Journal of Petroleum Science and Engineering

Journal of Petroleum Science and Engineering 67 (2009) 97 104 Contents lists available at ScienceDirect Journal of Petroleum Science and Engineering journal homepage: www.elsevier.com/locate/petrol Research paper A general approach for deliverability calculations of gas wells Hazim Al-Attar, Sulaiman Al-Zuhair Department of Chemical and Petroleum Engineering Department, UAE University, 17555 Al-Ain, United Arab Emirates article info abstract Article history: Received 2 September 2007 Accepted 14 May 2009 Keywords: gas deliverability test well dimensionless IPR performance This paper presents a general and a simplified method for deliverability calculations of gas wells, which among other advantages, eliminates the need for conventional multipoint tests. The analytical solution to the diffusivity equation for real gas flow under stabilized or pseudo-steady-state flow conditions and a wide range of rock and fluid properties are used to generate an empirical correlation for calculating gas well deliverability. The rock, fluid and system properties, used in developing previous correlations found in literature, were limited to reservoir pressure, reservoir temperature, gas specific gravity, reservoir permeability, wellbore radius, well drainage area, and shape factor. Additional key properties such as reservoir porosity, net formation thickness and skin factor are included in this work to develop a more general dimensionless Inflow Performance Relationship (IPR). It is found that the general correlation, developed is this study, presents the observed field data much closer than previous ones found in the literature. In addition, based on the larger data set, an empirical relation to predict future deliverability from current flow test data is also developed. The two modified and general relations developed in this work provide a simple procedure for gas deliverability calculations which greatly simplifies the conventional deliverability testing methods. The required data can be obtained from a buildup test, or a single-point flow test, instead of an elaborate multipoint flow test. Further, the broad range of practically all rock and fluid properties used in developing the modified dimensionless IPR curves should cover the majority of the field situations generally encountered. The use of the modified dimensionless IPR curves, the pseudopressure formulation and the sensitivity analysis indicate a generality of the approach presented in this paper, irrespective of the gas reservoir system under study. 2009 Elsevier B.V. All rights reserved. 1. Introduction Predicting the performance of a gas well is a process that has almost exclusively relied on using some form of multipoint well-testing procedure. The conventional back-pressure test or flow-after-flow test (Rawlins and Schellhardt, 1936), the isochronal test (Cullender, 1955), and the modified isochronal test (Katz et al., 1959) have been employed to predict the short- and long-term stabilized deliverability of gas wells. Typically, a well is produced at a minimum of four different flow rates, and the pressure-rate time response is recorded. Plotting the bottom hole pressure versus flow rate data obtained from the test, on log log paper, produces a straight line that reflects the stabilized deliverability of the well. The stabilized deliverability of a well may be defined as its ability to produce against a given back-pressure at a given stage of reservoir depletion. The empirically derived relationship given by Eq. (1) represents the equation of the stabilized deliverability curve. q = C P 2 r P 2 n wf ð1þ where, q is current gas flow rate, P r and P wf are current average reservoir pressure and bottom hole flowing pressure, respectively, and Corresponding author. Tel.: +971 33040; fax: +971 37624262. E-mail address: Hazim.Alattar@uaeu.ac.ae (H. Al-Attar). C and n are constants. The constant C reflects the position of the stabilized deliverability curve on the log log plot. The constant n represents the reciprocal of the slope of the stabilized deliverability curve and normally has a value between 0.5 and 1.0. The time to stabilization, t s, given by Eq. (2), can become very large when testing tight gas reservoirs. t s = 948 u μ c tr 2 e ð2þ k where, ϕ is porosity, μ is gas viscosity, c t is total system compressibility, r e is drainage area radius, and k is reservoir permeability. The stabilized deliverability curve, or the correlation derived from it, may be used to predict the inflow performance relationship (IPR) of a gas well and its absolute open flow potential (AOFP). The AOFP represents the theoretical maximum flow rate the well can sustain against a zero sandface back-pressure, P wf and is used mainly in wells comparisons. Properly conducted in the field, multipoint back-pressure tests yield very reliable deliverability projections. However, four-point tests are usually highly time-consuming and expensive, particularly in the case of low permeability reservoirs or where offshore rig time is involved. Brar and Aziz (1978) proposed methods for analyzing modified isochronal tests to predict the stabilized deliverability of gas wells using unstabilized flow data. Their methods, however, still require running a minimum of four flow tests on a well. 0920-4105/$ see front matter 2009 Elsevier B.V. All rights reserved. doi:10.1016/j.petrol.2009.05.003

98 H. Al-Attar, S. Al-Zuhair / Journal of Petroleum Science and Engineering 67 (2009) 97 104 Table 1 Rock, fluid and system properties used in developing correlations. Parameter and symbol Values ranges Units Reservoir pressure (P) 1000 a 8000 psia Reservoir temperature (T) 100 300 a F Gas gravity (γ) 0.5 a 1.0 Air=1 Reservoir permeability (k) 1 1000 (500 a ) md Wellbore radius(r w ) 0.25 a 0.5 ft Drainage area (A) 640 a 2640 acres Shape factor (C A ) 5.379 31.62 a dimensionless Porosity (φ) 0.1 0.3 (0.15 a ) fraction Net formation thickness (h) 20 500 a ft Mechanical skin factor (s) ( 6.0) ( 2.0 a ) dimensionless a Base case for sensitivity analysis. Mishra and Caudle (1984) developed a single dimensionless IPR curve for predicting the IPR of an unfractuned gas well at current conditions using a single-flow test. Their equation, given as a ratio of the current gas flow rate, q, to the current AOFP, q max, is shown in Eq. (3). q = 5 q max 4 1 5 h i! mðp wf Þ mp ð r Þ 1 where m(p) is the real gas pseudopressure, give by 2 (P/μz)dP. In addition, Mishra and Caudle (1984) proposed a second dimensionless curve to assist in the prediction of future performance. From this curve a correlation Eq. (4) is derived to predict the AOFP of a well from the future dimensionless IPR at some future average reservoir pressure. q max;f = 5 q max;i 3 1 0:4 ½ m ð P r; f Þ= mðp r;i ÞŠ ð3þ ð4þ where the subscripts f and i are future and initial conditions, respectively. Chase and Anthony (1988) demonstrated that the curves presented by Mishra and Caudle (1984) and their respective equations could also be used to predict the performance of some fractured gas wells. They also showed that for average reservoir pressures less than approximately 2000 psi (13.8 MPa), pressure-squared values could be substituted for pseudopressures, whereas for pressures above 2000 psi (13.8 MPa), the pseudopressures must be used. Equations (3) and (4), however, do not account for variation in skin factors, nor do they account for the presence of a hydraulically induced fracture. As opposed to using conventional four-point testing methods, Chase and Alkandari (1993) developed a method for predicting the deliverability of a fractured gas well using the average reservoir pressure, P r,the flowing bottom hole pressure, P wf, the stabilized flow rate, q, and either the ratio of radiuses of external boundary, x e to uniform fluracture,, or the skin factor, s, obtained from the analysis of a pressure buildup or drawdown test. They proposed the following general dimensionless IPR to predict the inflow performance of gas wells. Y =1 MX N where, Y = P pðp wf Þ P p ðp r Þ q X = x e q max; @ x e xf =1 = ð0:37x e Þe s = r w ð8þ logðmþ =0:004865 + 0:143121 log x e 0:00989 log x 2 e ð9þ 3 +0:00039 log x e logðnþ =0:296498 + 0:106181 log x e 0:0004278 log x e +0:00874 log x 2 e ð5þ ð6þ ð7þ ð10þ 3 In Eq. (6), P p (p) represents the real gas pseudopressure, give by 2 (P/μz)dP, similar to m(p) in Eqs. (3) and (4). Chase and Alkandari (1993) tested their dimensionless IPR against data from eight wells presented in the work of Brar and Aziz (1978) and found that the computed AOFP values compared favorably to those obtained from the modified isochronal method, with a maximum error of 15%. In addition, they reported that the skin factor, of either a fractured or unfractured well, can be converted to an x e / ratio using the apparent wellbore radius concept and that their new dimensionless IPR curve correlation can be then used to predict the performance of the well. Kamath (2007) outlined the five steps to predict deliverability loss caused by condensate banking. These steps are: (1) appropriate laboratory measurements, (2) fitting laboratory data to relative permeability models, (3) use of spreadsheet tools, (4) single-well models, and (5) full-field models (FFMs). He concluded that continued extensive testing of existing relative permeability models and more measurements in the high gas to oil relative permeabilities, k rg /k ro,and capillary-number region increases the confidence in the predictions. The present study expands upon the work of Mishra and Caudle (1984) to develop more accurate dimensionless IPR curves for stabilized Fig. 1. New dimensionless IPR for current conditions basic data. Fig. 2. Sensitivity analysis effect of pressure.

H. Al-Attar, S. Al-Zuhair / Journal of Petroleum Science and Engineering 67 (2009) 97 104 99 Fig. 3. Sensitivity analysis effect of temperature. Fig. 5. Sensitivity analysis effect of permeability. non-darcy flow in unfactured gas reservoirs. The rock, fluid and system properties, used in developing the correlations of Mishra and Caudle (1984), were limited to reservoir pressure, reservoir temperature, gas specific gravity, reservoir permeability, wellbore radius, well drainage area, and shape factor. Additional key properties such as reservoir porosity, formation thickness and skin factor are included in this work to develop a rather simple, accurate, and more general (IPR) that can be used as an alternative to the elaborate multipoint testing methods. 2. Development of new dimensionless IPR curves 2.1. Basic assumptions (i) A homogeneous, isotropic, unfractured reservoir with a closed outer boundary. (ii) A single, fully penetrating well. (iii) Stabilized conditions prevail, i.e. pseudo-steady state equations can be used to describe gas flow in the reservoir. (iv) Turbulent flow effects are characterized by a constant turbulence factor, D, and a rate dependant skin Dq. Under these conditions, the equation describing gas flow in a porous medium is given by Eq. (11). P p ðp r Þ P p ðp wf Þ = aq + bq 2 ð11þ 1637ðT = khþ a = log A = rw 2 + log ð 2:2458 = CA Þ +0:87s ð12þ b = 1422 TD kh D =2:715 10 15 βkmpsc hμ @Pwf β =1:88 10 10 k 1:47 u 0:53 ð13þ ð14þ ð15þ where, A is drainage area, T is reservoir temperature, C A is shape factor, h is net formation thickness, M is molecular weight of gas, P sc is standard pressure, μ @Pwf is gas viscosity measured at bottom hole flowing pressure (P wf ), r w is wellbore radius, and T sc is temperature at standard conditions. 2.2. Development of functional relationships for current and future well deliverability Solving Eq. (11) and taking the positive root to be q, yields: h i a + a 2 0:5 +4b P p ðp r Þ P p ðp wf Þ q = 2b ð16þ and, q max = AOFPðP wf =0Þ = h i a + a 2 0:5 +4bP p ðp r Þ 2b ð17þ Dividing Eq. (16) by Eq. (17) yields the following expression: q q max = h i a + a 2 0:5 +4b P p ðp r Þ P p ðp wf Þ h i 0:5 ð18þ a + a 2 +4bP p ðp r Þ The left-hand side of Eq. (18) is dimensionless and similar to the one derived by Vogel (1968) for gas drive reservoirs, but for s 0; where, Fig. 4. Sensitivity analysis effect of gas gravity. sv= s + Dq ð19þ

100 H. Al-Attar, S. Al-Zuhair / Journal of Petroleum Science and Engineering 67 (2009) 97 104 Eq. (18) can be rearranged to the following form: q = H P p P! ð wfþ q max P p ðp r Þ ð20þ where, H is some functional form (Mishra and Caudle, 1984). The objective therefore would be to generate the dimensionless groups (q/q max ) and (P p (P wf )/P p (P r )) from a variety of cases and develop an empirical correlation in the form of Eq. (20). This will then be the IPR for Current Deliverability. Designating future and current conditions by the subscripts f and c, respectively, Eq. (17) can be rewritten as, h i a + a 2 0:5 +4bP p P r;f q max;f = 2b ð21þ Thus, q max;f q max;c = h i a + a 2 0:5 +4bP p P r;f h i 0:5 ð22þ a + a 2 +4bP p P r;c Similar to Eq. (20), Eq. (22) can be rearranged to the following form: q max;f q max;c 0 = I@ P p P p P r;f P r;c 1 A ð23þ where I is some other functional form (Mishra and Caudle, 1984). The objective here would be to generate the dimensionless groups (q max, f /q max, c ) and (P p (P r,f )/P p (P r,c )) and develop a second empirical relation of the form of Eq. (23). This will then be the IPR for Future Deliverability. 2.3. Programming considerations Excel spreadsheet was used and a computer program was written in MATLAB software to perform four basic objectives. (i) Generate a database of pseudopressures and pressure for a broad range of temperatures and gas specific gravities using Excel spreadsheet. Fig. 7. Sensitivity analysis effect of drainage area. (ii) Generate a database of (q/q max ) and (P p (P wf )/P p (P r )) for a broad range of rock and fluid properties using MATLAB program, as given in Table 1. (iii) Evaluate the effects of changing rock and fluid properties, over the range given in Table 1, on a dimensionless IPR generated for a base case. The properties of the base case are highlighted in Table 1. (iv) Using the same conditions as in Eq. (2) to generate a data base of (q max, f /q max, c ) and (P p (P r,f )/P p (P r,c )). Correlations used in this program were: Lee et al. (1966) for gas viscosity, Smith et al. (2001) for gas deviation factor, and Swift and Kiel (1962) and Katz and Cornell (1955) for turbulence factor. 2.4. Development of general dimensionless IPRs and sensitivity analysis Employing the rock, fluid and system properties listed in Table 1, a set of 25,344 data points-pairs of (q/q max ) and (P p (P wf )/P p (P r )) was generated for all combinations of the variables investigated. The number of data points generated in this study is almost 2.5 times more than the 10,206 data points generated by Mishra and Caudle (1984).A strong trend of the data plot is observed as shown in Fig. 1. The data points were best fit by the sixth order polynomial given in Eq. (24) Fig. 6. Sensitivity analysis effect of wellbore radius. Fig. 8. Sensitivity analysis effect of porosity.

H. Al-Attar, S. Al-Zuhair / Journal of Petroleum Science and Engineering 67 (2009) 97 104 101 Fig. 9. Sensitivity analysis effect of net thickness. Fig. 11. Sensitivity analysis effect of shape factor. using Excel with R 2 value of 0.984, which indicates good presentation of the experimental data. Y = 0:7193 X 6 +0:6221 X 5 +0:3037 X 4 0:6108 X 3 +0:0756 X 2 0:6712 X +1:0006 where in Eq. (24), Y = q = q max ð24þ ð25þ to the correlation developed in this work, Eq. (24), over that developed by Mishra and Caudle, especially when considering wide range of skin effects. Based on the seven pressure levels used in developing Eq. (24), a data set comprising of 25,344 points of (q max, f /q max, c ) and (P p (P r,f )/P p (P r,c )) was generated and plotted as shown in Fig. 12. The data points were best fit by the sixth order polynomial given in Eq. (27) using Excel with R 2 value of 0.975, which also indicates good presentation of the experimental data. and, X = P p ðp wf Þ= P p ðp r Þ ð26þ Y =10:436 X 6 31:143 X 5 +33:876 X 4 15:374 X 3 +1:4779 X 2 +1:7044 X +0:0234 ð27þ Eq. (24) represents a modified general dimensionless IPR which can be used for calculating current gas deliverability. To study the effect of the variables listed in Table 1 on Eq. (24), a base case was selected for sensitivity analysis with respect to the properties given in Table 1. Each of the variables was varied over a range and the results are shown in Figs. 2 11. Among the ten variables considered in this study, only reservoir pressure, permeability, and skin factor were found to have significant effect on the dimensionless IPR. Similar observations were reported by Mishra and Caudle (1984), however, the skin effect was not accounted for. This gives superiority Where in Eq. (27), Y = q max;f = q max;c and, X=P p ðp r;f Þ=P p ð Pr;c Þ ð28þ ð29þ Eq. (27) represents a modified general dimensionless IPR which can be used for calculating future gas deliverability. As previously Fig. 10. Sensitivity analysis effect of skin factor. Fig. 12. New dimensionless IPR for future conditions basic data.

102 H. Al-Attar, S. Al-Zuhair / Journal of Petroleum Science and Engineering 67 (2009) 97 104 Table 2 Comparison of AOFP values (MMScf/D) estimated from multipoint and single-point tests. Wells Modified isochronal model Eq. (24) using P p Eq. (24) using P 2 Mishra and Caudle [5] Mishra and Caudle [5] using P 2 Chase and Alkandari [7] Wells presented by Brar and Aziz [1978] 1 2.128 1.607 1.983 1.481 1.424 1.895 2 2.289 2.253 2.380 2.052 2.191 2.237 3 2.391 2.064 2.210 1.896 2.118 2.417 4 5.340 5.255 5.278 4.880 4.904 5.200 5 6.847 6.825 6.821 6.326 6.324 7.012 6 17.296 17.995 17.000 17.406 15.903 15.412 7 20.005 20.388 19.316 19.206 18.060 22.137 8 184.167 213.074 196.040 207.870 188.548 202.987 Wells presented by Chase and Anthony [1988] 9 10.988 11.410 11.168 10.526 10.335 Unpublished data-fractured reservoir in the Middle East 10 135 137.94 128.978 129.316 121.040 11 130 126.64 117.269 124.70 115.435 12 40 38.38 37.175 35.198 34.225 13 50 47.88 45.938 44.183 42.392 14 22 18.99 18.220 17.513 16.805 15 50 48.02 46.200 43.950 42.460 Table 3 Associated error percent of AOFP values calculated by different models (Table 2). Well Eq. (24) Eq. (24) using P 2 Mishra and Caudle [5] Mishra and Caudle [5] Chase and Alkandari [7] Wells presented by Brar and Aziz [4] 1 24.483 6.814 30.404 33.083 10.95 2 1.558 +3.976 10.354 4.281 2.27 3 13.676 7.570 20.703 11.418 +1.09 4 1.592 1.161 8.614 8.165 2.62 5 0.321 0.380 7.609 7.638 +2.41 6 +4.042 1.711 +0.636 8.054 10.89 7 +1.915 3.444 3.994 9.698 +10.66 8 +15.696 +6.447 +12.870 +2.379 +10.22 Well presented by Chase and Anthony [6] 9 +3.84 +1.64 4.205 5.945 Unpublished data-fractured reservoir in the Middle East 10 + 2.178 4.461 4.210 10.341 11 2.585 9.793 4.077 11.204 12 4.050 7.063 12.005 14.438 13 4.240 8.124 11.634 15.216 14 13.682 17.182 20.395 23.614 15 3.960 7.600 12.100 15.080 mentioned, the corresponding correlation of Mishra and Caudle (1984) in this case is Eq. (4). 3. Evaluation of the new dimensionless IPR equation for current reservoir pressure The following published and unpublished field data are used to evaluate the new general correlations, Eqs. (24) and (27), against the previous correlations of Mishra and Caudle (1984) and Chase and Alkandari (1993). In addition, the ratio of (P p (P wf )/P p (P r )) was replaced with (P 2 wf /P 2 r ) to measure how close the squared-pressure approximation could represent the real gas pseudopressure. A comparison of the AOFP values calculated by the present technique and the existing methods versus field data is shown in Table 2 and Fig. 13. The associated percentage errors of this comparison are shown in Table 3. (i) The paper by Brar and Aziz (1978) contains results of both deliverability tests and pressure buildup or drawdown tests of eight gas wells that cover a spectrum of different reservoir conditions. (ii) The paper by Chase and Anthony (1988) contains complete deliverability test data from a single gas well. (iii) Unpublished modified isochronal test data of six gas wells completed in a fractured reservoir located in the Middle East. 4. Predicting the future performance of a gas well Mishra and Caudle (1984) proposed a future dimensionless IPR curve that can be used to find q max,f or the AOFP at some future P r. However, same as for their current conditions IPR curve, the curve AOFP developed did not take into account skin factor, porosity and net formation thickness. Nevertheless, their correlation was tested against twenty back-pressure tests of dry gas reservoirs and the results compared favorably with the field data. In order to evaluate the new AOFP correlation developed in this study, the calculations of future AOFP values by Eq. (27) are compared to those predicted using Eq. (4) at two Fig. 13. Broad comparison of new IPR model Eq. (24) with existing methods.

H. Al-Attar, S. Al-Zuhair / Journal of Petroleum Science and Engineering 67 (2009) 97 104 103 Table 4 Comparison of future AOFP calculation by the new IPR (Eq. (27)) and the Mishra and Caudle model [5] (Eq. (4)). Future reservoir pressure (psia) different future reservoir pressures, 1600 psia [11.04 MPa] and 1150 psia [7.935 MPa], respectively, and the results are shown in Table 4. 5. Discussion of results Pseudopressure ratio P p (P r,f )/P p (P r,c ) Estimated future AOFP (MMScf/D) using Eq. (4) 1600 0.706 7.23 7.28 1155 0.532 4.77 4.75 Estimated future AOFP (MMScf/D) using Eq. (27) In this work, an attempt to extend the work of Mishra and Caudle (1984) is done by accounting for additional key properties that characterize individual wells. These properties include the skin factor, porosity and net formation thickness. Including these variables resulted in the derivation of two new dimensionless Vogel (1968) type IPR models for current and future reservoir pressure conditions, respectively. The new IPR curve shown in Fig. 1 and expressed in Eq. (24) for current reservoir pressure seems to have significantly improved the computation of AOFP from a single-point test. Table 2 summarizes the data of the eight well tests presented in the paper of Brar and Aziz (1978), a single-well test in the paper of Chase and Anthony (1988), and six well tests from unpublished source in the Middle East. Also shown in Table 2 is a comparison between the AOFP values computed by the new model, Eq. (24), the new model using P 2 -approximation, Mishra Caudle model, Eq. (4), Mishra Caudle model using P 2 -approximation, and Chase Alkardani model, respectively, versus field modified isochronal tests. Within the first eight wells presented by Brar and Aziz (1978), and assuming the modified isochronal method is correct, the predicted values of AOFP by the five models in Table 2 are mostly of acceptable accuracy from a practical stand point. Nevertheless, the new IPR model presented in this work, Eq. (24), more accurately predicted AOFP values in six out of eight wells in comparison with Mishra Caudle model (1984) and in five out of eight wells in comparison to Chase Alkandari model (1993). This superiority is also reflected on the percentage errors shown in Table 3. Five out of eight wells have percentage errors less than 5%, while the maximum error observed is 24.48% for well number 1. On the other hand, using Mishra and Caudle (1984) model, the percentage errors of only two out of the eight wells is less than 5% and the maximum error observed is 30.4% for well number 1. Similarly, with the Chase and Alkandri (1993) model, the percentage errors of four wells out of eight is less than 5% and the maximum error observed was 10.95% for well number 1. The divergence in predicted AOFP values for the wells of low permeability, namely 1 and 8, is partly attributed to the fact that the back-pressure data of these wells is probably from the transient flow period, whereas the new model developed in this work, the Mishra Caudle (1984) model and the Chase Alkandari (1993) model, all assume stabilized flow. Another reason, which may have played a role in causing this divergence in the predicted AOFP values, is relying on assumed values of significant information, such as the gas gravity and composition, required in the calculations of the pseudopressures, due to the absence of this information in Brar and Aziz (1978) paper. On the other hand, Chase and Alkandari (1993) model shows a better accuracy in predicting the AOFP of well number 3, which happens to have a relatively high positive skin factor of +7.8. This high value of skin factor is outside the range considered in developing Eq. (24), and that may explain the superiority of Chase and Alkandari (1993) model for this case. Chase and Anthony (1988) pointed out that pressure-squared values can be substituted for pseudopressures in the dimensionless IPR graphs and equations, such as those developed by Mishra and Caudle (1984) and in the present work. However, this simplification is limited to values of the average reservoir pressure, or static bottom hole for a gas well, less than 2000 psi [13.8 MPa]. For average reservoir pressures above 2000 psi, pseudopressure must be used in the process of constructing IPR curves from the dimensionless plots. To further evaluate Eq. (24), it was used with pressure-squared method to predict current AOFP values. The percentage errors shown in Table 3 shows that five out of eight wells has errors less than 5% with maximum error observed for well number 3 of 7.57%. The predictions of Mishra and Caudle model using the pressure-squared approximation was also used in the comparison. The results show that only two out of eight wells have percentage errors less than 5% and maximum error of 33.08% is observed in well number 1. The results of this part are consistent with the Chase and Anthony's (1988) conclusion, regarding the applicability of using the pressure-squared ratio to replace the pseudopressures ratio, for reservoir pressures less than 2000 psi (wells 1 through 5 in Table 2). For further validation of the new dimensionless IPR model, Eq. (24), its prediction is compared to the test data of a single gas well presented in the paper of Chase and Anthony (1988). Referring to Tables 2 and 3, it is clearly seen that that the AOFP value predicted by Eq. (24) is more accurate than that of Mishra and Caudle (1984). In addition, the prediction of Eq. (24) using P 2 -approximation is just as good as that found when using the pseudopressure method. The Chase and Alkandari model (1993) was not included in this comparison due to the lack of information regarding the skin factor of this well. The new model was also validated against unpublished test data of six wells in a fractured gas reservoir located in the Middle East. Again here, the superiority of Eq. (24) over the Mishra and Caudle model (1984) is clearly seen in Tables 2 and 3, and Fig. 13 for predicting AOFP values. In addition, the very good predictions of Eq. (24) prove its applicability to the specific fractured reservoir attempted in this study. Predicting the future performance of a gas well is also investigated and a new dimensionless IPR model was developed as expressed in Eq. (27). This model is validated using the example presented in the paper of Mishra and Caudle. Table 4 shows the results of AOFP values computed at two pressure levels, 1600 psia [11.04 MPa] and 1150 psia [7.935 MPa], respectively, using Eq. (27) and Mishra Caudle model. These results are in excellent agreement indicating that the new model can be also used to predict future gas well deliverability with confidence. 6. Conclusions (1) A new dimensionless IPR model is developed for calculating the performance of fractured and unfractured gas wells from a single-point flow test data under current reservoir conditions. The accuracy, simplicity, applicability and generality of the proposed model make it more attractive over existing singlepoint flow test dimensionless IPR models and conventional multipoint tests. (2) For the field data used in this work, the new IPR developed in the present work is shown to have superiority when compared with the existing methods. (3) Another general dimensionless IPR is developed in this work for predicting future deliverability from current single-flow test data and is found to be as good as the existing correlation. (4) The application of the pressure-squared approximation for fractured and unfractured wells is found to be very accurate at reservoir pressures below 2000 psi. This conclusion is consistent with published literature. (5) Additional field data are necessary to test the proposed relationships and further verify their implementation in practice.

104 H. Al-Attar, S. Al-Zuhair / Journal of Petroleum Science and Engineering 67 (2009) 97 104 References Brar, G.S., Aziz, K., 1978. Analysis of modified isochronal tests to predict the stabilized deliverability potential of gas wells without using stabilized flow data. Trans. AIME 265, 297 304. Chase, R.W., Alkandari, H., 1993. Prediction of gas well deliverability from just a pressure buildup or drawdown test. Paper SPE 26915 presented at the Eastern Regional Conference and Exhibition, Pittsburgh, Nov.2 4. Chase, R.W., Anthony, T.M., 1988. A simplified method for determining gas-well deliverability. SPE Reserv. Eng. 1090 1096 (Aug.). Cullender, M.H., 1955. The isochronal performance method of determining flow characteristics of gas well. Trans. AIME 204, 137 142. Kamath, J., 2007. Deliverability of gas-condensate reservoirs field experiences and prediction techniques. JPT 94 100 (April). Katz, D.L., Cornell, D., 1955. Flow of natural gas from reservoirs. Notes on intensive course. InUniversity of Michigan Publishing Services, Ann Arbor, Michigan. Katz, D.L., et al., 1959. Handbook of Natural Gas Engineering. McGraw Hill Book Co., Inc., New York City. Lee, A.L., Gonzalez, M.H., Eakin, B.E., 1966. The viscosity of natural gasses. Trans. AIME 237, 997 1000. Mishra, S., Caudle, B.H., 1984. A simplified procedure for gas deliverability calculations using dimensionless IPR curves. Paper SPE 13231 presented at the SPE Annual Technical Conference and Exhibition, Houston, Sept. 16 19. Rawlins, E.K., Schellhardt, M.A., 1936. Back-pressure data on natural gas wells and their application to production practices. Monograph, vol. 7. U.S.Bur. Mines. Smith, J.M., Van Ness, H.C., Abbott, M.M., 2001. Intorduction to Chemical Engineering Thermodynamics, Sixth edition. McGraw Hill. Swift, G.W., Kiel, O.G., 1962. The prediction of gas well performance including the effect of non-darcy flow. Trans. AIME 225, 791 798. Vogel, J.L. (1968). Inflow Performance Relationship For Solution-Gas Drive Wells. JPT (Jan.) 83 92. Trans. AIME, 243. Glossary a: deliverability coefficient (psi 2 /cp MSCFD) A: drainage area (ft 2 ) AOFP: Absolute Open Flow Potential (MSCFD) B: deliverability coefficient (psi 2 /cp MSCFD 2 ) c t : total system compressibility (psi 1 ) C A : shape factor (dimensionless) C: constant reflects the position of the stabilized deliverability curve on the log log plot (MSCFD/psi 2n ) D: turbulence factor (MSCFD 1 ) h: net formation thickness (ft) k: reservoir permeability (md) m(p) or P p : real gas pseudopressure (psi/cp) n: reciprocal of the slope of the stabilized deliverability curve P: pressure (psia) P sc : standard pressure (14.7 psia) P r : current average reservoir pressure (psi) P wf : bottom hole flowing pressure (psi) q: current gas flow rate (MSCFD) q max : current AOFP (MSCFD) r w : wellbore radius (ft) r e : drainage area radius (ft) s: mechanical skin factor (dimensionless) s : total skin factor (dimensionless) t s : time to stabilization (h) T: reservoir temperature ( R) T sc : standard temperature (520 R) X: pseudopressure ratio=p p (P wf )/P p (P r ) (dimensionless) x e : radius of external boundary (ft) : radius of uniform fluracture (ft) Y: gas flow rate ratio=q/q max (dimensionless) z: gas deviation factor (dimensionless) Greek symbols β: coefficient of turbulence (ft 1 ) ϕ: porosity (dimensionless) μ: gas viscosity (cp) γ: gas specific gravity (Air=1) Subscripts c: current conditions f: future conditions i: initial conditions