The precipitation and deposition of scale pose serious injectivity and productivity problems. Several models have been developed for predicting oilfield scales formation and their effect on deliverability of the reservoir to aid in planning appropriate injection water programme. In this study an analytical model has been developed for predicting productivity index of reservoir with incidence of scale deposition in the vicinity of the well bore

Ako , C. T.

Fadairo, A. S. A.

Olugbenga , F.

Olusegun, O.

English

Covenant University Repository

Advances in Sustainable Petroleum Engineering and Science ISSN 1937-7991 2009, Volume 1, Issue 3, pp. © 2008 Nova Science Publishers, Inc. EFFECT OF OILFIELD SULPHATE SCALES ON PRODUCTIVITY INDEX Fadairo A. S. Adesina', C. T. Ako, Omole Olusegun and Falode Olugbenga Covenant University, Ota, Nigeria, University ofIbadan Nigeria ABSTRACT The precipitation and deposition of scale pose serious injectivity and productivity problems. Several models have been developed for predicting oilfield scales formation and their effect on deliverability of the reservoir to aid in planning appropriate injection water programme. In this study an analytical model has been developed for predicting productivity index of reservoir with incidence of scale deposition in the vicinity of the well bore. NOMENCLATURES Bo = Oil Formation volume factor, dimensionless Bw = Water Formation volume factor, dimensionless C = Concentration, g/m3 h = Thickness, m K = Instantaneous permeability, m2 K 0 = Initial permeability, m2 Kdep = Deposition rate constant rw = Well bore Radius, m R = Radial distance, m Sw = Water saturation, dimensionless SW = Connate water saturation, dimensionless c T = Temperature, K t = Production time, sec fJ o = Oil Viscosity, cp • Corresponding e-mail: adesinafadairo@yahoo.com 2 Fadairo A. S. Adesina, C. T. Ako, Omole Olusegun et al. J.1w =Water Viscosity, cp <Po =Initial Porosity, dimensionless <P = Instantaneous porosity, dimensionless P = density, g/m3 INTRODUCTION The magnitude of flow impairment induced by oilfield sulphates scale deposition around the well bore require description and classification of sulphate scales precipitation, scale build up (saturation), and their corresponding formation damage scenario at different operational and reservoirlbrine parameters such as scale concentration in the brine, viscosity of brine, formation volume factor of the brine, solid scale density, injection rate, pressure drawdown, reservoir temperature, reservoir thickness, brine velocity and radial distance from the vicinity of the well bore (Fadairo et aI, 2008; Civian, 200 I). Major factors that influence the mixing and scale formation have been described in the literature (Fadairo, 2004; Oddo and Tomson, ! 991). The details of how sulphate scales are deposited in different locations in the reservoir near the well bore region and the consequent formation damage has also been presented (Fadairo, 2004, Fadairo et aI, 2008). Mixing of incompatible waters take place in the water contacted portion of the reservoir during water flooding (Fadairo, 2004; Fadairo et ai, 2008; Civian, 2001; Bedrikovetsky et al., 2003a, 2004). For instance, when formation water containing barium ion and seawater containing sulphate ions are mixed together, barium sulphate (precipitate) is formed in the swept zone inside the reservoir and is deposited as scale around the well bore during waterflooding. In general the water-mixing zone moves from injection wells towards producers and precipitation of scales takes place in the mixing zone. Accumulation of precipitates does not depend upon mixing zone movement. The amount of scale precipitated at any point in the reservoir during such movement does not cause significant reduction in formation permeability (Civian, 2001; Bedrikovetsky et al., 2003a, 2004; Richards, 1968). Diffusion and intensive mixing increase close to the production well due to increase in fluid velocity which also causes increase in the rate of chemical reaction in this region (Civian, 2001; Bedrikovetsky et al., 2003a, 2004). These phenomenon lead to a higher rate of sulphate precipitation in the near well bore region than inside the reservoir. The overall effect of the above is that most of the sulphate precipitation and hence permeability reduction occur in the vicinity of the well (Fadairo et ai, 2008; Bedrikovetsky et al., 2003b). Studies (Fadairo et aI, 2008; Rosario and Bezerra, 2001; Rocha, 2001) have shown that formation damage caused by sulphate precipitation can be better described as an exponential function of the depositional rate constant, salt concentration and production time rather than by a hyperbolic function of these variables as proposed by Bedrikovetsky et a17 . Hence, there is the need to develop an expression for estimating the productivity index in wells producing from water-flooded reservoirs with possible incidence of SUlphate scale formation based on 3 Effect of Oilfield Sulphate Scales on Productivity Index the exponential function model. The purpose of this paper is to present the mathematical expression for achieving this purpose. MODEL DEVELOPMENT Consider the radial two-phase flow of oil and water at constant total flow rate q/; saturated with solid-state particle at a location r, from the well bore. Assuming an idealized flow equation, the pressure gradient is expressed as follows: (1) Fadairo et ai, 2008, recently expressed the effect of scale builds up on permeability variation based on exponential shape for both porosity and permeability damage function as (2) where K s is define as the instantaneous permeability as a result of solid scale saturation near the well bore region. The derivation of equation (2) is expressed in appendix A. Substituting equation (2) into (1) and re-arranging; we obtain (3) (4) Integrating equation (4); we have 4 Fadairo A. S. Adesina, C. T. Ako, Omole 01usegun et al. Therefore (7) The productivity index PI in a water-flooded reservoir with possible incidence of sulphate scale deposition around the well bore can be expressed as (8) At initial production time, when t = 0 and S s = 0 the expression degenerates to the normal Dupui formula for productivity index. (9) DISCUSSION OF RESULTS The model was validated using the data of Haarberg et ai (1991) on scale precipitation for given pore volume of sea water injected and fluid! reservoir properties datal, (Fadairo, 2004; Fadairo et ai, 2008; Richards, 1968) shown below in Tables1 and 2 respectively, as input into the model. Table 1. Amount of BaS04 and SrS04 precipitated as a function of pore volume of seawater injected (after Haarberg et a11991) Pore volume of seawater BaS04 SrS04 injected (%) Precipitate (g/m3 ) Precipitate (g/m3 ) 0 0.0 0.0 10 71.0 0.0 20 65.0 0.0 30 58.0 45.0 40 48.0 68.0 50 42.0 58.0 60 32.0 26.0 70 25.0 0.0 80 18.0 0.0 90 10.0 0.0 100 0.0 0.0 5 Effect of Oilfield Sulphate Scales on Productivity Index Table 2. Fluid and reservoir base case properties civan (2001) used as input in the scale prediction model Pay thickness (h) 26m Initial permeability 0.5922E-13mL (60mD) Initial porosity 0.04 Reservoir pressure 36600kpa Bottom hole pressure 22060kpa Reservoir temperature 353K (80C) Formation volume factor 0.254 Viscosity 0.0007Pa-s Connate water saturation 0.2 The result of the model show that productivity decline due to scale formation around the well bore is better described when the formation damage function was assumed to be an exponential function of the scale depositional rate constant, salt concentration and time than when hyperbolic shape was assumed as opined by Bedrikovetsky et of (2003a). The rate of decline of the productivity of a formation due to sulphate scale deposition may be sharp initially but usually the rate decreases exponentially as the pore volume of the seawater injected water increases (Civian et al 2001; Fadairo, 2004). The productivity decline caused by scale formation around the well bore was over estimated when the formation damage was assumed to be a hyperbolic function (figure I). The higher the average scale precipitation in the mixing zone along the reservoir, the lower the well productivity index (Table I). 0.000016 'iii 0.000014 n. >... Q 0.000012 1: x 0.00001 w Q ~ 0.000008 >­I­:> 0.000006 i= u :::l 0.000004Q a 0:: n. 0.000002 0 __ \ _ '\\ \\. \\ y~I--- \ '---\ 0 10 20 30 PORE VOLUM E OF SEAWATER INJECTED (%) Figure 1. Productivity Index ofa Well that Forms Sulphate Scale against Pore Volume of Seawater Injected. EXPONENTlA L SHA PE FOR FORM!\.TON DlIM'\GE FUNCTlON HY PERBOLIC SHAPE FOR FORJIMroN DlIM'\GE -­40 50 60 6 Fadairo A. S. Adesina, C. T. Ako, Omole Olusegun et a!. 0.000016 0.000014 c;;­o. >. 0.000012 ra c ~ 0.00001 X w C ~ 0.000008 >­f­:> 0.000006f= l) ::l c 0.0000040 lk: 0. 0.000002 o • EXPONENTIAL SHAPE J FOR FORMATION -•• • • ­• -o 10 20 30 40 50 60 PORE VOLUME OF SEAWATER INJECTED ("!o) Figure 2. Productivity Index of a Well that Forms Sulphate Scales against Pore Volume of Seawater Injected. Drastic productivity decline was observed at lower pore volume of seawater-injected ranges from 0% to 10% due to high permeability decline causes by deposited scaie at low pore volume of water injected. This is in agreement with the studies reported in the literature «Fadairo, 2004; Fadairo et ai, 2008; Civian, 2001; Bedrikovetsky et a!., 2003a, Tomson, 1991, Moghadasi et a!., 2006). This phenomenon might have been caused by heterogeneous nucleation that occurs at the early stage of scale build up around the well bore before re-dissolution of scale begins to take place at higher pore volume of injected water (Crabtee et a!., 1999). The increase in productivity index observed between 45% to 100% pore volume of water injected might have been due to scale re-dissolution (figure 2) CONCLUSION The following conclusions were drawn from the result of this study: At every given pore volume of sea water injected, the decline in productivity index for oil wells in water flooded reservoirs due to sulphate scale deposition depends upon oilfield solid scale saturation in the porous media. The rate of decline in productivity index due to sulphate scale deposition is the function of operational and reservoir/brine parameters such as scale concentration in the brine, viscosity of brine, formation volume factor of the brine, solid scale density, injection rate, pressure drawdown, reservoir temperature, reservoir thickness, brine velocity and radial distance from the well bore. 7 Effect of Oilfield Sulphate Scales on Productivity Index The developed model is capable of predicting productivity index decline due to scale deposition around the well bore in water-flooded reservoirs. ApPENDlXA. INSTANTANEOUS PERMEABILITY AS A RESULT OF SOLID SCALE SATURATION NEAR THE WELL BORE REGION Instantaneous local porosity can be defined as the difference between the initial porosity and damaged fraction of the pore spaces (Fadairo et ai, 2008; Moghadasi et aI., 2006). (AI) Therefore 2 (de )q -- .B .J!.f.A k dP T (A2) Damage fraction of the pore spaces ¢d can be defined as the ratio of the volume of scale deposited to bulk volume of the porous media or the fraction of minerals scale that occupied the total volume of porous media (Fadairo et ai, 2008; Moghadasi et aI., 2006). • A. volume of minerals scale deposited That IS 'f'd = ------------'---­bulk volume of the porous media Also Fadairo (2004); recently expressed the fraction of mineral scale that occupied the pore spaces at different radial distance from the well bore as follows: (A3) Re-arranging equation (A3), we have: (A4) 8 Fadairo A. S. Adesina, C. T. Ako, Omole Olusegun et al. where A¢ and Ak can be defmed as porosity damage coefficient and permeability damage coefficient respectively. (AS) Substituting equation (A3) in equation (A2), we have (A6) Dividing both side of equation (A6) by ¢o' we have (A7) Considering the relationship between the initial permeability and instantaneous permeability as a function of altered porosity and initial porosity defined by Frank et al (1991) as: (A8) Instantaneous permeability can be expressed as Fadairo, (2004): (A9) Equation (A9) expresses the effect of scale build up on permeability variation at different operational parameters and reservoirlbrine parameters such as scale concentration in the brine, viscosity of brine, formation volume factor of the brine, solid scale density, injection rate, pressure drawdown, reservoir temperature, reservoir thickness, connate water saturation against injection time and radial distance from the well bore vicinity. ApPENDIX B. PIRSON'S CORRELAnON Average relative permeability was expressed as a function of average water saturation was given below as follows (Ahmed, 1989): (B-1) 9 Effect of Oilfield Sulphate Scales on Productivity Index (B-2) _ [ {_)0.25 ] 0.5 Kro = (1- S,.) 1- ,Sw ..JS: (B-3) REFERENCES Ahmed, T. (1989) Introduction to Petroleum Reservoir Analysis, Gulf Publishing Company. Houston TX. Atkinson, G., Raju, K. and Howell, R.D. (1991) "The Thermodynamics ofScale Prediction", SPE 21021, pp.209-215, presented at the Society of Petroleum Engineers international Symposium on Oilfield chemistry Anaheim, Canada. Bedrikovetsky, P.G., Gladstone, P.M., Lope, Jr., Rosario, F.F., Silva, M.F., Bezerra, M.e. and Lima, E.A. (2003) Oilfield Scaling Part 1: Mathematical and Laboratory Modeling, SPE 81127, presented in SPE American and Caribbean Petroleum Engineering Conference in Port of Spain Trinidad West Indies. Bedrikovetsky, P.G., Gladstone, P.M., Lope, Jr., Rosario, F.F., Silva, M.F., Bezerra, M.e. and Lima, E.A. (2003b) Oilfield scaling part 11: Productivity Index Theory, SPE 81128, SPE Latin American and Caribbean Petroleum Engineering Conference, Port-of-Spain, Trinidad and Tobago. Bedrikovetsky, P.G., Gladstone, P.M., Lope, Jr., Rosario, F.F., Silva, M.F., Bezerra, M.e. and Lima, E.A. (2004) Barium Sulphate Oilfield Scaling: Mathematical and Laboratory Modeling, SPE 87457, SPE International Symposium on Oilfield Scale, Aberdeen, United Kingdom. Civan, F. (2001) Modeling Well Performance under Non Equilibrium Deposition Condition, SPE 67234, presented at SPE production and Operations Symposium Oklahoma, USA. Crabtee, M., Eshinger, D., Fletches, P., Johnson, A. and King, G (1999) Fighting Scale ­Removal and Prevention, Oilfield Review, Schlumberger Autumn. Fadairo, A.S.A. (2004) Prediction Scale Build Up Rate around the Well Bore, MSc Thesis, Department of Petroleum Engineering, University oflbadan, Nigeria. Fadairo, A.S.A. Omole, O. and Falode O. (2008) 'Effect of Oilfield Scale on Mobility Ratio', SPE 114488 Gas Technology Symposium 2008 Joint Conference held in Calgary, Alberta, Canada, 16-19 June 2008. Frank, F., Chang and Civan, F. (1991) Modeling of Formation Damage Due to Physical and Chemical Interaction between Fluid and Reservoir Rock, SPE 22856. SPE Annual Technical Conference and Exhibition, Dallas, Texasn Haarberg, T., Selm, 1., Granbakken, D.B., 0stvold, T., Read, P. and Schmidt, T. (1992) Scale Formation in Reservoir and Production Equipment during Oil Recovery II" equilibrium Model, SPE Journal Production Engineering, Volume 7, Number In Moghadasi, J., Sharif, A., Kalantari, A.M. and Motaie, E. (2006a) A New Model to Describe Particle Movement and Deposition in Porous Media, SPE 99391, presented at 15th SPE Europe Conference and Exhibition, Vienna, Austria. 10 Fadairo A. S. Adesina, C. T. Ako, Omole Olusegun et al. Oddo, 1.E. and Tomson, M.B, (1994) 'Why scale fonns in the oilfield and method of predict it', SPE 21710, SPE Journal Production and Facilities, Volume 9, Number In Richards, S.G. (1968) Effect of Brine Concentration and Pressure Drop Gypsum Scaling in Oil Well, SPE 1830, Journal ofPetroleum Technology, Volume 20, Number 6n Robert, B.E (1997) Effect of Sulphur Deposition on Gas Well Performance, SPE 36707, SPE Annual Technical Conference and Exhibition in Denver, Colorado. Rocha, A.A., Frydman, M., Fontoura, S.A.B., Rosario, F.F. and Bezzarra, M.C. (2001) Numerical Modelling of Salt Precipitation During Produced Water Re-injection, SPE 68336, International Symposium on Oilfield Scale, Aberdeen, United Kingdomn Rosario, F.F. and Bezerra (2001) Scale Potential of a Deep Water Field Water Characterization and Scaling Assessment, SPE 68332, International Symposium on Oilfield Scale, Aberdeen, United Kingdom. 

EFFECT OF OILFIELD SULPHATE SCALES ON

PRODUCTIVITY INDEX

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EFFECT OF OILFIELD SULPHATE SCALES ON PRODUCTIVITY INDEX

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