Cold, Hot, or Dilute: Modeling the Viscosity of Heavy Oil for In Situ Processes

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1 Cld, Ht, r Dilute: Mdeling the Viscsity f Heavy Oil fr In Situ Prcesses H.W. Yarrantn*, H. Mtahhari, Department f Chemical and Petrleum Engineering, University f Calgary, Calgary, Alberta, Canada hyarrant@ucalgary.ca M.A Satyr, Virtual Materials Grup, Calgary, Alberta, Canada S.D. Taylr, Schlumberger DBR Technlgy Center, Edmntn, Alberta, Canada J.J. van Drp, Shell Chemical Americas, Calgary, Alberta, Canada Summary Tw methds (the Expanded Fluid mdel and the Mdified Walther crrelatin) used fr fitting and predicting the viscsity f heavy il and slvents were assessed n a dataset including the viscsity and density f mixtures f bitumen and ethane, prpane, butane, pentane, heptane, and carbn dixide. Bth crrelatins were adapted t determine crude il viscsity based n C30+ GC assays. The methds prvided rder-f-magnitude viscsity estimates with n tuning and fit crude il viscsity data t within 30% after tuning t a single dead il experimental data pint. The crrelatins als predicted the diluted bitumen viscsities t within 30% at temperatures frm 20 t 80 C and pressures up t 0 MPa. Intrductin In situ prcesses fr heavy il recvery include cld prductin, thermal methds, slvent-based prcesses, and slvent assisted steam prcesses. These prcesses encmpass a brad range f temperatures, pressures, and cmpsitins in the reservir and at the surface. Since viscsity reductin is arguably the mst imprtant gal in any heavy il prcess, it is critical t develp a viscsity mdel that is suitable fr this brad range f cnditins. The viscsity mdels which extend t the full phase diagram including liquid and vapur regins are crrespnding states methds (Pedersen and Fredenslund, 987), Frictin Thery (Quiñnes- Cisners, 200), and the Expanded Fluid (EF) mdel (Yarrantn and Satyr, 2009). The Expanded Fluid crrelatin was develped specifically t include heavy il viscsities. This presentatin demnstrates hw t use this crrelatin fr a variety f heavy il prcess cnditins. The simpler mdified Walther crrelatin (Yarrantn et al., 202), which nly applies in the liquid state, is als examined. Methd EF Mdel This mdel (Yarrantn and Satyr, 2009) relates viscsity t the density f the fluid as fllws: 0.65 exp c () 2 (2) * 0.65 s exp where is the viscsity f the fluid (mpa.s), µ is the dilute gas viscsity, ρ is the fluid density, ρ s * is the density f the fluid in the cmpressed state and c 2 is a fitting parameter specific fr each fluid. The GeCnventin 203: Integratin

2 cmpressed state f the fluid is, by definitin, a hypthetical state f the fluid beynd which the fluid cannt be cmpressed withut incurring a slid-liquid phase transitin. It is assumed that the viscsity f the fluid appraches infinity as the fluid density appraches the cmpressed state density. The cmpressed state density is a functin f pressure as fllws: * s s exp( cp) 3 where ρ s is the cmpressed state density in vacuum, c 3 is a fitting cnstant in kpa -, and P is pressure in kpa. The mdel has three temperature independent parameters fr each fluid: c 2, c 3 and ρ s. The inputs t the mdel are the measured fluid density, pressure, and the dilute gas viscsity. Nte, the effect f temperature n viscsity is intrduced thrugh the density and the dilute gas viscsity bth f which are temperature dependent. The mdel is nly valid fr Newtnian fluids. The EF mdel treats a mixture as a single-fluid. The fluid-specific parameters f the mixture are calculated with fllwing mixing rules (Mtahhari et al., 202): ww 2 s, i s, j nc nc i j ij (4) s, mix i j c2, mix w w c2, c i j s, mix 2 s, i s, j nc nc i j i 2, j ij (5) nc w i 3, mix (6) i c 3, i c where nc is the number f cmpnents in the mixture, w i is the mass fractin f the cmpnent i in the mixture, and β ij is a binary interactin parameter with default value f zer. The binary interactin parameter can be used t tune the mdel when experimental viscsity data fr the mixture are available. The fllwing crrelatin was fund t prvide satisfactry results fr diluted bitumen: where fr ΔSG nrm <= 0.355: β sl-il = 0 (7a) fr ΔSG nrm >= 0.355: β sl-il = ΔSG nrm (7b) (3) where SG is specific gravity. Nte, the SG f bitumen is near unity while the effective SG f liquid slvents can be as lw as 0.4; fr example, fr disslved prpane. Mdified Walther Crrelatin The riginal Walther (93) crrelatin relates the kinematic viscsity f a liquid t temperature. Mehrtra and Svrcek (989) mdified the crrelatin t relate the dynamic viscsity f heavy il t temperature. Yarrantn et al. (202) mdified the crrelatin t accunt fr bth pressure and temperature as fllws: (8) (9) GeCnventin 203: Integratin 2

3 Viscsity (mpa.s) Viscsity (mpa.s) where i refers t the viscsity f a cmpnent (mpa.s) r a fluid mixture at a atmspheric pressure, T is the temperature in K, and P is the deviatin frm atmspheric pressure in kpa. A, B, and are fluid specific cnstants that were crrelated t mlecular weight fr crude il pseud-cmpnents. The crrelatin treats a mixture as a single-fluid and the parameters fr the mixture are calculated as fllws: (0) () Nte that n interactin parameters were required fr cmpnents with mlecular weights abve 44 g/ml (prpane). The mlecular weight f heavy ils and bitumens is in the rder f 500 g/ml. Examples The different appraches were tested n a dataset including the viscsity and density f mixtures f bitumen and ethane, prpane, butane, pentane, heptane, and carbn dixide as well as dead and live il viscsities f a range f cnventinal crude ils. Sme examples are prvided belw. Figure shws hw the EF mdel fits viscsity data fr a bitumen ver a range f temperature and pressures. Figure 2(a) shws the EF mdel predictins fr mixtures f prpane diluted bitumen. Similar results were btained fr ther n-alkanes as well as CO2 ver a brad range f cnditins (temperatures frm 20 t 80 C, pressures up t 0 MPa, and slvent cntents up t the nset f asphaltene precipitatin). In general, the mdel predicted the viscsities f mixtures with average abslute relative deviatins (AARD) less than 20%. Nte that the viscsity predictins are sensitive t the accuracy f the input densities. (2) (3) data, 00 kpa EF mdel K K 323 K data EF mdel Pressure (kpa) Figure : EF mdel fitted t viscsity f dead bitumen versus temperature (left) and pressure (right). 348 K 373 K 398 K 423 K 448 K GeCnventin 203: Integratin 3

4 Viscsity (mpa.s) Viscsity (mpa.s), WC-B-B3+7.6wt% C3 WC-B-B2+wt% C3 WC-B-B2+5wt% C3 WC-B-B3+6wt% C3 EF Mdel WC-B-B3+7.6wt% C3 WC-B-B2+wt% C3 WC-B-B2+5wt% C3 WC-B-B3+6wt% C3 Mdified Walther 0 0 (a) (b) Figure 2: Cmparisn f predicted and measured viscsity f prpane diluted bitumen at 0 MPa: a) EF mdel, the binary interactin parameter was calculated frm Eq. 7; b) Mdified Walther crrelatin. Figure 3 shws the Mdified Walther crrelatin fitted t viscsity data fr a cndensate, a heavy il, and sme bitumens. Figure 2(b) shws viscsity f prpane diluted bitumen predicted with the crrelatin. The results with the Mdified Walther crrelatin are cmparable t thse with the EF mdel. In general, the Mdified Walther predicted the viscsity f the same set f mixtures with average abslute relative deviatins (AARD) less than 30%. The Mdified Walther crrelatin des nt require a density input but is nly valid fr liquids. Bth the EF mdel and the Mdified Walther crrelatin were adapted t wrk with the pseudcmpnent characterizatins f crude ils used in equatin f state mdels (Mtahhari et al., 203, Yarrantn et al., 202). The il characterizatins were based n extraplatins f C30+ gas chrmatgraphic assays. The viscsities f a wide range f crude ils (including bitumen) were predicted within a factr f 3 (Mdified Walther) and 5 (EF) with n tuning. Single parameter tuning t a dead il viscsity data pint allwed the viscsity data ver a brad range f temperatures and pressures t be fitted t within 30% (Mdified Walther) and 20% (EF). Figure 3: Mdified Walther crrelatin fitted t viscsities f a cndensate, a heavy il, and three bitumen samples. GeCnventin 203: Integratin 4

5 Cnclusins The Expanded Fluid mdel fits pure cmpnent viscsity data and predicts mixture viscsities t within 30% ver a wide range f cnditins. The EF mdel is well suited fr simulatin applicatins where it is required t calculate viscsities fr gases, liquids, and fluids. Hwever, an accurate density input is required fr gd results. The Mdified Walther crrelatin des nt require a density input, prvides similar results, but is nly applicable t liquids. Bth crrelatins were adapted t determine crude il viscsity based n C30+ GC assays. The crrelatins prvided rder-f-magnitude viscsity estimates with n tuning and culd fit viscsity data t within 30% after tuning t a single dead il data pint. Acknwledgements We thank the spnsrs f the NSERC Industrial Reseach Chair in Heavy Oil Prperties and Prcessing: NSERC, Petrbras, Schlumberger, and Shell. References Mtahhari, H., Satyr, M.A., Yarrantn, H.W., 202, Viscsity Predictin fr Natural Gas Prcessing Applicatins: Fluid Phase Equilibria, , Mtahhari, H., Satyr, M.A., Taylr, S.D., Yarrantn, H.W., 203, Extensin f the Expanded Fluid Viscsity Mdel t Characterized Oils: Energy Fuels, Just Accepted, January 0, 203, DOI: 0.02/ef30575n. NIST Standard Reference Database; NIST/TRC Surce Database; WinSurce, Versin 2008 Pedersen, K. S.; Fredenslund, Aa., 987, An Imprved Crrespnding States Mdel fr the Predictin f Oil and Gas Viscsities and Thermal Cnductivities: Chem. Eng. Sci. 42, Quiñnes-Cisners, S. E.; Zéberg -Mikkelsen, C. K.; Stenby, E. H., 200, The Frictin Thery fr Viscsity Mdeling: Extensin t Crude Oil Systems: Chem. Eng. Sci. 56, Walther, C. 93. The Evaluatin f Viscsity Data: Erdl Teer 7, Yarrantn, H. W. and Satyr, M. A., 2009, Expanded Fluid-Based Viscsity Crrelatin fr Hydrcarbns: Ind. Eng. Chem. Res. 48, Yarrantn, H.W., van Drp, J.J., Verlaan, M.L., Lastvka, V., 202, Wanted Dead r Live: Crude Ccktail Viscsity: A Pseud- Cmpnent Methd t Predict the Viscsity f Dead Oils, Live Oils, and Mixtures: SPE Paper 6034, SPE Annual Technical Cnference and Exhibitin, San Antni, 8-0 Octber. GeCnventin 203: Integratin 5