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1 SPE Integration of Production Analysis and Rate-time Analysis via Parametric Correlations Theoretical Considerations and Practical Applications D. Ilk, Texas A&M University/DeGolyer and MacNaughton, J.A. Rushing, Apache Corp., and T.A. Blasingame, Texas A&M University Copyright 2011, Society of Petroleum Engineers This paper was prepared for presentation at the SPE Hydraulic Fracturing Technology Conference and Exhibition held in The Woodlands, Texas, USA, January This paper was selected for presentation by an SPE program committee following review of information contained in an abstract submitted by the author(s). Contents of the paper have not been reviewed by the Society of Petroleum Engineers and are subject to correction by the author(s). The material does not necessarily reflect any position of the Society of Petroleum Engineers, its officers, or members. Electronic reproduction, distribution, or storage of any part of this paper without the written consent of the Society of Petroleum Engineers is prohibited. Permission to reproduce in print is restricted to an abstract of not more than 300 words; illustrations may not be copied. The abstract must contain conspicuous acknowledgment of SPE copyright. Abstract Well performance analysis in unconventional reservoirs is a challenging task because of the non-uniqueness associated with estimating well/formation properties. In addition, estimation of reserves is often uncertain due to very long transient flow periods. Recently, new semi-empirical rate-time relations (Ilk et al and 2010) have been shown to properly model the rate-time behavior for wells in unconventional reservoirs. The success of these new rate-time relations has led us to focus on finding theoretical and empirical relationships between rate-time model parameters with well/formation properties. This work attempts to integrate model-based production analysis (i.e., semi-analytical/analytical solutions) and rate-time analysis by using parametric correlations. We perform production analysis and rate-time analysis for various tight gas and shale gas wells, and then correlate the various model parameters from the rate-time equations with the well/formation properties estimated using full (model-based) production data analysis. We demonstrate the application of the proposed methodology by using a sample of wells producing in tight gas and shale gas reservoirs. We can show that the integration of production analysis and rate-time analysis via parametric correlations is highly-dependent on the size of data sample (i.e., the number of wells) and the data quality. When high-quality data and ample production data are available, formation permeability and fracture half-length are well-correlated with the model parameters of the rate-time relations. Introduction Unconventional reservoir systems such as tight gas sands, shale gas, tight/shale oil, and coalbed methane reservoirs have recently become a significant source of hydrocarbon production and offer remarkable potential for reserves growth and future production. Unconventional reservoir systems can be described as hydrocarbon accumulations which are difficult to be characterized and produced by conventional exploration and production technologies. Complex geological and petrophysical systems describe unconventional reservoirs in addition to heterogeneities at all scales similar to conventional reservoir systems. Because of the low to ultra-low permeability of these reservoir systems, well stimulation operations (e.g., single or multi-stage hydraulic fracturing, etc.) are required to establish production from the formations at commercial rates. The common industry practice in unconventional reservoirs is to complete horizontal wells and perform multiple stage (transverse) fracture treatments. Therefore analytical/semi-analytical modeling of horizontal wells with multiple transverse fractures is important in terms of diagnosing well performance behavior of these wells. Soliman et al. (1990) present the production forecast of horizontal wells with multiple infinite-conductivity fractures. van Kruysdijk and Dullaert (1989) provide an analytical solution which introduces the "compound linear flow" concept. van Kruysdijk and Dullaert show that at early time dominant flow is linear, perpendicular to the fracture face until pressure transients of the individual fractures begin to interfere leading to a compound linear flow regime. Raghavan et al. (1994) provide a mathematical description of inflow into the late-time compound linear flow regime, similar to the model proposed by van Kruysdijk and Dullaert. Other analytical solutions to model the pressure transient behavior of horizontal wells include Guo and Evans (1993), Larsen and Hegre (1994) and Horne and Temeng (1995) solutions. Medeiros et al. (2006) provide a semi-analytical solution which models the entire range of flow regimes surrounding a horizontal well with multiple fractures. Medeiros, et al. include a dual permeability region near the fracture faces to represent complex fractured region surrounding primary the primary planar

2 2 D. Ilk, J.A. Rushing, and T.A. Blasingame SPE hydraulic fractures. On the other hand, reserves estimation in unconventional reservoir systems has been primarily performed using the conventional Arps' decline curve relations (Arps 1945). The application of Arps' relations (specifically the hyperbolic relation) for reserve estimates yields significant overestimates of reserves as Arps' relations are only applicable during boundary-dominated flow regime whereas unconventional reservoir systems exhibit extremely long transient flow periods. Recently two rate-time relations have been introduced to estimate reserves in unconventional reservoirs: Valko (2009) and Ilk et al. (2008 and 2010) provide new rate-time relations in the form of the "stretched exponential function" (Kohlrausch 1854). These relations have been proven to be successful in modeling the rate-time behavior properly and also these relations provide consistent and more realistic reserve estimates compared to Arps' decline relations. Recent developments in well completion technologies have transformed the unconventional reservoir systems into economically feasible reservoirs. However, the uncertainty associated with reserve estimates and non-uniqueness related with well/reservoir parameter estimation, are the main issues in future development of these reservoirs. The primary goal of this study is to link rate-time decline relations with model-based analysis results. Particularly, we try to put forward an initial basis for a theoretical understanding for why specific rate-time decline relations (i.e., power-law exponential or stretched exponential relations) approximate the rate-time data to a certain extent. Such understanding could offer a theoretical basis for the rate-time relation model parameters and could question the perception about the rate-time decline relations as only relations for curve-fitting purposes. To that end, in this paper we will present our results from three different shale gas fields and one tight gas field. As mentioned before, this is a study, which is in a beginning phase, and more work needs to be performed (obviously more data need to be analyzed) for improved correlations and better understanding of the behavior of the relations. Methodologies In this section we describe the rate-time relation and the model-based analysis methodologies which are used in this work. The original definitions of the "loss-ratio" and the "loss-ratio derivative", which were previously introduced by Johnson and Bollens (1927) are given as: 1 q( (Definition of the loss-ratio)... (1) D dq( / dt b d dt 1 D d dt q( dq( / dt (Derivative of the loss-ratio)... (2) Continuous evaluation of the "loss-ratio" and the "loss-ratio derivative" indicates power-law behavior (see Ilk et al. 2008). Therefore, the D-parameter trend can be modeled by using a power-law equation which is given as: (1 n) D( D1t... (3) Substituting Eq. 3 into the loss-ratio definition (Eq. 1) and solving the associated differential equation yields: q( D 1 exp t qˆ n i n... (4) Eq. 4 reduces in form to the power-law loss ratio rate decline relation as: ˆ exp[ ˆ n q( q D t ]... (5) i i

3 SPE Integration of Production Analysis and Rate-time Analysis via Parametric Correlations 3 Valko (2009) presents another form of Eq. 5, which is given as: n q( qˆ i exp[ ( t / ) ]... (6) Eqs. 5 and 6 are essentially same, and in the form of "stretched exponential function" which was introduced by Kohlrausch (1854) to describe the discharge of a capacitor. Williams and Watts (1970) utilize the stretched exponential function to characterize the dielectric relaxation rates in polymers. Kisslinger (1993) uses the stretched exponential function as an alternative to model aftershock decay rate as opposed to power-law functions. Phillips (1996) describes the stretched exponential nature of relaxation processes in disordered electronic and molecular systems. The general concept is that while empirical, stretched exponential function is successful in modeling decays particularly, decays (or relaxations) in randomly disordered and chaotic systems. Ilk et al. (2008) propose the following modified version (i.e., power-law exponential relation) of Eq. 5 to approximate late time behavior (i.e., boundary-dominated flow behavior) in unconventional reservoir systems: ˆ exp[ ˆ n q( q D t D t ]... (7) i i On the other hand, we utilize the following solutions for model-based analysis. For, hydraulically fractured vertical wells, we use the solutions proposed by Pratikno et al. (2003). The model parameters of interest for this solution are: Permeability (k), Fracture half-length (x f ), Fracture conductivity (F c ), Drainage area (A), Skin factor (s), For horizontal wells with multiple transverse fractures, we use the models proposed by van Kruysdijk and Dullaert (1989) and Larsen and Hegre (1994). The model parameters of interest for these solutions are: Permeability (k), Fracture half-length (x f ), Fracture conductivity (F c ), Drainage area (A), Well length (L w ), Number of fractures (n f ), Skin factor (s), In this work we focus on correlations based on permeability and fracture half-length. Other possible combinations are possible, but we will not discuss the other possibilities as we do not have any strong conclusions. Correlation of Rate-time Model Parameters versus Model Based Production Analysis Results This section attempts to correlate Eq. 5 parameters with model-based production analysis results. The ultimate objective of such correlation is to estimate well/reservoir properties such as permeability from rate-time model parameters (e.g., n, Dˆ i, etc.). By intuition we can state that such possible correlation requires a large sample (producing wells in a particular field) and high quality data. In fact our results indicate that this perception is correct. In this work we have performed the following rate-time analysis and model-based analysis: Holly Branch Field: 13 wells. Shale Gas Field A: 6 wells. Shale Gas Field B: 9 wells. Shale Gas Field C: 8 wells. The results of the rate-time and production analysis for these fields can be found in Ilk (2010). It is worth to note that production analysis of Holly Branch Field utilizes the "finite conductivity" fracture model for a vertical well. On the other hand, production analysis for all of the shale gas fields employs the horizontal well with multiple transverse fractures solution (Larsen and Hegre 1994).

4 4 D. Ilk, J.A. Rushing, and T.A. Blasingame SPE We first attempt to obtain correlations by cross-plotting a variety of combinations of Eq. 5 parameters versus the fractured well model variables. These cross-plots suggest that two parametric relations can be used as correlations from our results. First, permeability (k) can be correlated with Eq. 5 parameters; the proposed correlation is given as: b c d k a n Dˆ i qˆ i... (8) It is noted that the parameters in Eq. 8 vary for each field. We provide the correlation plots of model based permeability values versus calculated permeability values by Eq. 8 for each field in Figs It is worth to mention that the best correlation is obtained in Holly Branch Field, where the number of analyzed wells is the most and the Shale Gas Field B exhibits the worst correlation as the data quality is relatively lower. Fig. 1 Comparison of permeability calculated using the permeability correlation versus the permeability obtained using "model-based" production analysis Holly Branch Field.

5 SPE Integration of Production Analysis and Rate-time Analysis via Parametric Correlations 5 Fig. 2 Comparison of permeability calculated using the permeability correlation versus the permeability obtained using "model-based" production analysis Shale Gas Field A.

6 6 D. Ilk, J.A. Rushing, and T.A. Blasingame SPE Fig. 3 Comparison of permeability calculated using the permeability correlation versus the permeability obtained using "model-based" production analysis Shale Gas Field B.

7 SPE Integration of Production Analysis and Rate-time Analysis via Parametric Correlations 7 Fig. 4 Comparison of permeability calculated using the permeability correlation versus the permeability obtained using "model-based" production analysis Shale Gas Field C.

8 8 D. Ilk, J.A. Rushing, and T.A. Blasingame SPE Next, we develop the "permeability -fracture half-length" (k-x f ) correlation. We correlate the permeability-fracture halflength product versus the n-parameter in Eq. 5. This correlation is given as: k x ˆ exp[ ˆ f n]... (9) Again we would like to remind that the parameters in Eq. 9 vary for each field. Eq. 9 is a simple, yet promising correlation. We present the correlation plots for each field in Figs Our results indicate that best correlation is once again obtained in Holly Branch Field and correlation plot of the Shale Gas Field B shows the most scatter. These observations are in accord with our statement in the beginning on the sample size and data quality. We strongly believe more improved correlations can be obtained if we add more samples and have high quality data for rate-time and production analysis. While, our efforts in this work to establish correlations to estimate well/reservoir properties from rate-time relation model parameters are inconclusive, we believe that this effort could be promising to obtain predictive parametric models based on rate-time analysis relations. Fig. 5 Comparison of k-x f calculated using the k-x f correlation versus the k-x f obtained using "model-based" production analysis Holly Branch Field.

9 SPE Integration of Production Analysis and Rate-time Analysis via Parametric Correlations 9 Fig. 6 Comparison of k-x f calculated using the k-x f correlation versus the k-x f obtained using "model-based" production analysis Shale Gas Field A.

10 10 D. Ilk, J.A. Rushing, and T.A. Blasingame SPE Fig. 7 Comparison of k-x f calculated using the k-x f correlation versus the k-x f obtained using "model-based" production analysis Shale Gas Field B.

11 SPE Integration of Production Analysis and Rate-time Analysis via Parametric Correlations 11 Fig. 8 Comparison of k-x f calculated using the k-x f correlation versus the k-x f obtained using "model-based" production analysis Shale Gas Field C.

12 12 D. Ilk, J.A. Rushing, and T.A. Blasingame SPE Summary and Conclusions Summary: In general this work attempts to relate rate-time decline relations with model-based analysis results. Specifically, we try to establish parametric correlations between model parameters of rate-time decline relations and semianalytical/analytical solutions. For this purpose we have evaluated production data of a tight gas field and three different shale gas fields. We present two relations correlating permeability and fracture half-length with stretched exponential (power-law exponential) model parameters. Conclusions: We state the following conclusions based on this work: 1. We have demonstrated that it is possible to correlate the rate-time model parameters with model-based production analysis results. To this end we present two correlations to correlate permeability and permeability-fracture halflength versus rate-time model parameters. Based on our results we conclude that more sample size and improved data quality will yield improved correlations. 2. Although not presented in this work, we have also attempted to establish other correlations (e.g., EUR vs k and EUR vs x f, etc.). These correlations are possible, however the data quantity considered in this work does not let us derive strong conclusions. 3. This work is still in progress and our future efforts will mainly concentrate on improving the correlations presented in this work and also establishing other correlations particularly, correlating EUR from rate-time decline relations with model-based analysis parameters. Acknowledgements This work was supported by RPSEA (Contract No ) through the Ultra-Deepwater and Unconventional Natural Gas and Other Petroleum Resources Research and Development Program as authorized by the US Energy Policy Act (EPAc of Nomenclature Variables a = Model parameter (Eq. 8), (md-d 2 /MSCF) A = Drainage area, ft 2 b = Arps' decline exponent, dimensionless bˆ = Rate-time equation model parameter (Eq. 5 and Eq. 7), dimensionless b = Model parameter (Eq. 8), dimensionless c = Model parameter (Eq. 8), dimensionless d = Model parameter (Eq. 8), dimensionless D = Reciprocal of loss ratio, D -1 D 1 = Model parameter (Eq. 3), D -1 D = Rate-time equations model parameter, D -1 Dˆ i = Rate-time equations model parameter, D -1 EUR = Estimate of ultimate recovery, BSCF F c = Fracture conductivity, md-ft k = Formation permeability, md L w = Horizontal well length, ft n = Time exponent for Eq. 5 and Eq. 7, dimensionless n f = Number of transverse hydraulic fractures intersecting the horizontal wellbore q = Production rate, MSCF/D or STB/D qˆ i = Eq. 5 and Eq. 7 model parameter, MSCF/D or MSCF/Month in Eq. 6 s = Skin factor, dimensionless t = Production time, days = Fracture half-length, ft x f

13 SPE Integration of Production Analysis and Rate-time Analysis via Parametric Correlations 13 Greek Symbols ˆ ˆ = Model parameter (Eq. 9), dimensionless = Model parameter (Eq. 9), dimensionless = Characteristic time parameter in Eq. 6, months References Arps, J.J Analysis of Decline Curves. Trans. AIME 160: Guo, G. and Evans, R.D Pressure-Transient Behavior and Inflow Performance of Horizontal Wells Intersecting Discrete Fractures. Paper SPE presented at the SPE Annual Technical Conference and Exhibition, Houston, TX, 3-6 October. Horne, R.N. and Temeng, K.O Relative Productivities and Pressure Transient Modeling of Horizontal Wells with Multiple Fractures. Paper SPE presented at the SPE Middle East Oil Show, Bahrain, March. Johnson, R.H. and Bollens, A.L The Loss Ratio Method of Extrapolating Oil Well Decline Curves. Trans. AIME 77: 771. Ilk, D., Rushing, J.A., Perego, A.D., and Blasingame, T.A Exponential vs. Hyperbolic Decline in Tight Gas Sands Understanding the Origin and Implications for Reserve Estimates Using Arps' Decline Curves. Paper SPE presented at the SPE Annual Technical Conference and Exhibition, Denver, CO, September. Ilk, D., Currie, S.M., Symmons, D., Rushing, J.A., and Blasingame, T.A Hybrid Rate-Decline Models for the Analysis of Production Performance in Unconventional Reservoirs. Paper SPE presented at the SPE Annual Technical Conference and Exhibition, Florence, Italy, September. Ilk, D Well Performance Analysis for Low to Ultra-low Permeability Reservoir Systems. Ph.D. dissertation, Texas A&M U., College Station, Texas. Kisslinger, C The Stretched Exponential Function as an Alternative Model for Aftershock Decay Rate. Journal of Geophysical Research 98 (2): Kohlrausch, R Theorie des elektrischen Rückstandes in der Leidner Flasche. Poggendorff 91: Larsen, L. and Hegre, T.M Pressure Transient Analysis of Multifractured Horizontal Wells. Paper SPE presented at the SPE Annual Technical Conference and Exhibition, New Orleans, LA., September. Medeiros, F., Ozkan, E., and Kazemi, H A Semi-Analytical, Pressure Transient Model for Horizontal and Multilateral Wells in Composite, Layered, and Compartmentalized Reservoirs. Paper SPE presented at the SPE Annual Technical Conference and Exhibition, San Antonio, TX., September. Phillips, J.C Stretched Exponential Relaxation in Molecular and Electronic Glasses. Rep. Prog. Phys. 59: Pratikno, H., Rushing, J.A., and Blasingame, T.A Decline Curve Analysis Using Type Curves: Fractured Wells. Paper SPE presented at the SPE Annual Technical Conference and Exhibition, Denver, CO, October. Raghavan, R.S., Chen C.C., and Agarwal, B An Analysis of Horizontal Wells Intercepted by Multiple Fractures. SPEJ 2 (3): Soliman, M.Y., Hunt, J.L., and El Rabaa, W Fracturing Aspects of Horizontal Wells. JPT 42 (8): Valkó, P.P Assigning Value to Stimulation in the Barnett Shale: A Simultaneous Analysis of 7000 Plus Production Histories and Well Completion Records. Paper SPE presented at the SPE Hydraulic Fracturing Technology Conference, College Station, TX, January. van Kruysdijk, C.P.J.W. and Dullaert, G.M A Boundary Element Solution of the Transient Pressure Response of Multiply Fractured Horizontal Wells. Paper presented at the 2nd European Conference on the Mathematics of Oil Recovery, Cambridge, England. Williams, G. and Watts, D. C Non-Symmetrical Dielectric Relaxation Behavior Arising from a Simple Empirical Decay Function. Transactions of the Faraday Society 66:

14 SPE Integration of Production Analysis and Rate-time Analysis via Parametric Correlations Theoretical Considerations and Practical Applications D. Ilk, DeGolyer and MacNaughton, J.A. Rushing, Apache Corporation, and T.A. Blasingame, Texas A&M University Department of Petroleum Engineering Texas A&M University College Station, TX SPE Hydraulic Fracture Technology Conference The Woodlands, Texas January 2011 Integration of Production Analysis and Rate-time Analysis via Parametric Correlations (Ilk/Rushing/Blasingame) Thomas A. BLASINGAME Texas A&M University (24 January 2011) Slide 1/11

15 Presentation Outline Orientation Methodology: Model-based production analysis. Power-law exponential rate decline relation. (also known as the "stretched exponential" relation) Field Data Sources: Holly Branch Field (mature tight gas play) Shale Gas Field A (mature shale play) Shale Gas Field B (evolving shale play) Shale Gas Field C (evolving shale play) Correlations: Parametric Relation 1: Permeability (k) Parametric Relation 2: Permeability-fracture half-length (k-x f ) Parametric Relation 3: EUR Summary, Conclusions, and Recommendations 2011 SPE Hydraulic Fracture Technology Conference The Woodlands, Texas January 2011 Integration of Production Analysis and Rate-time Analysis via Parametric Correlations (Ilk/Rushing/Blasingame) Thomas A. BLASINGAME Texas A&M University (24 January 2011) Slide 2/11

16 Orientation The following tasks were performed in this work: Assembled data from various tight gas and shale gas wells: Reservoir data (reservoir properties). PVT data (reservoir fluids). Completion data (well construction/stimulation data). Production data (time-pressure-rate data). Data Analysis: Prepared data for analysis (QC, calculate BHP's, etc.). Model-based production analysis (time-pressure-rate) Decline curve analysis (time-rate-cumulative production). Correlation of Results: k f ( n, Dˆ i, qˆ i) kx f f (n) EUR f (n) Power Law Exponential Relation q( qˆ exp[ ˆ n i D t Di t ] Presentation/Interpretation/Discussion of Correlations SPE Hydraulic Fracture Technology Conference The Woodlands, Texas January 2011 Integration of Production Analysis and Rate-time Analysis via Parametric Correlations (Ilk/Rushing/Blasingame) Thomas A. BLASINGAME Texas A&M University (24 January 2011) Slide 3/11

17 Methodology: Model Based Production Analysis Vertical well with a single finiteconductivity vertical fracture: Pratikno et al 2003 Amini et al 2008 Model Parameters: Permeability (k) Fracture half-length (x f ) Fracture conductivity (F c ) Drainage area (A) Skin factor (s) Horizontal well with multiple vertical fractures: van Kruysdijk and Dullaert 1989 Larsen and Hegre 1994 Model Parameters: Permeability (k) Fracture half-length (x f ) Fracture conductivity (F c ) Drainage area (A) Skin factor (s) Well length (L w ) Number of fractures (n f ) 2011 SPE Hydraulic Fracture Technology Conference The Woodlands, Texas January 2011 Integration of Production Analysis and Rate-time Analysis via Parametric Correlations (Ilk/Rushing/Blasingame) Thomas A. BLASINGAME Texas A&M University (24 January 2011) Slide 4/11

18 Methodology: Power-law Exponential Relation Observed Behavior of Decline Parameter (D): (from data) D( 1 dq q dt D ndˆ i t (1 n) Flowrate Solution: (derived from D( behavior) q( qˆ exp[ ˆ n i D t Di t ] Literature: Kohlrausch (1854). Phillips (1996). Kisslinger (1993) Decays in random, disordered, chaotic, heterogeneous systems (e.g. relaxation, aftershock decay rates, etc.). Valkó (2009) q( qˆ i exp[ ( t / ) Jones (1942) and Arps (1945) q( 2011 SPE Hydraulic Fracture Technology Conference The Woodlands, Texas January 2011 Integration of Production Analysis and Rate-time Analysis via Parametric Correlations (Ilk/Rushing/Blasingame) Thomas A. BLASINGAME Texas A&M University (24 January 2011) q o n ] m 1 D exp o t 100( m 1) Slide 5/11

19 Correlation Work: Proposed correlations are based on the following production and rate-time analyses of tight gas and shale gas fields: (Ilk 2010) Holly Branch Field: 13 hydraulically-fractured vertical wells. Shale Gas Field A: 6 horizontal wells with multiple fractures. Shale Gas Field B: 9 horizontal wells with multiple fractures. Shale Gas Field C: 8 horizontal wells with multiple fractures. Proposed correlations are based on the assumption that the results of the "model-based" analyses are correlative with the results of the "rate-time" analyses. k, xf, A, Lw, etc. f ( n, Di, qˆ i, D )? ˆ Discussion: Objective Estimate RESERVOIR PROPERTIES from rate-time model parameters. Approach Use cross-plots of a variety of combinations of PLE parameters versus physical model parameters (k, x f, L w, etc.). Presentation Correlation plots for each field SPE Hydraulic Fracture Technology Conference The Woodlands, Texas January 2011 Integration of Production Analysis and Rate-time Analysis via Parametric Correlations (Ilk/Rushing/Blasingame) Thomas A. BLASINGAME Texas A&M University (24 January 2011) Slide 6/11

20 Correlation Work: k f ˆ ( n, D i, q ˆi ) Holly Branch (TG) "Shale Gas Field A" "Shale Gas Field B" "Shale Gas Field C" k an Dˆ qˆ d i Holly Branch Field: Tight gas sand. Very consistent correlation. Minor outlier(s). Shale Gas Field A: Apparent good correlation. 2 outliers (out of 6 points). Shale Gas Field B: Significant scatter. Very weak correlation for lowest k-value. Shale Gas Field C: Significant deviation from perfect trend, but good "clustering" about trend. Behavior could be due to reservoir quality SPE Hydraulic Fracture Technology Conference The Woodlands, Texas January 2011 Integration of Production Analysis and Rate-time Analysis via Parametric Correlations (Ilk/Rushing/Blasingame) Thomas A. BLASINGAME Texas A&M University (24 January 2011) b c i Slide 7/11

21 Correlation Work: kx f = f(n) k x f exp[ n] Holly Branch (TG) "Shale Gas Field A" "Shale Gas Field B" "Shale Gas Field C" Holly Branch Field: Tight gas sand. Minor outliers. Some discrepancies for lower kx f -values. Shale Gas Field A: Possible lack of correlation in these variables for this case. Small variance in values. Shale Gas Field B: Fair correlation. Variance in completions? Shale Gas Field C: Very good correlation. Minor outlier(s). Probably most coherent correlation case SPE Hydraulic Fracture Technology Conference The Woodlands, Texas January 2011 Integration of Production Analysis and Rate-time Analysis via Parametric Correlations (Ilk/Rushing/Blasingame) Thomas A. BLASINGAME Texas A&M University (24 January 2011) Slide 8/11

22 Correlation Work: EUR = f(n) EUR ˆ n ˆ Holly Branch (TG) "Shale Gas Field A" Holly Branch Field: Minor outliers = f(reservoir quality) (assumed). HP/HT (extreme). Shale Gas Field A: Very strong correlation. EUR related to production. Shale Gas Field B: Weak correlation. Variance in completion types and well locations. Shale Gas Field C: Excellent correlation. Very consistent well completion procedures. "Shale Gas Field B" "Shale Gas Field C" 2011 SPE Hydraulic Fracture Technology Conference The Woodlands, Texas January 2011 Integration of Production Analysis and Rate-time Analysis via Parametric Correlations (Ilk/Rushing/Blasingame) Thomas A. BLASINGAME Texas A&M University (24 January 2011) Slide 9/11

23 Summary, Conclusions, and Recommendations: Summary: Correlated results of Power-Law Exponential (PLE) rate-time decline relation with model-based analysis results. Created parametric relations for k, kx f and EUR using power-law exponential model parameters. Conclusions: Rate-time model results and model-based production analysis results CAN be correlated. Increased data sample sizes and improved data quality should yield better correlations. Strong evidence of correlation between EUR and PLE model parameters. No strong conclusions for other correlations (sample sizes?). Recommendations: Improve correlations with larger data sets (more wells). Attempt to establish rigorous parametric equations (inter-relation of rate-time and reservoir models) to directly predict production behavior for tight gas and shale gas reservoirs SPE Hydraulic Fracture Technology Conference The Woodlands, Texas January 2011 Integration of Production Analysis and Rate-time Analysis via Parametric Correlations (Ilk/Rushing/Blasingame) Thomas A. BLASINGAME Texas A&M University (24 January 2011) Slide 10/11

24 SPE Integration of Production Analysis and Rate-time Analysis via Parametric Correlations Theoretical Considerations and Practical Applications END OF PRESENTATION D. Ilk, DeGolyer and MacNaughton, J.A. Rushing, Apache Corporation, and T.A. Blasingame, Texas A&M University Department of Petroleum Engineering Texas A&M University College Station, TX SPE Hydraulic Fracture Technology Conference The Woodlands, Texas January 2011 Integration of Production Analysis and Rate-time Analysis via Parametric Correlations (Ilk/Rushing/Blasingame) Thomas A. BLASINGAME Texas A&M University (24 January 2011) Slide 11/11