Errors Introduced by Multiphase Flow Correlations on Production Analysis S.A. Cox and R.P. Sutton, Marathon Oil Co., and T.A. Blasingame, Texas A&M U.

Transcription

1 SPE Errors Introduced by Multiphase Flow Correlations on Production Analysis S.A. Cox and R.P. Sutton, Marathon Oil Co., and T.A. Blasingame, Texas A&M U. Copyright 2006, Society of Petroleum Engineers This paper was prepared for presentation at the 2006 SPE Annual Technical Conference and Exhibition held in San Antonio, Texas, U.S.A., September 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 300 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 First and foremost, production analysis techniques require accurate rate and bottomhole pressure histories. In most cases the pressure history of the well is not measured directly at the bottomhole condition, but is calculated from surface measurements by the use of single or multiphase flow correlations. In some cases significant error is introduced through the use of these correlations. This paper evaluates the magnitude of such errors for oil and gas producers with regard to the estimation of flow capacity, completion efficiency, and effective drainage area. Synthetic cases are used as control sets in order to evaluate the sensitivity of the results to the various multiphase flow correlations and flowing conditions. In addition to synthetic (simulated) performance behavior, field cases are presented and the variance in estimated reservoir and completion properties is evaluated. The technical contributions of this paper are: a. Systematic evaluation of the effect of errors in flow rates and bottomhole flowing pressures on production data analysis using both synthetic and field derived well performance data. b. Qualitative guidelines as the effect of errors in rate and pressure on estimated reservoir properties. c. Establishment of the most relevant pressure drop correlations for use in practice. Introduction Production analysis techniques can be used to provide an understanding of the flow capacity of a well, the completion efficiency of a well, and the effective drainage area (or volume). As a methodology, these techniques treat the long term production of a well as an extended constant rate drawdown test in order to interpret the well performance and to estimate the reservoir and well parameters. The well established analysis/interpretation techniques require both accurate production rates and flowing bottomhole pressures. In most cases the flowing bottomhole pressure is not measured directly, but is calculated based on the measured (surface) tubing pressure profile and flow rate data. Pressure drop correlations for multiphase flow are used to "convert" the surface pressure profile into a bottomhole pressure profile suitable for analysis and interpretation. Depending on the (multiphase flow) pressure calculation method that is selected, as well as the producing conditions, significant errors in the calculated flowing bottomhole pressure can (and will) result which affects the estimation of reservoir/well parameters. Three synthetic (simulation) cases were constructed for the purpose of serving as control data sets for this study. Each case represents a single well reservoir producing from the center of a radial flow geometry system. These simple scenarios are used to avoid any multiwell (interference) effects, as well as partial or irregular boundaries, etc. Specifically, the cases considered for this study include: Fracture stimulated well, low permeability gas reservoir, Unfractured well, low permeability oil reservoir, and Unfractured well, high permeability oil reservoir. An appropriate multiphase correlation for each case was selected to control the simulator. The actual rates and bottomhole pressures were used to validate the production analysis techniques. New bottomhole pressures were then calculated utilizing different multiphase flow correlations, and the evaluation process was repeated. The results of each analysis were compared to the parameters used in the simulator in order to establish the conclusions in this paper. As a comprehensive statement, the results of this work highlight the need for to acquire flowing gradients periodically to calibrate the multiphase flow correlation. Background Theory The use of well production data to characterize reservoir performance has been utilized by the oil industry for many years. Early application of this technology is based on the empirical equations presented by Arps 1 for rate-time decline curve analysis (semi-log rate-time plots). Decline curve analysis used the historical rate-time data of a given well to predict the future performance of that well. Production analysis techniques utilize time, rate, and pressure data to develop an interpretation and analysis, which provides estimates of reservoir properties and effective drainage area of a given producing well. This is accomplished by treating the long term production from the well as a variable rate transient test. During the life of the well, both rates and pressures

2 2 SPE change continuously however, the analytical solutions typically employed in production analysis require either constant rate or constant pressure production behavior. In order to overcome this issue, an equivalent time function must be incorporated into the analysis to account for the continuous changes in rates and pressures. Palacio and Blasingame 2 showed that the "equivalent time" function for oil is given by the following equation: Np te = q...(1) For gas wells the "equivalent time" function is defined as: ( μcg ) i t q( t ) dt ( μcg ) i z G t i i a = = Δ[ m( p) ]...(2) q( t) 0 μ( p) cg ( p) q( t) 2 pi For the gas well case, the average reservoir pressure profile must be known (or estimated) in order to calculate the correct equivalent time function. However the drainage area must be known in order to calculate the average reservoir pressure from material balance. Therefore, gas production analysis is inherently iterative in nature. Various plots are available to determine the effective drainage area (or volume) of the well. For oil wells, a plot of dimensionless rate (q Dd ) versus dimensionless cumulative production (Q Dd ) will form a straight line with an intercept of 1. For this plot q Dd and Q Dd are defined as: 1 Boμo 1 re 3 q Dd = ln q 3 o 7.08x10 kh ( pi pwf ) rwa 4...(3) Bo 1 QDd = Np...(4) φhact ( pi pwf ) For gas wells, a plot of reciprocal dimensionless pressure (1/p wd ) versus dimensionless cumulative production based on drainage area (Q DA ) will result in a straight line with an intercept of 1/2π during boundary dominated flow. 3 p wd and Q DA are defined as: 1 kh 1 pwd = [ m( pi ) m( pwf )]...(5) 1422 T q( t) T z [ ( ) ( ) = 4.5 igi m p i m p QDA...(6) φhapi [ m( pi ) m( pwf ) During the transient flow period the drawdown history can be used to estimate reservoir flow capacity and completion efficiency (analogous to a constant rate pressure transient test). The accuracy and frequency with which production and pressure data is gathered is the major limitation on the successful application of production analysis. Insufficient rate and pressure data through the transient period limits the accuracy of the analysis/interpretation and can lead to poor estimates of reservoir properties. If the bottomhole pressure is not measured directly with time, then we must estimate/calculate the bottomhole pressure profile from surface pressures utilizing multiphase flow correlations. A brief discussion of the correlations used for this study follows below. The accuracy of any bottomhole pressure calculation is dependent on the quality of the input data. The largest component of pressure drop in a well is normally the hydrostatic pressure constituent, which is dependent on oil, gas, and water specific gravities, as well as the ratios of each fluid phase relative to the other phases (GOR, WOR, GLR, etc). For multiphase flow, the pressure drop correlations develop their character from the manner in which the fluid density gradient is determined. The typical results from a number of standard correlations for oil and gas producers are shown in Figs. 1 and 2. These graphs depict the results of 16 flow correlations (refs. 4-22) which have been published in the literature. For reference, Brill 23 provides further discussion of these methods, their accuracy and applicability. For the purpose of this paper, the Hagedorn and Brown 16 correlation was used as the basis for simulation of the oil cases. This method was chosen because the Hagedorn and Brown method typically predicts pressure gradients that fall near the midrange value of the solutions offered by all of the pressure correlations. In other words, the Hagedorn and Brown method provides a consistent response of better than average accuracy. Using the Hagedorn and Brown method allows the effect of predicted pressures greater and less than the actual pressure to be evaluated with production analysis. For the gas case, the method proposed by Reinicke, et al. 21 was used. This method was developed for gas wells producing free water. Simulation Cases (Synthetic Performance) Three simulation cases were constructed and used as control sets to test the sensitivity of the production analysis results due to the errors introduced in the bottomhole pressure estimates from different multiphase flow correlations. In all cases the well is in the center of the simulation grid. The gas case uses a square simulation grid this case includes a hydraulic fracture. The oil cases (unfractured wells) are modeled using a radial grid. Table 1 presents the reservoir parameters common to all cases and Table 2 presents the specific parameters for each case. Simulation Case 1 Simulation case 1 is the case of a hydraulically-fractured well in a low permeability gas reservoir. The simulation model was initialized with a flow capacity of 2 md-ft and an in-place gas volume of 1,868 MMscf. For this case, the gas production rate was controlled by setting a maximum rate of 5,000 Mscf/D and a minimum flowing tubing pressure of 50 psia. The Reinicke, et al. multiphase flow correlation was used to construct the tubing performance curves for the simulation run. The water rate for this case was determined using a constant 10 Bbl/MMscf water-gas-ratio (WGR). Commercially available production analysis software was used to analyze the simulation results, which yielded estimates of the reservoir flow capacity and effective drainage volume of the well.

3 SPE Table 1 Model Parameters Parameter Value Unit Formation top, 10,000 ft Initial reservoir pressure 5,000 psia Average porosity 25 percent Net pay 40 ft Average water saturation 30 percent Reservoir temperature 225 F Water compressibility 3x10-6 1/psi Rock compressibility 4.6 x10-6 1/psi Water specific gravity 1.05 g/cc Oil case PVT properties: Oil gravity 32.7 API Solution GOR 350 Scf/Bbl Gas specific gravity 0.65 (air = 1) Bubblepoint pressure 2296 psia Gas case PVT properties: Gas specific gravity 0.65 (air = 1) Table 2 Case-Specific Parameters Case Value Unit Case 1 - Effective Permeability 0.05 md Case 1 - Fracture Half Length 200 ft Case 1 - Fracture Conductivity 500 md-ft Case 2 - Effective Permeability 0.05 md Case 3 - Effective Permeability 5 md The "rate-cumulative production" plotting technique was used to estimate the effective drainage volume for a given well. This technique was found to be very accurate as the resulting calculated volume was within 1 percent of the actual volume. The reservoir flow capacity was estimated to be 1.83 md-ft (using type-curve matching), where this result is within 10 percent of the actual value. Figures 3 and 4 present the "type curve" matches for this case. The flow rates and tubing pressures obtained from the simulation model were used to calculate the flowing bottomhole pressure responses for the well based on industry accepted multiphase flow correlations. Sixteen different correlations were used to estimate the flowing bottomhole pressure for the well. The new (bottomhole) pressure estimates were then used to estimate the flow capacity and effective drainage volume for the well. The production analysis results for each correlation are summarized in Table 3. Most of the correlations yielded acceptable errors in the estimate of flow capacity and in-place volumes. For the purposes of this work, an unacceptable error is considered to be an error in excess of 10 percent. Correlations resulting in greater than a 10 percent error in inplace volume were Baxendell 7, Chierici 10 and Poettmann 20. The Baxendell and Poettmann correlations which were developed primarily for use with oil wells resulted in errors in excess of 200 percent. These two correlations significantly over predicted flowing bottomhole pressures through the life of the well, and were found to have an increasing (pressure) slope after about one hundred days of production. Figure 5 compares the calculated bottomhole pressures to the actual bottomhole pressures for these three methods. As a result of over predicting the flowing bottomhole pressure, the flow capacity of the well is overestimated. In general, if the multiphase flow correlation overestimates the bottomhole pressure, then the estimated flow capacity will also be high. The slope of the flowing bottomhole pressure with time during boundary dominated flow controls the inplace volume estimate. An example of this would be the Kaya 17 correlation in Fig. 6. This correlation under predicts flowing pressures, which results in a large negative error in flow capacity, but this approach accurately predicts effective drainage volume. Table 3 Case 1: Tight Gas, Low Water Yield kh Error OGIP Error Correlation (md-ft) (percent) (Bscf) (percent) Simulation Ansari Aziz Baxendell Beggs Chierici Cornish Duns Fancher Gray Griffith Hagedorn Kaya Mukherjee Orkiszewski Poettmann Reinicke In Case 1 the impact of water yield was also explored to test sensitivity we increased the water yield to 50 Bbl/MMscf. Despite the increase in water, the calculated bottomhole pressures were similar to the previous evaluation as illustrated by Fig. 7. Simulation Case 2 Simulation case 2 is the case of an unfractured well in a low permeability oil case. The model was initialized with a flow capacity of 200 md-ft and for this case the oil production was controlled by setting a maximum oil rate of 500 Bopd and a minimum flowing tubing pressure of 50 psia. As noted earlier, the Hagedorn and Brown 16 multiphase flow correlation was used to construct the tubing performance curves for this simulation run. The drainage area was estimated from a plot of dimensionless rate versus dimensionless cumulative production as described earlier. Figure 8 illustrates the typical shape of the q Dd versus Q Dd plot and we note that the effective drainage area for the well can only be determined using production analysis after the well has reached boundary dominated flow. Boundary dominated flow was reached in this case after 48 days of production as evidenced by the vertical marker on the plot. We note an abrupt change in slope of the q Dd Q Dd plot after boundary dominated flow. It should be noted that for this case the flowing bottomhole pressure fell below the bubblepoint pressure near the end of the simulation run, which caused a gas accumulation in the near well region. This accumulation causes a change in the late time slope of the q Dd Q Dd plot. For this case, where the pressure declined below the bubblepoint pressure, the very late

4 4 SPE time data should not be used to estimate the drainage area for this well. We also note that, for this analysis, we assumed that the total system compressibility was a constant based on the initial pressure condition. This simplifying assumption introduced a slight error in the estimated drainage volume of the well the effective drainage volume based on the simulated bottomhole pressure was found to be 6.96 MMbls versus an actual value of 7.4 MMbls (i.e., the input volume) The flow capacity of the well was estimated from type curve matching the data in the transient flow period, again using a commercially available production analysis program. The reservoir flow capacity was found to be 208 md-ft or approximately 4 percent higher than the input value. The flow rates and tubing pressures from the simulation model were used to calculate flowing bottomhole pressure for this well, utilizing industry accepted multiphase flow correlations. As in Case 1, sixteen different multiphase correlations were considered in this work. The production analysis results for each correlation are summarized in Table 4. Table 4 Case 2: Low Permeability Oil Reservoir Correlation kh (md-ft) Error (percent) OOIP (MMstb) Error (percent) Simulation Ansari Aziz Baxendell Beggs Chierici Cornish Duns Fancher Gray Griffith Hagedorn Kaya Mukherjee Orkiszewski Poettmann Reinicke Most of the correlations resulted in unacceptable errors (> 10 percent) in the estimate of flow capacity and in-place volumes. Only the algorithms of Ansari and Fancher provided estimates of flow capacity that were within 10 percent error. Five correlations resulted in in-place fluid volume estimates which were within 10 percent of the input value. A performance review of the multiphase flow correlations provides some insight into these conclusions. The correlations depicted in Fig. 9 all yield a similar bottomhole pressure at a rate of 500 Bopd. Therefore the flow capacity determined by each of these methods should be (approximately) the same value. In Fig. 10, the slope of the bottomhole pressure versus flow rate at the point where boundary dominated flow is established controls the estimate of the in-place volume. Lines of constant slope were positioned over the three methods in this plot to illustrate this concept. Recall that the correlation presented by Hagedorn and Brown 16 was used to establish the results in the control model therefore, the slope (obviously) matches this method. The correlation of Chierici, et al. 9 exhibits a shallower slope, which results in a higher estimated in-place volume. Conversely, the Cornish 10 correlation exhibits a steeper slope, which results in a lower estimate for in-place volume. Figure 10 also illustrates the previous conclusion for flow capacity the Chierici, et al. correlation over predicts bottomhole pressure and also over predicts flow capacity, while the opposite is observed for the Cornish correlation. Simulation Case 3 Simulation case 3 represents the higher permeability oil case. The model was initialized with a flow capacity of 2,000 md-ft. For this case the oil production was controlled by setting a maximum oil rate of 1,500 Bopd and a minimum flowing tubing pressure of 50 psia. The Hagedorn and Brown 16 multiphase flow correlation was again used to construct the tubing performance curves for the simulation run. The drainage area was estimated from a plot of dimensionless rate versus dimensionless cumulative production (i.e., q Dd versus Q Dd ). The effective drainage area for the well can be determined from production analysis after the well has achieved boundary dominated flow. Boundary dominated flow was reached in this case after approximately 5 days of production (a product of the higher formation permeability) Since boundary dominated flow was reached in such a short time period, the pressures in the model remained relatively high and well above the bubblepoint pressure. Fig. 11 shows the bottomhole pressure versus rate performance for the16 multiphase flow correlations evaluated. In this case the results were in better agreement than the results observed in Case 2 because the primary flow regime in the tubing was single phase liquid. It should be noted that the flowing bottomhole pressure dropped below the bubblepoint pressure near the end of the simulation run, which as with the previous case, caused a gas accumulation in the near well region. This accumulation causes a change in the late time slope of the dimensionless rate versus dimensionless cumulative production plot which complicates the analysis of these data, as illustrated in Fig. 12. For this analysis we assumed that the total system compressibility was constant, evaluated at the initial pressure condition. As with Case 2, this assumption caused a slight error in the estimated drainage volume of the well. The effective drainage volume based on the simulated bottomhole pressure was found to be 6.96 MMbls versus an input value of 7.4 MMbls. The flow capacity of the well was estimated from type curve matching the data in the transient flow period using a commercially available production analysis program. The reservoir flow capacity was found to be 1,990 md-ft which is slightly lower than the input value. The production analysis results for each correlation are summarized in Table 5. Seven of the correlations resulted in unacceptable errors in the estimate of flow capacity for this case (i.e., errors > 10 percent). The errors were somewhat less than those found in the low permeability oil case. The Aziz 5 and Griffith 15 correlations yielded the highest errors in flow capacity for this case. Both of these correlations over predict pressures at early times, which results in an over prediction of flow capacity.

5 SPE Half of the correlations resulted in unacceptable error in the estimate of in-place volume. Table 5 Case 3: High Permeability Oil Reservoir Correlation kh (md-ft) Error (percent) OOIP (MMstb) Error (percent) Simulation Ansari Aziz Baxendell Beggs Chierici Cornish Duns Fancher Gray Griffith Hagedorn Kaya Mukherjee Orkiszewski Poettmann Reinicke Field Example 1 This well is producing from a sandstone reservoir at a depth of 15,000 ft with an average porosity of 9 percent, water saturation of 35 percent, and net pay of 100 ft. The initial reservoir pressure was 5000 psia. The well was fracture stimulated upon initial completion, and had an initial production rate of approximately 3.0 MMscf/D of wet gas and 120 Bw/D. Typical permeability values for this reservoir range from 0.01 md to 0.1 md. No measured bottomhole pressures exist for this well. Twophase flow correlations were used to estimate the flowing bottomhole pressure profile for this case and, due to the condensate and water production from the well, the pressure correlations resulted in a large variations in the estimated bottomhole pressures. These results are shown in Fig. 13. The effective gas permeability obtained using production analysis for this case ranged from a low of 0.03 md to 0.2 md where these values lie with the generally expected range of permeabilities for this reservoir. The effective fracture half length ranged from a low of 18 ft for the high permeability interpretation to a high of 289 ft for the low permeability interpretation. The effective drainage volume obtained from the normalized pressure plot averaged 1.5 Bscf over all of the correlations. The results for each correlation are summarized in Table 6. Field Example 2 This well is producing from a sandstone reservoir at a depth of 12,000 ft with an average porosity of 12 percent, water saturation of 35 percent, and net pay of 34 ft. The initial reservoir pressure was 4900 psia. The well had an initial production rate of approximately 350 Bopd, with a gas oil ration of 1100 scf/bo. As with the previous field case, no measured bottomhole pressures exist for this well. Table 6 Field Example 1: Tight Gas Correlation kh (md-ft) OGIP (Bscf) Aziz Baxendell Beggs Chierici Cornish Duns Fancher Gray Griffith Hagedorn Mukherjee Orkiszewski Poettmann Reinicke Multiphase flow correlations were used to estimate the flowing bottomhole pressure profile for the well. Figure 14 illustrates the range of flowing bottomhole pressures calculated for the well. The effective gas permeability obtained from production analysis for this well ranged from a low of 4.5 md to 7.1 md, with and average of 5.6 md. The effective drainage volume obtained from the normalized pressure plot ranged from 1.34 MMbo to 2.91 MMbo and averaged 1.5 Bscf considering all correlations. The results for each correlation are summarized in Table 7. Table 7 Field Example 2: Low Permeability Oil Correlation kh (md-ft) OOIP (MMstb) Aziz Baxendell Beggs Chierici Cornish Duns Fancher Gray Griffith Hagedorn Mukherjee Orkiszewski Poettmann Reinicke Observations and Conclusions 1. Multiphase flow correlations that over predict flowing bottomhole pressure also over predict flow capacity. The converse is true for methods that under predict bottomhole pressure. 2. The slope of the bottomhole pressure versus rate relationship for a multiphase flow correlation is related to the calculated in-place volume during boundary dominated flow. Slopes which are too high result in under prediction of in-place fluid volume, while slopes which are too low result in over prediction of in-place fluid volume. 3. For tight gas reservoirs, the drawdown in the system is very high therefore, any errors in the calculated bottomhole pressure have less effect on the flow capacity estimate. The bottomhole pressure versus rate

6 6 SPE relationship remains important for the correct determination of in-place volume. 4. The limitations of multiphase flow correlations need to be recognized so that these correlations can be used properly. Accurate production rates and pressures must be recorded, as errors in the rates and pressures affect the material balance of the system, as well as estimates of bottomhole pressure obtained from correlations. Periodic flowing pressure surveys are recommended to ensure that the pressure correlations are properly calibrated. In the absence of (measured) pressure surveys, the authors offer the following recommendations for computing/estimating flowing bottomhole pressures using multiphase flow correlations: Gas Wells Reinicke, Remer, Hueni Gray Hagedorn and Brown Cornish Oil Wells Hagedorn and Brown Duns and Ros Beggs and Brill Orkiszewski Kaya These recommendations are offered only as a guide we believe that it is helpful to examine the results using several methods in order to determine a range of uncertainty. Acknowledgments We thank the management of Marathon Oil Company for permission to print this article. Acknowledgment is due to various colleagues for providing production data for the field cases. Nomenclature A = drainage area, ft² B o = oil formation volume factor, RB/STB c t = total compressibility, psi -1 G = original gas in place, Mscf h = reservoir thickness, ft k = effective permeability to gas, md mp ( ) = real gas pseudo pressure, psi 2 /cp Δm( p) = mp ( i ) mp ( ), psi 2 /cp N p = cumulative oil production, bbl = bottomhole producing pressure, psia p wf p = average reservoir pressure, psia p i = initial reservoir pressure, psia p wd = dimensionless wellbore pressure q o = oil production rate B/D q() t = flow rate, Mscf/D Q DA = dimensionless cumulative production based on area r e = outer radius, ft r wa = effective radius, ft T = reservoir temperature, R t a = equivalent time gas, days t e z i = equivalent time oil, days = gas compressibility factor at p i φ = porosity, fraction μ = viscosity, cp π = Subscripts i = initial g = gas References 1. Arps, J.J. : "Analysis of Decline Curves", Trans., AIME (1945) 160, Palacio, J.C. and Blasingame, T.A.: "Decline-Curve Analysis Using Type Curves Analysis of Gas Well Performance Data," paper SPE presented at the 1993 Rocky Mountain Regional Meeting/Low Permeability Reservoirs Symposium and Exhibition, Denver, April. 3. Agarwal, R.G., Gardner, D.C., Kleinsteiber, S.W. and Fussell, D.D.: "Analyzing Well Production Data Using Combined-Type-Curve and Decline-Curve Analysis Concepts," SPEREE (October 1999) Ansari, A.M., Sylvester, N.D., Shoham, O., and Brill, J.P.: "A Comprehensive Mechanistic Model for Upward Two- Phase Flow in Wellbores," paper SPE presented at the 65 th Annual Technical Conference and Exhibition, New Orleans, LA (Sept , 1990). 5. Aziz, K.: Ways to Calculate Gas Flow and Static Head, Handbook Reprint from Pet. Eng., Dallas, TX (1963). 6. Aziz, K., Govier, G.W., and Fogarasi, M.: "Pressure Drop in Wells Producing Oil and Gas," J. Cdn. Pet. Tech. (July-Sept., 1972) Baxendell, P.B. and Thomas, R.: "The Calculation of Pressure Gradients in High-Rate Flowing Wells," J. Pet. Tech. (Oct., 1961) Brill, J.P. and Mukherjee, H.: Multiphase Flow in Wells, Monograph 17, SPE, Richardson, TX (1999). 9. Chierici, G.L., Ciucci, G.M. and Sclocchi, M.: "Two-Phase Vertical Flow in Oil Wells - Prediction of Pressure Drop," J. Pet. Tech. (Aug., 1974) Cornish, R.E.: "The Vertical Multiphase Flow of Oil and Gas at High Rates," J. Pet. Tech. (July, 1976) Cullender, M.H. and Smith, R.V.: "Practical Solution of Gas-Flow Equations for Wells and Pipelines with Large Temperature Gradients," Trans. AIME (1956) Vol. 207, Duns, H., Jr. and Ros, N.C.J.: "Vertical Flow of Gas and Liquid Mixtures in Wells," Proc., 6th World Petroleum Congress, Section II (1963) Fancher, G.H., Jr. and Brown, K.E.: "Prediction of Pressure Gradients for Multiphase Flow in Tubing," Soc. Pet. Eng. J. (March, 1963) Gray, H.E.: "Vertical Flow Correlation - Gas Wells," User Manual for API 14B, Subsurface Controlled Safety Valve Sizing Computer Program, App. B (Jan., 1978) Griffith, P., Lau, C.W., Hon, P.C., and Pearson, J.F.: "Two Phase Pressure Drop in Inclined and Vertical Pipes," Tech. Report No , Mass. Inst. Technol. (Aug., 1973). 16. Hagedorn, A.R. and Brown, K.E.: "Experimental Study of Pressure Gradients Occurring During Continuous

7 SPE Two-Phase Flow in Small-Diameter Vertical Conduits," J. Pet. Tech. (April, 1965) Kaya, A.S., Sarica, C., and Brill, J.P.: "Mechanistic Modeling of Two-Phase Flow in Deviated Wells," SPE Production and Facilities, (Aug., 2001) Mukherjee, H. and Brill, J.P.: "Liquid Holdup Correlations for Inclined Two-Phase Flow," J. Pet. Tech. (May, 1983) Orkiszewski, J.: "Predicting Two-Phase Pressure Drops in Vertical Pipe," J. Pet. Tech. (June, 1967) Poettmann, F.H. and Carpenter, P.G.: "The Multiphase Flow of Gas, Oil, and Water Through Vertical Flow Strings with Application to the Design of Gas Lift Installations," Drill. and Prod. Prac., API (1952) Reinicke, K.M., Remer, R.J., and Hueni, G.: "Comparison of Measured and Predicted Pressure Drops in Tubing for High-Water-Cut Gas Wells," paper SPE presented at the 59th Annual Technical Conference and Exhibition, Houston, TX (Sept , 1984). 22. Ros, N.C.J.: "Simultaneous Flow of Gas and Liquid as Encountered in Well Tubing," J. Pet. Tech. (Oct., 1961) Beggs, H.D. and Brill, J.P.: "A Study of Two-Phase Flow in Inclined Pipes," J. Pet. Tech. (May, 1973)

8 8 SPE Fig. 1 Multiphase Flow Correlations Oil Fig. 2 Multiphase flow correlations gas Infinite Conductivity Fracture in 1 to 1 Rectangular Boundary at 1 year Match Simulation Kh = 1.83 md-ft, 2.0 md-ft X f = 209 ft, 200 ft Area= 40 Acres, 40 Acres Effective Drainage Area 40 Acres Actual Analytical PwD or PwD' t DA Actual PwD Actual PwD' Analytical PwD Analytical PwD' 1/PwD Q DA Fig. 3 Sim. Case 1 - Type-curve match Fig. 4 Sim. Case 1 Rate Cumulative Decline Curve

9 SPE Simulation Baxendell & Poettman Chierici 4000 Simulation KAYA Bottomhole Pressure, Psia Bottomhole Pressure, Psia Time, Days Time, Days Fig. 5 Sim. Case 1 Multiphase Flow Correlation Comparison Fig. 6 Sim. Case 1 - Multiphase flow Correlation Comparison 2 Match Simulation Volume 6.96, 7.4 MMbo Time to BDF 1.5 q Dd Q Dd Fig. 7 Sim. Case 1 - Water rate sensitivity comparison Fig. 8 Sim. Case 2 - Normalized rate/cumulative production

10 10 SPE Fig. 9 Sim. Case 2 - Correlation comparison early time Fig. 10 Sim. Case 2 - Correlation comparison late time 2 Match Simulation Volume 6.96, 7.4 MMbo Time to BDF 1.5 q Dd Q Dd Fig. 11 Sim. Case 3 Correlation comparison Fig. 12 Sim. Case 3 - Normalized rate vs. comumulative production

11 SPE AZIZ ORKISZEWSKI REINICKE CHIERICI CORNISH FANCHER Bottomhole Pressure, Psia Bottomhole Pressure, Psia Time, Days Time, Days Fig. 13 Field Case 1 -- Calculated Bottomhole Pressures Fig. 14 Field Case 2 Calculated Bottomhole Pressures