Abstract A new simple method of establishing Inflow Performance Relationship for gas condensate wells is proposed. The proposed method uses transient pressure test data to estimate effective permeability as function of pressure and then uses it to convert production BHFP data into pseudopressure to establish well performance. Requirement of relative permeability as function of saturation thus has been completely eliminated. Effective permeability of either phase can be used to predict the production of second phase. A scheme has also been devised to estimate the effective permeability using well testing mathematical models available in literature. Also mathematical models of well deliverability loss due to condensate deposition when dew point pressure is reached, and deliverability gain due to condensate mobility when P is reached have been developed. Pseudopressure curves for both oil and gas phase have been developed for quick conversion of pressure data into pseudopressure. Relative permeability curves if available can also be used, however, the knowledge of saturation has to be known at all the stages of the depletion to be able to use them.
SPE 75503 Establishing Inflow Performance Relationship (IPR) for Gas Condensate Wells Sarfraz A Jokhio and Djebbar Tiab/University of Oklahoma, SPE MEMBERS Copyright 2002, Society of Petroleum Engineers Inc This paper was prepared for presentation at the SPE Gas Technology Symposium held in Calgary, Alberta, Canada, 30 April—2 May 2002 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 833836, Richardson, TX 75083-3836, U.S.A., fax 01-972-952-9435 Abstract A new simple method of establishing Inflow Performance Relationship for gas condensate wells is proposed The proposed method uses transient pressure test data to estimate effective permeability as function of pressure and then uses it to convert production BHFP data into pseudopressure to establish well performance Requirement of relative permeability as function of saturation thus has been completely eliminated Effective permeability of either phase can be used to predict the production of second phase A scheme has also been devised to estimate the effective permeability using well testing mathematical models available in literature Also mathematical models of well deliverability loss due to condensate deposition when dew point pressure is reached, and deliverability gain due to condensate mobility when P* is reached have been developed Pseudopressure curves for both oil and gas phase have been developed for quick conversion of pressure data into pseudopressure Relative permeability curves if available can also be used, however, the knowledge of saturation has to be known at all the stages of the depletion to be able to use them Gas condensate reservoirs are primarily gas reservoirs As the pressure declines with depletion, reservoir conditions of pressure may go below dew point and liquid begins to buildup Such reservoirs may go under liquid buildup without showing any trace of liquid production Sudden well deliverability loss and very high skin factor estimates from pressure tests are strong indicators of liquid buildup PVT characteristics like phase diagram help identify the problem too As the critical conditions are reached such reservoirs become two phase in nature Finally, a field example is analyzed to show the use of new method developed and a step-by-step procedure is used to establish the well performance Small operators, Independents, will benefit from this method at the most, since data acquisition like relative permeability curves require the laboratory experiments on cores, an expensive procedure Introduction Retrograde Gas-condensate systems have not been treated so intensively as solution gas reservoirs have been Main reason is the phase behavior of light (C1-C10) hydrocarbons in the reservoirs Retrograde gas-condensate reservoirs are primarily gas reservoirs A zone of liquid begins to form as the dew point pressure is reached The liquid keeps accumulating and does not flow until the critical liquid saturation is reached Pressure at this point in the reservoir is termed P* Interestingly, this liquid may re-vaporize as the pressure further crosses the lower line on two-phase envelope of phase diagram This behavior of re-vaporization of the oil phase is called the “Retrograde behavior.” Fig.2 through Fig.4 show the schematics of such phenomenon in vertical and horizontal well Deliverability loss in such conditions is mainly due to two reasons: a) Gas undergoing liquid phase and b) permeability impairment by the liquid Thus both have to be handled mathematically to predict the well performance with reasonable accuracy Fig Phase behavior of the condensate fluids 2 S A JOKHIO AND D TIAB Pe S wc Pd P* P wf Fig.2 Three regions in a gas condensate reservoir with vertical well Pi Pd P* Pwf Fig.3 Three regions indicating two-phase flow around the horizontal well, single-phase flow but with liquid buildup, and the free gas flow in the farther region Pi SPE 75503 Predicting production behavior of a well in gascondensate reservoirs has been a topic of continuous research lately Simple correlation for productivity index estimations for oil wells (J = q/∆P) was being used until 1968 for solution gas reservoirs too Vogel1, 1968, first published IPR for solution-gas reservoirs, which handles the two-phase flow of oil and gas Vogel using Weller’s concepts was able to generate family of IPR curve in terms of only two parameters flow rate and BHP Recently Raghavan and Jones4 discuss the issues in predicting production performance of condensate systems in vertical wells Fevang and Whitson5 model the Gas-Condensate well deliverability using simulator and by keeping the track of saturation with pressure and relative permeability The most recent work on the gas condensate well performance comes from Guehria15 Predicting well performance of gas-condensate wells is challenging and a necessity at the same time Its use in optimizing production equipment including tubing, artificial lift systems, pumps, and surface facilities is of paramount importance Mathematical Basis Flow of real gases in porous media in the presence of more than one phase can be expressed using Darcy's law Under pseudo-steady state conditions and in field units total gas flow rate is expressed as follows: (1) q gt = C ∆mPgt Or q gt = q g , free + q o Rs Pd P* Pwf Fig.4 Fluid and pressure distribution around the fully penetrating horizontal well For vertical wells 0.00708.h C= r ln e − 0.75 + S a rw And for horizontal wells 0.00708.b C= A1 / + ln C H − 0.75 + S a ln rw (3) (4) ∆mP, the pseudopressure for gas phase can be written as5 Pr Literature Review The quantitative two-phase flow in the reservoirs was first studied by Muskat and Evinger17 They were the first researchers who indicated that the curvature in IPR curve of solution gas drive reservoirs is due to the decreasing relative permeability of the oil phase with depletion Based on Weller’s2 approximations of constant de-saturation of oil and constant GOR at a given instant (not for whole life of the reservoir) in the reservoir, Vogel1was able to solve psuedosteady state two phase flow equation based on relative permeabilities of each phase, and provided the industry an equation that would revolutionize the performance prediction of solution gas drive reservoirs Camacho-Raghavan22, JonesBlount-Glaze18, Wiggins21, and Sukarno’s19 work on IPRs follows the Vogel’s1 work (2) ∆mPgt = ∫ Pwf k k ro k k rg Rs + Bo µ o B gd µ gd dp (5) For convenience we keep the ke = k.krg, the effective permeability inside the integral Eq.5 can further be divided into three equations representing Region-1, Region-2 and the Region-3 as discussed by Fevang and Whitson5 Region-1 (Inner wellbore region) P* ∆mPg1 = ∫ Pwf k k ro k k rg Rs + Bo µ o B gd µ gd dp Region-2 (Region where liquid develops) (6) ESTABLISHING INFLOW PERFORMANCE RELATIONSHIP (IPR) FOR GAS CONDENSATE WELLS P Pd k k rg dp ∆mPg2 = B gd µ gd * P Region-3 (Only gas region) ∫ (7) Pwf ∆mPg3 = k k rg ( S wi ) B gd µ gd Pd ∫ (8) k rg k + ro RS C Bg µ g Bo µ o q gT RP = = qOT k k rg Ro C ro + Bo µ o Bg µ g On simplification k rg Bo µ o − Ro RP RP = Rs + k ro Bg µ g k g = kk rg 13.0E+3 12.0E+3 10.0E+3 9.0E +3 5000 4800 4600 4400 4200 4000 3800 Pressure [psia] Fig Producing gas oil ratio as a function of pressure (Eq.12) 10000 P* = 4300 psi 100 (11) Bo µ o B µ g g 3900 −1 3950 4000 4050 4100 4150 4200 4250 4300 4350 Pressure [psi] (12) Fig.6 Ratio of gas relative permeability to oil relative permeability as a function of pressure (Eq.13) (13) 20000 18000 1/Ro (14) 16000 { } R (1 − R R ) P o S P )dp ( R p − Rs ) ( 14.0E+3 11.0E+3 krg/kro ) k rg k ro 15.0E+3 10 (1 − Ro RP ) µ o Bo kk rg k o = kk ro = (15) (RP − Rs ) µ g Bg Modeling Pseudopressure Function Substituting Eq.15 and 14 in Eq.6 and simplifying results the gas phase pseudopressure function in terms of gas and oil effective permeability, respectively Gas Phase ∫ 17.0E+3 1000 (R − Rs ) µ g B g {kk ro } = P (1 − Ro RP ) µ o Bo k.k rg ∆mPg1, g = (µ B Pwf g g (17) (10) ) P* ) ) dp P* Producing Gas Oil Ratio As the pressure drops below the dew point, producing gas oil ratio GOR, increases monotonically15, i.e., a one-to-one relationship exists between the producing gas oil ratio and the pressure as shown in Fig.5 It dives as the P* approaches and liquid becomes mobile However, it stabilizes as effective liquid permeability stabilizes By definition5,15 q gT q g , free + qo, free RS = RP = (9) qoT qo, free + q g , free Ro k rg Bo µ o + Ro R P = R s + k ro B g µ g Solving for krg/kro results, k rg (RP − Rs ) Bg µ g k = 1− R R B µ o P o o ro ( ( R − Rs Rs + p − Rs R p 16.0E+3 It is not likely that three regions occur altogether at the same time But it is most likely that any of the two exist at a given moment in time ( k k ro Bo µ o Oil Phase dp Producing GOR [scf/STB] PR ( ∫ ∆mPg1,o = ) (16) [scf/STB] SPE 75503 P* 14000 12000 Pd = 5000 psi Rp 10000 8000 5000 4900 4800 4700 4600 4500 4400 4300 4200 4100 4000 3900 3800 Pressure[psia] Fig Determination of P*, pressure at which liquid is mobile in a multiphase system 4 S A JOKHIO AND D TIAB In order to model oil phase Eq.1 can be written as qot = qofree + qg.Ro (18) Since oil phase is mobile in only Region-1 therefore the oil phase pseudopressure can be written as (19) Substituting Eq 14 and Eq 15 in Eq 19 respectively result the oil phase pseudopressure function in terms of oil and gas effective permeability, respectively P* ∆mPo1,o = ∫ Pwf P* ∆mPo1, g = ∫ Pwf k k ro Bo µ o − Ro R s − Ro R p ( ) dp − Ro R p k k rg + Ro B g µ g R p − Rs 0.1 Kg 0.08 (20) dp Effective Permeability [md] ∫ Pwf k k ro k k rg Ro dp + Bo µ o B g µ g (26) dmPws h (t + ∆t )µ g ct d ln ∆ t c µ gi ti SP Several gas well tests were simulated in order to establish relationship between pressure and effective permeability for gas wells (21) 0.06 0.04 Ko 0.02 Modeling Effective Permeability as a Function of Pressure: Vertical Wells (Pressure Drawdown Test) The effective oil and gas permeability during pressure transient period can be expressed as follows, respectively13: 70.6qo, free µ o Bo k o = kk ro = − (22) ∂Pwf h ∂ ln (t ) 70.6q g , free (23) k g = kk rg − ∂mPwf h ∂ ln (t ) SP Above equations are valid for a fully developed semi-log straight line Both the equation can also be written as 5500 5000 4500 4000 3500 3000 2500 2000 1500 1000 Pressure [psi] Fig Effective permeability from pressure test data in a multiphase system (Vertical Well) 0.1 0.09 0.08 0.07 Ko [md] ∆mPo1 = 70.6q g , free k g = kk rg = − q ot = C.∆mPot P* SPE 75503 0.06 0.05 0.04 0.03 0.02 0.01 Pressure Buildup 5000 4500 4000 3500 3000 2500 2000 1500 1000 500 P ressure [psi] 70.6q o µ o Bo ∂Pws h + ∆ t t ∂ ln ∆t (24) 0.01 0.009 0.008 Similarly k g = kk rg = − 70.6q g , free ∂mPws h t + ∆t ∂ ln ∆t SP To be more accurate following equation can be used Fig.9 Oil effective permeability as a function of pressure (Vertical Well) (25) Effective Permeability [md] k o = kk ro = − 0.007 0.006 0.005 0.004 0.003 0.002 0.001 5000 4500 4000 3500 3000 2500 2000 1500 1000 500 P ressure [psia] Fig 10 Gas effective permeability as a function of pressure during a pressure test SPE 75503 ESTABLISHING INFLOW PERFORMANCE RELATIONSHIP (IPR) FOR GAS CONDENSATE WELLS 0.2 From Left To Right qo [STB/D] 0.18 10 20 40 60 100 150 200 0.16 0.14 Ko [md] 0.12 0.1 0.08 0.06 0.04 0.02 5010 4760 4510 4260 4010 3760 3510 3260 3010 Pressure [psia] Fig 11 Effect of oil flow rate on effective oil permeability (Pd = 5000 psi) 0.016 From Left To Right qg [Mscf/D] 0.014 50 100 200 300 500 750 1000 0.012 Kg [md] 0.01 0.008 0.006 0.004 0.002 5500 5000 4500 4000 3500 3000 Pressure [psi] Fig 12 Effect of gas flow rate on effective gas permeability (Pd = 5000 psi) Horizontal Wells Earlty Time Radial Flow Regime Equation of this flow regime during a pressure drawdown test is k k t y z − qµB log (27) Pi − Pwf = 162.6 φ µ ct rw2 Lw k y k z 3.227 + 0.866s m According to Darcy law the flow rate of any phase towards the wellbore is the function of the preesure But pressure is function of the distance from the wellore 2π rLkk rm ∂P (28) q m = 1.127 x10 −3 µ m Bm ∂r w Where absolute permeability k = k H kv and kH and kv are the permeabilty in horizontal and vertical direction respectively For tD/rD2 ≥ 50 pressure is function of Boltzman variable z = r2/t Thus one can write ∂P ∂P ∂P dP r = z −2 (29) = −2t ∂ ln(t ) ∂r ∂t dz Substituting above equation in a Darcy law, one gets 2π Lkk rm ∂Pwf (30) q m = −1.127 x10 −3 µ m Bm ∂ ln(t ) Solving for Effective permeability, results 70.6q m µ m Bm kk rm = − ∂Pwf L ∂ ln(t ) For Oil phase 70.6qo, free µ o Bo kk ro = − ∂Pwf L ∂ ln(t ) And for gas phase 70.6q g , free kk rg = − ∂mPwf L ∂ ln(t ) SP Similarly for pressure buildup 70.6q o µ o Bo kk ro = − ∂Pws L ∂ ln(t H ) kk rg = − Fig.13 Early and late radial flow towards horizontal well16 70.6q g , free (31) (32) (33) (34) (35) ∂mPws L ∂ ln(t H ) SP Where tH is the Horner time Above equations are valid for a fully developed radial regime that appears for tD/rD2 ≥ 50 It is possible from a transient well pressure data to develop the relative permeability curves provided absolute formation permeability is known Such curves like the absolute permeability (in single phase systems) obtained from the S A JOKHIO AND D TIAB pressure transient data are the averaged values that capture the effects of fluid and formation properties If the radial line is masked by the wellbore effects or the linear flow regime, it should be extrapolated Several algorithms are available in the literature to calculate the log derivative of the pressure Early Time Linear Flow Regime This flow period is represented by SPE 75503 8.128qO BO d∆P hX h z d t Oil Phase k ey ( P) = Gas Phase k ey (P ) = µt 141.2qµB (s z + sm ) (36) + Pi − Pwf = φ c k y t Lw k y k z Lw h z Taking the derivative of pressure with respect to square root of time gives µ d∆ P 8.128qB (37) = k y φ ct d t Lw h z µO (44) φ ct 8.128q g µ g ( P) hZ h X d∆mPSP (45) φ ct d t 8.128qB ∆P & t.d∆P/dln(t) 1000 100 Solving for ky, the effective permeability in lateral direction, y, results k ey ( P ) = 8.128q o Bo µo φ ct d∆P Lw h z d t −1 For Gas phase Lw k y k z 10 100 1000 10000 100000 Fig.14 Simulated horizontal wellbore pressure response without wellbore storage and skin indicating early and late radial flow regimes N o F lo w U p p e r a n d L o w e r B o u n d a ry E ffe c ts (40) (s z + sm ) Taking the time log derivative of this equation, and then solving for effectve permeability, results Oil Phase 70.6qµ O B o k exy (P ) = k y k x = (41) dPwf hz d ln(t ) Gas Phase 70.6q g , free (42) k exy (P ) = k rg k y k x = dmPwf hz d ln(t ) SP Late Time Linear Flow This flow period during a drawdown pressure test is represented by 141.2qµ B µt 8.128qB ∆P = + (s x + s z + s m ) (43) hx hz k y φ ct Lw k y k z Thus effective permeability in y-direction from this period is estimated as follows 1 4900 4850 4800 4750 4700 4650 4600 4550 4500 4450 4400 P re s s u re [p s i] Fig.15 Profile of oil effective permability from horizontal well pressure data with upper and lower noflow boundary effects 0.31 0.29 0.27 0.25 Ko [md] 141.2qµ Bo (39) 0.1 Tim e[ hrs] Ko [md] 8.128q g k ey (P ) = d∆mPSP φ ct µ g ( P) L h z w d t Late Radial Flow Regime This flow regime is represented by 162.6qµ B o k x t − 2.023 + Pi − Pwf = log h z k y k x φµ ct Lw 10 0.01 (38) 0.23 0.21 0.19 0.17 0.15 49 00 48 00 47 00 46 00 45 00 44 00 43 00 P re ss u re [p s i] Fig 16 Profile of oil effective permability from horizontal well pressure data without upper and lower noflow boundary effects SPE 75503 ESTABLISHING INFLOW PERFORMANCE RELATIONSHIP (IPR) FOR GAS CONDENSATE WELLS 100 From Left to Right qo [STB/D] 0.9 10 10 20 40 60 100 150 200 0.7 Ko [md] ∆P & t.d∆P/dln(t) 0.8 0.6 0.5 0.4 0.1 0.3 0.2 0.01 0.01 0.1 10 100 1000 10000 100000 0.1 5000 Tim e[ hrs] 4900 4800 4700 4600 4500 4400 4300 Pressure [psi] Fig 17 An infinite acting (lateral direction) horizontal well pressure response without wellbore storage and skin factor.(Fully developed late radial flow regime) Fig.20 Effect of condensate flow rate on effective permeability to oil (Horizontal Well Pd = 5000 psi) 0.1 0.09 0.08 0.07 Kg [md] Ko [md] From Left to R ight qg [M scf/D ] 50 100 200 300 500 750 1000 0.06 0.05 0.04 0.03 0.02 0.01 5000 5100 4998 4996 4994 4992 4990 4988 4986 4984 4982 9 Kg [md] 8 7 6 5 4998 4996 4994 4992 4990 4900 4800 4700 4600 4500 4400 4300 Pressure [psi] Fig 18 Profile of oil effective permability from horizontal well pressure data with upper and lower noflow boundary effects 5000 5000 4980 P r e s s u r e [p s i] 4988 4986 4984 4982 P r e s s u r e [p s i] Fig.19 Gas effective permeability profile from pressure test in horizontal wells Fig.21 effect of condensate flow rate on effective permeability to gas (Horizontal Well Pd = 5000 psi) Effective Permeability With Measured Surface Rate In phase changing multiphase environment such as gas condensate systems it is hard to measure the free rate at surface The total rate is the combination of the free oil and gas flow and dissolved gas in oil and vapor phase in the gas phase Thus a scheme is devised to get effective permeability using the surface measured rate from well test analysis instead of free rate Pressure transient response in terms of pseudopressure can be represented as k ( P) − q g ,meas log(t ) + log e φµc r mPP < P* − mPwf = 162.6 t w h 3.2275 + 0.8686S (45a) Gas phase pseudopressure for Region-1 has been define by Eq.16 and 17 With equation 16, Eq 45a can be expressed as follows S A JOKHIO AND D TIAB P* ∫ Pwf k.k rg R P (1 − Ro R S ) (P )dp = ( µ B ) R p − Rs g g ( q g ,meas 162.6 h ) k ( P) log(t ) + log e φµc r t w 3.2275 + 0.8686S − (46) ∫ (µ Pwf R P (1 − Ro R S ) g Bg ( ) R p − Rs ) And Eq.16 is the pseudopressure in gas condensate reservoirs P* k.k rg RP (1 − Ro RS ) P )dp ∆mPg1, g = ( (16) (µ B ) R p − Rs g g Pwf ∫ (P )dp = log(t ) + log k e ( P) φµc r t w 3.2275 + 0.8686S q g ,meas 162.6 P* k.k (P )dp h rg P wf ∫ (47) − ∫ k.k rg q g ,meas (P )dp = 162.6 (48) d∆mPg1, g h d ln(t ) Gas phase effective permeability now is the derivative of the above equation Similarly oil phase effective permeability integral can be estimated as Pwf P* ∫ k.k q g ,meas (P )dp = 162.6 (49) d∆mPg1,o h d ln(t ) Oil phase effective permeability then is the derivative of above equation Using surface oil rate ro Pwf P* ∫ k.k rg (P )dp = 162.6 Pwf q o,meas d∆mPo1, g h d ln(t ) P* ∫ k.k ro (P )dp = 162.6 Pwf q o,meas d∆mPo1,o h d ln(t ) (50) (51) Establishing IPR Since pseudopressure has been developed, Rawlins and Schellhard20 equation can be used to establish well performance (51a) Gas phase q g = C ∆mPg n ( ) Oil phase qo = C (∆mPo ) n (51b) ( ) Comparing the integral in Eq.16 with single-phase gas pseudopressure in Eq 52, the difference is the gas phase recovery due to liquid production Effective permeability in Eq.16 is lower than that in Eq.52 The recovery term is equal to P* R P (1 − Ro R S ) (R p − Rs ) (P )d ∫ P * − Pwf Pwf Now gas phase effective permeability integral as a function pressure can be estimated as P* Well Deliverability Gain Due to Condensate Production in Region-1 Single-phase gas pseudopressure for gas reservoirs can be expressed as P* k k rg dp (52) ∆mPg,sp = B g µ g Pwf sp ∫ Re-arranging, yields P* SPE 75503 (53) p Or P* q g , sp ∫ (R Pwf R P (1 − RO R S ) p )( − R s P * − Pwf ) (P )dp = q gt ,2 P (54) Term in Eq 53 is the production gain factor in the Region-1 due to liquid mobility This can be converted into vapor equivalent as follows γ Veq = 133,000 o (54a) Mo Veq is the gas equivalent of the condensate Well Deliverability Loss Due to Condensation The recovery in the absence of liquid accumulation in Regio-1 would be qg,sp = C ∆mPg,sp (55) P k dp ∆mPg,sp = (56) B g µ g Pwf sp ∫ Since qg,sp > qgt,2P, (flow rate with condensate accumulation) therefore, well efficiency in this case can be expressed as q gt , P η w, p [%] = x100 (57) q g , sP And the damage factor then is q g , sP − q gt , P − η w, p = q g , sP (58) SPE 75503 ESTABLISHING INFLOW PERFORMANCE RELATIONSHIP (IPR) FOR GAS CONDENSATE WELLS P* ∫ C Pwf η w, p = k.k rg R P (1 − RO R S ) (P )dp R p − Rs ( µ g B g ) ( P C ( P* ∫ Pwf kk rg B g µ g ) Procedure to calculate Table ** Calculate the critical temperature and pressure I used correlation for California gases using following equation Tpc = 298.6 SG + 181.89 Tpc = 298.6 (0.94) +181.89 = 462.574 oR Ppc = -514.01 SG + 1788.2 SG - 2337.5 SG2 + 1305.3SG + 415.07 ) (59) dp sp k.k rg p R P (1 − Ro R S ) (P )dp (60) (kk rg ) sp R p − R s P * − Pwf ) Pwf Since effective permeability in single-phase gas reservoirs is equal to absolute permeability, therefore, above equation can be rewritten as ∫ η w, p = P* η w, p = ( k.k rg ∫ )2 P k Pwf ( )( ) R P (1 − Ro R S ) (R p − Rs )(P * − Pwf ) (P )dp Damage Factor in Region-2 In this region, only gas phase is mobile, therefore; Pd k.k rg P k P* DF2 = − (63) (Pd − P *) Equation 63 indicates that the delivery loss in Region-2 is the result of permeability loss due to condensation ∫ ) P1 0.9 0.8 Production Loss in Region-2 Pd 0.7 mPwf 0.6 0.5 Production Gain in Region-1 P* 0.4 0.3 0.2 0.1 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 Pwf 0.8 Table Well, reservoir and fluid data is given in following table Pi Pd GOR T Gas SG qg 6750 psia 6750 psia 9470 scf/STB 354 oF 0.94 [MW =27.17] 75.4 Mscf/D qc h φ rw API ∆T 2.8 STB/D 216.5 ft 0.062 0.54 ft 50 [Assumed] 2.85 oF/100FT (61) Eq.61 shows that the delivery loss in Region-1 is only due to relative permeability loss of the gas phase Partially the loss is recovered as liquid production ( 0.9 Qg Fig.22 Production trend in gas condensate systems Example-1 This example is taken from reference 12 The 11, 500 ft deep well KAL-5 (Yugoslavia) has following properties The initial conditions coincide with retrograde conditions In Table the mP values have been estimated using Eq 16 Once the derivative of the pseudopressure is estimated, the effective permeability integral is calculated using Eq.48 Ppc = -514.01 (0.94) + 1788.2 (0.94) - 2337.5 (0.94) + 1305.3(0.94) + 415.07 = 660.57 psi At 2200 psi Tr = T/Tpc = 354 + 460 /462.574 = 1.759 Ppr = P/Ppc = 2200/660.57 = 3.33 ** Calculate the compressibility factor using Gopal equations given in Appendix A Choose proper equation Following equation fits the above critical conditions of temperature and pressure Z =Pr (-0.0284Tr + 0.0625) + 0.4714Tr -0.0011 Z =(3.33) [-0.0284(1.759) + 0.0625] + 0.4714(1.759) -0.001 = 0.8699 zT ** Calculate the Bg using Eq.P-15 B g = 0.00504 P (0.8699)(354 + 460) =0.0016 bbl/scf B g = 0.00504 22 ** Calculate gas density using Eq.P-21 MW P ρ g = 1.601846 x10 − RT Table PVT Properties for example-1 P Ppr Z 200 600 1000 1400 1800 2200 2600 3000 3400 3800 4200 4600 5000 5400 5800 6200 6750 0.3028 0.9083 1.5138 2.1194 2.7249 3.3304 3.936 4.5415 5.147 5.7526 6.3581 6.9636 7.5692 8.1747 8.7802 9.3858 10.218 0.9818 0.9491 0.9186 0.8992 0.8797 0.8701 0.8777 0.8853 0.8929 0.8811 0.9149 0.9487 0.9825 1.0163 1.0501 1.0839 1.1304 Bg B/scf 0.0201 0.0065 0.0038 0.0026 0.002 0.0016 0.0014 0.0012 0.0011 0.001 0.0009 0.0008 0.0008 0.0008 0.0007 0.0007 0.0007 Vis Cp 0.015 0.016 0.016 0.017 0.018 0.019 0.02 0.022 0.023 0.025 0.027 0.029 0.031 0.034 0.037 0.04 0.045 Rso scf/B 42.45 150.7 271.7 400.6 535.3 674.7 818.1 965 1115 1267 1423 1580 1739 1901 2064 2229 2459 Ro B/scf -7.59E-06 4.83E-06 1.26E-05 1.90E-05 2.48E-05 3.03E-05 3.59E-05 4.16E-05 4.78E-05 5.45E-05 6.20E-05 7.03E-05 7.98E-05 9.05E-05 1.03E-04 1.16E-04 1.38E-04 Where R (10.73) is the universal gas constant, T is in oR and P is in psi The gas density is in gm/cc MW is the molecular weight of the gas 10 S A JOKHIO AND D TIAB (27.17)22,00 =0.10962 gm/cc (10.73)(354 + 460) ** Calculate the gas viscosity using Eq.P-16, (9.4 + 0.02M )T 1.5 X1 = 209 + 19M + T (9.4 + 0.02(27.17))(354)1.5 X1 = = 61.365 209 + 19(27.17) + (354) 986 X = 3.5 + + 0.01M T 986 X = 3.5 + + 0.01(27.17) = 6.557 354 X = 2.4 − 0.2 X X = 2.4 − 0.2(6.557) = 1.0886 ρ g = 1.601846 x10 −2 X µ g = 10 − X exp( X ρ ) ** Calculate Rso using Eq.P-2 I used following equation for light oils Rso = (P1.1535) (SG / 37.966) 10 (9.441 API / T) Rso = (2,2001.1535) (0.94 / 37.966) 10 (9.441 (50) / (354+460)) = 674.73 scf/STB ** Calculate vapor phase in gas phase, Ro [STB/MMscf], using following equation 42.3815 Ro = −11.66 + 4.706 x10 −9 Rs + 1.623 Rs − Rs Ro = −11.66 + 4.706x10−9 (674.73) + 1.623 674.73) − 42.3815 674.73 = 30.31233 STB/MMscf = 3.0312x10-5 STB/scf ** Producing gas oil ratio, Rp, is measured at surface during the well test, 9,470 SCF/STB Table Pressure and pseudopressure data, with Eq.16 P psi 6750 1083.1 1174.5 1226.7 1303.6 1490.6 1751.6 2046 2279.4 2759.4 3246.5 4210 5162 6161 6336.5 6406.1 6452.5 6487.3 6507.6 6526.5 6556.9 6574.3 6587.3 6601.8 mP1g,g Eq.16 248.3555 9.690342 11.4 12.4369 14.04406 18.34433 25.25937 34.35381 42.35781 60.66817 81.41431 127.6456 174.5628 221.9433 229.9477 233.0914 235.1772 236.7363 237.6437 238.4871 239.8407 240.614 241.1909 241.8336 Procedure to calculate Table ** Having calculated table convert the pressure data into pseudopressure using Eq.16 without the k.krg term P* R (1 − R R ) P O S (P )dp mPg1 = R p − Rs ( µ g B g ) Pwf ∫ ( ) The integral can be evaluated numerically as follows P* mPg1 = Pwf ∫ R (1 − R R ) P O S ( ) P dp R p − Rs ( µ g B g ) ( ) P* mPg1 = ∫ X (P )dp PB µ g = 10 −4 (61.365) exp(6.557)(0.1096)1.0886 ) = 0.011 cp Time hrs Pr = 0.167 0.333 0.5 12 16 22 28 34 42 50 58 68 82 97 112 141 SPE 75503 ∆mP 1.709663 2.746561 4.353722 8.653984 15.56903 24.66347 32.66747 50.97782 71.72397 117.9553 164.8725 212.2529 220.2574 223.4011 225.4869 227.046 227.9533 228.7967 230.1504 230.9236 231.5005 232.1433 X + X 200 (200 − 0) + 3242.079 mP(200) = (200 − 0) = 324207.9 = 3242 2 psi /cp 3242.079 + 9882.76 mP(600) = mP(200) + (600 − 200) = 3242.079 + 9882.76 mP(600) = 324207.9 + (600 − 200) = 2949175.7 an so on Procedure to calculate pseudopressure derivative group, t.d∆mP/d(ln(t) Using following equation ∆mp = mP-mP(t=0) d∆mPi +1 d∆mPi −1 ∆ ln(t ) i +1 + ∆ ln(t ) ∆ ln(t ) i −1 ∆ ln( ) t d∆mP i −1 i +1 = [∆ ln(t ) i +1 + ∆ ln(t ) i −1 ] d ln(t ) i mP(200) = Table Integral evaluation data t.d∆mP/d(ln(t) Integral[Keg] P 3.84810177 6.18010128 16.4412385 22.5880236 33.7942807 49.9686048 79.5896594 117.600946 133.490764 92.4258768 66.411804 20.7617509 12.3720492 7.66378648 7.0386556 6.60753927 4.96192743 5.41043564 3.83858505 Start of SLL 0.002727533 0.004577121 0.007389084 0.008045338 0.008570265 0.011412573 0.010466507 0.014752405 psi 200 600 1000 1400 1800 2200 2600 3000 3400 3800 4200 4600 5000 5400 5800 6200 6750 Bg Gas Vis Rso Ro X = Rp(1RoRs)/ [(Rp-Rso)(Bgµg)] [bbl/scf] [Cp] [scf/bbl] [B/scf] Rp = 9,470 0.020138962 0.01538971 42.4507256 -7.58E-06 3242.079135 0.00648931 0.01583345 150.745544 4.83E-06 9882.761598 0.003768687 0.0164451 271.735901 1.26E-05 16554.87436 0.002634882 0.0171969 400.595154 1.90E-05 22868.63006 0.00200499 0.0180827 535.308167 2.48E-05 28846.64708 0.00162264 0.01910453 674.732422 3.03E-05 34022.62432 0.00138497 0.0202691 818.123291 3.59E-05 37847.212 0.001210678 0.02158655 964.953491 4.16E-05 40893.98613 0.001077396 0.02306997 1114.82825 4.78E-05 43171.70082 0.000951253 0.02473525 1267.43994 5.45E-05 45676.80014 0.000893679 0.02660116 1422.54187 6.20E-05 45136.22568 0.000846117 0.02868952 1579.93115 7.03E-05 43948.96444 0.000806166 0.03102551 1739.43787 7.98E-05 42180.59821 0.000772133 0.03363803 1900.91724 9.05E-05 39887.95688 0.000742794 0.03656014 2064.24487 1.03E-04 37120.43519 0.000717241 0.03982965 2229.31177 1.16E-04 33921.35589 0.000687051 0.04497274 2458.94556 1.38E-04 28887.92587 At t = 68 hours and P = 6526.5 psi ESTABLISHING INFLOW PERFORMANCE RELATIONSHIP (IPR) FOR GAS CONDENSATE WELLS ∆mP = 511.067-23.3728 = 487.6942 At t = 82 hours and P = 6556.9 psi ∆mP = 511.9648-23.3728 = 488.592 d∆mP = ∆mP(t =82)- ∆mP(t =68) 488.592 – 487.6942 = 0.8978 d∆ln(t) = ln(82)-ln(68) = 0.1872 At t = 97 hours and P = 6574.3 psi ∆mP = 512.4781-23.3728 = 489.1053 d∆mP = 489.1053- 488.592 = 0.5133 ∆ln(t) = ln(97)-ln(82) = 0.16799 At t = 112 hours and P = 6587.3 psi ∆mP = 512.8614-23.3728 = 489.4886 d∆mP = 489.4886 – 489.1053 = 0.3833 d∆ln(t) = ln(112)-ln(91) = 0.143787 Then the derivative at 97 hours, P = 6574.3 is d∆mPi-1 = 0.8978 ∆ln(t)i-1 = 0.1872 d∆mPi+1 = 0.3833 ∆ln(t)i+1 = 0.143787 0.3833 0.8978 0.1872 0.143787 + d∆mP 1872 0.143787 = [0.1872 + 0.143787] d ln(t ) i = 3.590871565 Where the point i is the point where derivative is calculated and point i-1 is the point before it and i+1 is the point after it ∆ln(t) = ln(t1) –ln(t2) ** Plot the pseudopressure and its derivative and locate the start of radial straight line This is the semi-log straight line on the semi-log plot of pressure vs time The effective permeability The integral [Keg] is calculated from the straight line portion and onwards using following equation q g ,meas dmP −1 d ln(t ) h P ∫ (k.k rg (P ))dp = 162.6 Pwf 6000 5000 1000 0.1 10 100 1000 Time [hr] Fig.23 Transient pressure semi-log plot Table Pressure and Pseudopressure data Time hrs Pr = 0.167 0.333 0.5 12 16 22 28 34 42 50 58 68 82 97 112 141 P psi 6750 1083.1 1174.5 1226.7 1303.6 1490.6 1751.6 2046 2279.4 2759.4 3246.5 4210 5162 6161 6336.5 6406.1 6452.5 6487.3 6507.6 6526.5 6556.9 6574.3 6587.3 6601.8 mP1g,o ∆mP t.d∆mP/d(ln(t) Integral[Keo] Eq.17 MM psi2/Cp 517.6423 23.3728 25.82054 2.447743 27.24284 3.870043 29.37082 5.998017 4.876688764 34.71134 11.33854 7.493499072 42.57468 19.20188 17.59814272 52.05665 28.68385 23.02276104 60.07426 36.70146 33.95911145 78.13077 54.75797 50.2170588 99.00624 75.63344 86.65745905 151.2229 127.8501 180.0784224 233.9581 210.5853 524.924176 500.2031 476.8303 142.9481323 505.4348 482.062 323.2790984 Start of SSL 507.5021 484.1293 13.60094325 0.004163561 508.8777 485.5049 8.151117177 0.006947313 509.908 486.5352 5.062244746 0.011186413 510.5084 487.1356 4.655564686 0.012163586 511.067 487.6942 4.376948091 0.012937864 511.9648 488.592 3.290109705 0.017211694 512.4781 489.1053 3.590871565 0.015770088 512.8614 489.4886 2.549689479 0.022209905 513.2888 489.916 1000 100 Un-e xpe cte d anom aly ∆ Pwf 3000 ∆ q g , meas dmP −1 d ln(t ) h ∫ (k.k rg (P ))dp = 162.6 4000 2000 The effective permeability integral is calculated using following equation, after the semi-log straight line has developed P 11 7000 Shutin Pressure [psi] SPE 75503 P ∫( Pwf ) 75.4 *1000 k k rg (6574.3) dp = 3.5908715x10 216.5 = 0.01577 Oil effective permeability Use same procedure for table with equation 17 instead of Eq 16 to calculate pseudopressure and following equation to calculate oil effective permeability P q g , meas ∆mP′ h 162.6 ∫ (k.kro (P ))dp = Pwf 10 162.6 0.1 10 100 1000 T im e [h rs] Fig.24 Pseudopressure and its derivative vs time The unexpected anomaly is observed The initial reservoir pressure is equal to dew point pressure Thus it is suspected that the anomaly is the approaching P* 12 S A JOKHIO AND D TIAB Two-point numerical derivative can also be used to calculate effective permeability as a function of pressure Integral[kg ] − Integral[kg ] k k rg = P2 − P1 It is possible that the producing gas oil ratio estimated at the surface may have human error in it Thus a sensitivity analysis was performed by increasing the GOR by 10% and see its impact on the effective permeability and skin factor since in gas condensate systems skin factor is also added due to change in effective permeability This was done by using the skin factor equation at different values of gas effective permeability 0.025 0.02 0.015 0.01 0.005 6300 6350 6400 6450 6500 6550 6600 P re ssu re [p si] Fig 27 Oil effective permeability integral as function of pressure Vertical solid line is the start of semi-log straight line [Eq.17] 0.012 0.01 0.008 Table Effect of 10% increase in GOR on oil effective permeability E x p e c te d P * 0.006 P psi 6406.1 6452.5 6487.3 6507.6 6526.5 6556.9 6574.3 6587.3 0.004 0.002 6650 SPE 75503 6600 6550 6500 6450 6400 6350 6300 P re ssu re [p si] Fig.25 Gas effective permeability integral as function of pressure Vertical solid line is the start of semi-log straight line [Eq.16] Keo Rp = 9,470 5.73045E-05 5.99946E-05 0.000121813 4.81366E-05 4.09671E-05 0.000140586 8.28509E-05 0.000495371 Keo Rp = 10,417 5.16527E-05 5.45406E-05 0.000110739 4.37605E-05 3.72428E-05 0.000127806 7.5319E-05 0.000450337 % Error 9.862689 9.090909 9.090909 9.090909 9.090909 9.090909 9.090909 9.090909 For oil phase effective permeability, slope of Eq 51 can be used q g ,meas dmP −1 d ln(t ) h P ∫ (k.k ro (P ))dp = 162.6 Pwf Table Effect of 10% increase in producing GOR on gas effective permeability Fig.26 Gas effective permeability integral extrapolated to zero pressure Table Gas effective permeability as function of pressure Pressure 500 1000 1500 2000 2500 3000 3500 Keg Pressure 6.005e-08 5.681e-08 6.159e-08 7.107e-08 8.575e-08 8.597e-08 1.418e-07 Keg 4000 4500 5000 5500 6000 6500 1.971e-07 2.952e-07 4.936e-07 9.949e-07 2.974e-06 4.104e-05 Time hrs P psi 34 42 50 58 68 82 97 112 141 6406.1 6452.5 6487.3 6507.6 6526.5 6556.9 6574.3 6587.3 6601.8 Keg md Rp = 9,470 2.69E-05 3.99E-05 8.08E-05 3.23E-05 2.78E-05 9.35E-05 5.44E-05 0.00033 Keg md Rp =10,417 2.78E-05 4.11E-05 8.33E-05 3.34E-05 2.87E-05 9.64E-05 5.59E-05 0.00034 % Error 3.02190686 3.06048534 3.04016961 3.21625527 3.35208414 3.07862887 2.88401789 3.08949186 Using following equation for various values of pressure and effective permeability, skin factor was estimated as function of pressure Table indicates that the increase in gas oil ratio also causes increase in skin factor This may be due to the fact that the increase in gas rate gives rise in the non-Darcy flow Condensed liquid occupies more space thereby reducing the rate and the non-Darcy flow effects ∆mPg M g h k eg ( P ) + 3.2275 − log S1 = 1.1513 φµc r q g ,meas t w SPE 75503 ESTABLISHING INFLOW PERFORMANCE RELATIONSHIP (IPR) FOR GAS CONDENSATE WELLS Table Absolute error in skin factor to gas with 10 % increase in producing GOR P Psi 6452.5 6487.3 6507.6 6526.5 6556.9 6574.3 6587.3 Skin Rp = 9,470 -3.53405 -3.92994 -3.53555 -3.53051 -4.18602 -4.01019 -4.92164 Skin Rp = 10,417 -3.488564948 -3.866652757 -3.467571977 -3.45896314 -4.098223812 -3.929811734 -4.813667252 13 Use Eq.20 without k.kro term to calculate pseudopressure P* % Error ∆mPo = 1.287002 1.610467 1.922726 2.026399 2.097282 2.004447 2.193882 o Pwf − Ro R s − Ro R p ∫ B µ o dp P q (k.k ro (P ))dp = 162.6 o,meas Use equation h Pwf ∫ dmPo −1 d ln(t ) to calculate oil effective permeability integral 8000 Procedure to calculate IPR Chose the pressure data as shown in Table 10, column Convert the pressure data into pseudopressure as we did earlier in this example without Krg term This is equal to mP/Mg (Column-2) Using the same pressure data (Column 1) evaluate integral using equation given in Fig 26 This is the term Mg (Column-3) Now calculate the final value of pseudopressure by multiplying the mP/Mg with Mg to get mP (Column-4) Plot the mP Vs flow rate on a log-log plot and calculate the sole n, and intercept C In this example we assumed values such that they match the rate and BHFP during the well test since we did not have production data for this well Estimate these parameters separately for oil and gas phases Now establish IPR using Rawlins and Schellhardt20 equation Gas phase: q g = C ∆mPg n ( ) Oil phase qo = C (∆mPo )n 0.8 0.7 0.6 0.5 0.4 0.3 7000 6000 5000 4000 3000 2000 1000 0 10 20 30 40 50 60 70 Fig 29 Gas phase IPR against pressure Table 10 Well performance data [n = 0.8, C = 0.948, Assumed Values] P 200 600 1000 1400 1800 2200 2600 3000 3400 3800 4200 4600 5000 5400 5800 6200 6750 mP/Mg 0.32339411 2.94400525 8.25361881 16.1918666 26.6565599 39.5642106 54.3308111 70.6711157 88.3323739 107.419393 127.150589 146.954463 166.651224 186.091089 205.150979 223.731447 248.355527 Integral[Keg] Mg 7.40445E-05 0.000100002 0.000122767 0.000146064 0.000171361 0.000199845 0.000232845 0.000272102 0.000320103 0.00038065 0.000459941 0.000568898 0.000728781 0.000987312 0.001478542 0.002779552 0.003 mP MM psi2/cp 2.39456E-05 0.000294406 0.001013273 0.002365048 0.004567893 0.007906711 0.01265068 0.019229763 0.028275479 0.040889153 0.058481785 0.083602079 0.121452239 0.183729879 0.303324261 0.621873294 0.74506658 q Scf/D 74.91424 74.91232 74.89056 74.83273 74.72395 74.54659 74.27757 73.89491 73.36341 72.63107 71.60676 70.17197 68.11042 64.97424 59.72925 49.31097 17.75325 0.2 0.1 0 10 20 30 40 50 60 70 80 G a s F lo w R a re [M sc f/D ] Fig.28 Gas Phase IPR vs pseudopressure [n = 0.8 and C = 0.0948, assumed and closely matched with rate during well test, since we did not have the production data for this well] Oil Phase For oil phase use following equations Pseudo-critical Temperature, Eq P-26 Pseudo-critical Pressure, Eq.P-27 Oil formation Volume Factor (Bo), Eq.P-28 4.Viscosity, Eq.P-30 80 P re ssu re [p si] Fig.30 Oil effective permeability integral 14 S A JOKHIO AND D TIAB SPE 75503 Table 11 Time, pressure, pseudopressure, and effective permeability to oil data 0.00001 0.000009 0.000008 Time P mP1o,o ∆mP 0.000007 0.000006 0.000005 0.000004 0.000003 0.000002 0.000001 0 1000 2000 3000 4000 5000 6000 7000 P re ssu re [p si] Fig 31 Oil phase effective permeability, derivative of Eq.17 10000 ∆ ∆ 1000 100 10 0.1 10 100 t.d∆mP/d(ln Integral[K eo] (t)) Hrs 0.167 0.333 0.5 12 16 22 psi 1083.1 1174.5 1226.7 1303.6 1490.6 1751.6 2046 2279.4 2759.4 3246.5 4210 5162 6161 Psia /cp 37.69242 45.06127 49.60332 56.74562 76.42196 109.62 155.6 198.9084 308.5168 450.2727 829.7878 1339.958 2012.652 Eq.20 7.368851 11.9109 19.05319 38.72953 71.92376 117.9054 161.216 270.8244 412.5802 792.0953 1302.266 1974.959 17.46048 28.77838 82.02722 120.4391 191.8662 321.6509 603.1635 1133.067 1594.884 1104.705 28 6336.5 2143.882 2106.189 969.7653 34 42 50 58 68 82 97 112 141 6406.1 6452.5 6487.3 6507.6 6526.5 6556.9 6574.3 6587.3 6601.8 2196.913 2232.571 2259.472 2275.226 2289.935 2313.675 2327.308 2337.515 2348.921 2159.22 2194.878 2221.78 2237.534 2252.242 2275.982 2289.615 2299.823 2311.229 344.0685 210.5204 131.9755 121.9627 115.2834 86.96564 95.23596 67.81678 Start of SSL 0.006112 0.009989 0.015934 0.017242 0.018241 0.024181 0.022081 0.031009 Keo 0.0000567 0.0000836 0.0001708 0.0000644 0.0000529 0.0001954 0.0001207 0.0006867 1000 Tim e [hrs] Table 12 Oil Phase IPR Fig.32 Oil phase pseudopressure and its derivative P 100 90 80 Pseudopressure [psia2/cp] 70 60 50 40 30 20 10 0 0.5 1.5 2.5 3.5 Oil flow Rate [STB/D] Fig.33 Condensate pseudopressure phase well performance vs 6000 Pressure [psi] 5000 4000 3000 2000 1000 2.5 2.55 2.6 2.65 2.7 2.75 2.8 2.85 Oil Flow Rate [STB/D] Fig.34 Oil phase well performance against pressure 2.9 200 600 1000 1400 1800 2200 2600 3000 3400 3800 4200 4600 5000 5400 5800 6200 6600 6750 mP1o,o/Mo Eq 20 1.005179 10.36004 31.6242 66.47398 116.5378 183.47 268.93 374.5329 501.7112 651.6465 825.1444 1022.557 1243.743 1488.069 1754.464 2041.501 2347.504 2466.777 Integral Mo [Fig.30] 7.89E-05 0.000139 0.00019 0.000242 0.000299 0.000362 0.000435 0.000522 0.000628 0.000762 0.000937 0.001178 0.00153 0.002099 0.003177 0.006013 0.034292 0.04 mP Psi2/cp 7.93358E-05 0.00143703 0.006010048 0.01609866 0.034792975 0.066391755 0.117008362 0.195527471 0.315218734 0.496653232 0.773404912 1.204296865 1.903079384 3.123445954 5.573699342 12.27577953 80.50032368 98.67109403 qo STB/D 2.862683 2.862681 2.862644 2.862518 2.86224 2.861724 2.860853 2.859458 2.857294 2.853995 2.848993 2.841363 2.829481 2.810206 2.776527 2.708841 2.52324 0.573717 Conclusions New method of projecting performance of gas condensate wells have been introduced that integrates well test transient pressure data and the production test data Well test data is used to estimate effective permeability of each (gas and condensate) phase and then is used to convert production pressure data into pseudopressure data Thus relative permeability curves have been completely eliminated SPE 75503 ESTABLISHING INFLOW PERFORMANCE RELATIONSHIP (IPR) FOR GAS CONDENSATE WELLS Well test equations have been modified in order to provide effective permeability of each phase as a function of pressure The effective permeability of one phase can also be used to convert the pressure data into pseudopressure of other phase This is very useful in case only one phase production data is available Sensitivity analysis shows that 10% increase in producing gas oil ratio causes 9% absolute error in oil effective permeability and 3% in gas effective permeability Nomenclature Bo = Oil FVF, RB/STB Bgd = Dry gas FVF cf/scf kro = Oil relative permeability krg = Gas relative permeability qg = Gas flow rate, scf/D Rs = Solution GOR, SCF/STB Rsgw = Solution gas water ratio, scf/STB Rp = Producing GOR, scf/STB (qg/qo) Rpgw = Producing gas water ratio, scf/STB Rpow = Producing oil water ratio, STB/STB S = skin SSL = Semi-log straight line SOC = Critical oil saturation, fraction Xe = a = Reservoir width, ft mP = pseudo-pressure function, MMpsia2/cp = Oil viscosity, cp µo = Gas viscosity, cp µg Subscripts g = Gas o = Oil w = Water r = relative e = effective z = in Z direction x = in X direction y = in y direction meas = Measured hr = One hour w = wellbore (In well testing equations) cor = Corrected b = Bubble d = Dew trans = Transient sp = Single phase sp-trans = Single phase from transient test wf = wellbore flowing s = shut-in t = total = Region-1 = Region-1 = Region-1 g1,o = gas phase in Region-1 using oil effective permeability g1,g = gas phase in Region-1 using gas effective permeability 15 o1,o = Oil phase in Region-1 using oil effective permeability o1,g = Oil phase in Region-1 using gas effective permeability References Vogel, J.T.: “Inflow Performance Relationships for Solution-Gas Drive Wells,” JPT Jan 1968, (83-92) Weller, W.T.: “ Reservoir Performance During Two Phase Flow,” JPT Feb.1966 (240-245) Fetkovich, M.D., Guerrero, E.T., Fetkovich, M.J., and Thomas, L.K.: “Oil and Gas Relative Permeabilities Determined from Rate-Time Performance Data,” paper SPE 15431 presented at the 1986 SPE Annual Technical Conference and Exhibition, New Orleans, Oct 5-8 Raghavan, R., Jones, J.R.: “Depletion Performance of Gas-Condensate Reservoirs”, JPT Aug 1996 Fevang, O and Whitson, C.H “Modeling GasCondensate deliverability,” Paper SPE 30714 presented at the 1995 SPE Annual Technical Conference and Exhibition, Dallas, Oct 22-25 Gopal, V.N.: “Gas Z-Factor Equations Developed For Computer,” Oil and Gas Journal (Aug 8, 1977) 58-60 Aguilera, R et al.: Horizontal Wells, Gulf Publishing Co., Houston TX.(185-187) McCain, W.D Jr.: The Properties of Petroleum Reservoir Fluids, Second Edition, PennWell Publishing company., Craft, B.C and Hawkins, M.F: Applied Petroleum Reservoir Engineering, Second Edition, prentice Hall PTR Publishing Company 10 Gopal, V.N.: “Gas Z-Factor Equations Developed For Computer,” Oil and Gas Journal (Aug 8, 1977) 58-60 11 Standing, M.B and Katz, D.L.: “Density Of Natural Gases,” Trans., AIME (1942), 146, 140-149 12 Penuela, G and Civan, F.: “Gas-Condensate Well Test Analysis With and Without Relative Permeability Curves”, SPE 63160 13 Serra, K.V., Peres, M.M., and Reynolds, A.C.: “WellTest Analysis for Solution-Gas Drive Reservoirs: Part-1 Determination of Relative and Absolute Permeabilities” SPEFE June 1990, P-124-131 14 Economides M.J et al “The Stimulation of a Tight, VeryHigh-Temperature Gas Condensate Well” SPEFE March 1989, 63-72 15 Guehria, F.M “Inflow Performance Relationships for Gas Condensates”, SPE 63158 16 Horne N.R., Modern Well Test Analysis, Second Edition, Petroway Inc., 1998 17 Evinger, H.H and Muskat, M.: “Calculation of Theoretical Productivity Factors,” Trans.,AIME (1942) 146, 126-139 18 Jones, L.G., Blount, E.M and Glaze, O.H.: “Use of Short Term Multiple Rate Flow Tests to Predict Performance of Wells Having Turbulence,” paper SPE 6133 presented at the 1976 SPE Annual Technical Meeting and Exhibition, New Orleans, Oct 3-6 19 Sukarno, P and Wisnogroho, A.: “Genaralized Two Phase IPR Curve Equation Under Influence of Non-linear Flow Efficiency,” Proc of the Soc of Indonesian 16 S A JOKHIO AND D TIAB Petroleum Engineers Production Optimization International Symposium, Bandung, Indonesia, July 2426, 1995, 31-43 20 Rawlins, E.L and Schellhardt, M.A.: Backpressure Data on Natural Gas Wells and Their Application to Production Practices, USBM (1935) 21 Wiggins, M.L.: “Inflow Performance of Oil Wells Producing Water,” PhD dissertation, Texas A&M U., College Station, TX (1991) 22 22 Camacho V and Raghavan R., “Inflow Performance Relationships for Solution-Gas Drive Reservoirs.” JPT (May 1989), P-541-550 Appendix A: Fluid Properties Used in This Study Light Oil Properties (API > 31.1) Bubble point Pressure: To estimate the bubble point pressure of the liquid phase of the condensate system Standings modified correlation was chosen 0.7857 R 10 0.0009T (P-1) 0.0148 API Pb = 31.7648 s γ g 10 Solution Gas Oil Ratio (Rso): Modified Kartoatmodjo's Correlation ( R s = 0.01347 γ g ,corr )0.3873 (Pb )1.1715 x 12.753 API T + 460 10 (P-2) Where Psp (P-3) γ g,corr = γ g Psp 1+ 0.1595.API0.4078Tsp −0.2466 log 114.7 Dead oil viscosity (µd) (Modified Egbogah-Jack's Correlation) log log(µod +1) = 1.8513− 0.025548.API − 0.56238 logTg (P-4) ( ) ( ) Gas saturated oil viscosity: (Modified Beggs and Robinson Correlation µ o1 = −0.032124 + 0.9289.F − 0.02865.F [ ] SPE 75503 Pseudo critical pressure Californian Gases Psp(psia) = -44.906(γg,cor)3 + 93.189(γg,cor)2 - 108.17(γg,cor) + 717.85 (P-12) Oklahoma gases Psp(psia) = -514.01(γg,cor)4 + 1788.2(γg,cor)3 - 2337.5(γg,cor)2 + (P-13) 1305.3(γg,cor)+ 415.07 Gas formation volume factor (Bg) zT Bg = 0.02829 , cu ft/SCF (P14) P zT Bg = 0.00504 , bbl/SCF (P-15) P Natural gas viscosity (µg) For its convenient mathematical form Lee and Gonzalez model for viscosity is used X µ g = 10 − X exp( X ρ ) (P-16) Where ρg is the gas density in g/cc and µg is the gas viscosity in cp, and (9.4 + 0.02M )T 1.5 (P-19) 209 + 19M + T 986 X = 3.5 + + 0.01M (P-18) T X = 2.4 − 0.2 X (P-20) MP (P-21) ρ g = 1.601846 x10 − RT Where T is in oR, ρ is in lb/cu ft, P in psia, R is 10.732 psiacuft/[lb-mole-oR] Gas compressibility (Z) For gas compressibility Gopal6 equations generated for computer use have been selected (Table A) Gas gravity at reservoir conditions: Three stage separation R1γ g + 4,602γ o + R γ g + R3γ g γg = (P-22) 133,316γ o R1 + + ( R + R3 ) Mo Two stage separation, R1γ g + 4,602γ o + R3γ g γg = (P-23) R1 + 133,316γ o M o−1 + R3 Also R1γ g + 4,602γ o + G pa g (P-24) γg = R1 + Veq X1 = ( (P-5) ] (P-6) µ o1 = 25.1921(Rso + 100)−0.6487 µ od [2.7516(Rso +150) Condensate specific gravity (γo) 141.5 γo = (P-7) 131.5 + API Molecular weight of condensate (Mo) 5,954 Mo = (P-8) API − 8.811 42.43γ o Mo = (P-9) 1.008 − γ o Natural Gas Properties For the temperature range of 300-700 oF and gravity range of 0.5-1.8 the following parameters are estimated as Pseudo Critical Temperature Standing correlation for California gases Tsp (oR) = 295.48γg,cor + 181.89 (P-10) Standing correlation for Oklahoma gases Tsp (oR) = 298.6 γg,cor + 179.44 (P-11) −0.2135 ( ) ) Condensates Pseudo-critical temperature Tsp (oR) = -71.647(γg,cor)2 + 333.52(γg,cor) + 182.2 Pseudo-critical Pressure Psp(psia) = -22.334(γg,cor)2 - 35.575(γg,cor) + 704.99 Oil formation Volume Factor (Bo) Standing co-relation Bo = 0.972 + 0.000147F 1.175 (P-26) (P-27) (P-28) SPE 75503 ESTABLISHING INFLOW PERFORMANCE RELATIONSHIP (IPR) FOR GAS CONDENSATE WELLS 0.5 γ g Where F = Rso + 1.25T , T = oF (P-29) γo For crude oil viscosity (In Pa-S), Miadonye et al one parameter correlation is available 350 Gas Gravity From TopBottom 340 330 320 0.60 0.65 0.70 0.75 0.80 0.85 0.90 0.95 1.00 1.05 310 300 290 280 −d T − 30 ln µ o = 2.30259b1 + − 6.912375 303.15 Where b = log µ (@ 30o C ,0 MPag ) + 3.002 17 270 260 (P-30) 250 240 230 (P-31) Rp = 5000[scf/ST B] T = 200 F API = 45 SG = 0.6 220 210 And d = 0.006694b + 3.5364 Where T is in oC Table A-1Gopal6 Equations for Estimating Gas Compressibility Factor (Z) Pr Tr Equations 0.2 To 1.2 1.2 + To 2.8 1.05 To 1.2 1.2 + To 1.4 1.4+ To 2.0 2.0+ To 3.0 1.05 To 1.2 1.2 + To 1.4 1.4+ To 2.0 2.0+ To 3.0 Pr Pr Pr Pr Pr Pr Pr Pr (1.6643 Tr - 2.2114) - 0.367 Tr + 1.4385 (0.5222 Tr - 0.8511) - 0.0364Tr *+ 1.0490 (0.1391 Tr - 0.2988) + 0.0007Tr * + 0.9969 (0.0295 Tr - 0.0825) + 0.0009Tr * + 0.9967 (-1.3570 Tr +1.4942) + 4.6315 Tr - 4.7009 (0.1717 Tr - 0.3232) + 0.5869 Tr +0.1229 (0.0984 Tr - 0.2053) + 0.0621Tr + 0.858 (0.0211 Tr - 0.0527) + 0.0127Tr + 0.9549 2.8 + To 5.4 1.05 To 1.2 1.2 + To 1.4 1.4+ To 2.0 2.0+ To 3.0 Pr Pr Pr Pr (-03278Tr + 0.4752) +1.8223Tr -1.9036 (-0.2521Tr + 0.3871) +1.6087Tr -1.6635 (-0.0284Tr + 0.0625) + 0.4714Tr -0.0011* (0.0041Tr + 0.0039) + 0.0607 Tr +0.7927 mP[MM psi2/cp]/Mg1 200 190 180 170 160 150 140 N o 3+ 4+ 5+ 130 120 110 100 90 80 70 60 + 50 9+ 10 40 30 20 10 0 500 1000 1500 2000 2500 3000 3500 4000 4500 5000 5500 6000 Pressure [psi] + 11 12 Fig.B-2 Gas phase pseudopressure Region-1[Eq.16 ] [T = 200 oF] 1.05 To 3.0 Pr (0.711 + 3.66Tr)-1.4667 -1.637/(0.319Tr + 0.522) + 5.4 2.071 13 + To 15 *These terms may be ignored +For a very slight loss in accuracy, Equations and and and 10 can, respectively, be replaced by the following two equations: ++Preferably use this equation for Pr up to 2.6 only For Pr = 2.6+, equation will give slightly better results Also, preferably, use Equation for 1.08 ≤Tr ≤ 1.19 and Pr ≤1.4 300 G as G ravity From TopBottom 290 280 0.60 0.65 0.70 0.75 0.80 0.85 0.90 0.95 1.00 1.05 270 260 250 240 230 Appendix B: Pseudopressure Function Charts Gas Phase Region-1 220 210 200 350 G a s G r a v it y Fr o m T o p Bo tto m 340 330 180 320 290 280 270 260 250 240 170 mP[MM psi2/cp]/Mg1 0 0 0 0 0 10 300 Rp = 5000[scf/S TB ] T = 300 F AP I = 45 190 160 150 140 130 120 110 230 100 220 Rp = 0 [ s c f /S T B] T = 150 F A PI = 45 S G = 10 200 19 18 90 80 70 17 60 16 50 15 40 14 13 30 12 20 110 10 10 0 90 80 500 1000 1500 2000 2500 3000 3500 4000 4500 5000 5500 6000 Pressure [psi] 70 60 Fig.B-3 Gas phase pseudopressure Region-1[Eq.16 ] [T = 300 oF] 50 40 30 20 10 0 500 10 0 15 0 2000 2500 3000 3500 4000 4500 5000 5500 6000 P r e s s u r e [ p s i] Fig.B-1Gas phase pseudopressure Region-1[Eq.16 ] [T = 150 oF] 18 S A JOKHIO AND D TIAB Effect of API Gravity Effect of Producing Gas Oil Ratio, Rp 45 350 G as G ravity F ro m To pB o tto m 44 43 42 330 320 0.60 0.65 0.70 0.75 0.80 0.85 0.90 0.95 1.00 1.05 39 38 37 36 35 34 33 32 31 30 Rp = 5000 [sc f/S TB ] T = 50 F AP I = 50 29 28 27 26 290 280 270 260 250 240 230 23 22 21 20 19 Rp =6000 [scf/S T B] T = 150 F AP I = 45 220 210 24 300 200 190 180 170 160 150 140 18 17 130 16 120 15 110 14 100 13 12 90 11 80 10 70 90 60 80 70 50 60 40 50 30 40 20 30 10 20 10 0 50 10 00 15 00 20 00 25 00 30 00 35 00 40 00 45 00 50 00 55 00 500 1000 1500 2000 2500 3000 3500 4000 4500 5000 60 00 P re ssure [p si] P ressure [p si] Fig.B-6 Gas phase pseudopressure Region-1[Eq.16 ] [Rp = 6,000 scf/STB] Fig.B-4 Gas phase pseudopressure Region-1[Eq.16 ] [API = 50] 600 Gas Gr avity Fr o m T o p Bo tto m 575 30 G as G ravity F ro m Top B o tto m 29 550 0.60 0.65 0.70 0.75 0.80 0.85 0.90 0.95 1.00 1.05 525 500 475 450 425 28 27 0.60 0.65 0.70 0.75 0.80 0.85 0.90 0.95 1.00 1.05 26 25 24 23 22 400 21 Rp = 5000[s cf/ST B] T = 150 F A PI = 55 375 350 325 20 18 17 300 275 250 Rp =7 000[scf/S T B] T = 50 F AP I = 45 19 mP[MM psi /cp]/Mg1 25 0.60 0.65 0.70 0.75 0.80 0.85 0.90 0.95 1.00 1.05 310 mP[MM psi /cp]/Mg1 40 G as G ravity F ro m To p B o tto m 340 41 mP[MM psi /cp]/Mg1 SPE 75503 16 15 14 13 225 12 200 11 175 10 90 150 80 125 70 60 100 50 75 40 50 30 25 20 10 0 500 1000 1500 2000 2500 3000 3500 4000 4500 5000 5500 6000 P re ssu re [p si] 50 10 00 15 00 20 00 25 00 30 00 35 00 40 00 45 00 50 00 P ressure [p si] Fig.B-5 Gas phase pseudopressure Region-1[Eq.16 ] [API = 55] Fig.B-7 Gas phase pseudopressure Region-1[Eq.16 ] [Rp = 7,000 scf/STB] SPE 75503 ESTABLISHING INFLOW PERFORMANCE RELATIONSHIP (IPR) FOR GAS CONDENSATE WELLS 300 280 G as G ravity F ro m To pB o tto m 25 G as G ravity F rom To pB o ttom 290 19 24 23 270 0.60 0.65 0.70 0.75 0.80 0.85 0.90 0.95 1.00 1.05 260 250 240 230 220 210 0.60 0.65 0.70 0.75 0.80 0.85 0.90 0.95 1.00 1.05 1.10 22 21 20 19 18 17 180 160 mP[MM psi /cp]/Mg1 170 150 140 130 120 110 Rp =8000[scf/S T B] T = 150 F AP I = 45 190 Pseudopressure [MMpsi /cp]/Mo1 200 16 R p = 5000 S C F /S TB T = 00 F AP I = 45 µ d = 0.5 c p P b = 100 p si 15 14 13 12 11 10 100 90 80 70 60 50 40 30 20 10 0 500 1000 1500 2000 2500 3000 3500 4000 4500 5000 500 1000 1500 2000 Oil Phase Region-1 28 27 26 25 24 23 22 21 20 24 4000 4500 5000 5500 6000 G as G ravity F ro m Top B o tto m 0.60 0.65 0.70 0.75 0.80 0.85 0.90 0.95 1.00 1.05 1.10 21 23 18 Rp = 5000 SC F/ST B T = 150 F A PI = 45 µ d = 0.5 cp Pb = 1000 ps i 17 16 15 14 13 12 20 19 18 17 16 R p = 5000 S C F /S TB T = 50 F AP I = 45 µ d = 0.5 c p P b = 1000 p si 15 14 13 12 11 10 11 10 0.60 0.65 0.70 0.75 0.80 0.85 0.90 0.95 1.00 1.05 1.10 22 19 Gas Gr avit y Fr o m T o p Bo tto m Pseudopressure [MMpsi /cp]/Mo1 29 /cp]/Mo1 3500 25 30 3000 Fig.B-10 Oil phase pseudopressure Region-1[Eq.21] [T=200 oF] Fig.B-8 Gas phase pseudopressure Region-1[Eq.16 ] [Rp = 8,000 scf/STB] Pseudopressure [MMpsi 2500 P ressu re [p si] Pressure [p si] 0 500 1000 1500 2000 2500 3000 3500 4000 4500 5000 5500 6000 500 1000 1500 2000 2500 3000 3500 4000 4500 5000 5500 6000 P ressu re [p si] Pr e s s u r e [p s i] Fig.B-9 Oil phase pseudopressure Region-1[Eq.21] [T=150 oF] Fig.B-11 Oil phase pseudopressure Region-1[Eq.21] [T=250 oF] 20 S A JOKHIO AND D TIAB G as G ravity F ro m To pB o tto m 20 19 18 0.60 0.65 0.70 0.75 0.80 0.85 0.90 0.95 1.00 1.05 1.10 17 16 15 14 Pseudopressure [MMpsi /cp]/Mo1 13 R p = 5000 S C F /S TB T = 00 F AP I = 45 µ d = 0.5 c p P b = 100 p si 12 11 10 0 500 1000 1500 2000 2500 3000 3500 4000 4500 5000 5500 6000 P ressu re [p si] Fig.B-12 Oil phase pseudopressure Region-1[Eq.21 ] [T= 400 oF] G as G ravity F ro m To pB o tto m 30 29 28 27 0.60 0.65 0.70 0.75 0.80 0.85 0.90 0.95 1.00 1.05 1.10 26 25 24 23 22 21 Pseudopressure [MMpsi /cp]/Mo1 20 19 Rp = 10,0 00 S C F /S TB T = 50 F AP I = 45 µ d = 0.5 c p P b = 100 p si 18 17 16 15 14 13 12 11 10 0 500 1000 1500 2000 2500 3000 3500 4000 4500 5000 5500 6000 P ressu re [p si] Fig.B-13 Oil phase pseudopressure Region-1[Eq.21 ] [Rp = 10,000 scf/STB] SPE 75503