Wellhead pressure (MPa) PROCEEDINGS, Thirty-Ninth Workshop on Geotheral Reservoir Engineering Stanford University, Stanford, California, February 4-6, 014 SGP-TR-0 Nuerical siulation on fluctuation in wellhead pressure of geotheral well Haruhiro INAGAKI, Ryuichi ITOI,Naoto KUMAGAI,Takaichi IWASAKI Departent of Earth Resources Engineering Faculty of Engineering, Kyushu University, Fukuoka 819-0395, Japan h-inagaki@ine.kyushu-u.ac.jp Keywords: wellbore flow, unsteady-state, unsteady state ABCTRACT Geotheral wells copleted with ulti-feedzones ay lead to unstable production characteristics such as oscillations of wellhead pressure and discharge rate. Reservoir paraeters were exained for the oscillation phenoenon of well characteristics with nuerical siulations of wellbore flow. Siulated results showed that depths of flashing point are affected by a degree of inflow of low teperature fluid fro shallow feed zone. 1. INTRODUCTION Producing stea consistently is iperative for stable power generation of a geotheral power plant. Production wells with ulti-feedzones are copleted to enhance stea productivity. However, fluctuations of pressure and stea production rate at wellhead were observed (Iwata et al., 00). The production well finally stopped producing stea because wellhead pressure fell below the iniu pressure to produce stea. An unstable stea production will pose an obstacle for a stable operation of geotheral power plant. Thus, it is iportant fro the view of resource anageent to understand its echanis. For this purpose, nuerical analysis with a coupled odel of wellbore and reservoir is needed. Tokita and Itoi (004) developed a odel for analyzing stea-water two phase steady flow in wellbore coupled with a reservoir odel. But this steady odel can not analyze the fluctuation of wellhead pressure and production rate with tie. In this study, we used a coupled odel of wellbore and reservoir to analyze transient two-phase flow and to understand the echanis of the phenoenon by exaining the effects of pereability-thickness of reservoir on the flow in the wellbore.. FLUCTUATION OF WELLHEAD PRESSURE AT SUMIKAWA The Suikawa geotheral field is located in Akita Prefecture, northern Japan. The power plant with installed capacity of 50MW started operation in 1995 with 7 production wells and 10 injection wells. Figure 1 shows a history of wellhead pressure in Well SA-6 (Itoi et al., 013). This well has two feedzones at 000 and 1700 depths and shows fluctuation of wellhead pressure. The wellhead pressure began to fluctuate soon after producing stea, and its aplitude is 0.1 MPa and cycle period is 100 inutes. The aplitude gradually increases with decreasing iniu of wellhead pressure, and the well stops production1 days after starting operation. But after the well is taken a brief stop, the well can be restarted. 0.8 0.7 0.6 0.5 0.4 0.3 0. 5 Nov 30 Nov 5 Dec 10 Dec Date Figure 1:Fluctuation of wellhead pressure in Well SA-6 1
Inagaki, Itoi, Kuagai, Iwasaki 3. SIMULATION MODEL We used the WELLBORE siulation code developed by Miller (1983). WELLBORE is a coputer progra that siulates one diensional transient non-isotheral flow of single-phase water and stea-water two-phase in a wellbore. We used the code odified for siulating wellbore flow with two feedzones because WELLBORE can treat only one feedzone. Therodynaic properties of water were calculated by using a software package for therophysical properties of fluids naed PROPATH (PROPATH group, 1999). Figure shows a conceptual odel of the fluid flow in the wellbore and reservoir. The well has two feedzones through which single-phase fluid enters. The fluid enters at deep feedzone fro deep reservoir and flows upward and then it ixes with the fluid fro shallow reservoir at shallow feedzone. The ixed fluid further flows upwards in the wellbore, then start flashing and increasing its stea fraction up to the wellhead. Flashing point Water single-phase Two-phase 3.1 Reservoir odel Figure Conceptual odel of fluid flow in wellbore and reservoir Reservoir pressure in radial coordinate syste is given by a conventional pressure diffusion equation for a slightly copressible fluid as (Matthews and Russel, 1967): P k P 1 t c r r P r (1) where c is the fluid copressibility (1/Pa), k is the rock pereability ( ), P is pressure (Pa), r is radial distance (), t is tie (s), is porosity, and is the coefficient of viscosity (Pa s). In this study, heat transfer between wellbore and surrounding rock is considered so the heat conduction equation is needed : T 1 T r c r r t r r r () where c r is the specific heat of the rock (J/kg K), T is the rock teperature o C), is the heat conductivity of rock (W/ o C) and r is the rock density (kg/ 3 ). 3. Wellbore odel Transient two-phase flow in the wellbore is described by the ass, oentu and energy conservation law (Miller, 1983; Atoic Energy Society of Japan, 1993): t ( G ) 0 z (3)
Inagaki, Itoi, Kuagai, Iwasaki G t P ( Gv ) g sin F w (4) z z t E P / ( GE ) q (5) where, z E e P / (6) F w f v (7) 4 r w G v (8) q H T T r w (9) r w where e is the internal energy per unit ass (J/kg), E is the specific enthalpy or total energy per unit ass (J/kg), f is the coefficient of pipe friction, F w is the frictional pressure loss per unit volue (Pa/), g is the gravitational acceleration (/s ), G is the ass flow rate per unit area (kg/s- ), H is the coefficient of heat transfer (W/ o C ), q is the heat transfer per unit volue (W/ 3 ), r w is the wellbore radius (), T r is the rock teperature surrounding the well ( o C), T w is the fluid teperature in the wellbore ( o C), v is the average fluid velocity (/s), is the inclination angle of the well (rad), and ρ is the average fluid density (kg/ 3 ). An additional equation of state is required to correlate fluid density, pressure and energy, P e (10) P e Coefficient of heat transfer included in Eq. (9) is calculated by Holan s forula (Holan, 1976) as: 0.8 v r w H 0.03 (11) where μ is the fluid viscosity (Pa s). Friction factor of pipe for water single-phase flow is calculated using Karan s forula (Nakayaa,007) : 1 (1) (1.14 log D ) where is the surface roughness of pipe () and D is the diaeter of pipe (). In two-phase flow area, the friction factor is applied 1.1 ties value of that in single-phase area. 3.3 Fluid flow in wellbore with two feedzones Figure 3 shows scheatic of fluid ixing at the shallow feed zone. At the shallow feed zone, ass flow rate of ixed fluid, M total is given as: M = M total 1 + M (13) where M 1 is the ass flow rate of fluid fro deep feed zone of wellbore and M is the ass flow rate fro shallow reservoir. Mass flowrate fro each reservoirs are calculated by: 3
Inagaki, Itoi, Kuagai, Iwasaki M kh P r r w (14) where kh is the pereability-thickness (darcy ) and r w is the wellbore radius (). Specific enthalpy of ixed fluid h total is given as: h total M h 1 1 M h (15) M t where h 1 and h are the specific enthalpy of shallow reservoir fluid and deep reservoir fluid, respectively. 4. NUMERICAL SIMULATION Figure 3 Fluid ixing at shallow feedzone In this study, we assued a vertical well of,000 depth with a unifor diaeter, 0.. Shallow feedzone and deep feedzone exist at 1,700 and,000 depth, respectively. For evaluating the effects of pereabilitythickness product (kh) of shallow reservoir on well perforance, three kh values of shallow reservoir are given whereas that of deep reservoir kept constant: 3 darcy. Table 1 suarizes conditions of each reservoir. The boundary condition of wellhead pressure was given as sinusoidal in tie with cycle 6,000 sec and aplitude 1. bar as shown in Figure 4. This boundary condition was taken fro the easured data of wellhead pressure in Well SA-6 Table 1 Siulation conditions of each reservoirs Shallow reservoir Shallow reservoir Pressure (bar) 9 1.6 Teperature ( o C) 00 40 Pereabilitythickness (darcy ).0, 3.0, 4.0 3.0 4
Production rate (kg/s) Wellhead pressure (bar) Inagaki, Itoi, Kuagai, Iwasaki 8.0 7.5 7.0 6.5 6.0 Tie (s) 5. RESULTS OF CALCULATION Figure 4 Boundary condition of wellhead pressure Figure 5 shows calculated production rate at wellhead in three cases of shallow reservoir pereability-thickness (kh). In this study, production rate indicates the su of stea rate and water rates. The flowrate for kh= darcy shows salls fluctuation in early ties, then reains constant at 4.0 kg/s for the rest of tie. The flowrate for kh=3 darcy ranges fro 15 to 30 kg/s and this aplitude tends to be saller with tie. The flowrate for kh= 4 darcy also shows the fluctuation of production rate in the range fro 10 to 30 kg/s. The aplitude of fluctuation for kh=4 darcy is larger than that for kh=3 darcy. 35 30 5 0 15 10 5 0 darcy 3 darcy 4 darcy Tie (s) Figure 5 Calculated production rate at wellhead Figure 6 shows flowrate fro shallow reservoir into wellbore at shallow feedzone. The flowrate for kh= darcy is about kg/s and hardly fluctuates except in the early tie. The flowrate for kh=3 darcy fluctuates between 0 and 5 kg/s and the agnitude grows saller with tie in the sae way of the production rate at wellhead in Figure 5. The iniu flowrate for kh=4 darcy shows a negative value around - kg/s. The negative flowrate expresses a flow of fluid fro wellbore to reservoir. 5
Specific enthalpy (kj/kg) Flow rate (kg/s) Inagaki, Itoi, Kuagai, Iwasaki 10 8 6 B 4 0 - -4-6 A C darcy 3 darcy 4 darcy Tie (s) Figure 6 Flowrate fro shallow reservoir Figure 7 shows the specific enthalpy of ixed fluid at shallow feedzone. There is a quick drop in the specific enthalpy fro A to B. The value of specific enthalpy at A is 1037 kj/kg, which is equivalent to saturated water at 40. The specific enthalpy decreases to 995 kj/kg due to ixing with the fluid fro shallow reservoir whose teperature is 00 (A to B). Fro B to C, the specific enthalpy for kh=4 darcy increases to 1037 (kj/kg) again and the value reains constant at 1037 (kj/kg) for about 1300 s. The specific enthalpy for kh=3 darcy also shows the fluctuation as is the case with 4 darcy. However, a agnitude of fluctuation is 30 kj/kg in early tie while it becoes about 10 kj/kg in latter tie. This indicates that the aplitude of fluctuation becoes saller with tie. Although the specific enthalpy for kh= darcy fluctuates until 5000 s, subsequently the value is alost constant at 10 kj/kg. 1050 1040 A C 1030 100 1010 1000 990 980 B darcy 3 darcy 4 darcy Tie (s) Figure 7 Specific enthalpy of ixed fluid at shallow feedzone 6
Flashing depth () Pressure (bar) Inagaki, Itoi, Kuagai, Iwasaki Figure 8 shows histories of the flashing point depth and pressure of shallow feedzone for kh=4 darcy. This figure shows that there is an oscillation of flashing depth and pressure of shallow feedzone with inverse correlation between flashing depth and pressure of shallow feedzone. Fro D to E in the figure, the flashing point oves fro 1,01 to 904 depth while the pressure of shallow feedzone increases fro 87 to 91.4 bar. The reason why the flashing depth change is a decrease of saturation pressure of the fluid due to lowering the specific enthalpy of ixed fluid at shallow feedzone (A to B in Figure 7). Figure 9 deonstrates pressure distributions in wellbore at D and E in Figure 8. The flashing depth is 101 which eans that a length of water-phase colun fro shallow feedzone is 688, and the pressure of shallow feedzone is 87 bar at D. At E, the flashing depth is 904 and the pressure is 91.4 bar. Thus the length of waterphase colun is 796 which is 108 longer than that of D. The changes of the length of water colun result in the pressure increase fro 87 to 91.4 bar. The length water-phase colun controls the pressure of shallow feedzone. Then, the flow rate fro the shallow reservoir into the wellbore at shallow feedzone declines with ascent of the pressure of shallow feedzone ( B to C in Figure 6), and the specific enthalpy of ixed fluid at shallow feedzone increases to 1037 kj/kg. The flashing depth oves to deeper depth again by an increase of specific enthalpy of ixed fluid, which leads to descent of the pressure of shallow feedzone because the length of water-phase colun shortens. (E to F in Figure 8). The cycle entioned above is a echanis of fluctuation of production rate at wellhead occurring in Well SA-6 at Suikawa. 1090 94 1040 D E F 9 90 990 D F 88 86 940 84 890 840 E 8 Depth 80 Pressure 78 Tie (s) Figure 8 Histories of flashing point depth and pressure of shallow feedzone 7
Depth () Inagaki, Itoi, Kuagai, Iwasaki 0 Pressure (bar) 0 50 100 150 00 400 600 800 1000 Flashing depth Point D Point E 100 1400 1600 1800 000 Figure 9 Pressure distributions in the wellbore The echaniss of the phenoenon discussed so far are suarized in Figure 10. The cyclic discharge fro shallow reservoir causes the change of specific enthalpy of ixed fluid at the shallow feedzone. This causes a change of flashing depth and then the pressure at shallow feedzone fluctuates. This leads to a change of flowrate fro the shallow reservoir into the wellbore. Cyclic discharge fro shallow reservoird Fluctuation of pressure at shallow feedzoned Changes of specific enthalpy at shallow feedzoned Up and down of flashing depthd figure 10 The echanis of cyclic discharge 6. CONCLUSIONS 1) Unsteady stea-water two-phase flow in the wellbore with two feedzones was siulated. ) The larger pereability-thickness of shallow reservoir is, the larger fluctuation of production rate at wellhead is observed and the phenoenon did not occur in sall pereability-thickness case. 8
Inagaki, Itoi, Kuagai, Iwasaki 3) The cyclic discharge at wellhead is essentially controlled by the changes of specific enthalpy at shallow feedzone due to fluid fro the shallow reservoir. REFFERENCES Atoic Energy Society of Japan, 1993. Nuerical analysis of vapor water two phase flow (in Japanese), Asakura Shoten. Holan, J.P.,1976. Heat Transfer, McGraw Hill. Itoi. R, Katayaa. Y, Tanaka.T, Kuagai. N, Iwasaki. T. 013. "Nuerical siulation of instability of geotheral production well", Geotheral Resources Council Trans., vol.37, 837-841 Iwata S., Y. Nakano, E. Granados, S. Butler, and A. Robertson-Tait, 00. Mitigation of Cyclic Production Behavior in a Geotheral Well at the Uenotai Geotheral Field, Japan, Geotheral Resources Council Transactions, v.6, pp. 193-196. Matthews, C. S and Russell, D. G., 1967. Pressure Buildup and Flow Tests in Wells, Society of Petroleu Engineers. Miller, C., 1980. Wellbore User s Manual, Lawrence Berkeley Laboratory, University of California, LBL- 10910. Nakayaa Y, 007. "The echanics of fluid" (in Japanese), Youkendo. PROPATH group, 1999. PROPATH A progra package for therophysical properties of fluids Version 11.1. Tokita, H. and R. Itoi, 004. Developent of the MULFEWS Multi-Feed Wellbore Siulator, Proc. 9 th Workshop on Geotheral Reservoir Engineering, Stanford University, SGR-TR-175. 9