Evaluation of Property Methods for Modeling Direct-Supercritical CO₂ Power Cycles

Combustion of fossil fuels in oxygen results in combustion products that are primarily CO₂ and H₂O, from which the water can be condensed to yield a reasonably high-purity CO₂ stream for use or storage. Although there are several power systems capable of operating under oxy-fuel conditions, those that employ open cycle turbines are attractive due to the potential to leverage high efficiencies common to modern gas turbine cycles. A recent report by the International Energy Agency Greenhouse Gas R&D Program compared several oxy-combustion turbine power plants and found that the potential for highest plant efficiency and lowest cost of electricity came from direct-fired supercritical carbon dioxide (sCO₂) power plants [1]. This is due in part to the properties of CO₂ near its critical point (CP) of 31 °C and 73.7 bar, where its high density reduces the power required for compression to improve net power output. Further, these cycles are efficient due to their high degree of recuperation and also produce a relatively high-purity CO₂ stream near storage-ready pressures as a byproduct of the process. Direct-fired sCO₂ cycles are a fairly recent innovation and are well described by the works of Allam et al. [2,3].

A block flow diagram (BFD) of a simplified direct sCO₂ cycle is shown in Fig. 1, with accompanying state points for the numbered streams shown in Table 6 in Appendix  A. This BFD is derived from a more detailed plant design that includes coal gasification, syngas cleanup, and thermal integration with the sCO₂ power cycle. Additional details about the process configuration and balance of plant unit operations are provided by Weiland et al. [4]. Note that the BFD and state point table are not intended to represent a complete process, as only major process streams and equipment are shown.

The sCO₂ cycle begins with the introduction of the fuel which in this case is a stream of cleaned and pressurized syngas that has been preheated in a syngas cooler. The syngas is mixed with the recycle working fluid that has been preheated by the recuperator. The mixed stream is further preheated in the syngas cooler and fed to the oxy-combustor along with a stream of 99.5 mol % oxygen from an air separation unit. The combustion products leave the oxy-combustor at 1149 °C and are expanded in the turbine (T) to generate electric power. The turbine exhaust preheats the portion of the working fluid that is recycled using a recuperator. The cooled stream leaving the recuperator (7) undergoes further cooling to knock out most of the water generated during combustion. The other products of combustion are removed in a purge stream that is sent to a CO₂ purification unit in preparation for sequestration. At the final stage of cooling, the working fluid is liquefied and pumped to the peak cycle pressure and then preheated in the recuperator.

Coal-fueled systems in which coal is first gasified, and the resulting syngas is fired in the sCO₂ cycle, was proposed by Allam et al. [2] and has recently been studied by Lu et al. [5], EPRI [6], and Weiland et al. [4]. A few recent studies have also been undertaken in the area of natural-gas fired sCO₂ cycles, most notably those of Allam et al. [2,3] and IEAGHG [1].

Due to the high pressures throughout the cycle and the already small size of the turbine, the development of small-scale direct sCO₂ test units is all but cost prohibitive. As a result, modeling becomes a very cost-effective system design and component development tool, though there is a considerable lack of modeling experience in the temperature, pressure, and composition space required for this application.

Modeling of sCO₂ power cycles requires high accuracy in determining the physical properties of CO₂, particularly near its critical point. The Span–Wagner equation of state (EOS) [7] is the most accurate property method available for processes consisting of pure CO₂ [8]. The Span–Wagner EOS is incorporated into the reference fluid thermodynamic and transport properties (REFPROP) physical property method developed by the National Institute of Standards and Technology [9] and is used by most researchers in modeling indirect sCO₂ power cycles. For a direct-fired sCO₂ power cycle, however, the working fluid is not pure CO₂ and it changes composition at various points in the cycle. REFPROP was developed for a limited set of pure components and mixtures and the species set encountered in coal-fired direct sCO₂ cycles is not one of those mixtures. Using REFPROP on streams containing CO₂, O₂, H₂, N₂, Ar, H₂O, NH₃, and HCl generated severe errors in the Aspen Plus^® (Aspen, Bedford, MA) physical property system. Furthermore, there are a number of species present in a coal-fueled direct-fired sCO₂ cycle which encounter temperature limitations in REFPROP's representation of those fluids. Per REFPROP's documentation, temperature limits for relevant species are: hydrogen, 727 °C; methane, 352 °C; carbon monoxide, 227 °C; ammonia, 427 °C; hydrogen sulfide, 487 °C; and sulfur dioxide, 252 °C [9]. As a result of these temperature limits, computations fail if significant fuel preheating or incomplete combustion conditions are considered. Even with a relatively simplified system with the trace components eliminated and complete combustion assumed, simulations made using REFPROP required long computation times and are impractical for rapid parametric studies.

A series of comparative analyses were performed to identify the best physical property method in Aspen Plus to use for direct-fired sCO₂ cycles. These analyses include assessment of property methods for matching saturated liquid and vapor states of pure CO₂, superheated CO₂ vapor properties, and vapor/liquid equilibria of CO₂–H₂O mixtures. Finally, the various property methods are compared against REFPROP as a standard in predicting the performance of various unit operations in a simplified direct sCO₂ cycle.

Based on the recommendations in the Aspen physical property selection tool and the technical documentation (accessible through the help system in the aspen plus software), ten physical property methods were selected for detailed assessment. These methods are: REFPROP, Lee–Kesler–Plöcker property method (LK-PLOCK), Peng–Robinson EOS with Boston–Mathias alpha function property method (PR-BM), Benedict–Webb–Rubin–Starling property method (BWRS), Benedict–Webb–Rubin–Lee–Starling property method (BWR-LS), Soave–Redlich–Kwong property method (SRK), Redlich–Kwong–Soave (RKS) property method, Schwarzentruber and Renon property method (SR-POLAR), Grayson property method (GRAYSON), and perturbed-chain statistical associating fluid theory property method (PC-SAFT). This set is similar to that examined in a previous National Energy Technology Laboratory (NETL) report [10]. Property methods used in other direct sCO₂ system studies include PR-BM [4], the Peng–Robinson EOS [1,5], RKS EOS [5], and UNIFAC [6,11], though little justification is given for these selections. UNIFAC uses the Redlich–Kwong EOS and thus is expected to produce similar results to the RKS and SRK property methods used in this work.

Table 1 lists the basic features of the physical property methods examined. All of these methods are recommended for mixtures of light gases and all are significantly more accurate than the IDEAL (ideal gas) physical property method for conditions encountered in sCO₂ power cycles. No custom binary interaction parameters are used. Additional details on these physical property methods can be found in the aspen plus technical documentation.

The initial evaluation is made using data from the pure CO₂ vapor–liquid saturation line, as shown in Table 2 [12]. The data in this table were generated using REFPROP and the Span–Wagner EOS, which has been shown to reproduce highly accurate saturated CO₂ density experimental data to within 0.01% below 293 K and to within 0.5% up to the CP [7]. The Aspen vapor–liquid flash is used to calculate the saturation line at the data points listed. The initial comparison is based on specific volume results of the vapor and liquid phases. Comparisons are based on root-mean-square (RMS) relative deviation from the data set of Table 2.

Figure 2 shows an example comparison of the REFPROP data against the calculated results for the LK-PLOCK property method. For this figure, the saturated vapor and liquid results are shown on the upper and lower portions of the curve, respectively. In general, results show very good agreement in calculating the specific volume of saturated liquid and vapor states, with significant error only at the critical point.

Figure 3 shows a comparison of the relative errors in predicting the data in Table 2 for each of the property methods studied. In general, vapor-specific volumes are consistently overpredicted for the GRAYSON, PC-SAFT, SR-POLAR, RKS, and SRK property methods, though all the methods have large error near the critical point for this property. The CO₂ liquid-specific volume is poorly calculated throughout the temperature range by the SR-POLAR, SRK, and PR-BM property methods. Each of the remaining methods predicts the liquid-specific volume well, except for large deviations at the last two data points near the critical point (300 K and 304.2 K).

Table 3 shows the average RMS relative deviations calculated for the saturated liquid and vapor molar volumes for all the nine methods, sorted by increasing deviation. Lee–Kesler–Plöcker property method had the smallest deviation followed by RKS. The methods GRAYSON and PC-SAFT had larger deviations due to difficulties noted earlier in calculating CO₂ saturated vapor-specific volumes, but their accuracy is still deemed to be good. The results are shown graphically in Fig. 4 for the liquid and vapor states separately and show the relative strengths and weaknesses of each of the property methods in modeling the liquid and vapor states of CO₂.

An analogous comparison was made to a second pure CO₂ property data set of 84 points, based on REFPROP calculations for superheated CO₂ [12]. The temperature range for the data was 300–1000 K and the pressure range was 3–30 MPa, focusing on sCO₂ cycle conditions of interest. The Aspen pure component property analysis feature was used to calculate superheated data at these conditions. In this case, only superheated vapor properties were calculated. Comparisons are based on average RMS deviation of the specific volume from REFPROP data. Table 4 lists the physical property methods ranked by the magnitude of the deviations.

For this second pure CO₂ property evaluation, the most accurate methods are BWR-LS, PC-SAFT, and LK-PLOCK. Figure 5 shows bubble plots of the relative error for these property methods as a function of temperature and pressure, which are useful for selecting the most accurate property methods for particular sCO₂ component operating conditions.

One area where direct sCO₂ cycle models may be challenged is in correctly calculating the water knock-out process on the low-pressure side of the cycle. Depending on the fuel composition and CO₂ recycle conditions, the predominantly sCO₂ process fluid passing through the turbine and hot side of the recuperator may contain 2–7% water vapor by volume [1,6]. As the process fluid is cooled, water vapor condenses out into liquid water, typically at temperatures ranging from 20 °C to 100 °C and pressures from 2.5 MPa to 4 MPa [1–6]. Accurate modeling of this process is required for two reasons: First, depending on cycle conditions, water may begin to condense out within the recuperator, which typically leads to an internal temperature pinch point that limits recuperator effectiveness and cycle efficiency. This can be managed to regain effectiveness if the onset and extent of the internal condensation are properly predicted. Second, following the water knock-out stage, the remaining water vapor in the sCO₂ process fluid acts as an impurity that increases the required cycle compression power, due to its much lower density than sCO₂ [6]. Accurate modeling of the remaining water vapor content will better predict the cycle's compression power requirements and hence its efficiency.

Due to the importance of this process, another property evaluation was performed for the CO₂:H₂O binary mixture using experimental data taken from Ref. [10]. The data used are plotted in Fig. 6 and show the saturated water content in a CO₂:H₂O mixture as a function of temperature and pressure. The calculated data were obtained by performing a vapor–liquid equilibrium two-phase flash in Aspen with the selected physical property method. Deviations from the experimental data were measured as average RMS of the differences in log10 of the ratio of moles of saturated H₂O per mole CO₂.

Figures 9–18 in Appendix  B show plots of the calculated data (as lines) compared to the experimental data (dots) for each of the physical property methods. Note that in some cases, the calculated data do not extend to the high pressures in the experimental data. This is because the flash calculation failed for those conditions. Of the 26 data points for which calculations were attempted, all the property methods were able to calculate at least 20 data points, with BWRS, REFPROP, and SRK successfully calculating 23, 24, and 25 data points, respectively. Note that failed calculations are occurring at higher pressures than those presently employed in direct sCO₂ cycle water knockout stages.

Figure 7 plots the average RMS deviation from the data in Fig. 6 for all the ten physical property methods in order of increasing error. In this case, the most accurate methods are REFPROP, PR-BM, BWR-LS, RKS, and LK-PLOCK.

As a final evaluation, a preliminary sCO₂ cycle [4] was modeled using different physical property methods and the results compared. In the absence of a model validation data set for a direct sCO₂ power cycle, comparisons are made to a single converged solution of the cycle model obtained using REFPROP with a reduced chemical species set (without HCl, NH₃, H₂S, and SOx), due to restrictions or error conditions from Aspen. The results for this baseline cycle are shown in Table 6 in Appendix  A and were compared to results using six physical property methods. These were LK-PLOCK, PC-SAFT, RK-SOAVE (RKS), PR-BM, BWRS, and BWRS-REF, a version of BWRS that used binary interaction parameters that were fit to REFPROP data. The latter model is included here for comparison to prior internal modeling efforts, while RK-SOAVE and PR-BM are chosen due to their use in other studies [1,5]. Lee–Kesler–Plöcker property method and PC-SAFT are included as the two best-performing property methods overall from the earlier analyses.

The comparison is based on a subset of stream data and unit operations block outputs that are considered important for accurately characterizing the performance of the system. To isolate the impact of deviations in the physical property model predictions, the feed stream to each process unit was set equal to the feed stream calculated in the converged REFPROP case.

Initially, 26 process variables were examined, but it became apparent that most of the deviations were contained in 12 of the variables. As expected, the major differences arose for process units that operate near the CO₂ critical point, and negligible differences were seen between the property methods in the outputs of the turbine and oxy-combustion processes. Table 5 shows the list of 12 process variables used to quantitatively compare the six physical property methods.

For stream vector entries, an average RMS relative deviation was calculated for the enthalpy and density stream variables that were calculated by the physical property method.

Figure 8 shows the calculated relative deviation for the 12 key process variables listed in Table 5, for each of the six physical property methods tested. In this case, LK-PLOCK and PC-SAFT produced results most consistent with those from REFPROP.

In cases where the stream vector variable resulted in large discrepancies, differences in bulk fluid densities compared to those from REFPROP are generally the root cause. This is shown to be a problem for BWRS and BWRS-REF, which is consistent with BWRS's poor performance in predicting vapor molar volumes relative to the subset of property methods used in this analysis, per Table 4. The large errors for all the property methods for the precompressor stream vector result from the existence of a condensate stream per the REFPROP calculations (stream 13 in Fig. 1 and Table 6), which does not appear for any of the other property methods. As noted in Figs. 9–18, water content is typically underpredicted at 25 °C and low pressures for most property methods and often results in a failure to execute the calculation at higher pressures for this temperature. This is also consistent with the relative errors in the water vapor fraction exiting the CO₂ cooler, where Figs. 8 and 18 show that PC-SAFT performs well at these conditions.

Also shown in Fig. 8 are large errors in the cold-end recuperator approach temperature relative to REFPROP, which is nominally 10 °C per Table 6. PC-SAFT overestimated this approach temperature, but all the other property methods underestimated it, with BWRS-based methods predicting about 1 °C approach temperature. This is due in large part to the fact that some water vapor condensation occurs within the recuperator (stream 8 in Fig. 1 and Table 6). The latent heat of vaporization affects the recuperator temperature profiles, underscoring the importance of accurate property methods for recuperator and cycle design purposes.

One final observation from Fig. 8 is that the pump exit temperature is overpredicted by several property methods, which leads to errors in required pump power relative to REFPROP. Factoring this into the performance of a direct sCO₂ plant, a 10% error in the predicted pump power requirements roughly equates to 0.5% points in the plant's net thermal efficiency [4]. This points again to the importance of utilizing accurate property methods in the modeling of direct sCO₂ power plants.

This work examines the ability of various physical property methods to accurately model fluid properties for direct sCO₂ power systems. General observations and recommendations are as follows:

1. (1)

   For pure CO₂ process fluids at near-supercritical conditions, REFPROP is by far the best-performing property method, as concluded in other studies [8]. LK-PLOCK and PC-SAFT also perform well under these conditions.

2. (2)

   In binary CO₂:H₂O mixtures, the most accurate methods for determining saturated water content at direct sCO₂ cycle conditions are REFPROP, PR-BM, BWR-LS, LK-PLOCK, and RKS. Most of these property methods, with the exception of REFPROP, give errors in aspen plus for conditions at or below the CO₂ critical temperature of 31.04 °C and above the critical pressure of 7.37 MPa, which may be problematic depending on the cycle design.

3. (3)

   REFPROP is the recommended property method for direct sCO₂ power cycle modeling, however, it may not be compatible with the species set required for accurate modeling of syngas-fired direct sCO₂ cycles.

4. (4)

   In these cases, performance indicators for various cycle processes were computed for several property methods and compared to REFPROP under a reduced species set. Results show that LK-PLOCK and PC-SAFT perform most similarly to REFPROP under the cycle conditions studied.

5. (5)

   Given its superior performance in predicting saturated CO₂ properties and saturated water content in binary CO₂:H₂O mixtures, LK-PLOCK is the recommended property method if REFPROP cannot be used due to species compatibility or computational time constraints. LK-PLOCK has also been recommended for CO₂ compression studies [10,13]. PC-SAFT is the next best option after LK-PLOCK, though it tends to underpredict saturated water content in sCO₂, whereas LK-PLOCK tends to overpredict this quantity.

Based on the results of this effort, the preliminary analysis of the direct sCO₂ power cycle by the authors in Ref. [4] was modified to change the property method from PR-BM to LK-PLOCK to improve the accuracy of the results.

The property method analysis performed in this work is certainly not exhaustive, but should serve to guide the selection of property methods for modeling direct sCO₂ systems, particularly those with an expanded species set as encountered in syngas-fired systems. Additional comparisons to calorific data, where available, may also be pursued in future work to improve the utility of these results. The experimental data available for comparing property methods in this temperature, pressure, and composition space are sparse, however, particularly for CO₂ mixtures. Future analyses would benefit greatly from a more expansive data set at these conditions for model validation purposes, which will hopefully arise out of increased development and construction of these cycles in the coming years.

This report was prepared under the Mission Execution and Strategic Analysis (MESA) Contract No. DE-FE00025912 for the United States Department of Energy (DOE), National Energy Technology Laboratory. This work was performed under MESA Activity 25912.02.2300.201.005. All images in the report are source from NETL.

The authors wish to acknowledge the excellent guidance, contributions, and cooperation of the NETL staff, particularly, Richard Dennis, Walter Shelton, and Travis Shultz.

• Office of Fossil Energy (Contract No. DE-FE00025912).

BWRS =

Benedict–Webb–Rubin–Starling property method

BWR-LS =

Benedict–Webb–Rubin–Lee–Starling property method

CP =

critical point

EOR =

enhanced oil recovery

EOS =

equation of state

GRAYSON =

Grayson property method

h_f =

saturated liquid enthalpy

h_g =

saturated vapor enthalpy

LK-PLOCK =

Lee–Kesler–Plöcker property method

P =

pressure, pump

PC =

precompressor

PC-SAFT =

perturbed-chain statistical associating fluid theory property method

PR-BM =

Peng–Robinson EOS with Boston–Mathias alpha function property method

Recup =

recuperator

REFPROP =

reference fluid thermodynamic and transport properties

RKS =

Redlich–Kwong–Soave property method

RMS =

root mean square

sCO₂ =

supercritical carbon dioxide

SR-POLAR =

Schwarzentruber and Renon property method

SRK =

Soave–Redlich–Kwong property method

T =

temperature, turbine

v_f =

saturated liquid specific volume

v_g =

saturated vapor specific volume

Referring to Fig. 1, the fuel (stream 1) adiabatically mixes with the heated recycle CO₂ (stream 17) to form the partially preheated mixed fuel and sCO₂ (stream 2). This stream is heated in the syngas cooler where zero heat loss is assumed to create the final preheated fuel and sCO₂ (stream 3). This stream along with the oxygen (stream 4) enters the combustor where 100% conversion of the combustible species occurs. No heat loss is assumed in the combustor and the pressure drop is set at 0.69 MPa. One percent excess oxygen is fed to the combustor. The combustor effluent (stream 5) is expanded in the turbine which has an isentropic efficiency of 0.927. The turbine effluent (stream 6) passes through the hot side of the recuperator. The outlet (stream 7) is partially condensed. After a small purge is taken (stream 9), additional cooling and partial recompression remove most of the remaining water. The partially recompressed stream (stream 14) is further cooled to 27 °C and recompressed to 30.0 MPa. Both compressors have isentropic efficiencies of 0.85. The high-pressure cool recycle sCO₂ (stream 16) then enters the cold side of the recuperator to complete the cycle. The heat exchanger units in the cycle have a total of 0.45 MPa pressure drop.