Many gas-condensate wells show a significant decrease in productivity once the pressure falls below the dew point pressure. A widely accepted cause of this decrease in productivity index is the decrease in the gas relative permeability due to a buildup of condensate in the near wellbore region. Predictions of well inflow performance require accurate models for the gas relative permeability. Since these relative permeabilities depend on fluid composition and pressure as well as on condensate and water saturations, a model is essential for both interpretation of laboratory data and for predictive field simulations as illustrated in this article.S lr ϭmin ͩ S l ,S lr high ϩ S lr low ϪS lr high 1ϩT l ͑ N T l ͒ l ͪ . ͑4͒

Summary An analytical method for calculating an effective non-Darcy flow coefficient for a heterogeneous formation is presented. The method presented here can be used to calculate an effective non-Darcy flow coefficient for heterogeneous gridblocks in reservoir simulators. Based on this method, it is shown that the non-Darcy flow coefficient of a heterogeneous formation is larger than the non-Darcy flow coefficient of an equivalent homogenous formation. Non-Darcy flow coefficients calculated from gas well data show that non-Darcy flow coefficients obtained from well tests are significantly larger than those predicted from experimental correlations. Permeability heterogeneity is a very likely reason for the differences in non-Darcy flow coefficients often seen between laboratory and field data. Introduction In this paper, we present an analytical method for calculating an effective non-Darcy flow coefficient for a heterogeneous reservoir. The effect of heterogeneity on the non-Darcy flow coefficient is also shown using numerical simulations. Non-Darcy flow coefficients calculated from the analysis of welltest data from a gas condensate field are compared with experimental correlations. Such a comparison allows us to more accurately assess the importance of non-Darcy flow in gas condensate reservoirs. Literature Review As early as 1901, Reynolds observed, in his classical experiments of injecting dye into water flowing through glass tubes, that after some high flowrate, flow rate was no longer proportional to the pressure drop. Forchheimer1 also observed this phenomena and proposed the following quadratic equation to express the relationship between pressure drop and velocity in a porous medium: d P d r = μ k u + β ρ u 2 . ( 1 ) This equation has come to be known asForchheimer's equation. At low Reynolds number (creeping flow conditions), the above equation reduces to Darcy's law. Tek2 developed a generalized Darcy equation in dimensionless form which predicts the pressure drop with good agreement over all ranges of Reynolds numbers. Katz et al.3 attributed the phenomenon of non-Darcy flow to turbulence. Tek et al.4 proposed the following correlation for?: β = 5.5 × 10 9 k 5 / 4 ϕ 3 / 4 . ( 2 ) Gewers and Nichol5 conducted experiments on microvugular carbonate cores to measure the non-Darcy flow coefficient. They also studied the effect of the presence of a second static fluid phase and the effect on plugging due to fines migration. They found that ? decreases and then increases with liquid saturation. Wong6 studied the effect of a mobile liquid saturation on ?. He used distilled water as the liquid phase and water saturated nitrogen as the gas phase on the same cores used by Gewers and Nichol. He plotted ? vs liquid saturation and found that there is an eight-fold increase in ? when the liquid saturation increases from 40% to 70%. He concluded that ? can be approximately calculated from the dry core experiments by using the effective gas permeability. Geertsma7,8 introduced an empirical relationship between ?,k and ? based on a combination of experimental data and dimensional analysis. He noted that the observed departure from Darcy's law was due to the convective acceleration and deceleration of the fluid particles. He also defined a new Reynolds number as ?k??/?, and suggested the following correlation for ? with a constant C (k is in ft 2, ?is in 1/ft). β = C k 0.5 ϕ 5.5 . ( 3 ) For the case of gas flowing through a core with a static liquid phase, he suggested the following correlation: β = C ( k k r g ) 0.5 [ ϕ ( 1 − S w ) ] 5.5 . ( 4 ) Phipps and Khalil9 proposed a method for determining the exponent in a Forchheimer-type equation. Firoozabadi and Katz10 presented are view of the theory of high velocity gas flow through porous media. Evanset al.11 reviewed the various correlations. They conducted an experimental study of the effect of the immobile liquid saturation and suggested a correlation based on dimensional analysis. Nguyen12performed an experimental study of non-Darcy flow through perforations on a synthetic core using air. These experiments showed that non-Darcy flow exists in the convergence zone and the perforation tunnel. Results of this study showed that Darcy flow equations can over predict well productivity by as much as 100%. Jones13 conducted experiments on 355 sandstone and 29 limestone cores. These tests were done for various core types: vuggy limestones, crystalline limestones, and fine grained sandstones. He presented the following correlation: β = 6.15 × 10 10 k − 1.55 . ( 5 ) He also points out that the group ?k? which is the characteristic length used for defining a Reynolds number for porous media, should be proportional to the characteristic length k/ϕ. He developed an approximate multilayer flow model that demonstrates that the departure from the above relation is due to permeability variations. Jones suggested that heterogeneity may be the reason why all correlations involving ? exhibit so much scatter.

ReservoirsThe University of Texas at Austin scheme for computing the gas and condensate relative permeabilities as a finction of the capillary trapping model and with only data at low trapping number (high IFT) as input and have found good agreement with the experimental data in the literature. We then used this model and typical parameters for gas condensates in a compositional simulation study of a single well to better understand the PI behavior of the well and the significance of the condensate buildup.

Copyright1SSS,Societyd Pa4roieum Engirwem,Ir?c, This pap-wwas pmpamd for pmssntakm d tha 1S98 SPE Gas TachnobgySymposium hsld In Ck@av, Nbarta, Cansda, 1S-18 MwctI 1W3 Tim papar was sebcted for pmsemtstion by an SPE ProgramCcinrmltaefolkmving rwiaw cf infw'nation wntainad III sn abstracteubmittadby the at.ithor(s)ContentsM tha papar, as pmsmted, have not bsen reviewedby tha Sccisty G4PatmlaumEngineamand am wkjact to corractiorrby tha authcf(s) The mat~ial, ss presented, ti not necasssrily mflecl sny PMW of tha Scdaty of PetroleumE@naam. its Micws, or mambam Papws pnmrntadst SPE meetings are subjectto publicafiiri review by Edlorial Committals of ths Soc4etyof PetrolaurnEnginsars Elactrmic mpmdudii, dstrih+ii, or atorsgeof any PSI d lhIs pspar for @nmmarda4 purpa.ss witlwuttha Wlten cunsantc+tha Sccietyof Pdoiaum Enginasmis pr&ibilOd Parmiswonto mpmduca in * u mstrtded to qn ** * notmom than 203 words; illustrations may not ba copiad Tha abstract must contain conspicuous ackmwbdgrnsnt C4wimre and by whomlha paperwas presented VWa Libmriem, SPE, PO. BoxS32826, Rbmdswi. TX 7SOSHS36, U.S A.. fax 01-972-9S2-943S AbstractAn analytical method for calculating an effective non-Darcy flow coetllcient for a heterogeneous formation is premnted, The method presented here can be used to calculate an effective non-Darcy flow coefficient for heterogeneous gridblocks in reservoir simulators. Based on this method, it is shown that the non-Darcy flow coefficient of a heterogeneous formation is larger than the non-Darcy flow coefllcient of an equivalent homogeneous formation, This result is confirmed using numerical simulations. Non-Darcy flow coefficients calculated from analysis of well test data from a gas condensate field show that non-Darcy flow obtained tlom well tests that are significantly larger than those predicted from experimental correlations. Permeability heterogeneity is, therefore, a very likely reason for differences in non-Darcy flow coefllcients often seen between lab and field data.

fax 01-972-952-9435. AbstractThe objective of this work was to provide a more accurate prediction of well and reservoir performance for gas and gas condensate reservoirs by investigating near-wellbore effects. Specifically, the effects of non-Darcy flow and changes in relative permeability due to interfacial tension (1FT), and flow rate (modeled based on capillary number) on well productivity are considered. These effects are shown to be important factors affecting the productivity index (PI) of gas condensate wells. When only non-Darcy effects are considered, the condensate bank can cause an order of magnitude reduction in the PI. Hence, immediate remediation steps might be necessary for formations with high non-Darcy flow coefficients. The reduction in PI with increasing non-Darcy flow coefficient is also highly non-linear. The relative permeability improvement obtained at high capillary numbers on the other hand counteracts the PI reduction due to non-Darcy flow effects. This effect reduces the drop in PI due to condensate buildup and makes the drop in PI more gradual. Hence, both effects should be considered while studying the production performance of a gas condensate reservoir. The capillary -now at ARCO Exploration & Production Technology Co, 285 number effect can in some cases overshadow the two-phase non-Darcy effects. Interestingly, when both non-Darcy and capillary number effects are present, the rate of decrease in the PI at or below the dew point is smaller than the case with the capillary number effect only. A case study of a lean-gas condensate reservoir, similar to the Arun field, was considered and a history match with the production data was performed. Simulation results are presented which clearly show that accurate prediction of PI based on laboratory measurements is possible using both non-Darcy and capillary number effects.