Variable pressure power cycle and control system

A variable pressure power cycle and control system that is adjustable to a variable heat source is disclosed. The power cycle adjusts itself to the heat source so that a minimal temperature difference is maintained between the heat source fluid and the power cycle working fluid, thereby substantially matching the thermodynamic envelope of the power cycle to the thermodynamic envelope of the heat source. Adjustments are made by sensing the inlet temperature of the heat source fluid and then setting a superheated vapor temperature and pressure to achieve a minimum temperature difference between the heat source fluid and the working fluid.

BACKGROUND OF THE INVENTION 
1. Field of the Invention 
This invention relates generally to power cycles and control systems for 
power cycles. More particularly, this invention concerns a variable 
pressure power cycle and control system which is capable of adjusting 
pressure on the heating phase of the cycle in response to a variable heat 
source fluid inlet temperature. 
2. Description of the Prior Art 
In the past, a typical approach to designing the parameters for a power 
cycle has been to first select the cycle and then a working fluid for the 
cycle. The power cycle is selected based on its geometric compatibility 
with a heat source and a heat sink. The working fluid is selected based on 
the physical constraints imposed by the mechanics of the process. 
The heat source and heat sink define a thermodynamic envelope within which 
the power cycle must operate. That is, because of the inefficiencies of 
heat transfer, a temperature difference will exist between the working 
fluid and heat source fluid in a heat exchanger and also between the 
working fluid and the heat sink. 
The objective of the process designer is to devise a thermodynamic cycle 
that will encompass the largest possible area within the thermodynamic 
envelope defined by the heat source and the heat sink in order to maximize 
work output. For a constant heat source, i.e., a condensing vapor heat 
source, the rectangular shaped Carnot cycle describes a theoretically most 
efficient means of power generation. In practice, the conventional 
subcritical Rankine cycle, which has a boiling working fluid, most 
efficiently utilizes the available heat from a condensing vapor heat 
source. 
When, however, the heat source is a liquid phase heat source in which the 
temperature of the heat source fluid drops through the heating phase of 
the cycle, the simple Rankine cycle is inefficient. Examples of liquid 
phase heat sources include liquid dominated geopressure-geothermal 
resources and processed waste liquids from processes such as 
petrochemical, nuclear and the like. The increase in energy demand makes 
recovery of the available energy from these resources an economically 
feasible proposition. 
Many techniques have been used to alter the shapes of simple power cycles 
to approximate a series of Carnot cycles, either horizontally or 
vertically assembled, to match the declining temperature thermodynamic 
envelope of the heat source. For example, double boiling cycles have been 
utilized to more closely approximate the thermodynamic envelope. A major 
drawback of this system is that the cycle requires complex equipment 
including a two-phase heat exchanger, a mist extracter and a complex 
control system. 
Recent studies have shown that a supercritical Rankine cycle is superior to 
the subcritical cycle in liquid phase heat source applications. Although a 
supercritical heat exchanger may have a larger surface area than a 
subcritical exchanger, it is simpler in mechanical design than the 
two-phase heat exchanger and mist extracter required for subcritical 
cycles. More pump work is generally required by the supercritical process 
due to the higher working pressures required for operation which in turn 
require more structural material in the piping and heat exchanger. In the 
past, the increased capital requirements for heavier hardware have led to 
economic compromises in cycle design based upon cheap fuel in favor of 
lower pressure processes. Further, higher heat transfer coefficients for 
two phase systems imply a reduction in heat exchanger surface area and 
hence a reduction in construction material requirements. These traditional 
arguments in favor of two phase systems have been weakened by a major 
shift in the cost relationship between energy and capital equipment 
brought about by increased energy demand. 
Traditionally, power plant cycles are designed based on a fixed maximum 
pressure for the cycle. This maximum pressure occurs during the heating 
phase of the cycle and is maintained by varying the flow rate of the 
working fluid through the system. 
These fixed pressure power cycle systems work well when the heat source 
maintains a constant inlet temperature and flow rate over time. However, 
when the inlet temperature of the heat source varies (e.g., a 
geopressure-geothermal heat source) or if it is desirable to move the 
power plant from one heat source to another heat source having a different 
inlet temperature or flow rate (e.g., moving the power plant from one 
geothermal well to another), a fixed pressure power cycle possesses an 
inherent shortcoming--inflexibility. Specifically, a fixed pressure cycle 
defines a thermodynamic envelope that is incapable of adjusting to 
substantially fill the changing thermodynamic envelope that is defined by 
a changing heat source or different heat sources. For variable heat source 
applications, it is therefore desirable to provide a power cycle in which 
the maximum pressure developed during the heating phase of the cycle can 
be varied, thereby varying the temperature over the heating phase to more 
closely match the temperature of the heat source for maximum heating 
efficiency. Further, it is desirable that a control system be provided to 
automatically adjust the heating phase pressure of the cycle in response 
to a changing heat source. 
SUMMARY OF THE INVENTION 
By means of the present invention, there is provided a variable pressure 
power cycle and control system which is capable of automatically adjusting 
the pressure of the working fluid over the heating portion of the cycle in 
response to a change in the inlet temperature or flow rate of the heat 
source liquid. 
In one embodiment of the present invention, there is provided a variable 
pressure power cycle comprising a Rankine cycle having a variable 
thermodynamic envelope that substantially fills the thermodynamic envelope 
defined by a variable heat source. The variable cycle envelope has a 
temperature and pressure at a turbine inlet that is adjustable according 
to the inlet temperature of the variable heat source so that a minimum 
temperature difference between the heat source fluid and the working fluid 
over the heating phase of the cycle is maintained at a predetermined 
minimal temperature difference for efficient heat exchange. 
In another embodiment of the present invention, the variable pressure power 
cycle comprises a supercritical Rankine cycle wherein the variable heat 
source comprises a liquid phase heat source. 
In a further embodiment of the invention, there is provided a method of 
controlling a variable pressure supercritical Rankine power cycle. The 
first step of the method involves sensing the inlet temperature of the 
heat source liquid. Based on the heat source liquid inlet temperature and 
the working fluid and turbine utilized, a superheated vapor point for the 
working fluid is selected which defines an isobaric pressure curve for the 
working fluid over the heating phase of the cycle. This isobaric pressure 
curve has a temperature substantially approaching the temperature of the 
heat source fluid at a point along the heating phase of the cycle. The 
back pressure immediately upstream of a turbine inlet is then set to the 
pressure selected for the superheated vapor point. The next step is 
sensing the temperature of the working fluid at the superheated vapor 
point. The flow rate of the working fluid through the heating phase of the 
cycle is then regulated so that the temperature of the working fluid at 
the superheated vapor point is maintained. 
In another embodiment, the method of the present invention further 
comprises sensing the temperature and pressure in the floating pressure 
condenser. The expansion curve for the turbine is then calculated based on 
the saturated vapor temperature and pressure for the existing conditions. 
In a still further embodiment of the invention, there is provided an 
apparatus for controlling a variable pressure supercritical Rankine power 
cycle having means for sensing the inlet temperature of the heat source 
fluid. The apparatus also has means for selecting a superheated vapor 
point for the working fluid based on the heat source fluid inlet 
temperature and the working fluid and turbine utilized. This superheated 
vapor point defines an isobaric pressure curve for the working fluid over 
the heating phase of the cycle having a temperature substantially 
approaching the temperature of the heat source fluid at a point along the 
heating phase of the cycle. The apparatus further includes means for 
setting the back pressure immediately upstream of the turbine inlet to the 
pressure selected for the superheated vapor point, and means for sensing 
the temperature of the working fluid at the superheated vapor point. 
Further means regulates the flow rate of the working fluid through the 
heating phase of the cycle so that the temperature of the working fluid at 
the superheated vapor point is maintained. 
In still another embodiment of the apparatus of the present invention, the 
back pressure setting means comprises a back pressure valve and the flow 
rate regulating means comprises a temperature control valve downstream of 
the feed pump. The working fluid comprises a paraffinic hydrocarbon and 
the heat source liquid comprises a geothermal brine. 
In yet another embodiment of the apparatus of the present invention, the 
apparatus further comprises means for sensing the discharge temperature of 
the heat source liquid. If the discharge temperature is rising over time, 
the apparatus has means for reducing the flow rate of the heat source 
liquid or means for adding a parallel power cycle to the system. 
It is therefore an advantage of the present invention that the power cycle 
is capable of adjusting to a changing heat source in order to maximize 
efficient heat exchange from the heat source to the working fluid and 
optimize work output. 
Another advantage of the present invention is that the maximum pressure of 
the power cycle is automatically adjusted by a control system in response 
to changes in the heat source. 
A further advantage of the invention is that a variable pressure design 
permits one basic plant design to suffice for any application within a 
wide range of heat sources.

DETAILED DESCRIPTION OF THE PREFERRED EMBODIMENTS 
Referring first to FIG. 1, there is shown a temperature-Enthalpy diagram of 
the supercritical variable pressure power cycle of the present invention 
for a geopressure-geothermal resource in which propane is the working 
fluid and brine is the resource liquid. Propane is the working fluid of 
choice for the supercritical cycle in the particular 
geopressure-geothermal application considered. It is desirable that the 
working fluid have a temperature somewhat below that of the expected range 
of temperatures to be encountered in the geopressure-geothermal resource 
liquid. Expected brine temperature will vary from 240.degree. F. to 
360.degree. F. By comparison, propane has a critical temperature of 
260.degree. F. and critical pressure of 616 psia. The power cycle 
operating pressure for the heating phase of the cycle will vary from the 
critical pressure of the working fluid up to approximately 1200 psia at 
which point the propane will have a temperature of 290.degree. F. Thus, 
the propane temperature range substantially matches the expected 
temperature range for the geopressure-geothermal resource. 
For heat source liquid temperatures above 360.degree. F., it is desirable 
to utilize a paraffinic hydrocarbon having a higher molecular weight. For 
example, in the temperature range of 360.degree. F. to 410.degree. F., 
isobutane possesses the requisite critical pressure and temperature 
properties, while pentane is preferred between 410.degree. F. and 
520.degree. F. Above 450.degree. F., cracking of the working fluid, which 
creates non-condensable gases, becomes an increasing problem. Conventional 
flash steam systems are more appropriate for applications to resources at 
these higher temperatures. 
The maximum working pressure is limited to 1200 psia by practical 
limitations on the power system. First, there are obvious mechanical 
limitations on handling pressures higher than 1200 psia. Second, there is 
a diminishing return between the incremental power generated at higher 
pressures and the propane pump work required to feed the heat exchanger. 
Applying reasonable expander and pump efficiencies to the calculations 
results in the conclusion that the incremental increase in power output is 
small between 1200 psia and 2000 psia and possibly negative above 2000 
psia due to pump-expander irreversibilities. Consequently, working 
pressures above 1200 psia (600 psia ASME flanges) are considered to be 
economically impractical at this time. 
The supercritical variable pressure power cycle is indicated generally at 
10 in FIG. 1. Power cycle 10 has a saturated liquid propane point 12, high 
pressure liquid propane points 14a, 14b, 14c, 14d and 14e, variable 
superheated vapor points 16a, 16b, 16c, 16d and 16e, and a near saturated 
vapor point 18. 
Between saturated liquid propane point 12 and high pressure liquid propane 
points 14a to 14e, the liquid propane is pumped from a condenser pressure 
of 150 to 300 psia and corresponding temperature of 80.degree. to 
140.degree. F. up to a pressure at or above the critical value. The 
pressure range shown extends from 700 psia at point 14e to 1200 psia at 
point 14a. This pumping phase of the cycle is indicated at 20. 
The high pressure liquid is then isobarically heated in the heat exchanger 
from the temperature at points 14a to 14e to a higher temperature at the 
superheated vapor points 16a to 16e. This heating phase of the variable 
pressure power cycle is indicated by lines 22a, 22b, 22c, 22d, and 22e 
corresponding to the variable pressure superheated vapor points 16a, 16b, 
16c, 16d, and 16e. 
Line 24 represents the expansion of the working fluid in a turbine having 
an 80% efficiency as compared to the 100% isotropic expansion line shown 
at 26. Vapor is fed into the turbine where it expands to produce work and 
is exhausted at the turbine outlet as a near saturated vapor, indicated at 
point 18. Condensing of the working fluid occurs between points 18 and 12 
as indicated by line 28 utilizing ambient air as the heat sink. 
Turbine expansion line 24 is established based on the type of turbine and 
working fluid selected for the process. Preferably, the power cycle 
operates with a floating condenser to match the ambient air temperature. 
The advantage of a floating condenser is a significant increase in plant 
efficiency. The disadvantage lies in operating the turbine at off-design 
conditions which can reduce plant capacity. It is preferable that a radial 
inflow single stage turbine be utilized in connection with the floating 
condenser because this turbine design is more flexible with regard to 
operation at off-design conditions than more conventional multi-stage 
machines associated with conventional steam generation plants. A further 
constraint on the turbine design is that it must also operate with a 
variable inlet pressure. For a turbine of radial inflow design, condensate 
in the exhaust stream can be tolerated at levels of less than 5%. A radial 
inflow turbine having a specific speed of 0.6, yielding an expander 
efficiency slightly above 80%, is operable within the imposed constraints. 
Thus, based on propane as the working fluid and a radial inflow turbine, 
the 80% expansion line 24 is established. Expansion line 24 represents a 
locus of points for required turbine inlet temperature and pressure 
conditions to achieve a saturated vapor turbine exhaust at point 18. 
Referring to FIG. 2, a line 30 is a plot of temperature versus pressure at 
the turbine inlet for propane in order to produce a saturated vapor 
turbine exhaust at point 18. This curve is generated by analyzing the 
expansion process for the selected radial inflow turbine and working 
fluid, propane. 
Again referring to FIG. 1, points 16a, 16b, 16c, 16d and 16e are plots of 
the variable turbine inlet temperature and pressure conditions for the 
propane working fluid at variable pressures of 1200 psia, 1000 psia, 900 
psia, 800 psia, and 700 psia, respectively. It will be appreciated that 
plotting of these five discrete points is for illustration purposes only. 
In operation, there is a continuous series of temperature and pressure 
turbine inlet points ranging from a maximum operating pressure for the 
cycle of 1200 psia down to a minimum critical pressure for propane of 616 
psia. 
Based on the variable pressure superheated vapor points at 16a to 16e, the 
isobaric pressure lines 22a to 22e are established. The brine cooling 
curve over the heat exchange phase of the cycle is indicated generally at 
32. As shown in FIG. 1, the brine has a heat exchanger inlet temperature 
of 300.degree. F. indicated at point 34 and a discharge temperature of 
approximately 160.degree. F. at point 36. Brine cooling curve 32 is 
assumed to have a constant slope due to a constant specific heat for 
brine. On the other hand, the curvatures of the supercritical propane 
heating curves are pronounced. As the pressure of the propane increases 
from curves 22e to 22a, the curvature of the propane heating curves is 
reduced which allows better differential temperature matching between the 
brine and propane in the heat exchanger. This in turn provides more 
complete utilization of the heat in the brine. 
The operating pressure for the power plant is a function of maximum 
achievable propane temperature. In practice, inefficiencies in the heat 
exchange process will create a temperature difference between the heat 
source liquid and the working fluid. This is dictated by practical 
limitations in heat exchanger design. Heat exchangers are typically 
designed for a minimum temperature difference over the heating cycle of 
10.degree. F. 
Referring to FIG. 1, the desired 10.degree. F. temperature difference for a 
brine resource having a 300.degree. F. inlet temperature is achieved by 
setting the superheated vapor point pressure and temperature at point 16a 
and defining the heating curve for propane at 22a. If, on the other hand, 
the inlet temperature of the brine resource liquid drops to 285.degree. F. 
as shown by the brine cooling curve at 32', the propane heating curve 22a 
is no longer operable. This is because the temperature of the propane 
following heating curve 22a would actually exceed the temperature of the 
resource as shown by the crossing lines 22a, 32'. For a brine resource 
having a cooling curve 32', the propane heating curve of choice would be 
that shown by line 22b. Thus, by varying the supercritical pressure at 
points 16a to 16e on the heating curve of the cycle, an efficient 
operating temperature difference can be maintained between the heat source 
liquid and the working fluid. 
The heating curve for the propane is adjusted according to the inlet 
temperature of the brine resource by a control system that first senses 
the inlet temperature of the brine at 34. Optionally, the control system 
may also sense the ambient air temperature conditions of the condenser. If 
so, the control system will determine the appropriate 80% expansion line 
24 based on the saturated vapor pressure and temperature for the existing 
atmospheric conditions. If not, an expansion line 24 is assumed which best 
fits the range of possible ambient conditions. 
The control system then chooses an appropriate superheated vapor point 
temperature and corresponding pressure for the propane based on the 
pressure-temperature relationship for propane defined by curve 30. The 
initially chosen superheated vapor point simply seeks a predetermined 
temperature difference between the heat source inlet temperature and the 
superheated vapor point temperature. Following this initial selection, the 
controller calculates the minimum temperature difference over the heating 
phase of the cycle between the heat source liquid and the working fluid. 
This calculation is based on a predetermined cooling curve for the heat 
source liquid. Through an iterative process, the controller recalculates 
the superheated vapor point and adjusts the heat source liquid flow rate 
through the heat exchanger until the desired temperature difference 
between the heat source and working fluid is obtained at some point along 
the heating phase of the cycle. 
Based on the selected superheated vapor pressure, the controller sends a 
signal to a back pressure valve located just upstream of the turbine inlet 
to establish the desired back pressure on the heating phase of the cycle. 
The process controller then senses the temperature at the turbine inlet 
and relays this information to a cutoff valve downstream of the feed pump. 
The required turbine inlet temperature, based on the pressure-temperature 
relationship defined by line 30, is achieved by varying the flow rate 
through the heating phase of the cycle. Thus, if the temperature at the 
turbine inlet is lower than that required for the proper 
pressure-temperature relationship for propane, the cutoff valve will 
reduce the flow of propane through the heating phase of the cycle. By 
reducing the flow, the propane is able to achieve a higher temperature in 
the heat exchange process. The process controller system continuously 
monitors resource inlet temperature and adjusts the system accordingly to 
achieve optimum efficiency. 
A schematic diagram of a preferred form of the variable pressure 
supercritical power cycle and process control system is shown in FIG. 3 
incorporated into a natural gas processing system. The brine, as shown by 
the heavy dashed line, is diverted from the brine and gas production 
equipment shown generally at 50 through a level control valve 52 and into 
a shell and tube heat exchanger 54 on the shell side. The brine then flows 
to disposal at 56. The brine may be bypassed through a shutoff valve 58 
(shown in a normally closed condition) for maintenance of the heat 
exchanger by closing shutoff valves 60, 62. Any liquid or gaseous process 
stream may be cooled in this manner. The working fluid, in this instance 
propane, is circulated in counterflow through heat exchanger 54 through 
block valves 64, 66 to a back pressure control turbine throttle valve 68. 
The propane then flows through an expansion turbine 70 and to a condensor 
inlet header 72. An alternate route may be taken through a back pressure 
sensing expansion valve 74 (shown in a normally closed condition) which 
functions in a similar manner but at a higher pressure setting to act as a 
safety device or bypass for routine maintenance. 
The low pressure vapor exhaust is fed to an air cooled condenser 76. The 
subcooled liquid passes through shutoff valve 78 and is stored in an 
accumulator 80 which serves as the working fluid reservoir and 
contamination detection point. Any brine entering the process fluid can be 
collected, detected and dumped through shutoff valve 82 (shown in a 
normally closed condition) to a sump 84. Accumulator 80 also acts as the 
head tank to feed the process feed pump 86. Feed pump 86 boosts liquid 
pressure, forcing the propane through a primary check valve 88 into a 
nitrogen charged pulsation damper 90. Feed pump 86 flow is controlled by a 
temperature sensing bypass valve 92 (shown in a normally closed condition) 
that can act singly or be part of the pump valve unloading process. Bypass 
valve 92 maintains working fluid discharge temperature from heat exchanger 
54 at the desired temperature required for the process pressure level. 
The process control device 94, which controls the entire power cycle, can 
be a digital, mechanical analog, or electrical analog device, although a 
digital device is preferred for its programming capabilities. Process 
controller 94 in turn receives information from sensors and transmits 
information to control valves through either a hydraulic, pneumatic, or 
electrical transfer system. 
The function of the process controller can be described as follows. 
Controller 94 senses the temperature of the heat source liquid, in this 
case geothermal brine, at a point 96 where it enters heat exchanger 54. 
Using the temperature at point 96, controller 94 logically generates the 
high side process pressure setting for back pressure control valves 68, 74 
and the setting for temperature control valve 92 based on the 
pressure-temperature relationship for propane at the superheated vapor 
point. The required pressure settings are transmitted to valves 68, 74 
from controller as shown at 98, 100, respectively. Likewise, the proper 
temperature setting is transmitted to valve 92 as shown at 102. Valves 68, 
74 regulate the process pressure against which feed pump 86 is circulating 
the working fluid. 
Temperature control valve 92 regulates process fluid temperature by 
altering the flow rate through heat exchanger 54. This is done by first 
sensing the temperature of the working fluid at point 104, the turbine 
inlet. Temperature control valve 92 then compares the working fluid 
temperature at point 104 with the temperature required for propane as 
defined by the pressure-temperature relationship for propane at the 
superheated vapor point at the turbine inlet. If the temperature of the 
working fluid at point 104 is below this required temperature, this 
indicates that the capacity of heat exchanger 54 has been exceeded. In 
response, bypass valve 92 reduces the flow rate through heat exchanger 54. 
Bypass valve 92 recirculates part of the flow through condenser 76 to 
accumulator 80, thereby reducing flow through one side of heat exchanger 
54. If the working fluid temperature at point 104 exceeds the required 
temperature, bypass valve 92 closes, allowing more working fluid to pass 
through heat exchanger 54. 
The control system is designed to maximize heat transfer through exchanger 
54 or to make maximum use of the heat that is available from the brine. 
Further, the control system is designed to maximize cycle efficiency with 
regard to wet expansion considerations for turbine 70. 
A further refinement of the system is illustrated by referring once again 
to FIG. 1. An alternate brine cooling curve is shown at 32" in which the 
outlet temperature has risen to 270.degree. F. A high brine discharge 
temperature implies that the power plant is not removing heat and hence is 
not functioning efficiently. A slow rise in temperature over a period of 
weeks is indicative of scaling in the heat exchanger. 
Referring to FIG. 3, diagnostics can be generated by sensing the brine 
discharge temperature at 106. Diagnostic system 108 can then determine 
whether the brine discharge is rising over time. If so, diagnostic system 
108 can either reduce the flow rate of the brine or add one or more 
parallel power cycle units to the system. Alternatively, diagnostic system 
may simply alert an operator that the discharge temperature is rising and 
the operator can take the appropriate action. 
Any parallel power unit added will automatically adjust its operation to 
optimum on its portion of the split resource liquid stream. The stream 
splitter can be as simple as parallel adjustable chokes or a sophisticated 
flow control system. 
Additional diagnostics may be provided to sense the flow rate of the 
propane through the last cycle added to the system at pump 86. A low flow 
rate indicates that the last cycle is not operating economically. That is, 
the flow rate may be so low that costs of operating the last cycle exceed 
output of the cycle. Diagnostic system 108 can compare the measured flow 
rate to a predetermined minimum flow rate and remove the last power cycle 
from the system or alert an operator to do so. 
The variable pressure concept as applied to a conventional subcritical 
Rankine cycle is illustrated by the temperature-Enthalpy diagram of FIG. 
4. The subcritical Rankine cycle is indicated generally at 110. 
Subcritical cycle 110 obtains heat from a condensing vapor heat source 112 
which has a constant temperature over the heating phase of the cycle. It 
can be seen from the diagram that when the heat resource fluid temperature 
increases as shown by line 112', the temperature difference between the 
working fluid of subcritical cycle 110 and the resource fluid temperature 
112' increases, causing a reduction in heat exchange efficiency. A 
variable pressure subcritical cycle adjusts the pressure and temperature 
over the heating phase of the cycle to 110' in order to more closely match 
the increased temperature of the heat resource 112'. 
It may be appreciated that when a power plant is installed in an industrial 
processing facility and the heat source fluid is an industrial product, 
such as ammonia, it is preferable to choose ammonia as the working fluid 
of choice because those operating the plant will be most familiar with 
this product. 
The foregoing description has been directed to particular embodiments of 
the invention in accordance with the requirements of the patent statutes 
for the purposes of illustration and explanation. It will be apparent, 
however, to those skilled in this art that many modifications and changes 
in the apparatus and processes set forth will be possible without 
departing from the scope and spirit of the invention. It is intended that 
the following claims be interpreted to embrace all such modifications and 
changes.