INVESTIGATION OF HYDRODYNAMIC PROCESSES IN GEOTHERMAL PLANT

Transcription

1 th World Congress on Computational Mechanics (WCCM XI) 5th European Conference on Computational Mechanics (ECCM V) 6th European Conference on Computational Fluid Dynamics (ECFD VI) M. Bogdevicius, J. Januteniene, S. Razmas, M. Draksas, R. Didziokas and V. Nikit INVESTIGATION OF HYDRODYNAMIC PROCESSES IN GEOTHERMAL PLANT MARIJONAS BOGDEVICIUS*, JOLANTA JANUTĖNIENĖ **, SAULIUS RAZMAS **, MINDAUGAS DRAKSAS **, RIMANTAS DIDZIOKAS, VADIM NIKITIN* * Department of Transport Technological Equipment Vilnius Gedimas Technical university Plytes st. 7, LT-005 Vilnius, Lithuania tti@vgtu.lt, web page: ** Department of Mechanical Engeerg Klaipeda University Bijunu st. 7-03, LT-955 Klaipeda, Lithuania mik.jtf@ku.lt, web page: Mechatronics Science Institute Klaipeda University Bijunu st. 7-03, LT-955 Klaipeda, Lithuania mmi@ku.lt, web page: Key words: geothermal system, hydrodynamics equations, stability. Abstract. Durg the experimental studies physical properties of underground water and gases mixture were analyzed and a correlation between pressure and gas content liquid was determed. Correlation between pressure, temperature and other parameters (density, fluid bulk modulus, sound velocity) were determed with respect to the results of the experiments. It was determed that the amount of released gas directly correlates with creased liquid-gas mixture compressibility and slowed down hydrodynamic processes, which changes workg properties of centrifugal pump reduces the natural frequency of the system subsurface centrifugal pump pipe le/system. Paper analyses an existg geothermal energy extraction system, which consists of a long pipe system and a large number of hydraulic and mechanical elements. Therefore, as the first step of the analysis, were decided to compile a mathematical model of the geothermal system, usg the method of concentrated parameters. Mathematical models of asynchronous motor, multilevel depth centrifugal pump mechanical system, depth centrifugal pump (6 levels), absorption pump, pipg system and other elements of geothermal energy extraction system were made. Also a universal mathematical model of depth centrifugal pump was made. Mathematical model of hydrodynamic processes of geothermal system (pumps, pipg, heat exchangers and filters) was made. A numerical analysis of hydrodynamic equations of geothermal system was made.

2 M. Bogdevicius, J. Januteniene, S. Razmas, M. Draksas, R. Didziokas and V. Nikit.. INTRODUCTION In scientific research geothermal system performance, the ma features and problems are quite widely described. Articles related to geothermal systems are analyzed [-5]. Transitional fluid flow processes are vestigated the work []. The transitional process pipg was examed two cases: when the fluid pipeles are used for temporary storage and transportation, and when the flow field the pipe is examed with periodic changg flow. The study was done by one-dimensional fluid flow assumption. The differential equations have been solved by characteristics method. Liquid-gas mixture flowg up vertical direction pressure drop was analyzed [6]. In order to avoid the exact prediction of the mixture density authors have suggested to use the energy balance method stead momentum method which is more commonly used. One dimensional steady and transient numerical modelg describg the heat and fluid dynamic transport side geothermal wells has been conducted Garcia-Valladares et al. study []. In this case, the mathematical model was established for both transitional and the settled flow analysis. Hydrodynamic processes of geothermal system are vestigated this paper.. PHYSICAL PROPERTIES OF GOETHERMAL WATER Durg experimental studies were determed the dependence between the pressure and the amount of gasses liquid. The regression relation of the amount of gas and the pressure is deduced. The dependence is described usg five degree polynomial function. Accordg to the dependence on gas pressure was determed relationship between the relative volume of the liquid and the gas pressure: ε V g /V () p 0, 003-0, p+ 0, 4040 p -0, p + 0, 3040 p -0, 950 p () where relative gas volume liquid; V g is gas volume, m 3 ; V is gas-liquid mixture volume, m 3 ; p is pressure, Pa. Based on the results were determed relationship between the geothermal fluid bulk modulus of elasticity and pressure accordg to the formula: K K s K s p where K and K S are geothermal fluid and liquid bulk modulus, Pa, is adiabatic dex. The dependence of geothermal fluid bulk modulus of elasticity and the relative gas volume are presented Fig. a). Geothermal fluid bulk modulus of elasticity dependence on the pressure is shown Fig. b). (3)

3 M. Bogdevicius, J. Januteniene, S. Razmas, M. Draksas, R. Didziokas and V. Nikit. a) b) Figure : a) The dependence between geothermal fluid bulk modulus of elasticity and the relative gas volume; b) The dependence between geothermal fluid bulk modulus of elasticity and pressure Geothermal fluid density and pressure dependence was determed by the formula: p sp (4) ZRT where s is liquid density, kg/m 3. Z is gas compression coefficient, R is gas constant, T is temperature. Speed of sound the fluid was determed by the formula: K(, p) a (5), p where a is sound velocity. The speed of sound and relative gas dependence is shown Fig.. Figure : Dependence between sound velocity and relative gas volume. CENTRIFUGAL DEPTH PUMP PIPE SYSTEM STABILITY Focus of this vestigation was assessment of fluence of energy sources (centrifugal pumps) and physical properties of transported fluid to hydrodynamic processes analyzed geothermal system. Dependance of developed pressure on flow rate p ( Qs, ) was determed paper [8] as ma charactersitic of centrifugal extraction pump. With addition of gas to the geothermal fluid, pump characteristic p (Q) becomes sufficient to accurately describe real operatg mode of the pump. In this case pump characterstic could be shown more accurately by usg 3

4 M. Bogdevicius, J. Januteniene, S. Razmas, M. Draksas, R. Didziokas and V. Nikit. pressure to mass flow rate dependance, which is G Q. Pump characteristic when relative volume of gas is 0 and 0 is shown Fig. 3. a Figure 3: The pressure dependence on the mass flow rate and the impeller rotation frequency (f=30-60 Hz): a normal liquid 0 ; b geothermal liquid 0 This scheme consists of extraction well, centrifugal depth pump, which is submerged side the well at the depth of H 0 and a vertical pipe (Fig. 4). Computational scheme of vestigated system Deep well multi-level centrifugal pump - pipele is shown Fig. 5. Hydrodynamic processes of the vestigated system Deep well multi-level centrifugal pump - pipele could be described by equation system [7]: Q s F Qs p ms p Qs Qp C Qs Qs F Qs p Qs ph psh signq s s s signq s A A, (7) s L V There: m ; C ; ( Qs ) is the ma characteristic of the multi-level centrifugal A Kp pump ; p, p H, p SH are the fluid pressures the suction pipe, pump suction cavity and hydrostatic pressure, respectively; L, A the length and cross-sectional area of suction pipe;, S are densities the let and pump volumes; is the pressure loss coefficient. Parameters of steady state process, that are characterizg hydrodynamic processes the system Deep multi-level centrifugal pump pipele can be determed from (6) equation system: b (6) F Qs0 p Qs 0 Qp (8) 4

5 M. Bogdevicius, J. Januteniene, S. Razmas, M. Draksas, R. Didziokas and V. Nikit. Fig.4. Scheme of the extraction well. Figure 5: System Deep well multi-level centrifugal pump - pipele stability determation scheme Nonlear algebraic equation system is solved and solution Q s 0, p 0 obtaed by usg Newton method. By learizg equation system (6) pot Q s 0, p 0 settg, system of lear equations was obtaed. Qs Qs0 Q and p p 0 p. After transformations of equation system (8), by removg pressure p, second degree differential equation respect of Q: m s Input parameters: Q dq p dq p df Q df Q s m Q s s Q 0 (9) dq C dp C dp dq Q dq p df, dq dp s0 0 K C m s p df Q dq 0 s0 K, (0) dp dq K K3. m C s 5

6 M. Bogdevicius, J. Januteniene, S. Razmas, M. Draksas, R. Didziokas and V. Nikit. Parameter K 3 is the natural frequency of the system [7]. Instability of hydrodynamic processes which are occurrg system centrifugal depth pump pipe could be determed from conditions: K 0 - dynamic stability; K 0 and K static stability. System centrifugal depth pump pipe is stable, when parameters K, K 0, K By assessg geothermal parameters of extraction well and physical properties of transported fluid, range of this system stability was determed. System is unstable, when rotation frequency of the pump impeller is with range of Hz. More formation about this vestigation is provided articles [7,8]. 4. MATHEMATICAL MODEL OF HYDRODYNAMIC PROCESSES The deep centrifugal pump is immersed a depth H 0 (Fig.5). The water column height is a variable when the well s fluid and the gas mixture is pumped from the depths (H well =35 m). The equations of the water column height variation are equal to: H Q well QsignQ A, () well, where: Q well discharge of fluid, Q well A wel well depth p depthl p Q - the fluid flow enterg the centrifugal pump; depth the bottom of the well; well wel sign p depth p wel, () - the liquid and the gas density at - the liquid and the gas density at the bottom before the filter; p ( p ) g H H H p ; pgas - gas pdepth - the pressure at the bottom of the well, well depth well 0 gas (nitrogen, N ) extracted at the well top, p gas CgasVgas ; Vgas - the volume of gas; well - the pressure loss coefficient; A well - the cross-section of the filter. All values of geometrical parameters are presented table. Table : Values of geometrical parameters Parameter H 0 H H H S H H gr H gr D V D V D V3 L Value, m ,34 0,778 0,5 0 Fluid flow enterg the pump is described by the equation: Q m p p p H p signq Q A Q p p (3) 6

7 M. Bogdevicius, J. Januteniene, S. Razmas, M. Draksas, R. Didziokas and V. Nikit. p, H ( p ) gl ; - the pressure loss coefficient of the pump the let pipe: 5. NUMERICAL ANALYSIS L Local, Re, n. (4) D Calculation scheme of all geothermal system was created (Fig. 6). This scheme was used for the numerical analysis. Geometrical parameters of pipeles of geothermal system are presented Table. Fig.6. Calculation scheme of geothermal system In the itial stage of work process water column height is a variable (formula ). Results of variation of water column height are presented Fig 0. Results of numerical calculations are presented Fig.7-0. Numerical calculation was performed different steps of centrifugal pump and pipeles of geothermal system. Pressure and discharge different steps of centrifugal pump are presented Fig.7 and Fig.8. In Fig.9 are presented changes of relative volume of gas depends on the different deep. Table. Geometrical parameters between concentrated volumes Parameter L L S L S- L -3 L 3-4 L 4-5 L 5-6 L 6-7 L 7-8 L 8-9 L 9-0 L 0- Value, m 0 3 7,8 7,8 7,8 7, Parameter D D S D S- D -3 D 3-4 D 4-5 D 5-6 D 6-7 D 7-8 D 8-9 D 9-0 D 0- Value, m 0,78 0,78 0,78 0,78 0,78 0,78 0,5 0,5 0,35 0,38 0,34 0,3 Calculation was performed nodes for every 30 meters of a long vertical pipele of deep well. Pressure and discharge different steps of pipeles are presented Fig. -6. In Fig.3 and Fig.5 are presented changes of relative volume of gas depends on the different deep and different water column height H. 7

8 M. Bogdevicius, J. Januteniene, S. Razmas, M. Draksas, R. Didziokas and V. Nikit. Fig.7: Pressure different steps of pump, H =00 m Fig.8: Changes of relative volume of gas depends on the different deep of well, H =00 m Fig.9: Discharge different steps of pump, H =00 m Fig.0: Water column height variation, H =00 m Fig.: Pressure different nodes of pipele, H =00 m. Fig.: Discharge different nodes of pipele, H =00 m. 8

9 M. Bogdevicius, J. Januteniene, S. Razmas, M. Draksas, R. Didziokas and V. Nikit. Fig.3: Changes of relative volume of gas depends on the different deep of well, H =00 m. Fig.4: Pressure different nodes of pipele, H =00 m. Fig.5: Changes of relative volume of gas depends on the different deep of well, H =00 m. Fig.6: Discharge different nodes of pipele, H =00 m. 6. NUMERICAL AND EXPERIMENTAL RESULTS COMPARISON Daily data of discharge, pressure and temperature of geothermal system were selected for statistical analysis. Measurement pots selected scheme of geothermal system are presented Fig.7. Fig.7: Scheme of measurement pots of parameters 9

10 M. Bogdevicius, J. Januteniene, S. Razmas, M. Draksas, R. Didziokas and V. Nikit. Parameters were monitored and captured every second. For this analysis the data of every 0 seconds was chosen. For numerical analysis and experimental measurements comparison a geothermal systems node above extractive deep pump at the begng of the pipe was chosen. Results of numerical analysis of discharge at the pot from start-up to steady state are presented Fig.8 and Fig.0. Measured values of pressure and discharge at the same pot of the system are presented Fig 9 and Fig.. Fig.8: Results of numerical analysis of discharge from start-up to steady state Fig.9: Results of measured discharge at steady-state Fig.0: Results of numerical analysis of pressure from start-up to steady state Fig.: Results of measured discharge at steady-state Averages data of measurement the pot of system (Fig.7) are followg: pressure p - 4,95± 0,04 Bar; discharge Q- 85,43±,3 m 3 /h; and temperature T 37,76 ± 0,03, 0 C. CONCLUSIONS. Evolved gas (N nitrogen) geothermal fluid has fluence to hydrodynamics and thermodynamic processes of system "Deep-well - multi-level centrifugal pump - pipele".. The extraction well system Deep well- multi-level centrifugal pump - pipele is stable when rotation frequency of pump impeller is higher than 40 Hz. The stability of the system is less sensitive to fluid flow rate variation. It was determed that a low Hz natural frequency of the system is a result of the combation of high compressibility of the underground water and the large amount of water side the pipes. 0

11 M. Bogdevicius, J. Januteniene, S. Razmas, M. Draksas, R. Didziokas and V. Nikit. 3. The mathematical model of geothermal well extraction with a multi-stage centrifugal pump was developed. The basis of this model has established the geothermal pipele parameters on the centrifugal pump. It was found that the variation of the height of water column the well has an fluence on the quantity of gas; decreasg the water column height then creases the amount of gases. In each stage of the pump, the relative volume of gas is different and varies from 0.0 to 0.0. ACKNOWLEDGMENTS This work has been supported by the Research Council of Lithuania with the project Simulation software and the vestigation of thermo-hydrodynamic processes the geothermal loop, project No. MIP-090/0. REFERENCES [] Ouchuha, Z., Loraud, J.,C. Ghezal, A., et al. An vestigation of highly pressurized transient fluid flow pipeles. Int. Journal of Pressure Vessels and Pipg (0) 9:06-4. [] Garcia-Valladares, O., Sanchez-Upton, P. and Santoyo, E. Numerical modelg of flow processes sided geothermal wells. An approach for predictg production characteristics with uncertaties. Energy Conversion and Management (006) 47: [3] Popecu, D. E. Some Aspects About the Reliability Analysis of a Phased-Mission Geothermal Power Plant. Proceedgs World Geothermal Congress 00, 5-9 April 00 Bali, Indonesia. [4] Hepbasli A. A review on energetic, exergetic and exergoeconomic aspects of geothermal district heatg systems (GDHSs). Energy Conversion and Management (00) Vol. 5, Issue 0: [5] Kaya, E., Zarrouk, S.J. and O Sullivan. Rejection geothermal fields: A review of worldwide experience. Renewable and Sustaable Energy Rewiews (004) 5: [6] Lombardi, C., Cammi, A. and Faimali, E. Pressure drops prediction gas-liquid mixtures flowg upflow vertical ducts. Progress Nuclear Energy (04) 7:4-5. [7] Bogdevičius, M., Janutėnienė, J., Didžiokas, R., et al. Investigation to the stability of hydrodynamic processes the dept centrifugal pump and pipele system. TRANSBALTICA 03. The 8th International Conference (03) -4. [8] Bogdevičius, M., Janutėnienė, J., Razmas, S., et al. Mathematical modellg of hydrodynamic processes geothermal plant. V conference on Computational Methods for Coupled Problems Science and Engeerg, COUPLED PROBLEMS 03, 7-9 June 03, Ibiza, Spa.