Coupled Reservoir, Wellbore and Surface Plant Simulations for Enhanced Geothermal Systems

Transcription

1 PROEEDINGS, Thirty-Ninth Workshop on Geothermal Reservoir Engineering Stanford University, Stanford, alifornia, February 24-26, 2014 SGP-TR-202 oupled Reservoir, Wellbore and Surface Plant Simulations for Enhanced Geothermal Systems Manish S. Nandanwar, Brian J. Anderson Department of hemical Engineering, West Virginia University, Morgantown, WV, 26506,USA Keywords: ombined model, Enhanced Geothermal Systems, Wellbore model, Surface plant model ABSTRAT To enable the complete optimization of a geothermal system requires fully-coupled models that include the reservoir, the wellbore, and the surface plant. In order to find a true global optimum for the operation of a geothermal system over its lifetime requires that one should be able to integrate the subsurface and the surface, including operating parameters and the subsequent capital cost as well as operating costs. Integrating these simulations together could allow for a reduction in the levelized cost of electricity (LOE) or directuse heat (LOH) as well as decreased simulation time due to the implicit coupling of the three major components of a geothermal system. This paper presents a combined model to simulate flow in reservoir as well as in the wellbore and evaluates the LOE and LOH from Enhanced Geothermal Systems. The components of this combined model includes two dimensional unsteady state single phase wellbore simulator coupled with the reservoir simulator TOUGH2-EGS (Xiong et al., 2013) plus a surface plant model. The wellbore and surface plant models are incorporated implicitly as subroutines in the TOUGH2-EGS main program. A single input file is read in to the combined model and the flow in reservoir and wellbore is solved in fully-coupled manner. The output parameters at the production well head are then taken as an input in to surface model which provides an estimate of the LOE or LOH. The coupling procedure is explained in detail in this paper. Two example problems are shown to demonstrate use of the model. 1. INTRODUTION Geothermal energy is one of the few renewable sources of energy with the potential to provide clean, reliable and abundant direct-use heat and electricity (Tester J.W. et al., 2006). A geothermal system consists of geothermal reservoir and a surface plant. Unlike traditional hydrothermal system reservoirs, Enhanced or Engineered Geothermal System (EGS) reservoirs are created by injecting high pressure cold water in hot dry rock either creating a network of fractures or causing existing fractures to slip, which results in increased rock permeability and transmissivity. Development of any EGS system involves geothermal field exploration, well drilling and stimulation, and surface plant installation. Due to the high costs associated with these operations and the uncertainties involved in longterm productivity of the reservoir, complete modeling of an EGS system is required to assess its economic feasibility and long term performance. Estimation of levelized cost of electricity (LOE) or levelized cost of heat (LOH) for direct-use systems from an EGS is necessary to compare it with other modes of power generation. Modeling of geothermal system involves wellbore, reservoir and surface plant modeling which is usually done separately. For accurately modeling an EGS reservoir, one needs to consider the flow through wellbore along with the reservoir flow. This can be done by coupling wellbore model with the reservoir model. For complete optimization of geothermal system, it is required to integrate wellbore-reservoir model with the surface plant model. It could allow us to simulate a geothermal system for various scenarios and different operating conditions resulting into optimization of operating parameters and reduction in LOE/LOH. This paper describes the coupling of wellbore and surface plant model with TOUGH2-EGS reservoir simulator. A combined model is developed which simulates the wellbore-reservoir flow in coupled manner and estimates the LOE and LOH from Enhanced Geothermal Systems. This paper first discusses each individual model in detail. Then the coupling procedure and simulation logic is explained. Finally, two example problems are given which demonstrates the utility of the combined model. 2. WELLBORE MODEL A two dimensional unsteady state wellbore simulator is developed to model fluid flow and heat transfer in the injection and production wells. This model is written in FORTRAN 95 and can handle single phase pure water flow for any well depth and wellbore radius. The wellbore model takes into account the fluid pressure, temperature and fluid mass flow rate as an input and determines the pressure, temperature and other thermo-physical properties of fluid at a given depth in form of output. The fluid pressure calculations as a function of depth are modeled by using Navier-Stokes momentum equation given as: 2 dp dv V V g f 0 (1) dz dz 2d where P is fluid pressure, Z is the vertical distance, ρ and V are fluid density and velocity, f is friction factor and d is well diameter. The friction factor, f, for the flow in vertical pipe is given as (hen et al., 1979) 1

2 f log d log d (2) Re Re where ε is pipe roughness factor and R e is Reynolds number. To determine the fluid temperature, T f, as a function of well depth and production or injection time, the approach given by Hasan and Kabir (2002) is used in this model. The energy balance across the formation leads to diffusivity equation given as: 2 Te 2 r 1 Te r r ee T K t e e (3) where T e is formation temperature at arbitrary depth at time, t, and distance, r, measured from the center of the wellbore; e, ρ e and K e are the formation heat capacity, density and thermal conductivity respectively. Hasan and Kabir (2002) solved this equation in terms of dimensionless variables and the solution obtained as: T 0.2t t D e D D ln ( e ) t (4) D where t D is dimensionless time and T D is dimensionless temperature. The energy balance for the wellbore fluid can be expressed as: dt f dz J dp 1 Q dv g V (5) dz m dz P where J is Joule-Thompson coefficient, p is specific heat capacity of fluid, m is mass flow rate of fluid and Q is heat flow per unit length which is defined by heat transfer equation: Q r U ( T T ) (6) 2 to to f wb where r to is outer radius of well casing, U to is overall heat transfer coefficient and T wb is the temperature at wellbore and formation interface. The negative sign of Q in equation implies production well and the positive sign implies injection well. On solving equation (5), the expression for fluid temperature, T f, for the production well at any depth Z can be obtained as: T f T eibh g G ( Z (1 e ( L Z) Lr L) L r ) (7) Similarly for injection well the fluid temperature can be given as: T f T eiwh g G ( (1 e Z Lr Z) L r ) (8) where T eibh represents bottom hole temperature, T eiwh represents wellhead temperature, g G represents geothermal gradient and Lr is the relaxation parameter which is defined as (Ramey et.al, 1962) L r 2 rtou toke (9) PW Ke ( rtou totd ) The major input parameters for the wellbore model are: Fluid Pressure, Temperature and Mass flow rate Well depth, wellbore diameter, wellbore casing diameter Injection or Production time 2

3 Some of the assumptions made in this model are: Fluid velocity, pressure and temperature does not vary in radial direction Acceleration term in momentum equation (1) is negligible Vertical heat diffusion is neglected while deriving diffusion equation 3. TOUGH2-EGS TOUGH2-EGS is a numerical simulator developed by Xiong et al. (2013) for solving thermal, hydrological, mechanical and chemical processes in enhanced geothermal reservoirs in a fully coupled manner. This simulator is built by incorporating geomechanical and reactive geochemical model into existing structure of TOUGH2 (Pruess et al., 1999), a numerical simulator for multidimensional fluid and heat flows of multiphase, multi-component fluid mixtures in porous and fractured media. Geo-mechanical processes are modeled as mean stress equations which are solved simultaneously with fluid and heat flow equations. The solution of fluid and heat flow equation provides fluid velocity and phase saturation which are then used to solve chemical processes in a sequential manner. Although TOUGH2-EGS is capable of solving thermal-hydrological-mechanical-chemical (THM) processes in coupled manner, the provision is made for the user to select specific coupling process such as TH, THM, TH or THM in a simulation. In TOUGH2-EGS, EOS3 module of TOUGH2 family is used to calculate thermo-physical properties of water and air flow. The primary thermodynamic variables are pressure, temperature and air mass fraction for single phase flow, while pressure, temperature and gas phase saturation for two phase flow. Multiphase extension of Darcy's law is used to describe fluid flow through porous medium whereas heat flows are governed by conduction and convection. In order to model fluid and heat flow through fractured porous media, Multiple Interacting ontinua (MIN) approach (Pruess and Narasimhan, 1985) is used. At each time step, a set of coupled non-linear algebraic equations obtained from space and time discretization of continuum equations, are solved for primary and secondary variables for each grid block using Newton-Rapson method. Injection or production well is modeled as sink or source. Sink or source is specified as grid block in the reservoir domain, where the injection or production of fluid occurs at a constant rate or time dependent rates. Among the various options, one of the option for injection well is to specify injection fluid mass flow rate and enthalpy. For production well, fluid can be produced at constant mass flow rate, or the well on Deliverability option can be used where the cell produces to a fixed pressure. 4. SURFAE PLANT MODEL Surface plant model is developed which consists of set of correlations to evaluate plant capital and operation & maintenance costs and estimate the levelized cost of electricity (LOE) or direct-use heat (LOH) from Enhanced Geothermal Systems. The model can be divided into three parts. : 1) alculation of net electricity or direct-use heat generated, 2) alculation of capital and operation & maintenance (O&M) costs and, 3) alculation of LOE or LOH. 4.1 alculation of Net Electricity or Direct-use Heat Generated Depending on the end use, user has an option to choose either electricity mode or direct-use heat mode. In electricity mode, all the heat extracted from the geothermal reservoir is used to generate electricity. The power generated is given as: P ub (10) where η u is utilization efficiency of the power plant and B is the exergy or availabiltiy of geothermal fluid. The availability of geothermal fluid is given as: B m h h T ( S S )) (11) ( p a a p a where m is production fluid mass flow rate, h is specific enthalpy, S is specific entropy and T a is ambient temperature. The net electricity generated is calculated by subtracting geothermal fluid pumping power from the total power generated given by equation (10). The correlations used in equation (10) and (11) are taken from GEOPHIRES (Beckers et al., 2013). In direct-use heat mode, all the heat extracted from geothermal fluid is used in direct-use heat applications. It is expressed in MMBtu. The geothermal fluid pumping power consumption is modeled as an operating cost with user defined electricity cost. 4.2 alculation of apital and Operation & Maintenance (O&M) osts Total apital ost The total capital cost is calculated as the sum of geothermal well drilling and completion costs ( cap,well ), power plant costs ( cap,pp ), reservoir stimulation costs ( cap,stim ), fluid distribution costs ( cap,distr ) and resource exploration costs ( cap,expl ). cap (12) cap, well cap, PP cap, stim capdistr, cap,expl. The geothermal well drilling and completion cost is given by the following correlation (in M$) (Lukawski et al., 2013): cap, well MD (13) 3

4 1600 MD 9000 where MD is the well depth in meters. In electricity mode, the power plant capital cost is calculated as: cap, PP ( cap,pp P for 15MW e) 15MW 0.06 (14) where P is capacity of power plant in MW e. cap,pp for 15MW is calculated first, based on the correlations used in GEOPHIRES (Beckers et al., 2013). For direct use heat mode, the power plant cost depends on the application. User can manually specify the cost or it is calculated by the model using built-in correlation. The reservoir stimulation cost is taken as M$ 2.5 per injection well in the model, based on the assumption by Mines et al. (2013). Fluid distribution costs and resource exploration costs are calculated using the correlations similar to that used in GEOPHIRES (Beckers et al., 2013) Operation & Maintenance (O&M) osts The annual operation and maintenance (O&M) cost is given as sum of power plant O&M costs ( O&M,PP ), well field O&M costs ( O&M,wf ) and make up water costs ( O&M,w ). Again, all the correlations used for O&M cost calculation are taken from GEOPHIRES (Beckers et al., 2013). O& M O & M, PP O & M, wf O & M, w (15) The power plant O&M cost is estimated as the sum of 75% of total labor cost ( lab ) and 1.5% of power plant capital cost. Labor costs are estimated by using built-in correlation. O& M, pp lab cap, PP (16) The well field O&M costs are estimated as the sum of remaining 25% of labor cost and 1% of well capital costs: O& M, wf lab cap, well (17) alculation of Levelized ost of Electricity (LOE) or Direct-use Heat (LOH) To calculate the LOE or LOH, two different types of models are provided in the surface plant model. I) Fixed charge rate model, II) Standard Levelized ost model. Both the models are taken from the GEOPHIRES. I. Fixed harge Rate Model (FR) In this model, the LOE or LOH is given as: FRcap O & M LOE/ LOH (18) W where cap is total capital cost, O&M is the operation and maintenance cost and W is the average annual electricity output in kwh or direct-use heat generation in MMBtu. FR is the factor which is multiplied by the total capital cost to obtain annual capital cost. It is determined based on several financial parameters such interest rate, tax rates, depreciation etc. II. Standard Levelized ost Model In this model, LOE or LOH is given as: LOE/ LOH cap n t n t 1 O& M, t t 1 (1 i) Wt t (1 i) (19) where cap is capital investment, O&M is operation and maintenance cost and W t is electricity or direct heat generated in year t. 'i' is the discount rate and 'n' is number of years of production. 4

5 5. OUPLING OF WELLBORE AND SURFAE PLANT MODEL WITH TOUGH2-EGS Wellbore and surface plant model are integrated with TOUGH2-EGS simulator and a single combined model is developed. Both the models, wellbore and surface plant, are incorporated in the TOUGH2-EGS main program as subroutines. Figure 1 shows the flow diagram for coupled simulation. The coupling procedure is explained in detail as follows: 1) TOUGH2-EGS main input file is modified to include input parameters for wellbore as well as surface plant model. Thus all the input parameters are read once in the main program routine. 2) At each time step, an explicit call is made to WBINJ, a subroutine for injection well. This subroutine takes the injection fluid mass flow rate, pressure and temperature at the wellhead as an input and calculates the enthalpy of fluid at the well bottom which serves as an input to the TOUGH2-EGS main program. 3) TOUGH2-EGS solves the reservoir flow and update the primary variables such as pressure and temperature for each grid block. Again an explicit call is made to subroutine WBPRO for production well, which takes the production well bottomhole pressure and temperature as an input and calculates the enthalpy of fluid at the surface. 4) For the same time step, using the calculated enthalpy values, subroutine POWAL calculates the total heat extracted from the geothermal fluid. If the electricity mode is specified in the input file by the user then net electricity generated is calculated. 5) Step 2 to step 4 is repeated for every time step and the net electricity output or the direct-use heat is calculated and stored. 6) At the end of the simulation, subroutine OSTAL first calculates the average annual electricity output or direct-use heat and then using the cost correlations it calculates the total capital cost and the operation & maintenance cost of the power plant. 7) Finally the subroutine LOST calculates LOE or LOH using one of the models discussed earlier in this paper. Some of the major changes in the TOUGH2-EGS original code are: 1) Many new records or code blocks are added in the subroutine INPUT to read the input parameters for wellbore as well as surface plant model. For example injection well input parameters are given under the record name 'INJ' in the main input file. 2) Subroutine WBINJ is called inside the subroutine YIT at the beginning of each time step. The calculated values of enthalpy at the injection well bottom-hole are given to the subroutine QU. Subroutine QU in TOUGH2-EGS main program deals with all the terms arising from sink and sources. 3) Just after the subroutine ONVER, subroutine WBPRO is called inside the YIT. It uses updated bottom-hole pressure and temperature values to calculate the fluid properties at the surface. 4) Subroutine POWAL is called inside the WBPRO at every time step. Subroutine OSTAL and LOST are called at the end of the simulation. A small code block is written to print the output of the surface plant model. No changes are made in the original output file of TOUGH2-EGS. Unlike TOUGH2-EGS, in our combined model, input for injection well has to be given separately through the input file under the record 'INJ'. Injection fluid pressure, temperature and constant mass flow rate at the wellhead are the input parameters. Also while specifying the name of sink or source, same name must be given to the elements of a particular Sink or Source. For example 'INJ01' must be the name of all the source elements in a particular injection well. The combined code deals only with constant mass rate production and injection. It is not capable of handling time dependent mass injection rate. Also the wellbore model is developed only for single phase flows and thus the combined model is not capable of handling two-phase flows. 5

6 START Read INPUT file Time step 1 all WBINJ alculate fluid enthalpy at injection well bottom-hole TOUGH2-EGS iterations all WBPRO alculate fluid enthalpy at the surface all POWAL alculate total heat extracted or the electricity generated More time steps YES NO all OSTAL STOP simulation alculate capital costs and O & M costs all LOST alculate LOE/LOH Figure 1: Schematic diagram showing the simulation logic and procedure 6. APPLIATION EXAMPLES 6.1 Example 1 An example problem is given to demonstrate the use of coupled model. In this example problem, the reservoir model based on five-spot geometry for geothermal injection and production presented in TOUGH2-User's guide (Pruess et al., 1999) is used. Injection well is taken at the center while the production wells are located equidistant from the injection well. Fractures are modeled using the method of 'Multiple Interacting ontinua' (Pruess and Narasimhan, 1985). Table 1 shows the reservoir material properties and initial conditions used in this simulation. All the reservoir data is taken from the hot spot region in West Virginia, USA (Bedre et al., 2012). This reservoir falls under the category of low-temperature geothermal reservoir with a geothermal gradient of 28 /km, reaching the temperatures of 150 to 200 for a depth range of 4.5 to 6 km. Electricity can be generated from the surface plant if the fluid temperature exceeds 150. Fluid temperatures below 150 can be used for various direct-use heat applications. Thus in this example, for electricity generation, reservoir temperature is taken as 190 at a depth of 6 km and for direct-use heat calculations reservoir temperature is 150 at a depth of 4.5 km. 6

7 Tables 2 and 3 show the input parameters for the wellbore and surface plant model. onsidering the ideal case scenario, 0% water loss is assumed. In this simulation, Standard Levelized ost model is used to calculate the levelized cost of electricity and direct-use heat. It should be noted that all the input data for reservoir, wellbore and surface plant is given through the single input file. Table 1: Reservoir material properties and Initial conditions Parameter For electricity Generation For direct-use heat Reservoir pressure 600 bar 465 bar Reservoir temperature Porosity(Volume fraction) Thermal conductivity 0.5 W/(m ) 0.5 W/(m ) Permeability m m 2 Rock grain density 2600 kg/m kg/m 3 Table 2: Wellbore model input parameters Parameter For electricity Generation For direct-use heat Injection flow rate 60 kg/s 60 kg/s Injection fluid temperature Well depth 6000 m 4500 m Water loss 0% 0% Well asing diameter 0.22 m 0.22 m Table 3: Surface plant model input parameters Pump efficiency 0.8 Discount rate 8 % Inflation rate 1.6% Plant lifetime 30 years Ambient temperature 15 While running the simulation, at each time step, injection wellbore model calculates the fluid pressure and temperature at the well bottom. Figures 2 and 3 shows the injection wellbore pressure and temperature profiles for three different injection time periods for the case of direct-use heat. It can be seen from Figure 2 that pressure profile of injection well remains almost same for all the injection times. Figure 3 shows that the slope of temperature profile increases with increase in injection time. This means that due to continuous injection of cold water, the rock formation surrounding the wellbore cools down and thus the fluid temperature difference between wellhead and well bottom decreases as the injection time increases. Production well produces at a constant pressure of 3 MPa with the temperature profiles at different production time periods as shown in Figure 4. Final results obtained from the simulations are shown in Table 4. LOE of $0.67/kW e and LOH of $19/MMBtu are obtained from a geothermal plant with capacity 2.7 MW e for electricity generation and 16.7 MW th for direct-use heat. From the economic point of view, LOE of $0.67 /kwh and LOH of $19/MMBtu do not look attractive. High values for total capital costs are due to high well drilling costs. 6.2 Example 2 Drilling costs and production flow rate are the important subsurface variables that affect the LOE/LOH significantly (Mines et al., 2013). In this example problem, effect of injection/production flow rate on LOH is studied using the combined model. Keeping all the surface and subsurface parameters same as that in example 1, LOH is calculated for different flow rates and the results are plotted in Figure 5. 7

8 It can be seen from Figure 5 that LOH decreases very rapidly with increase in production flow rate up to certain value. This is due to the increase in generating capacity of geothermal plant as the production is increased. But beyond certain flow rate, not much decrease in LOH is observed. This can be explained by the fact that as the production flow rate increases, pumping power also increases and thus the pumping cost comes in to effect after certain flow rate, which increases the total operating cost. Increase in operating cost reduces the effect of increased generating capacity and thus LOH does not change significantly with further increase in production flow rate. Figure 2: Injection wellbore pressure profile at different times Figure 3: Injection wellbore temperature profile at different times 8

9 Figure 4: Production wellbore temperature profile at different times Table 4: Output results Parameters Electricity mode Direct-use heat mode Generating capacity 2.7 MW e 16.7 MW th Total capital cost $120MM $70MM Total O&M cost $2.2MM $1.8MM LOE/LOH $0.67/kWh $19/MMBtu Figure 5: Plot of LOH versus Injection/production flow rate 7. ONLUSION This paper presents a combined model which simulates wellbore and reservoir flow in a coupled manner and estimates the LOE or LOH from Enhanced Geothermal Systems. Individual models are discussed first and then their coupling procedure is described in detail. At last, two example problems are given to demonstrate the use of the model. In first example problem, an EGS reservoir is simulated using the field data for hot spot region in West Virginia, USA and LOE & LOH are estimated. It is found that the LOE & LOH obtained, are not economically competitive as compared to other modes of power generation. In the second example problem, effect of production flow rate on LOH is studied. From the results it can be concluded that the optimization of operating parameters is required to minimize the LOH or LOE. Both the examples illustrate the utility and requirement of the combined model. The wellbore model is built only for single phase flows and thus the combined model is not capable of handling two-phase flows. Future work involves modifying wellbore model to handle both single phase as well as two-phase flows. 8. AKNOWLEDGEMENT The authors would like to thank Mr. P. Fakcharoenphol from olorado School of Mines for his useful guidance and Mr. K. Beckers for providing GEOPHIRES source code. Authors would also like to thank Mr. J. Peluchette, Mr. X. He, Mr. S. Velaga, Mr. A. Taiwo, Ms. P. Sridhara and other lab members for their constructive remarks and suggestions. 9

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