Two-Phase Modeling of Gravity Drainage of Bitumen from Tar Sand Using In-Situ RF Electrical Heating

Transcription

1 Excerpt fro the Proceedings of the COMSOL Conference 008 Boston To-Phase Modeling of Gravity Drainage of Bituen fro Tar Sand Using In-Situ RF Electrical Heating Arin Hassanzadeh*, Pyrophase Inc. *14 S. Princeton Ave., Chicago, IL 60616, Abstract: To-phase oveent of bituen and air in tar sand porous deposit is odeled using COMSOL ultiphysics. A syste of non-linear PDE(s) for the oveent of each of the phases is coupled ith heat transfer equation to account for heat diffusion through the edia. The deposit is heated voluetrically and locally by using insitu RF technology that as developed by Pyrophase, Inc. The effects of variation in properties of bituen and reservoir edia due to teperature and pressure are considered. These properties are derived fro experiental data (e.g. viscosity, capillary pressure and relative pereability) obtained fro earlier easureents by IIT Research Institute (IITRI). The Van Genuchen odel is used to relate the data to the paraeters in the to-phase odel. The COMSOL syste deonstrates acceptable capability and flexibility in solving the equations and setting logical boundary and initial conditions to odel flo under conditions of teperature and pressure variation. Keyords: In-situ electrical heating, radiofrequency heating, ultiphase flo odeling, gravity drainage, bituen recovery, tar sand, IITRI. 1. Introduction The existing orld energy deand is currently doinated through the use of conventional hydrocarbon resources, hich supply about 85 percent of the orld s energy [1]. World energy consuption is projected to increase by 71 percent fro 00 to 00 [1], hile these conventional resources (especially oil) are diinishing. With the current high prices of crude oil, extraction of non-conventional hydrocarbon resources such as tar sand and oil shale becoe ore econoically feasible. The large aount of such resources around the orld (especially in the US and Canada), are encouraging the energy producing copanies to invest ore on developing innovative technologies for extraction fro these resources. In-situ electrical heating technologies are aong the ost recent technologies used for bituen recovery fro tar sand and oil shale. These technologies have liited environental ipact because there is little disturbance of the land, and ater and solvents are not used. IIT Research Institute (IITRI) back in the 80 s as a pioneer in using radio-frequency (RF) energy to voluetrically heat a large block of tar sand or oil shale []. The in-situ RF technology is being further developed by the sae tea of inventors orking for Pyrophase Inc. since then. In this technology, the non-conventional resource of tar sand is voluetrically heated to reduce the viscosity of the bituen product, hich then flos by gravity to collection points over a period of a fe onths. Capillary pressure and relative pereability of the oil and air affect drainage because these forces are coparable to the gravity gradient. Modeling of such processes requires a siulator ith ulti-physics flexibility and coputational capabilities. This ork is focused on odeling of to-phase oveent of bituen and air/gas ithin the porous edia of tar sand deposit. A unifor RF heating pattern is assigned for the heat transfer equation and this equation is coupled ith the to continuity equations for the to existing phases.. Objective The ain objective of this ork is to test the COMSOL odeling techniques in a D geoetry by using to different heating ethods for reducing the bituen viscosity. In the first ethod, the heat source is assued to be inside the production ell using a hot pipe, as ith RFT heating process (Pyrophase Inc. []). In this, a constant teperature is assued at the boundary of the ell. In the second ethod, a unifor heat distributed through the entire volue is assued. According to the experiental results of tri-plate line RF heating of a tar sand and oil shale edia (deonstrated by IITRI, 198 []), this ethod can uniforly heat up the edia ith approxiately a constant rate until the evaporation teperature of ater is reached. The heating rate drops as the edia 1

2 dries up but unifor teperatures of ore than 50ºC can be reached ith this ethod.. Description of the Geoetry A cylindrical perforated production ell is assued to be vertically inserted into a hoogeneous tar sand reservoir hile the edia is heated. The geoetry is syetrical around the perforated; therefore the proble can be solved in D hich significantly speeds up the nuerical calculations (Figure 1). Tar Sand Media Perforated Well D Modeled Geoetry Figure 1. Cylindrical Geoetry of the Tar Sand Media and the Perforated Well COMSOL Multiphysics as used to solve the inter-connected equations nuerically. Figure represents the slice of the tar sand volue (shon in Figure 1) along ith a perforated ell (on the left side) in a D geoetry. The esh distribution used for the nuerical calculations is also shon in this figure. For the first part of this study, a edia ith a diaeter of 5 and a depth of is nuerically odeled and later the results are extended to a 45- depth volue. Prod uction We ll Open to atosphere z r Perforated Boundary Open to atosphere 5 Bituen Reservoir Figure. D Geoetry Nuerically Solved ith COMSOL 4. Matheatical Model 4.1 Governing Equations To continuity equations can be derived for each of the etting and non-etting phases. By substituting Richard s equation (odified Darcy s La) into a continuity equation, the folloing equations can be derived for each of the phases: ( θ ) ( θ ) n n krk + η + n k rnk η n ( p + gd) = 0 (1) ( p + gd) = 0 n n () Where, k : Absolute Pereability, D: Elevation direction, k r & k rn : Relative pereabilities of etting and non-etting phases, diensionless θ & θ n : Volue fraction of etting and non-etting phases, diensionless η & η n : Dynaic viscosities of etting and non-etting phases, Pa.s p & p n : Pressure of etting and nonetting phases, Pa & n : Molar densities of etting and non-etting phases, kg/ The capillary capacity of the etting phase in contact ith the non-etting phase is defined as the slope of the capillary head curve versus the etting phase volue fraction. θ θ C = = g hc pc Where the capillary pressure is defined as pc = pn p. In this ork, C is re-expressed in ters of and to be consistent ith p c reference [4]. It is assued that the etting phase (i.e. bituen) is incopressible but the non-etting phase (i.e. air or gas) is copressible. According to the ideal gas la, variation in the non-etting phase pressure and teperature has a direct effect on the density of this phase as follos:

3 p T n 0 n = po T o Where the subscript o represents the nonetting phase characteristics at abient condition. By substituting all the above assuptions into Equations 1 and, and by using the chain rule, the folloing equations can be derived: C pn g n p krk + η () ( p + gd) = 0 C p pn ot0 pn ot0 pn T + θ n θ n g pot po T k rnk + n ( pn + n gd) = 0 η n (4) The ters for copressibility of the nonetting phase are the second and third ters on the left side of Equation 4. Equations and 4 can be solved siultaneously for unknon pressures of the etting and non-etting phases. Equations and 4 sho that the flo of each phase is initiated due to the pressure gradient (i.e. p ) as ell as the fluid eight gradient (i.e. ( gd) ). If there is a teperature gradient ithin the edia, a significant gradient is generated in the fluid density that resulted in generation of a force in the opposite direction of the density gradient. As entioned before, to ethods of heating are used in the edia to increase the bituen teperature. For the hot pipe ethod, the heat is generated at the boundary of the production ell but for the voluetric RF heating ethod the heat is generated internally. An overall heat balance, including conduction and heat source ters, is defined as follo: T C p + ( k T ) = Q& (5), h Where, k : Heat conductivity of the reservoir edia, W/ºK C p, : Heat capacity of the reservoir edia, J/kgºK : Density of the reservoir edia, kg/ Q & : Rate of heat generation due to h voluetric RF heating, W/ In COMSOL ultiphysics, it is possible to define ulti-dependent variables for each of the differential equations separately. For tiedependent equations, there is a atrix of ass coefficients for all the dependent variables that change ith tie. This atrix can be easily edited for any special purpose of odeling. To define equation 4 in COMSOL, for instance, the ass coefficients for each of the dependent variables are as follo: for p : C n g for pn : C n + θ g for T : ot0 pn θ n p T o n ot0 p T 4. Initial and Boundary Conditions For Equations and 4 the folloing initial conditions ere assigned: at t=0 p ( ) = g D pc, int at t=0 pn = g( D) According to experients on Asphalt Ridge saples (IITRI Report []), about 10%v/v of the reservoir is occupied ith air or volatile coponents. Since the average porosity of the edia are about 6 to percent, ore than 0%v/v of the pore volue of reservoirs are initially epty. According to the van Genuchen odel [5], the initial epty space corresponds to an initial capillary pressure ( p c,int ) that, on average, initially is present all along the reservoir. Since the capillary pressure is defined as the difference beteen pressures of the etting and non-etting phases, the definition of initial pressures for the etting and non-etting phases should be consistent ith this assuption (see above initial conditions). Referring to Figure, the folloing expressions are the defined boundary conditions. No flo is assued across the geoetry boundaries. That corresponds to the case here another siilar volue, using the sae process, is adjacent. At the top it is assued that there is no flo of the etting phase across the boundary, but the non-etting phase can flo into the top of the perforated ell: ( p + gd) = 0 p = (open to atosphere) n p at o

4 At the botto, both of the phases can flo in/out of the perforated ell: p (open to atosphere) = p at p (open to atosphere) n = p at In the first heating ethod, the heat is assued to be generated inside the production ell and gradually transfers across the edia through conduction. To constant teperature cases of 600ºC and 00ºC are assued for the pipe at the boundary of the ell, hile the reservoir is initially assued to be at abient teperature. No heat flo is assued across the geoetry boundaries. In the RF heating ethod, a unifor voluetric heat is assued to increase teperature of the edia. A constant heat rate of Q h =0 W/ is assued for the entire volue. Ongoing RF odeling attepts fro this author sho that ith an average electric field of 1000 V/, the above heating rate is achievable for 45- long tri-plate line electrodes. 4. Model Paraeters The folloing physical characteristics are used for the etting phase, non-etting phase and reservoir. The experiental data ere obtained fro IITRI report for Asphalt Ridge tar sand []. = 1000 kg / = 1.8 kg / = 00 kg / k = 1.0 W / K θ s = k = 9.8e C p, ( 1 Darcy) n, int 5 ηn = e Pa. s θ = r = 100 J / kg K Figure shos the changes in the bituen viscosity as a function of teperature obtained experientally by IITRI []. A constant viscosity of 6.0 cp is assued for teperatures ore than 150ºC. Viscosity, cp As entioned before, it is assued that about 70 percent of the edia porosity is initially occupied ith bituen and the rest is a ixture of air and volatile coponents []. To adjust the odel paraeters to the initial bituen content, an initial capillary pressure of 900 Pa is used through the entire edia, corresponding to the initial volue fraction of the non-etting phase. 5. Results and Discussions Figures 4 through 7 sho the changes in bituen content and the teperature distribution after heating the reservoir boundary to 00ºC. The background color shos the extractable (effective) bituen volue fraction, in hich red is 100 percent bituen and blue is zero. The hite lines indicate strealines of velocity field of etting phase across the reservoir and the black arros sho the flo direction of this phase. The strength of the bituen velocity is proportional to diensions of the arros in each graph, independently. The colors of the vertical lines represent the teperature distribution, indicated by the scale on the far right side of each graph. By decreasing the bituen viscosity near the production ell, bituen flos into the ell and drains at the botto of the ell. Gravity is the ain force for floing bituen in the edia but gas expansion, due to teperature, also affects the bituen oveent. Figures 5 though 7 represent that soe of the bituen flos to the botto right side of the edia, aay fro the production ell (see the velocity strealines). Because of the flo bottleneck at the boundary of the production ell, there is accuulation of bituen at the botto of the edia shon in red color in these figures (bituen fraction, S e, close to 1). Figures 8 through 11 sho the sae paraeters for the case of voluetric heating of the edia. In this case, teperature changes uniforly through the entire edia. By using a heating rate of 0 W/, teperature of 187ºC is reached after 6 onths (Figure 11) Tep, C Figure. Bituen Viscosity versus Teperature (IITRI Report []) 4

5 Figure 4. Hot Pipe Boundary Heating Result in Less than an Hour Figure 8. Voluetric RF Heating Result in Less than an Hour Figure 5. Hot Pipe Boundary Heating Result after One Month Figure 9. Voluetric RF Heating Result after One Month Figure 6. Hot Pipe Boundary Heating Result after Three Months Figure 10. Voluetric RF Heating Result after Three Months Figure 7. Hot Pipe Boundary Heating Result after Six Months Figure 11. Voluetric RF Heating Result after Six Months 5

6 A siilar case to Figures 4 through 7 is odeled by assuing boundary teperature of 600ºC. Changes in the bituen fraction are integrated along the entire edia and copared for each of the cases in Figure 1. Initial bituen content is assued to be about 70 percent and it decreases as bituen extracted fro the edia. Copared to the hot pipe boundary heating ethod, the voluetric RF heating ethod shos loer extracted bituen at the first 150 days of production. The rate of bituen extraction significantly increases for the voluetric heating ethod after 100 days of heating and it shos significantly higher bituen extraction at the first year of production. This result represents that there is a delay tie for the voluetric heating ethod until bituen reaches its floing teperature. Because of the voluetric heating, the part of edia aay fro the production ell (that contains a significant volue of the entire cylindrical edia) can reach higher teperatures in less tie, copared to the hot pipe boundary heating results. extracted bituen beteen the RF voluetric heating ethod and the hot pipe boundary heating ethod. Figure 1. Bituen Fraction in a 45- Height Media after One Year (Production through Perforated Well Using RF Voluetric Heating Method) 0.75 Bituen Fraction in Media Voluetric Heating (0 W/^) 0.5 Boundary Heating T=00 C Boundary Heating T=600 C Tie, days Figure 1. Integrated Bituen Fraction for Three Modeling Cases In this ork, the to ethods of heating are also odeled for a case of 45- depth cylindrical edia ith 5 radius to evaluate the effect of the height of bituen layer on the bituen production rate. Figures 1 and 14 sho distribution of the bituen fraction in a 45deep volue after one year of heating. Except for the edia depth, Figures 1 and 14 are siilar to Figure ith the perforated pipe on the left side. A significant advantage of the voluetric heating ethod in extracting higher bituen fraction can be observed in these figures. Figure 15 confirs that there is a significant difference in the aount of the Figure 14. Bituen Fraction in a 45- Height Media after One Year (Production through Perforated Well Using Hot Pipe Boundary Heating Method at 600ºC) Bituen Fraction in Media Tie, days Voluetric Heating Boundary Heating T=600 C Figure 15. Integrated Bituen Fraction for 45- Depth Deposit 6. Conclusion A -diensional cylindrical geoetry as successfully odeled ith COMSOL ultiphysics to siulate to-phase oveent of etting and non-etting phases in a porous edia. With the help of COMSOL flexibility and capability, the copressibility effect of the non- 6

7 etting phase and the effect of capillary pressure are considered in this odeling. Heating the edia at the boundary of the production ell, by aintaining a constant teperature of a hot pipe, causes bituen to start floing quicker copared to voluetrically heating the entire reservoir (Figure 1). The difference beteen the response ties of the heating ethods is less significant for the case of 45-depth edia (Figure 15). By using unifor heating rate of 0 W/, the reservoir can reach teperatures of 107ºC and 187ºC after onths and 6 onths, respectively. In the case of voluetric heating, the rate of bituen extraction increases rapidly after 150 to 00 days of heating (Figures 1 and 15), hen the bituen viscosity drops to a lo value by the increase in teperature. After a year of production, the voluetric RF heating ethod produces significantly higher bituen fraction copared to the hot pipe boundary heating ethod (Figure 1), and this difference is ore significant for 45-depth edia (Figure 15). 7. References 1. IEO006 Report, International Energy Outlook 006, Energy Inforation Adinistration (EIA), Office of Integrated Analysis and Forecasting, US departent of Energy (006).. Sresty, G.C. and Bridges, J., The IITRI RF Process to Recover Bituen fro Tar Sand Deposits-A Progress Report, International Conference on Heavy Crude and Tar Sands, III, 1-4 (198).. Bridges, Jack, Radio Frequency Technology Heater for Unconventional Resources, US patent application nuber US007/ , Pyrophase Inc. (Pending). 4. Chen, J., Hopans J.W. and Griser, M.E., Paraeter estiation of to-fluid capillary pressure-saturation and pereability functions, Advances in Water Resources,, 5, (1999). 5. van Genuchten, M. Th., A closed-for equation for predicting the hydraulic conductivity of unsaturated soils. Soil Sci. Soc. A. J., 44, (1980). 7