1030639.pdf

GRC Transactions, Vol. 37, 2013

The Reduced Pumping Power Requirements from Increasing the Injection Well Fluid Density Benjamin M. Adams1, Thomas H. Kuehn1, Jimmy B. Randolph2, and Martin O. Saar2 1

Department of Mechanical Engineering, University of Minnesota, Minneapolis, MN 2 Department of Earth Sciences, University of Minnesota, Minneapolis, MN [email protected]

Keywords

It is not uncommon for a binary geothermal plant to consume 30-40% of its gross generated power with parasitic loads; the Heber Binary plant in Heber, California has a parasitic load of 34%, 7% of which is used by brine production and reinjection pumps (DiPippo, 2012). Reduction in parasitic pumping load may come from more than just increasing pump efficiency. We have shown for a CO2based geothermal system that pumps can be all but eliminated due to the density-driven “thermosiphon effect” (Adams, Kuehn, Bielicki, Randolph, & Saar; In preparation, 2013b). However, we have also shown that the effect is applicable not only to CO2—a 20 wt% brine solution may generate a flowrate of 50 kg s-1 without pumps for a single injection-production well pair as shallow as 3.5 km. The flow is created through the difference in densities in the injection and production wells, and is not negligible—even for brine systems. Therefore, production flowrates may be increased through the manipulation of wellbore densities, not just pumping. When a fluid is injected through a well, it increases in pressure based on its depth and density, as shown in Equation 1 for a frictionless well. For an incompressible substance, as water is generally considered, the increase in pressure throughout the well reduces to the product of density, the gravitational constant, and depth. This is the hydrostatic pressure.

Parasitic losses, CO2, thermosiphon, reverse osmosis, operational efficiency, pumping, thermodynamics

Abstract The reduction of parasitic loads is a key component to the operational efficiency of geothermal power plants, which include reductions in pump power requirements. Variations in fluid density, as seen in CO2-based geothermal plants have resulted in the elimination of pumping requirements, known as a thermosiphon; this effect, while less pronounced, is also found in traditional brine geothermal systems. Therefore, we find the reductions in pumping power requirements for traditional 20 wt% NaCl brine and CO2 geothermal power systems by increasing the injection fluid density. For a reduction in temperature of 1°C at a 15°C surface condition, a traditional brine system was found to require up to 2kWe less pumping power. A CO2 system in the same condition was found to require up to 42 kWe less power. When the density of the injected brine was increased by increasing the salinity of the injected fluid to 21 wt% NaCl, the injection pumping requirement decreased as much as 45 kWe. Both distillation and reverse osmosis processes were simulated to increase the salinity while producing 7 kg s-1 fresh water. The pumping power reduction does not account for the increased energy cost of salination; however, this may still be economical in locations of water scarcity.

z

ΔPwell,isentropic =

∫ ρ ⋅ g ⋅ dz

(1)

0

A change in the density of the injected fluid will have an effect on the pressure change through the well, even if the density remains constant while doing so. The pressure change and density are proportional for an incompressible fluid; therefore an increase in density of 10% would cause the pressure change in the well to also increase by 10%. If the downhole pressure of the injection well remains constant, increasing the density in the well will decrease the required injection wellhead pressure at the surface, and therefore decrease pumping power. In this paper, we look at the effect of changing the injection density of both 20 wt% NaCl brine and CO2 in geothermal systems.

1. Introduction Geothermal power systems operate from lower temperature thermal resources than most other types of power production, which leads to inherently lower thermal efficiency. While they can still be profitable, increased attention must be paid to increasing power conversion efficiencies, decreasing parasitic losses, and reducing the number of costly components. One such parasitic load in traditional brine geothermal is injection pumping power. 667

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m i = ρi AVi

2. Method

(4)

Pure CO2 and a 20 wt% NaCl brine system were modeled using Engineering Equation Solver (EES). EES is a simultaneous equation solver with built-in property data for many substances. The thermodynamic property data within EES for CO2 is from Span and Wagner (1996). Brine property data is based on water data from the IAPS-84 Steam Tables (Haar et al., 1984), and converted to brine values from relations provided by Driesner (2007). The pump power reduction was simulated for changes in injection fluid density in three different ways. First, the fluid density was increased by decreasing the fluid temperature by one degree Celsius through the use of a closed-circuit cooling tower. Second, the brine density was increased by increasing the salinity of the brine +1 wt% through a partial-vacuum distillation process. Last, the brine density was increased by increasing the salinity of the brine +1 wt% through a reverse osmosis (RO) process. In all cases, the reduction in pump power was determined by differencing the surface pump power before and after the density was varied.

The last term in Equation 3 accounts for the deviation from isentropic flow in the wellbore, due to frictional losses. The Darcy friction factor, f, is found using the Reynolds number and surface roughness of the piping, ε, using the Moody Chart (Moody, 1944). The surface roughness was chosen as a conservative value for oil & gas industry bare CR13 piping as reported by Farshad and Rieke (2006), found in Table 1. Wellbore heat transfer was assumed to be negligible based on previous work (Randolph, Adams, Kuehn, & Saar, 2012). Once the pressure at State 5 was determined, the temperature of the state was found using the isentropic efficiency relation for a pump described in Equation 5. The subscript ‘s’ denotes the exit state of the pump if it were an isentropic process. The injection pump was assumed to have an isentropic efficiency of 90%.

2.1 Simple Cooling

The pumping power, Ppump, was determined from the enthalpy difference across the pump and mass flowrate, as shown in Equation 6.

ηs =

In the simple cooling case, the fluid temperature was reduced 1°C to increase the fluid density. This was achieved using a closedcircuit cooling tower, as shown in Figure 1. The incoming fluid at State 1 is cooled one degree to State 2 at constant pressure. Then it is pumped to a pressure at State 5 such that the downhole pressure at State 6 is 5 MPa higher than hydrostatic pressure at that depth. State 6 was set at a 5 MPa over-pressurization to ensure the surface pumping power was positive.

(h − h ) (h − h ) 5,s

2

5

2

(

(5)

)

 h5 − h 2 Ppump = m⋅

(6)

The parasitic power requirements for cooling the fluid from State 1 to State 2 were derived from published Baltimore AirCoil FXV and PC2 series industrial cooling and condensing tower data (Adams, Kuehn, Bielicki, Randolph, and Saar, In Preparation, 2013a). Parasitic power requirements were then found using Equations 7 and 8.

Pparasitic = λcooling ⋅Qsurface

(7)

 h2 − h 1 Qsurface = m⋅

(8)

(

)

2.2 Partial-Vacuum Distillation Another method to increase the density of the brine is to increase the salinity of the solution. One way this is accomplished is through distillation. This is a popular method by which ocean water is desalinated for human consumption. In a distillation process, the brine is boiled, separating water vapor from the brine mixture. Vacuum distillation is performed by decreasing the brine pressure below its saturation vapor pressure, causing the mixture to boil. This differs from a thermal distillation process where the mixture is heated to its boiling point. Vacuum distillation is preferred in this geothermal process due to the already low pressures and pumps available at the surface and the large heat input needed for thermal distillation. A schematic of this process is diagramed in Figure 2. The entering brine is boiled by throttling the fluid to a partial vacuum below the vapor pressure (State 3), separating the liquid and vapor components (States 4 and 4’), condensing the distillate (State 5’), and then pressurizing to atmospheric pressure (State 6’). Likewise, the resulting brine is pressurized (State 5) to that required downhole to match the reservoir over-pressurized state (6). The mass flowrate of the injected brine is reduced by a factor of (1-x) and the injection well pressure profile is numerically

Figure 1. A Simple Cooling Process Diagram. Incoming fluid (1) is decreased in temperature through a surface heat exchanger (2) and then increased in pressure (5) to a state needed to achieve the appropriate downhole pressure (6).

To find the wellhead injection pressure given the downhole pressure, the well must be numerically integrated from State 5 to 6. This is required because the fluid cannot be assumed incompressible, as we are chiefly concerned in the small variations in density that occur. The well was divided into 100m segments. Across each segment, an energy balance, the patched Bernoulli equation, and continuity equation were performed as described in Equations 2, 3, & 4, respectively.

hi+1 + gzi+1 = hi + gzi Pi+1 + ρi+1gzi+1 = Pi + ρi gzi − f

(2) 2 L ρiVi D 2

(3)

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2.3 Reverse Osmosis An alternate method for increasing the salinity of the injected brine is through Reverse Osmosis (RO). RO is gaining popularity for the desalination of seawater, especially through Europe (Fritzmann, Lowenberg, Wintgens, & Melin, 2007). Reverse Osmosis differs from distillation in that the pure water is separated from the solution by forcing the water through a membrane that is impermeable to NaCl. This is generally more economical than distillation as much of the pumping energy can be recovered, as opposed to the lost thermal energy required to boil water. A schematic of this process is shown in Figure 3.

Figure 2. A Partial-Vacuum Distillation Process Diagram. Incoming fluid (1) is heated to 64°C (2), then throttled to a pressure (3) where a quality X is achieved to produce a 21 wt% NaCl brine (4) at a 30°C, which is pumped to a pressure (5) needed to achieve required downhole reservoir pressure (6). The fresh water vapor (4’) is condensed to a liquid (5’) and then pumped to atmospheric pressure (6’).

integrated as described previously. It is assumed the reservoir can accommodate the decrease in fluid mass. To achieve an increase in the salinity from 20 wt% NaCl to 21 wt% NaCl, the liquid solution must be throttled to a quality of x=0.059, which generates 7.14 kg s-1 desalinated water. At a quality of 0.059, the fluid exists as a mixture of 5.9% water vapor and 94.1% 21 wt% NaCl. The distillation boiler is assumed to be a constant pressure process, and its energy balance is given in Equation 10. The mass of NaCl does not change through the process, so the enthalpy of solution is neglected.

h2 = h 3 h3 = x ⋅ h4' '+ (1− x ) ⋅ h4

Figure 3. A Reverse Osmosis (RO) Process Diagram. Incoming brine (1) is pumped to above the osmotic pressure of 20 wt% NaCl brine (2), where X salt-free water is forced through a filter (5’), leaving higher concentration brine behind (3). The high-pressure products are expanded to atmospheric pressure (6’ and 4), recapturing the initial pump energy. The brine is then pressurized (5) to achieve the appropriate downhole pressure (6).

(9) (10)

In the reverse osmosis system, the incoming brine (State 1) is pumped up beyond its osmotic pressure (State 2), near an osmotic membrane. During this separation process, the fluid is assumed to drop in pressure by 0.2 MPa (States 3 & 6’), which is significantly dependent on the separation rate and filter area available (Fritzmann, et al., 2007). The brine with increased salinity is depressurized through a liquid expander (State 4), and then pumped to the surface pressure (State 5) required to achieve the appropriate downhole over-pressurization (State 6). In practice, the RO Expander and Primary Surface Pump would be combined; however, they were kept separate so the decrease in primary surface pumping could be measured before and after desalination. Reverse osmosis is based on a material property of membranes known as semi-permeability, where the material will allow water to pass-through, but resist Na+ and Cl- ions. The pressure required to force the water through is the osmotic pressure, π, given by Van’t Hoff’s law in Equation 12 (Fritzmann, et al., 2007).

As the brine is separated, its temperature decreases. The vacuum distillation process is a constant-energy process (Equation 10); therefore, the energy required to vaporize the 5.9% water vapor component is equivalent to that needed to reduce the temperature in the remaining brine. The vapor must be condensed after it is boiled to minimize compression costs, so the condensing temperature must also be above ambient temperature. A condensing temperature of 30°C was chosen to minimize condensing parasitic power costs, fixing State 4 and 4’ (P4=4.2 kPa, T4=30C, x=0.059). Thus, State 3 is also fixed (T3=64°C, P3=100 kPa), because the pressure on both sides of the throttling value is know and each has equivalent enthalpy (Equation 9). Therefore, incoming brine must be heated (or cooled) to 64°C from State 1 to 2 to achieve the desired output salinity. Alternatively, preheating the brine may be avoided if there is some flexibility in the output salinity. The parasitic power of the condensing tower is found in the same manner as the cooling tower, using EQUATIONEQUATION.

Pparasitic = λcondensin g ⋅Qsurface

π = ϕ ⋅C ⋅ R ⋅T

(12)

The concentration, C, is the Colligative concentration, which is the number of ions per unit volume, or twice the normal concentration for NaCl, or 7.89 mol L-1 for 20 wt% NaCl. The osmotic coefficient is a correction factor used to account for non-ideal

(11) 669

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3. Results & Discussion

behavior of the solution, and is 1.13 for 20 wt% NaCl (Hamer & Wu, 1972). Therefore, a 20 wt% NaCl solution has an osmotic pressure of 21.3 MPa. This is a factor of 8 greater than the osmotic pressure of 3.5 wt% seawater. A substantial amount of energy is Table 1. Model Parameters. used to compress the Working Fluids 100% CO2 (CO2) brine to above 22 MPa, 20 wt% H20-NaCl (Brine) therefore a method to ηpump 0.9 recover this energy D 0.27 m is necessary. Either a g 9.81 m s-2 pump/turbo-expander ṁ 120 kg s-1 set or a work ex8000 kPa (CO2) changer may be used Pfluid, initial (P1) 100 kPa (Brine) to compress and dePreservoir (P5) Hydrostatic + 5 MPa compress the brine. A R 8.314 L kPa K-1 mol-1 pump/expander pair of Tfluid, initial (T1) 15ºC to 64 ºC devices may be used z 0.5 km to 5 km as shown in Figure 3, λcondensing 0.017 kWe kWth-1 and have an overall λcooling 0.019 kWe kWth-1 recovery efficiency of ε 0.000055 m 90% (Fritzmann, et al., φ 1.13 2007). The recovery efficiency is the output of the expander divided by the input to the pump. A direct “work exchanger” may also be used, where the exiting fluid is used to directly pressurize the incoming fluid, and may have a recovery efficiency of up to 96% (Fritzmann, et al., 2007).

The results for the simple cooling scenario are shown in Figure 4. In every case, there is a net positive reduction in pump power required. This is due to the increase in density which consistently occurs when the temperature is decreased 1°C. The density change in CO2 is larger than brine; when the temperature is decreased from 15°C to 14°C, the density increases from 869 kg m-3 to 877 kg m-3, whereas the brine density increases from 1140.8 kg m-3 to 1141.2 kg m-3 for the same conditions. The result is a substantial reduction in pump power required for all CO2 cases, and a smaller, <2 kWe change for the brine scenarios. Also, the density changes for CO2 become larger as it nears its critical point (31°C), causing the power savings to be even greater near those temperatures. On each curve in Figure 4, the electrical power needed to produce the increase in density is shown; this is the parasitic load needed to power the cooling tower. It is clear that for most CO2 cases at a depth greater than 1km, the energy reduction in pumping power is greater than the energy needed to cool the fluid. Conversely, in all brine cases, the energy required to increase the density is more substantial than that saved by its increase. The density of the injected fluid may also be increased through salination, and the result is shown in Figure 5. The density changes from 1140.8 kg m-3 at 20 wt% NaCl to 1148.8 kg m-3 at 21 wt% NaCl. Therefore, at a depth of 1 km, the +8 kg m-3 density increase results in a pump power reduction of 12 kWe, which increases to 45 kWe at 5 km. To obtain the energy cost required for the salination, the method through which this is accomplished must be considered. The salination may be accomplished in several ways; two methods shown here are: Distillation and Reverse Osmosis. The energy requirements for distillation of the brine to achieve +1 wt% NaCl are shown in Figure 5. The energy requirements for distillation are dependent on the inlet temperature, T1. To achieve a resulting fluid temperature at least 15°C above ambient conditions (30°C), the brine must be heated to 64°C before it is throttled. This is indicated by the di-

2.4 Model Parameters Initial surface pressures for the system were different for both CO2 and Brine, chosen for typical surface values in each system. These parameters are shown with others used in simulation in Table 1, unless specifically stated otherwise. The CO2 pressure used is large, but typical of what would be found at the surface in a supercritical, CO2-based system.

Figure 4. Pump Power Reduction at varying depths for CO2 and 20 wt% brine when you decrease the injection fluid by 1°C. The pump power reduction for increasing the salinity of brine +1 wt% is also shown. The power quantities shown on each line are the parasitic power requirements to achieve the 1°C reduction in each fluid.

Figure 5. Pump and fan power requirements to achieve a +1 wt% increase in brine salinity using a distillation process.

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pumping power is 24 kWe, and 7 kg s-1 fresh water is produced. Therefore, the net cost of producing fresh water is reduced from 17 to 14 kWe per kg s-1. If a wholesale electric rate of $0.05/kWhr is assumed, the additional energy cost of the geothermal plant to produce one unit (100 ft3) of fresh water is $0.55/unit, and the plant would produce 213 units per day.

minishing heat input required up to an inlet value of 64°C. Below this threshold value, the condensing temperature (T4’) will always be the same, requiring the same amount of fan parasitic power to condense the vapor. Above the threshold value of 64°C, the condensing temperature increases, increasing the approach temperature of the condenser, causing a reduction in parasitic power. At an inlet temperature of 75°C, the condensing temperature is 41°C; similarly, at a temperature of 90°C, the condensing temperature is 56°C. Reverse Osmosis (RO) provides an alternate way to increase the salinity of the brine. It has the advantage of only requiring pumping of the fluid—no thermal input or extraction is necessary. However, the pressure required to overcome the osmotic pressure of 20 wt% brine (21 MPa) is substantial and can be costly based on the type of energy recovery used. Figure 6 shows the energy cost for Reverse Osmosis, given varying degrees of overall recovery efficiency of the process. The recovery efficiency is the gross power recovered by the turbo-expander, divided by the gross input RO pump power.

4. Conclusions In this paper, the reduction in injection pumping power was found for three scenarios: a decrease in CO2 surface temperature of one degree Celsius, a decrease in temperature of 20 wt% brine by one degree Celsius, and an increase in salination of the injection brine by 1 wt%. A summary of these scenarios is plotted in Figure 7.

Figure 7. Pump Power Reduction per Input Power Required for CO2 and Brine. Values greater than 1 indicate the pump power reduction at the injection well is larger than the power needed to decrease the temperature or increase the salinity of the fluid. Figure 6. Net power requirement for Reverse Osmosis process for a given overall recovery efficiency of the Reverse Osmosis system. In addition, the Pump Power Reduction per Input Power at 2.5 km ant 5 km is plotted on the right axis logarithmically.

For each scenario, the decrease in pumping power required at the injection well was divided by the input power required to produce the change in temperature or salination. Therefore, values greater than one indicate energy is saved by performing the listed action. Only the CO2 scenarios are able to save pumping power by reducing the fluid temperature. However, in some brine scenarios, additional benefit may come from the fresh water produced during the desalination process. Additionally, we have shown: The injection pumping power requirement decreases as injection density increases. The pressure change in the injection well is proportional to the injection density. Therefore, increasing the average injection density by 10% increases the pressure change in the injection well by 10%. Given the same downhole injection pressure, this decreases the required injection wellhead pressure, decreasing the injection pumping requirement. The CO2 injection pump energy savings is very likely to be greater than the energy required to decrease the CO2 temperature. At a 15°C to 14°C change in surface temperature and a 2.5 km depth, the pumping power is reduced by 24 kWe, at an energy cost of only 6 kWe to reduce the temperature. Conversely, the pump power reduction for 20 wt% brine is never greater than the energy required to do so.

For a 2.5 km brine system, the pumping power reduction for a +1% NaCl salinated fluid is 24.4 kWe. The right axis in Figure 6 shows the fraction of energy which is recovered due to the salination process. At a pump power reduction per power input of one, all the power used in the reverse osmosis process is recovered through the reduction in injection pumping power required. This occurs at overall reverse osmosis recovery efficiencies near 99% and 98% for a 2.5 km and 5 km system, respectively. A 90% overall recovery efficiency represents the state-ofthe-art for a pump and turbo-expander pair with 95% isentropic efficiencies, which have a net power requirement of 320 kWe and a gross pumping requirement of 3100 kWe (Fritzmann, et al., 2007). However, using a “work exchanger,” a 96% recovery may be possible, reducing the net power required to 120 kWe. The cost of producing fresh water can be reduced by the pump power reduction made through salination of the geothermal brine. In the 2.5 km scenario with a 96% overall reverse osmosis efficiency, the RO power requirement is 120 kWe, the reduction in 671

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6. Nomenclature

Large amounts of thermal energy are required to distill the brine to increase salinity, unless the inlet temperature is near 64°C. At greater inlet temperatures, the energy cost to distill the water decreases dramatically. However, the energy cost to condense the vapor is never less than the energy reduction in pump power. Reverse osmosis can provide a more energy effective way of increasing the injection salinity. However, the energy required for Reverse Osmosis is still more than that saved in pumping power. Therefore, a producer would have to find 14 kWe per kg s-1 of fresh water cost effective.

The nomenclature for parameters used is shown in Table 2.

7. References Adams, B., Kuehn, T.H., Bielicki, J., Randolph, J.B., & Saar, M.O. (In Preparation, 2013a). A comparison of CO2 and Brine geothermal systems from depths between 1km and 5km, temperature gradients from 20C/km to 50C/km, and pipe diameters from 14cm to 41cm. Energy. Adams, B., Kuehn, T.H., Bielicki, J., Randolph, J.B., & Saar, M.O. (In Preparation, 2013b). The Importance of the Thermosiphon Effect in CO2 Plume Geothermal (CPG) Power Systems. Energy.

5. Acknowledgements Funding from the National Science Foundation (Award ID# 1230691) is gratefully acknowledged. We would also like to thank the Initiative for Renewable Energy & the Environment (IREE), at the Institute on the Environment, University of Minnesota for initial seed funding.

Dipippo, R. (2012). Geothermal power plants: Principals, applications, case studies, and environmental impact. 3rd ed. Elsevier: Waltham. Driesner, T. (2007). The System H20-NaCl. Part II: Correlations for Molar Volume, Enthalpy, and Isobaric Heat Capacity from 0 to 1000 °C, 1 to 5000 Bar, and 0 to 1 XNaCl. Geochimica et Cosmochimica Acta, 71, 4902-4919.

Table 2. Nomenclature.

C D f g h L

ṁ

P Ppump Q R T V x z ε λ η ρ π φ

Farshad, F. & Rieke, H. (2006). Surface-roughness design values for modern pipes. SPE Drilling & Completion, 21, 212-215.

Colligative Concentration [mol L-1] Well pipe diameter [m] Darcy friction factor [dim] Gravitational constant [m s-2] Specific Enthalpy [kJ kg-1] Pipe length [m] Mass flowrate [kg s-1] Pressure [kPa] Pumping Power [kWe] Heat Transfer Rate [kWth] Ideal gas Constant [L kPa K-1 mol-1] Temperature [C] Fluid Velocity [m s-1] Mass Fraction [dim] Elevation [m] Pipe surface roughness [m] Parasitic Cooling Load [kWe kWth-1] Efficiency [dim] Density [kg m-3] Osmotic Pressure [kPa] Osmotic Coefficient [dim]

Fritzmann, C., Lowenberg, J., Wintgens, T., Melin, T. (2007). State-of-the-art of reverse osmosis desalination. Desalination, 216, 1-76. Haar, L., Gallagher, J.S., & Kell, G.S. (1984). NBS-NRC Steam Tables: Thermodynamic and Transport Properties and Computer Programs for Vapor and Liquid States of Water in SI Units. Hemisphere. Hamer, W., & Wu, Y. (1972). Osmotic Coefficients and mean activity coefficients for uni-univalent electrolytes in water at 25C. Journal of Physical Chemistry Reference Data, 1, 1047-1100. Moody, L., 1944, “Friction Factors for Pipe Flow,” Transactions of the ASME, 66, 671-684. Randolph, J.B., Adams, B., Kuehn, T.H., & Saar, M.O. (2012). Wellbore heat transfer in CO2-based geothermal systems. Geothermal Resources Council Transactions, 36, 549-554. Span, R. & Wagner, W. (1996). A New Equation of State for Carbon Dioxide Covering the Fluid Region from the Triple-point Temperature to 1100 K at Pressures up to 800 MPa. J. Phys. Chem. Ref. Data, 25, 1509-1596.

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