniques in the barnett shale usin microseismic fracture mappin, in Proceedins of the SPE Annual Technical Conference,SPE-951,Houston,Tex,USA,September. [16] C. L. Cipolla, E. P. Lolon, M. J. Mayerhofer, and N. R. Warpinski, Fracture desin considerations in horizontal wells drilled in unconventional as reservoirs, in Proceedins of the SPE Hydraulic Fracturin Technoloy Conference, SPE-119366, pp. 366 375, The Woodlands, Tex, USA, January 9. [17] C. L. Cipolla, E. P. Lolon, and B. Dzubin, Evaluatin stimulation effectiveness in unconventional as reservoirs, in Proceedins of the SPE Annual Technical Conference and Exhibition 9, ATCE 9,SPE-183,pp.3397 317,NewOrleans,La, USA, October 9. [18] M.J.Mayerhofer,E.P.Lolon,N.R.Warpinskietal., Whatis stimulated reservoir volume? SPE Production & Operations, vol. 5, no. 1, pp. 89 898, 6. [19] C. L. Cipolla, E. P. Lolon, J. C. Erdle, and B. Rubin, Reservoir modelin in shale-as reservoirs, SPE Reservoir Evaluation & Enineerin,vol.13,no.,pp.638 6653,1. [] C. L. Cipolla, N. R. Warpinski, M. J. Mayerhofer, E. P. Lolon, and M. C. Vincent, The relationship between fracture complexity, reservoir properties, and fracture treatment desin, in Proceedins of the SPE Annual Technical Conference and Exhibition, SPE-115769, Denver, Colo, USA, 8. [1] T. Voel, H. H. Gerke, R. Zhan, and M. T. Van Genuchten, Modelin flow and transport in a two-dimensional dualpermeability system with spatially variable hydraulic properties, Journal of Hydroloy,vol.38,no.1-,pp.78 89,. [] CMG, IMEX User s Guide, Computer Modelin Group, 11. [3] D. I. Potapenko, S. K. Tinkham, B. Lecerf et al., Barnett Shale refracture stimulations usin a novel diversion technique, in Proceedins of the SPE Hydraulic Fracture Technoloy Conference, SPE-119636, The Woodlands, Tex, USA, 9. [] W. Yu and K. Sepehrnoori, Simulation of as desorption and eomechanics effects for unconventional as reservoirs, in Proceedins of the SPE Western Reional Meetin, SPE-165377, Monterey, Calif, USA, April 13.
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