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1 SPE Integrating Short-Term Pressure Buildup Testing and Long-Term Production Data Analysis to Evaluate Hydraulically-Fractured Gas Well Performance J.A. Rushing, SPE, Anadarko Petroleum Corp. and T.A. Blasingame, SPE, Texas A&M University Copyright 23, Society of Petroleum Engineers Inc. This paper was prepared for presentation at the SPE Annual Technical Conference and Exhibition held in Denver, Colorado, U.S.A., 5 8 October 23. 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, as presented, have not been reviewed by the Society of Petroleum Engineers and are subject to correction by the author(s). The material, as presented, does not necessarily reflect any position of the Society of Petroleum Engineers, its officers, or members. Papers presented at SPE meetings are subject to publication review by Editorial Committees of the Society of Petroleum Engineers. Electronic reproduction, distribution, or storage of any part of this paper for commercial purposes 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 3 words; illustrations may not be copied. The abstract must contain conspicuous acknowledgment of where and by whom the paper was presented. Write Librarian, SPE, P.O. Box , Richardson, TX , U.S.A., fax Abstract This paper presents an integrated approach for evaluating the post-fracture performance of gas wells completed in tight gas sands. Our technique focuses on a methodology for evaluating the stimulation effectiveness of hydraulically fractured gas wells. Rather than relying on a single evaluation technique, we integrate short-term pressure buildup testing with long-term production data analysis using decline type curves. We illustrate the applicability and efficacy of our technique with examples from more than twenty wells completed in tight gas sands. The results of our paper also demonstrate the value and function of short-term pressure buildup tests performed in tight gas sands. Introduction Most wells completed in tight gas sands require stimulation to achieve economic production. Depending on the type and size of stimulation treatment, hydraulic fracturing may be very expensive, often representing a significant portion of the total well completion costs. Since the economic viability of many wells completed in low-permeability reservoirs depends on minimizing costs, then it is imperative to optimize fracture treatments. Fracture optimization is achieved by finding the proper balance between stimulation costs and well productivity. A key component in achieving this balance is a post-fracture evaluation program to determine stimulation effectiveness, principally effective fracture conductivity and propped fracture length. A number of techniques have been developed by the petroleum industry for evaluating hydraulically-fractured gas well performance. Unfortunately, no single methodology is perfect. Theoretical assumptions, model applicability, and/or data requirements limit each analysis technique. Therefore, we employ an integrated approach in which we capture the benefits and utilize the strengths of several types of fractured well diagnostic techniques. Several previous papers have illustrated the effectiveness of such an integrated approach. 1-7 Cipolla and Wright 8,9 have identified and grouped fractured well diagnostic techniques into three general categories: direct far-field, direct near-wellbore, and indirect. We focus on the integration of indirect techniques, particularly pressure transient testing and production data analysis. Pressure buildup testing is the most effective indirect technique for evaluating the stimulation effectiveness of hydraulically fractured gas wells. But, knowledge of reservoir permeability, either from the well test or from an independent source, is required to compute fracture properties. If a well is shut in for a sufficient time to reach the pseudoradial flow period, then we can uniquely determine reservoir permeability. Unfortunately, wells completed in tight gas sands usually require very long shut-in times to reach pseudoradial flow. Most operators are reluctant to shut in a well for extended periods, especially under favorable gas product pricing scenarios. If, however, we have an estimate of reservoir permeability from an independent source, then shorter duration pressure buildup tests in tight gas sands become practical. Conventional decline type curve analysis 1-13 of production data is a viable alternative for evaluating well performance without shutting in the well. Unlike pressure transient test analysis, decline type curves do not rely upon identification of characteristic flow regimes for the analysis. As a result, we cannot always obtain unique estimates of fracture half-length, especially when using poor-quality production data. Other production analysis techniques consider the production data to be an extended drawdown test. 14,15 Accordingly, these techniques use variable-rate pressure transient testing theory and superposition plotting functions to analyze the production data. Unlike conventional decline type curve analysis techniques, these methods allow us to identify specific flow regimes. However, we still cannot quantify fracture properties unless we have an estimate of reservoir permeability. Evaluation Methodology To overcome these problems with post-fracture evaluation techniques, we have developed an analysis methodology that integrates short-term pressure buildup testing and long-term production data analysis using conventional decline type curves. Although several decline type curves are applicable, we selected the material balance decline type curve (MBDTC) methodology developed by Palacio and Blasingame. 12

2 2 SPE Theoretical aspects of the MBDTC analysis technique have been discussed previously and will not be repeated in detail in this paper. In general, the type curve method is applicable to variable rate, variable bottomhole flowing pressure, or combinations of these flowing conditions. Use of three different type curve plotting functions normalized rate, rate integral, and rate derivative against material balance time allows us to obtain more unique type curve matches, even from typical field data with significant scatter. Since the plotting functions were developed in terms of pseudopressures 16 and pseudotime 17 variables, then the type curves are applicable to gas well production data analysis. Moreover, the type curves were developed for an infiniteconductivity vertical fracture, so they may not be appropriate for all fractured well conditions, especially those wells with very low fracture conductivities. Our iterative technique begins with initial estimates of permeability and fracture half-length from decline type curve analyses of the well production data. We then use the pressure derivative plot of the pressure buildup data to identify flow regimes characteristic of hydraulically fractured wells. Depending on the type of flow regimes present, we may then use special plotting functions and analysis techniques to compute fracture properties. Next, we use an automatic history-matching process to analyze the test data. Estimates of formation permeability from the decline type curve analysis and fracture properties from the special analyses are used to establish initial estimates and reasonable ranges for the parameters during the history-matching process. We then iterate between analyses until consistent results are obtained. Integrated Analysis Procedure. The procedure outlined below assumes that a pseudoradial flow period will not be present. If, however, the well test exhibits pseudoradial flow, then that data should be incorporated into the analysis. The working equations are also derived based on a pseudopressure and normalized pseudotime formulation. Note that the equation format will change if different pressure and time functions are used. 18 A step-by-step procedure is as follows: 1. Analyze the post-fracture gas production data using a decline type curve methodology. For this paper, we use the material balance decline type curves (MBDTC). 12 Estimate effective gas permeability (k g ) and effective fracture half-length (L f ). 2. Prepare a plot of pseudopressure change and derivative of pseudopressure change against normalized equivalent or superposition 19 pseudotime function using the pressure buildup test data. Identify all flow regimes characteristic of hydraulically fractured wells from the shape of the derivative data. 3. If the bilinear flow period 2-22 is present, prepare a Cartesian plot of pseudopressure against the fourth root of normalized pseudotime function. Compute the slope (m B ) of the line drawn through the bilinear flow period identified from Step 2. Using k g from the MBDTC analysis and m B from the bilinear plot, compute effective fracture conductivity, w f k f : w f k f q gt 1 =...(1) hm B φµ g ct k g 4. If the formation linear flow period 21,23,24 is present, prepare a Cartesian plot of pseudopressure against the square root of normalized pseudotime function. Compute the slope (m L ) of the line drawn through the formation linear flow period identified from Step 2. Using k g from the MBDTC analysis and m L from the formation linear plot, compute effective fracture halflength, L f : L f 4.925q gt 1 =...(2) hm L φµ g ct k g 5. Compute the dimensionless fracture conductivity, F CD, using estimates of w f k f, L f and k g : CD w f k f L f k g F =...(3) 6. Use an automatic history-matching 25 process to analyze the test data. Estimates of formation permeability from the decline type curve analysis and fracture properties from the special analyses are used to establish initial estimates and reasonable ranges for the parameters during the history-matching process. Iterate between analyses until consistent results are obtained. Application of our integrated approach is illustrated with several field examples from the Bossier tight gas sand play in the East Texas Basin. All of these wells were stimulated with various types of water-frac techniques. 26 Field Example 1 The first field case is an example of a well completed with a small conventional water-frac. The well was drilled and completed in August of 21. Following a water-frac with 5,281 bbl slick water and 28,65 lbs 3/5 proppant pumped at an average rate of 67 bpm, the well produced at an initial rate of slightly more than 2, Mscf/day (Fig. 1). The well was shut in December 13, 21 for a two-week pressure buildup test. Initial estimates of permeability and fracture half-length were obtained from a material balance decline type curve (MBDTC) analysis of the production data. 12 The type curve match shown in Fig. 2 is a log-log plot of normalized rate, integral of normalized rate, and derivative of rate integral against material balance time. 12 Note that all rate functions are derived in terms the pseudopressure function, 16 while the time variable is derived in terms of the pseudotime function. 17 The solid lines in Fig. 2 correspond to the dimensionless type curves, while the discrete points represent the corresponding dimensional discrete field data. We estimate k g =.169 md and L f = 45.7 ft.

3 SPE Gas Production Rate, Mscf/d 2,5 2, 1,5 1, 5 24-Aug-1 14-Sep-1 5-Oct-1 26-Oct-1 16-Nov-1 7-Dec-1 Date Fig. 1 Post-fracture gas production history, Field Example 1. Again, assuming we have identified the correct straight line, then we can this line slope, m L, to estimate effective fracture half-length as defined by Eq. (2). Using the slope of this line and k g estimated from MBDTC analysis, we compute L f = 41.8 ft, which is very similar to the value estimated from the decline type curve analysis. s, psia 2 /cp/mmscfd Bilinear Flow Formation Linear Flow Derivative Pseudotime Superposition, hr Fig. 3 Log-log plot identifying flow regimes characteristic of hydraulically fractured wells, Field Example 1. Fig. 2 Material balance decline type curve analysis of postfracture gas production, Field Example 1. Because of the significant rate changes prior to shutting in the well, we analyzed the pressure buildup data using both pseudopressure and pseudotime superposition functions. A log-log plot of the pseudopressure change and pseudopressure derivative functions against the normalized pseudotime superposition 19 function is shown in Fig. 3. Possible flow regimes characteristic of hydraulically fractured wells are indicated by the solid black lines. The one-quarter slope line identifies bilinear flow, while the line with a slope of one-half indicates formation linear flow. Note that, although we cannot positively identify a pseudoradial flow period, it may be developing at the end of the test as indicated by the flattening of the pressure derivative. As we mentioned previously, the next step is to use special plotting functions to validate various flow patterns identified from the log-log derivative plot. The bilinear flow regime is indicated by the straight line on a plot of pseudopressure against the fourth root of pseudotime superposition function shown in Fig. 4. If we have identified the correct straight line on the curve, then we can use the bilinear flow line data slope to estimate effective fracture conductivity as defined by Eq. (1). On the basis of the line slope from Fig. 4 and k g from the MBDTC analysis, we estimate w f k f is 6.2 md-ft. Moreover, if we substitute L f and k g from the MBDTC analysis and w f k f from Fig. 4 into Eq. (3), we compute F CD = 8.. Similarly, the formation linear flow regime is indicated by a straight line on the plot of pseudopressure against the square root of pseudotime superposition function shown in Fig. 5., psia 2 /cp Fourth-Root of Pseudotime Superposition, (hr) 1/4 Fig. 4 Fourth-root-of-time plot showing bilinear flow regime from two-week pressure buildup test, Field Example 1., psia 2 /cp Square-Root of Pseudotime Superposition, (hr) 1/2 Fig. 5 Square-root-of-time plot showing formation linear flow regime from two-week pressure buildup test, Field Example 1. On the basis of the derivative plot in Fig. 3, we did not observe the pseudoradial flow regime. As a result, we cannot use conventional semilog analysis techniques to compute formation permeability from the well test. Instead, we used an

4 4 SPE automatic history-matching process during which we allowed k g, L f, and F CD to vary. To assess the importance of non-darcy flow in the well test analysis, 27,28 we also included a ratedependent skin factor defined by the non-darcy flow coefficient, D. Estimates of formation permeability from the decline type curve analysis and fracture properties from the special analyses were used to establish initial estimates and reasonable ranges for the parameters during the historymatching process. We then iterated several times until we obtained consistent results from all analyses. The final and best history match is shown in Fig. 6. The solid lines drawn through the well test data represent the final history-matched solution. Note that results from the pressure buildup test analysis are very similar to that from the decline type curve analysis. We estimate k g and L f are.134 md and 44.1 ft, respectively. In addition, the results suggest the stimulation treatment generated a short fracture with relatively low conductivity. We compute w f k f = 13.7 md-ft corresponding to F CD = s, psia 2 /cp/mmscfd Well Test Results k =.134 md FCD = 23.3 L f = 44.1 ft D = 4.17x1-9 (Mscf/d) -1 Pseudotime Superposition, hr Fig. 6 Results from automatic history-match of two-week pressure buildup test, Field Example 1. Field Example 2 The next example illustrates a well with a very conductive and long effective fracture half-length. The stimulation treatment for this well began by injecting 5,45 bbl slick water with 2,5 gal 15% HCl and 5, lbs 4/7 sand followed by 2,857 bbl of 3 lbs/1 gas cross-linked gel with 25, lbs 2/4 proppant. The initial rate was slightly less than 12, Mscf/day (Fig. 7). The well produced for about six months before being shut in for a two-week pressure buildup test. Gas Production Rate, Mscf/d 14, 12, 1, 8, 6, 4, 2, 17-Mar-1 17-Apr-1 17-May-1 17-Jun-1 17-Jul-1 17-Aug-1 17-Sep-1 Fig. 7 Post-fracture gas production history, Field Example 2. Date The MBDTC analysis of the post-fracture production data is shown in Fig. 8. The evaluation yielded k g =.261 md and L f = 26.6 ft. Fig. 8 Material balance decline type curve analysis of postfracture gas production, Field Example 2. A log-log plot of the pseudopressure change and pseudopressure derivative functions against the pseudotime superposition function is shown in Fig. 9. We observe both bilinear and formation linear flow periods, as indicated by the solid black lines with slopes of one-quarter and one-half, respectively. We do not, however, see evidence of pseudoradial flow. s, psia 2 /cp/mmscfd Derivative Bilinear Flow Pseudotime Superposition, hr Formation Linear Flow Fig. 9 Log-log plot identifying flow regimes characteristic of hydraulically fractured wells, Field Example 2. The bilinear and formation linear flow regimes are also identified and validated by the plots of pseudopressure against fourth-root and square-root of pseudotime superposition functions shown in Figs. 1 and 11, respectively. Using m B from the line drawn through the bilinear flow period in Fig. 1 and k g estimated from the MBDTC analysis, we compute w f k f = md-ft. Further, if we use k g and L f estimates from the MBDTC analysis of the production data, we estimate F CD = As indicated by the straight-line on the plot of pseudopressure against the square root of pseudotime superposition function shown in Fig. 11, the formation linear flow period is very well defined. Using m L from the line drawn through the formation linear flow period and k g estimated from the MBDTC analysis, we compute L f = 26.1 ft. Again, the fracture half-lengths estimated from the

5 SPE MBDTC and square-root-of-time analyses are generally in agreement., psia 2 /cp s, psia 2 /cp/mmscfd Well Test Results k =.276 md F CD = 23.1 L f = 29 ft D = 1.1x1-6 (Mscf/d) -1 Fourth-Root of Pseudotime Superposition, (hr) 1/4 Fig. 1 Fourth-root-of-time plot showing bilinear flow regime from two-week pressure buildup test, Field Example 2. Pseudotime Superposition, hr Fig. 12 Results from automatic history-match of two-week pressure buildup test, Field Example 2. 12,, psia 2 /cp Gas Production Rate, Mscf/day 1, 8, 6, 4, 2, 8-Oct-99 8-Dec-99 8-Feb- 8-Apr- 8-Jun- 8-Aug- 8-Oct- 8-Dec- Date Fig. 13 Post-fracture gas production history, Field Example 3. Square-Root of Pseudotime Superposition, (hr) 1/2 Fig. 11 Square-root-of-time plot showing formation linear flow regime from two-week pressure buildup test, Field Example 2. Like the first field example, we did not see evidence of a pseudoradial flow period on the log-log plot of the pressure derivative. Consequently, we could not use conventional semilog techniques to compute permeability. Again, we used an automatic history-matching process to analyze the well test data. The final and best history match for Field Example 2 is shown in Fig. 12. Note that results from the pressure buildup test analysis are very similar to those estimated from the decline type curve analysis. We estimate k g and L f are.276 md and 29.1 ft, respectively. The results also suggest the stimulation treatment generated a long and very conductive fracture. We compute w f k f = 25.9 md-ft corresponding to F CD = Field Example 3 The next field example illustrates a successful large conventional water-frac stimulation treatment. The well was hydraulically fractured on October 8, 1999 with 8,175 bbl slick water and 237, lbs 2/4 proppant. As shown by the production history in Fig. 13, the initial gas rate was almost 12, Mscf/day. After producing for about 14 months, the well was shut in for a two-week pressure buildup test on December 31, 2. We compute k g =.219 md and L f = ft from the material balance decline type curve analysis of the post-fracture production data, as shown in Fig. 14. Fig. 14 Material balance decline type curve analysis of postfracture gas production, Field Example 3. A log-log plot of the pseudopressure change and pseudopressure derivative functions against the pseudotime superposition function is shown in Fig. 15. The solid black lines identify bilinear and formation linear flow regimes. Note that, similar to the previous examples, we did not observe development of a pseudoradial flow period. The bilinear and formation linear flow patterns are also identified and validated by plots of pseudopressure against fourth-root and square-root of pseudotime superposition functions shown in Figs. 16 and 17, respectively. Using m B from the line drawn through the bilinear flow period as well as k g from the MBDTC analysis, we compute w f k f = md-ft. Similarly, if we use k g and L f estimated from the MBDTC

6 6 SPE analysis of the post-fracture production data, we also estimate F CD = s, psia 2 /cp/mmscfd Pseudotime Superposition, hr Fig. 15 Log-log plot identifying flow regimes characteristic of hydraulically fractured wells, Field Example 3., psia 2 /cp Fourth-Root of Pseudotime Superposition, (hr) 1/4 Fig. 16 Fourth-root-of-time plot showing bilinear flow regime from two-week pressure buildup test, Field Example 3. Similar to Field Example 2, the formation linear flow regime is very well defined and is indicated by the straight-line on the plot of pseudopressure against the square root of pseudotime superposition function shown in Fig. 17. As described by Step 4 in the analysis procedure, we use m L from the line drawn through the formation linear flow period as well as k g estimated from the MBDTC analysis to compute L f = ft., psia 2 /cp Bilinear Flow Derivative Square-Root of Pseudotime Superposition, (hr) 1/2 Formation Linear Flow Fig. 17 Square-root-of-time plot showing formation linear flow regime from two-week pressure buildup test, Field Example 3. Like the previous examples, the absence of a pseudoradial flow period precludes use of conventional semilog analysis techniques to compute permeability from the well test. Alternatively, we used an automatic history-matching process to analyze the well test data. The best history match is shown in Fig. 18. We estimate k g and L f are.272 md and ft, respectively. In addition, these results indicate the stimulation treatment generated a long and very conductive fracture. We compute a fracture conductivity of 25.9 md-ft corresponding to a dimensionless fracture conductivity of s, psia 2 /cp/mmscfd Well Test Results k =.272 md F CD = 39.2 L f = ft D = 1.4x1-2 (Mscf/d) -1 Pseudotime Superposition, hr Fig. 18 Results from automatic history-match of two-week pressure buildup test, Field Example 3. Validation of Integrated Evaluation Technique To assess the validity of our integrated evaluation technique, we analyzed several pressure buildup tests numerically. We then compared the results to the integrated analytical approach. We illustrate the results of the numerical well test analysis for Field Example 4. Because this well has a very low-conductivity fracture, it represents an extreme test case for our integrated (analytical) evaluation technique. Integrated (Analytical) Well Test Analysis. The last field example illustrates a large conventional water-frac stimulation treatment that generated a fracture with long effective halflength but very low effective conductivity. The well was stimulated in three stages, with each stage being composed of 8,5 to 1, bbl slick water and 17, to 23, lbs 2/4 proppant. The well produced for about two years before being shut in for a two-week pressure buildup test. The gas production and flowing wellhead pressure histories are shown in Fig. 19. The MBDTC analysis of the post-fracture production data, shown in Fig. 2, yielded k g =.11 md and L f = 11.7 ft. A log-log plot of the pseudopressure change and pseudopressure derivative functions against the pseudotime superposition function is shown in Fig. 21. The solid black line with a one-quarter slope indicates a significant portion of the test was dominated by bilinear flow. We do not observe either a formation linear or a pseudoradial flow period. The presence of bilinear flow is validated by the straight line on the plot of pseudopressure against fourth root of pseudotime superposition function shown in Fig. 22. From Eq. (1), we compute a very low effective fracture conductivity

7 SPE of 2.8 md-ft. Similarly, if we use k g and L f estimated from the MBDTC of the production data, we also estimate F CD = 2.5. Gas Production Rate, Mscf/d 7, 6, 5, 4, 3, 2, Gas Production Flowing Wellhead Pressure 7, 6, 5, 4, 3, 2, Flowing Wellhead Pressure, psig, psia 2 /cp 1, 1, 6-Sep- 4-Jan-1 4-May-1 1-Sep-1 3-Dec-1 29-Apr-2 Date Fig. 19 Post-fracture gas production and wellhead flowing pressure, Field Example 4. Fourth-Root of Pseudotime Superposition, (hr) 1/4 Fig. 22 Fourth-root-of-time plot showing bilinear flow regime from two-week pressure buildup test, Field Example 4. s, psia 2 /cp/mmscfd Well Test Results k =.68 md F CD = 1.97 L f = ft D = 4.3x1-5 (Mscf/d) -1 Pseudotime Superposition, hr Fig. 2 Material balance decline type curve analysis of postfracture gas production, Field Example 3. s, psia 2 /cp/mmscfd Bilinear Flow Pseudotime Superposition, hr Derivative Fig. 21 Log-log plot identifying flow regimes characteristic of hydraulically fractured wells, Field Example 3. As shown by the history-matched solution in Fig. 23, we estimate k g and L f are.68 md and ft, respectively. The results suggest the stimulation treatment generated a long effective half-length but very low effective conductivity. Note also that the fracture half-length from the MBDTC analysis was significantly less than that computed from the well test. Recall that the material balance decline type curves 12 were derived assuming an infinite-conductivity vertical fracture. Consequently, the MBDTC will underestimate the effective fracture half-length for a low finite conductivity fracture. Fig. 23 Results from automatic history-match of two-week pressure buildup test, Field Example 4. Numerical Well Test Analysis. To demonstrate the validity of our analysis technique, we present the results of the numerical well test analysis for Field Example 4. We developed a two-phase (gas-water), three-dimensional, multilayer finite-difference model. To reduce computational time, we simulated one quarter of the reservoir with a Cartesian grid system. Moreover, we used a Cartesian rather than a radial grid system so that we could more accurately model the linear flow patterns characteristic of hydraulically fractured wells. We used data from a comprehensive core description and evaluation program to populate the grid blocks vertically. The core data suggested significant reservoir heterogeneity in the vertical direction, so we built the model using 12 hydraulic flow units distributed over an interval of about 3 ft. The flow units were generated using a methodology described in References 29 and 3. Water saturations were distributed vertically using core-derived capillary pressure curves. We input the gas production history shown in Fig. 19 and history-matched the well flowing and shut-in pressures. Fracture properties, including effective fracture half-length and fracture permeability, as well as absolute permeability and effective porosity were varied until we matched the pressure history. Our best match, shown in Fig. 24, was obtained with a fracture permeability of 1 md, a fracture half-length of 27 ft. On the basis of the modeled fracture grid width of.5 ft, we compute an effective fracture conductivity of 5 md-ft,

8 8 SPE which is very close to that estimated from the pressure buildup test analysis. Similarly, the simulated effective fracture halflength of 27 ft agrees with the value estimated from the integrated well test and decline type curve analyses. Although not shown in this paper, we have successfully matched results from the analytical and numerical techniques on several other wells. Consequently, we feel that our technique is valid for evaluating hydraulically-fractured gas well performance. 3,5 kg from MBDTC Analysis, md o Line Bottomhole Shut In Pressure, psi 3, 2,5 2, 1,5 1, Elapsed Shut In Time, hr Measured Bottomhole Pressure Simulated Bottomhole Pressure Numerical Well Test Results k =.7 md wfk f = 5 md-ft Lf = 27 ft F CD = 2.6 Fig. 24 Numerical well test analysis of two-week pressure buildup test, Field Example 4. Results of Post-Fracture Performance Analysis We have applied our integrated post-fracture performance evaluation technique to 22 wells producing from the Bossier tight gas sand play in both the East Texas and North Louisiana Salt Dome Basins. All of these wells were stimulated using various water-frac techniques, ranging from water-fracs with little to no sand, water-fracs with large sand concentrations, and a hybrid water-frac technique. 26 Results from both the material balance decline type curves and well test analysis are shown in Figs. 25 and 26. As shown by Fig. 25, we generally observed good agreement between effective gas permeability computed from the material balance decline type curve and the pressure buildup test analyses. Similarly, we see good agreement with effective fracture half-lengths computed from both methods. Most of the differences, especially in estimated fracture halflengths, can be attributed to wells with low or very low conductive fractures. Since the current version of the MBDTC used in this study was derived for infiniteconductivity vertical fractures, then we would not necessarily expect close agreement. New type curves for finiteconductivity fractures have been developed. 31 Based on our experiences with the MBDTC analysis technique, we believe these decline type curves are an excellent tool for well performance analysis, reservoir surveillance and monitoring, and reservoir characterization studies, particularly in tight gas sands. However, a critical element in the successful application of the decline type curve methodology is directly related to the frequency and quality of the well production data. We have had the most success with well performance evaluations when accurate daily production data, including well flowing pressures, are used. Fig. 25 A comparison of effective gas permeabilities computed from the material balance decline type curve and well test analyses. Fig. 26 A comparison of effective fracture half-lengths computed from the material balance decline type curve and well test analyses. Summary and Conclusions We have developed an integrated approach for evaluating the post-fracture performance of gas wells completed in tight gas sands. Our technique focuses on application of short-term pressure buildup testing and long-term production data analysis using decline type curves for evaluating the stimulation effectiveness of hydraulically fractured gas wells. This integrated technique captures the benefits and advantages of each method, thus both complementing and supplementing each technique. Application of this evaluation technique demonstrates the tremendous value of short-term pressure buildup testing in tight gas sands. Acknowledgments We would like to express our thanks to the management of Anadarko Petroleum Corporation for permission to publish the results of our study. Nomenclature D = non-darcy flow coefficient, (Mscf/d) -1 F CD = dimensionless fracture conductivity = w f k f /k g L f k f = fracture permeability, md k g = effective permeability to gas, md = effective fracture half-length, ft L f Lf from MBDTC Analysis, ft k g from Well Test Analysis, md L f from Well Test Analysis, ft 45 o Line

9 SPE q g = gas flow rate, Mscf/day T = reservoir temperature, o R w f k f = effective fracture conductivity, md-ft References 1. Agarwal, R.G., Carter, R.D., and Pollock, C.B.: Evaluation and Performance Prediction of Low-Permeability Gas Wells Stimulated by Massive Hydraulic Fracturing, J. Pet. Tech. (March 1979) ; Trans. AIME, Lee, W.J. and Holditch, S.A.: Fracture Evaluation with Pressure Transient Tests in Low-Permeability Gas Reservoirs. Part I: Theoretical Background, paper SPE 7929 presented at the 1979 SPE Symposium on Low Permeability Gas Reservoirs, Denver, CO, May Holditch, S.A. and Lee, W.J.: Fracture Evaluation with Pressure Transient Tests in Low-Permeability Gas Reservoirs. Part I: Theoretical Background, paper SPE 793 presented at the 1979 SPE Symposium on Low Permeability Gas Reservoirs, Denver, CO, May Bostic, J.N., Agarwal, R.G., and Carter, R.D.: Combined Analysis of Postfracturing Performance and Pressure Buildup Data for Evaluating an MHF Gas Well, J. Pet. Tech. (Oct. 198) Holditch, S.A., Lee, W.J., and Gist, R.: An Improved Technique for Estimating Permeability, Fracture Length and Fracture Conductivity from Pressure Buildup Tests in Low Permeability Gas Wells, paper SPE 9885 presented at the 1981 SPE Symposium on Low Permeability Gas Reservoirs, Denver, CO, May Lee, W.J. and Holditch, S.A.: Fracture Evaluation with Pressure Transient Testing in Low-Permeability Gas Reservoirs, J. Pet. Tech. (September 1981) Cipolla, C.L. and Mayerhofer, M.J.: Understanding Fracture Performance by Integrating Well Testing & Fracture Modeling, paper SPE 4944 presented at the 1998 SPE Annual Technical Conference and Exhibition, New Orleans, LA, September Cipolla, C.L. and Wright, C.A.: Diagnostic Techniques to Understand Hydraulic Fracturing: What? Why? And How?, paper SPE presented at the 2 SPE/CER Gas Technology Symposium, Calgary, Alberta, Canada, April 3-5; SPE Prod. & Facil. (February 22) Cipolla, C.L. and Wright, C.A.: State-of-the-Art in Hydraulic Fracture Diagnostics paper SPE presented at the 2 SPE Asia Pacific Oil and Gas Conference and Exhibition, Brisbane, Australia, Oct Fetkovich, M.J.: Decline Curve Analysis Using Type Curves, J. Pet. Tech. (June 198) Carter, R.D.: Type Curves for Finite Radial and Linear Gas Flow Systems: Constant Terminal Pressure Case, Soc. Pet. Engr. J. (Oct. 1985) Palacio, J.C. and Blasingame, T.A.: Decline-Curve Analysis Using Type Curves-Analysis of Gas Well Production Data, paper SPE 2599 presented at the 1993 SPE Joint Rocky Mountain Regional and Low Permeability Symposium, Denver, CO, April Agarwal, R.G., et al. Analyzing Well Production Data Using Combined Type Curve and Decline Curve Analysis Concepts, paper SPE presented at the 1998 SPE Annual Technical Conference and Exhibition, New Orleans, LA, September Hager, C.J. and Jones, J.R.: Analyzing Flowing Production Data with Standard Pressure Transient Methods, paper SPE 7133 presented at the 21 SPE Rocky Mountain Petroleum Technology Conference, Keystone, CO, May Poe, B.D., Jr., et al.: Advanced Fractured Well Diagnostics for Production Data Analysis, paper SPE 5675 presented at the 1999 SPE Annual Technical Conference and Exhibition, Houston, TX, Oct Al-Hussainy, R, Ramey, H.J. and Crawford, P.B., et al.: The Flow of Real Gases Through Porous Media, J. Pet. Tech. (May 1966) ; Trans., AIME, Agarwal, R.G.: Real Gas Pseudo-Time-A New for Pressure Buildup Test Analysis of MHF Gas Wells, paper SPE 8279 presented at the 1979 SPE Annual Technical Conference and Exhibition, Las Vegas, NV, Sept Lee, W.J. and Wattenbarger, R.A.: Gas Reservoir Engineering, Textbook Series, SPE, Richardson, TX (1996) 5, Chap Agarwal, R.G.: A New Method to Account for Producing Time Effects When Drawdown Type Curves are Used to Analyze Pressure Buildup and Other Test Data, paper SPE 9289 presented at the 198 SPE Annual Technical Conference and Exhibition, Dallas, TX, Sept Cinco-Ley, H. and Samaniego-V., F.: Effect of Wellbore Storage and Damage on the Transient Pressure Behavior of Vertically Fractured Wells, paper SPE 6752 presented at the 1977 SPE Annual Technical Conference and Exhibition, Denver, CO, Oct Cinco-Ley, H. and Samaniego-V., F.: Transient Pressure Analysis for Fractured Wells, J. Pet. Tech., (Sept. 1981) Cinco-Ley, H., Samaniego-V., F., and Rodriguez, F.: Application of the Pseudolinear Flow Model to the Pressure Transient Analysis of Fractured Wells, paper SPE 1359 presented at the 1984 SPE Annual Technical Conference and Exhibition, Houston, TX, Sept Ramey, H.J., Jr. and Gringarten, A.C.: Effect of High Volume Vertical Fractures on Geothermal Steam Well Behavior, Proc., Second United Nations Symposium on the Use and Development of Geothermal Energy, San Francisco, CA, May 2-29, Raghavan, R.: Some Practical Considerations in the Analysis of Pressure Data, J. Pet. Tech., (Oct. 1976) Pansystem Manual, Edinburgh Petroleum Services, Ltd, Edinburgh, Scotland, UK (22) Chapter Rushing, J.A. and Sullivan, R.B.: Evaluation of a Hybrid Water-Frac Stimulation Technology in the Bossier Tight Gas Sand Play, paper SPE presented at the 23 SPE Annual Technical Conference and Exhibition, Denver, CO, Oct Umnuayponwiwat, S. et al.: Effect of Non-Darcy Flow on the Interpretation of Transient Pressure Responses of Hydraulically Fractured Wells, paper SPE presented at the 2 SPE Annual Technical Conference and Exhibition, Dallas, TX, Oct Alvarez, C.H., et al.: Effects of Non-Darcy Flow on Pressure Transient Analysis of Hydraulically Fractured Wells, paper SPE presented at the 22 SPE Annual Technical Conference and Exhibition, San Antonio, TX, Sept. 29-Oct Newsham, K.E. and Rushing, J.A.: An Integrated Work-Flow Model to Characterize Unconventional Gas Resources: Part I-Geological Assessment and Petrophysical Evaluation, paper SPE presented at the 21 SPE Annual Technical Conference and Exhibition, New Orleans, LA, Sept. 3-Oct Rushing, J.A. and Newsham, K.E.: An Integrated Work-Flow Model to Characterize Unconventional Gas Resources: Part II-Formation Evaluation and Reservoir Modeling, paper SPE presented at the 21 SPE Annual Technical Conference and Exhibition, New Orleans, LA, Sept. 3-Oct Pratikno, H., Rushing, J.A., and Blasingame, T.A.: Decline Curve Analysis Using Type Curves; Fractured Wells, paper SPE presented at the 23 SPE Annual Technical Conference and Exhibition, Denver, CO, October 5-8.