Endpoint Mobility Ratios for Vertical and Horizontal Wells with Incidence of Scale Deposition

Transcription

1 e Open Petroleum Engineering Journal, 2009, 2, Open Access Endpoint Mobility Ratios for Vertical and Horizontal Wells it Incidence of Scale Deposition A. Olufemi Bamidele *,1, A.S. Fadairo 2 and O.A. Falode 1 1 Department of Petroleum Engineering, University of Ibadan, Ibadan, Nigeria 2 Department of Petroleum Engineering, Covenant University, Otta, Nigeria Abstract: One of te most difficult and profit urting problems found in te oil field is te build-up of scale deposits in te bore, production string, flo lines and even in storage tanks. ese deposits act as a restriction during build-up in te bore causing a gradual decrease in production and, in many cases, as a solid barrier fobore fluid flo. is paper presents an analytical model based on te existing termodynamic model soing te endpoint mobility ratios for bot vertical and orizontal s it te incidence of scale precipitation and deposition at te neabore region during ater flooding. e results revealed tat Endpoint mobility ratio for a vertical it radial flo approaces unity 1 faster tan for te orizontal it elliptical flo. And orizontal s are good candidates for managing scale precipitation and deposition during aterflooding. INRODUCION Scaling penomenon is a major problem tat occurs en ater is injected for oil displacement and pressure maintenance in oilfields [1-3]. is penomenon of precipitation and accumulation of oilfield scale is due to incompartibility beteen formation and te injected ater induced around te bore after ater breaktroug at reduced reservoir pressure [4,5]. e effects result in formation damage ic negatively impact reservoir performance, bore performance and te success of aterflooding project tat depends on mobility ratio [6,7]. Supplementary recovery results from increasing te natural energy of te reservoir, usually by displacing te ydrocarbons toards te producing s it some injected fluid. By far te most common fluid injected is ater because of its availability, lo cost and ig specific gravity ic facilitates injection. e basic mecanics of oil displacement by ater can be understood by considering te mobilities of te separate fluids. e mobility of any fluid is defined as: KKr (1) μ ic, considering Darcy's la [8], can be seen to be directly proportional to te velocity of flo. Also included in tis expression is te term kr /μ, ic is referred to as te relative mobility. e favourable type of displacement ill only occur if *Address correspondence to tis autor at te Department of Petroleum Engineering, University of Ibadan, Ibadan, Nigeria; el: ; s: ofemidele@yaoo.com, ofemidele@gmail.com K K ro M 1 (2) ere M is knon as te end point mobility ratio and, since bot K ro and K are te end point relative permeabilities, is a constant. If M 1 it means tat, under an imposed pressure differential, te oil is capable of travelling it a velocity equal to, or greater tan, tat of te ater. Since it is te ater ic is pusing te oil, tere is terefore, no tendency for te oil to be by-passed ic results in te sarp interface beteen te fluids. is displacement is called "piston-like displacement". Its most attractive feature is tat te total amount of oil tat can be recovered from a linear reservoir block ill be obtained by te injection of te same volume of ater. is is called te movable oil volume ere, 1( MOV ) (1 S or S c ) (3) e unfavourable displacement ic unfortunately is more common in nature, occurs en M > 1. In tis case, te ater is capable of travelling faster tan te oil and, as te ater puses te oil troug te reservoir, te latter ill be by-passed. Water tongues develop leading to te unfavourable ater saturation profile. Aead of te ater front oil is again floing in te presence of connate ater. is is folloed, in many cases, by a aterflood front, or sock front, in ic tere is a discontinuity in te ater saturation. ere is ten a gradual transition beteen te sock front saturation and te maximum saturation, S 1 S or (4) At a constant rate of ater injection, te fact tat muc more ater must be injected, in te unfavourable case, / Bentam Open

2 18 e Open Petroleum Engineering Journal, 2009, Volume 2 Bamidele et al. protracts te time scale attaced to te oil recovery and tis is economically unfavourable. In addition, pockets of bypassed oil are created ic may never be recovered. MODE DEVEOPMEN Assuming an idealised flo, Fadairo and Omole [6,7] expressed te effect of scale build up on permeability variation, skin factor and additional pressure drop across te skin based on exponential sape for bot porosity and permeability damage function as; K i 1 F dc ere is defined as te instantaneous permeability as a result of solid scale saturation near a vertical bore region it exponent of 3 [2,9]. e effect of oil field scale build up on te skin factor at different pore volume of sea ater injected can be expressed as; K [1F dc (5) 1] ln r s (6) Endpoint Mobility ratio for a radial flo of ater it te incidence of scale deposition around a vertical bore can terefore be expressed as: KK M P n r oil μ + q n r ater + s (7) Wile Endpoint Mobility ratio for an elliptical flo of ater it te incidence of scale deposition around a orizontal bore can be expressed as: 141.2P KK + q ln a + a 2 + ( 2) 2 + ln 2 2r + s orizontal M ln a + a2 + ( 2) 2 + ln 2 2r e details of te derivation can be seen in te Appendix A and B. RESUS AND DISCUSSION Horizontal Well engt: Fig. (1) revealed tat as te orizontal lengt increases, mobility ratio also increases, and, beyond 1300 ft it becomes unfavourable and greater tan unity resulting in premature breaktoug of ater. Pore Water Injected: As te ater injected increases, mobility ratio increases and faster to approac te value of unity 1 (for a stable and pistonlike displacement to occur) for 1500ft orizontal lengt. Hoever, it least approac unity for a 100ft reservoir (Fig. 2). Skin Factor: It is son in Fig. (3) tat mobility ratio increases it increasing formation damage. As te orizontal lengt increases from 100 feet (ft) to 600 feet (ft), mobility ratio is greater tan unity and becomes muc more unfavourable for reservoir tickness of 60ft. Mobility Ratio of Radial and Elliptical Flo: Endpoint mobility ratio for a vertical radial flo approaces unity 1 faster tan for te orizontal elliptical flo. is results in te by-passing of oil and consequently te premature breaktroug of ater (Fig. 4). (8) Fig. (1). Endpoint mobility ratio versu lengt, 20ft. Fig. (2). Endpoint mobility ratio versus ater flo rate at varied orizontal lengt.

3 Vertical and Horizontal Wells it Incidence of Scale Deposition e Open Petroleum Engineering Journal, 2009, Volume 2 19 Fig. (3). Mobility ratio and skin factor, 60 for orizontal it elliptical flo. Fig. (4). Endpoint mobility ratios of a vertical radial flo and orizontal elliptical flo. CONCUSION e folloing conclusions ere dran from te results of tis study: able 1. Fluid and Reservoir Parameters used as Input in te Scale Prediction Models [2,5,10,11] a r o K Kro P dc 85 o C 1114ft Varies 0.365ft Varies 1.02 bbl/d 1.6cp 1cp 0.04mD 2.5mD Varies 5.0E-15mg/m 3 -pa Endpoint mobility ratio of bot vertical and orizontal s due to sulpate scale deposition is te function of operational and reservoir/brine parameters suc as scale concentration in te brine, viscosity of brine, formation volume factor of te brine, solid scale density, injection rate, pressure dradon, reservoir temperature, reservoir tickness and brine velocity. Mobility ratio increases it increasing formation damage. ick reservoir approaces unfavourable mobility ratio faster tan tin oil reservoirs it incidence of scale deposition. Endpoint mobility ratio for a vertical radial flo approaces unity 1 faster tan for te orizontal elliptical flo. APPENDIX A Model Development Pressure gradient due to te presence of scale in te flo pat as follos [3,4].

4 20 e Open Petroleum Engineering Journal, 2009, Volume 2 Bamidele et al. dr qμbe ( 3k dep Ct) 2 kr s (A-1) In ic e 3k dep C.t and 3k dep C is defined as formation damage coefficient. From tis equation, te formation damage coefficient is a function of time. Instantaneous local porosity is defined as te difference beteen te initial porosity and te damaged fraction of te pore spaces i.e. te fraction of te mineral scale tat occupied te total volume of te porous media. at is, dc μb m 4 2 r 2 s 2. By substituting (A-7) into (A-2) m o ere m o dc μb 4 2 r 2 s 2 o., ic is te pore volume occupied by scale. (A-7) (A-7.1) s 0 m s 0 1 m 0 s 0 volume scale volume pores (A-2) (A-3) Expressing tis volume as a fraction of te total pore volume occupied by oil, e ten ave: s 1 m 1 o 0 dc μb 4 2 r 2 s 2 o. (1 S c ) (A-8) e volume of scale dv ic drops out and get deposited in te volume element over te time interval, dt, is given as follos: [2] dv q dc.dt (A-4) dc ere is defined as te cange in saturated solid scale content per unit cange in pressure at constant temperature. Hence, te cange in porosity due to scale deposition over time interval is given as: q dc d m ( qμbe 3k dep Ct ).dr.dt 2 kr s 2r s dr dc ( μbe 3k dep Ct ) dt d m 4 2 r 2 s 2 Integrating equation (A-5) m ere dc ( μbe 3k dep C.t ) 4 2 r 2 s 2.3k dep C 3k dep C dc μb k m 4 2 r 2 s 2.3k dep C and e 3k dep Ct (A-4.1) (A-5) (A-6) (A-6.1) et F s 1 F dc o μb 4 2 r 2 s 2 o. (1 S c ) ere, dc is determined by te termodynamic model of eac salt involved [12]. By expressing te initial and instantaneous permeabilities as a function of altered porosity [2,9] e ave: K o 0 0 By substituting te skin formula e ave (A-8.1) (A-8.2) K o 1 F dc (A-9) And simply, skin factor can be expressed as K 1 K s ln r s (A-10) We can express te relationsip beteen orizontal and vertical damage as [13]: ( / ) (A-10.1) ( ) (A-10.2) / ( k k s ) 1 ln ( r r s ) Substituting (A-9) into (A-10), e ave:

5 Vertical and Horizontal Wells it Incidence of Scale Deposition e Open Petroleum Engineering Journal, 2009, Volume 2 21 K [1F dc 1] ln r s (A-10.3) We also ave for te orizontal skin factor due to scale as: K [1F dc 1] ln r s (A-11) At te initial start of production, en time is zero, q 0, and since F depends on q, F is also equal to zero, and te initial permeability is equal to te intantaneous permeability i.e K K o and tere ill be no skin due to scale, i.e 0, By subtituting (A-11) into orizontal fluid flo equation [10,11], e ten ave: a + a 2 ( 2) 2 q 141.2p B K ln μ / 2 + ln 2r + s orizontal And for productivity index: ln a + a2 ( 2) 2 2 J q p 141.2k μ / + ln 2r + k H [1F dc k 0 For and 2 ( ) 0.9r eh (A-12) (A-13) 1] ln r s ere, J is te orizontal productivity index. If k v k, 1, ic implies tat, vertical permeability is equal to te orizontal permeability. And, a is te alf of te major axis of a drainage ellipse in a orizontal plane in ic te is located and can be reformulated as: a reh and fluid flo in porous media for a vertical into a orizontal fluid flo pattern. q 141.2p o K o / ln a + a 2 2 μ o 2 ( ) 2 + ln 2r Assuming tat te vertical injection is located around te producing orizontal and te flo around te orizontal is elliptical. e total pressure drop as a result of ater pusing oil can be expressed as: P t P o + P + P g + P scale For Oil Pase: P o B o A KK ro, For Water Pase: P q B A KK, For Gas Pase: P g q g μ g B A g KK rg, and, For Scale: P scale q KK, et, A ln a + a2 2 2 and, ( ) 2 K [1F dc + ln 2r 1] ln r s (A-14) (A-15) (A-16) (A-17) (A-18) Since gas does not carry any particle and assumed to be a non-etting pase, terefore, P g 0. en equation (12) becomes: P B A o KK ro q B A KK q KK (A-19) ( ) 2 ln a2 + a ln 2r is a dimentional factor tat converts te conventional Darcy [8] equation of P B o A KK ro q KK A + s orizontal (A-20)

6 22 e Open Petroleum Engineering Journal, 2009, Volume 2 Bamidele et al. P A KK ro dividing te equation by 141.2P KK q KK KK KK ro KK A + A q B A + s orizontal By (A-21) 141.2P KK q A q B A + s orizontal (A-22) M A 141.2P KK + q A P KK + q A + M A 141.2P KK + q ln a + a 2 + ( 2) 2 + ln 2 2r + s orizontal M ln a + a2 + ( 2) 2 + ln 2 2r (A-23) (A-24) (A-25) K [1F dc K 0 1] ere, ln r s APPENDIX B Consider te simultaneous radial flo of oil and injected ater, saturated it solid mineral scale particle at location r, from a vertical bore. e total pressure drop across te vertical bore is te summation of te pressure drop due to flo of oil and ater. at is: P P + P o + P s (B-1) KK M P n r + q oil n r ater + s r (B-6) ere s is te skin factor, ic can be expressed as: K [1F dc Symbols Used C Salt Concentration V Volume of scale q Flo rate bbl/day Density 1] ln r s t Production time, ours (rs) emperature, Degree Celcius ( o C) r Radius feet (ft) m Damaged fraction porosity, (%) K P B K dep Permeability milli-darcy (md) Reservoirickness, feet (ft) Pressure lb/in 2 (psi) Formation Volume Factor rb/sb Deposition rate constant Formation damage coefficient o Initial Porosity, percent (%) s Instantaneous porosity, percent (%) S c Connate ater saturation, percent (%) (B-7) P q n r ater μ o 1 F dc 2 KK ro 2 KK By rearranging tis e ave; q P n r ater + 1 F dc 2 KK q o n r oil 2 KK ro 2 KK P q n r ater + 1 F dc 2 KK n r oil q + n r n r ater + 1 F dc oil 1 n r s r n r s r n r s r Mn r oil r n r s r M (B-2) (B-3) (B-4) (B-5) K o r s r K ro K K g P Initial Permeability, milli-darcy (md) Altered Permeability, milli-darcy (md) Horizontal Well engt, feet (ft) Radius of te altered zone, feet (ft) Wellbore radius, feet (ft) Oil relative permeability, dimensionless Water relative permeability, dimensionless Gas Relative Permeability, dimensionless Pressure Drop, lb/in 2 (psi) Viscosity centi-poise (cp) Horizontal Skin factor, dimensionless J Productivity Index, bbls/d/psi M Mobility Ratio, dimensionless

7 Vertical and Horizontal Wells it Incidence of Scale Deposition e Open Petroleum Engineering Journal, 2009, Volume 2 23 a Half of te major axis of drainage ellipse in a orizontal, feet (ft) Square root of permeability ratio, k H / k v Subscripts H orizontal V Vertical s skin eh drainage for orizontal orizontal o oil g gas ater ACKNOWEDGEMEN e autor gratefully acknoledge te effort of Esso Exploration & Production imited an ExxonMobil Subsidiary for providing fund to sponsor tis project. SI Metric Conversion Factors bbl E-01m 3 psi E-00Kpa ft 48* E-01m cp 1.0* E-03Pa.s md E-04m 2 ( o F-32)/1.8 E-00 o C REFERENCES [1] P. G. Bedrikovetsky, P. M. Gladstone, ope, Jr., F. F. Rosario, Silva, M. F., M. C. Bezerra and E. A. ima, Oilfield Scaling. Part II: Productivity Index eory, SPE Paper 81128, 2003 [Online] [2] F. Civan, Modelling Well Performance under Non Equilibrium Deposition Condition, SPE Paper 67234, 2001 [Online] [3] A. S. Fadairo, O. Omole, and O. Falode, Effect Of Oilfield Scale Deposition On Mobility Ratio, SPE Paper , 2008 [Online] [4] A. S. Fadairo, Modeling Formation Damage Induced by Oilfield Scales. M.Sc tesis, University of Ibadan, Ibadan, Nigeria, [5] O. J. Veter and V. Kandarpa, Prediction of CaCO 3 Scale Under Boreole Conditions, SPE Paper 8991, 1980 [Online] [6] F. Frank, Cang and F. Civan, Modeling of Formation Damage Due to Pysical and Cemical Interaction beteen Fluid and Reservoir Rock, SPE Paper 22856, 1991 [Online] [7]. Haarberg, I. Selm, D. B. Granbakken,. Østvold, P. Read and. Scmidt, Scale Formation in Reservoir and Production Equipment during Oil Recovery II, equilibrium Model, SPE J. Prod. Eng., Vol. 7, no. 1, [8] H. Darcy, es Fontaines de la Ville de Dijon, Victor Dalmont, Paris, 1856 [Online] Available:.spe.org/elibrarysearc [Assessed Feb.19, 2009]. [9] J. Mogadasi, A. Sarif, A. M. Kalantari and E. Motaie, A Ne Model to Describe Particle Movement and Deposition in Porous Media SPE Paper 99391, 2006 [Online] Available:.spe.org/elibr arysearc [Assessed Feb.19, 2009]. [10] S. D. Josi Augmentation of Well Productivity it Slant and Horizontal Wells, J. Petrol. ecnol., pp , 1988 [Online] [11] D. Josi Sada, Horizontal Well ecnology. Josi ecnologies International, Inc. ulsa, Ok, USA, Penn Well Books: pp. 1-91, [12] G. Atkinson, K. Raju and R. D. Ho, e ermodynamics of Scale Prediction, SPE Paper 21021, 1991 [Online] Available:.spe.org/elibrarysearc [Assessed Feb. 19, 2009]. [13] G. I. Renard and J. M. Dupuy, Influence of Formation Damage on te Flo Efficiency of Horizontal Wells, SPE Paper 19414, 1990 [Online] Available:.spe.org/elibrarysearc [Assessed Marc 3, 2009]. Received: June 12, 2009 Revised: June 26, 2009 Accepted: June 29, 2009 Bamidele et al.; icensee Bentam Open. is is an open access article licensed under te terms of te Creative Commons Attribution Non-Commercial icense (ttp://creativecommons.org/licenses/bync//) ic permits unrestricted, non-commercial use, distribution and reproduction in any medium, provided te ork is properly cited.