New equations calculate Claus unit sulfur-recovery efficiency

Michael Anderson
Brimstone Engineering Services Inc.
Chino Hills, Calif.

A method has been developed that allows direct, accurate calculation of recovery efficiency for Claus sulfur-recovery units (SRU). The calculation combines feed-gas data and tail-gas composition to calculate flow rates for combustion air and tail-gas streams.

Because the recovery calculation quantifies tail-gas flow and composition, it allows direct, exact calculation of conversion efficiency, recovery efficiency, and plant sulfur emissions.

The recovery-efficiency algorithm or calculation has been designed to accommodate a wide variety of plant configurations without need for modification. The method accounts for feed-stream water vapor, hydrocarbons, and ammonia and results in accurate calculation of combustion air and tail-gas flow rates.

Need for calculation

Many facilities that operate Claus sulfur-recovery units have a need to calculate on-line operating recovery efficiency.

Some refineries and gas plants calculate on-line recovery efficiency for general, internal monitoring of Claus-unit performance. This can be useful for optimizing plant operations, improving catalyst management, and early discovery of operating or mechanical problems.1-3

In other cases, operating facilities have been required by local environmental agencies to report on-line operating efficiency for their Claus sulfur-recovery units.

For example, one California refinery must report Claus recovery efficiency during any period when the tail-gas unit (TGU) is temporarily out of service and Claus tail gas is routed directly to incineration. In another case, a refinery must provide backup to its continuous emissions-monitoring system for determining and reporting on-line recovery efficiency.

Plants that utilize tail-gas treating sometimes need to demonstrate compliance with a minimum level of recovery efficiency for the Claus train. In such cases, there may be adequate instrumentation on the TGU for reporting of overall SRU/TGU recovery efficiency, but no means exist to determine real-time efficiency for the Claus unit by itself.

There are smaller, often older plants which include single Claus trains that operate with thermal incinerators rather than TGUs and do not currently have incinerator-stack continuous emission-monitoring systems (CEMs).

In these cases, rather than installing a complete stack CEM system to report operating efficiency, another option exists that may offer an improved solution for some operators.

The use of an accurate tail-gas H₂S/SO₂ analyzer instead of a CEM system allows the calculation and reporting of plant emissions along with improved control of the process. Installing such an analyzer allows efficiency-reporting requirements to be met, and emissions can be reduced through proper tail-gas H₂S and SO₂ ratio control.

This approach has been accepted by state environmental authorities in New Mexico and Wyoming and implemented in facilities in those states. In one of these cases, on-line feed-gas analysis was an additional requirement.

Calculation basis

The general approach of this calculation is straightforward. Based on the feed and tail-gas compositions and feed rate, the quantity of combustion air required to produce the desired tail-gas composition can be directly calculated. This is accomplished through the initial assumption that all H ₂S is converted completely to elemental sulfur.

Because such an assumption would produce a tail gas consisting of nothing but nitrogen, carbon dioxide, and water, adjustments are made to that "ideal" air value based on the presence of other tail-gas components (for example, hydrogen, carbon monoxide, carbonyl sulfide, and carbon disulfide) and their concentrations.

Note that since flow rates for combustion air and tail gas are calculated, concentrations of nonsulfur tail-gas components (H₂ and CO) are necessary for the calculation.

Once the flow rates of combustion air and tail gas are calculated, tail-gas composition is derived based on the tail-gas flow and tail-gas component concentrations.

Comparing the quantity of tail-gas sulfur with the inlet sulfur yields the unit's recovery efficiency. In addition, all significant tail-gas components are calculated, including CO₂ and water.

For plants that utilize direct reheat with acid gas, the reheat acid gas would be treated as part of the overall acid-gas feed. In the case of fuel gas-fired reheats, the total reheat fuel gas should be treated as an additional feed stream.

Metered combustion air is not used as an input in the calculation but rather is calculated as an intermediate result, as discussed earlier. This calculated result can be used as an external check against the metered air flow rate.

Be aware that combustion-air metering in many plants is of poor quality and will often be in poor agreement with calculated values.

The recovery calculation has been tested against a large number of cases prepared using TSweet version 96.0, a commercial simulator for amine, Claus, and tail-gas units.4 These simulator cases included rich and lean-feed plants and plants with large and small amounts of hydrocarbons and ammonia in the feeds.

In all test cases, accuracy in the calculated combustion air and tail-gas flows was greater than 99.95%. Average absolute error between calculated percentage recovery and that for the test cases was less than 0.01%. Calculated values for tail-gas carbon dioxide and water were accurate to within 2%.

In addition to the simulator, several plant design cases were also tested with the algorithm, and extremely close agreement was found in all cases. The accuracy of the calculation is limited only by the quality of the input data. The only guarantee offered with this algorithm is that if poor quality input data are used, the output will also be of poor quality.

This calculation can be easily constructed in spreadsheet form for use on a PC. Some users may want to install the calculation within their process-control systems. The algorithm has been built in a generalized form to allow application to a wide variety of needs.

In cases where a plant needs to match on-line or occasional emissions compliance testing, the algorithm-calculated recovery efficiency can be adjusted upward or downward to match results from external testwork, if necessary, through the use of an offset factor. This may prove useful when there exists a discrepancy between the calculated recovery value and one derived from external testing (for example, stack testing results).

Input data

Like any other, this calculation relies on accurate input data to achieve reliable output results. The required feed data include inlet or feed-stream flow rates, compositions, and stream conditions.

Feed-stream flow, temperature, and pressure are readily available in nearly all plants. Reliable feed composition, however, is somewhat more difficult to obtain. Some plants can analyze for H₂S in the Claus feed streams, either on-line or with laboratory test methods. Such test methods include stain tubes, Tutweiler analysis, or gas chromatography.

As an alternative, accurate measurement of the feed-gas flows combined with sulfur-production data can provide a reasonable calculated feed H₂S concentration. Accurate feed concentrations for hydrocarbons and ammonia are not as commonly available, but plant design data, field-test data, or estimates may be adequate.

Tail-gas compositional data required for the recovery calculation include sulfur components (H₂S, SO₂, COS, CS₂, sulfur vapor, and entrained liquid sulfur) along with H₂ and CO. Tail-gas components which are accurately known include sulfur vapor in the tail gas (which can be calculated based on stream conditions) and on stream tail-gas analyzer output for H₂S and SO₂.

Because H₂S and SO₂ represent a large fraction of the total sulfur in the tail gas and tend to vary with time, it is important that their values be as accurate as possible. Because of the "leverage" effect inherent in recovery-efficiency calculations, the final recovery result depends much more on the tail-gas composition than on the feed-gas composition.

To maximize accuracy and reliability of the calculated recovery efficiency, it is recommended that the tail-gas analyzer be periodically calibrated against H₂S and SO₂ external standards (at the same time, if possible, to eliminate interferences).

For other sulfur and nonsulfur tail gas components, there are generally three available sources: historical data from field test work; estimated concentrations based on plant configuration or operation; or general default values.

Concentration values derived from actual analysis of the process streams will yield the most accurate recovery-calculation results. Because the non-H₂S and SO₂ components do not change rapidly with time, recent historical test data will provide the most accurate source of input data.

The next best option would be to use "customized" estimated values based on specific plant configuration and operation. If neither of these options is available, general default values are shown here that should provide reasonably accurate results.

Procedure

Process-recovery efficiency can be calculated with the equations and data that follow. Use of the algorithm involves five calculations:

• For inlet feed-stream flow rate, water content, and sulfur content
• For feed hydrocarbon concentration and composition
• For tail-gas sulfur vapor concentration
• For combustion air and tail-gas flow rates
• For recovery efficiency and sulfur emissions.

Calculation No. 1

Step 1: For each feed stream, calculate water vapor pressure at the feed-stream temperature.1 Inputs: stream temperature (T in °R.). Vapor pressure for water is calculated using the following equation:

ln (Vp_H2O) = a + bT + c/T + d/T²

where:

a = 14.1313

b = 0.000145628

c = -6609.292

d = -767871.1

with "Vp_H2O" in psi and T in degrees Rankine [R. = °F. + 459.7]) Step 2: Calculate water concentration in each feed stream. Inputs: barometric pressure (inches of Hg) and feed-stream pressure (P; psig). The following calculates water concentration (%) in the feed:

% H₂Ofeed = 100 * Vp_H2O/(stream pressure + ambient pressure) = 100 * Vp_H2O/(P + BP/2.303) where:

Hg (in.)/2.303 = psi

Step 3: Calculate lb/hr sulfur (S) in the feed stream.

S = Feed flow * 2.637 * dry %H₂Sfeed/100 * (100 - %H₂O_feed)/100 * 32.064 = 1,000 std. cu ft/hr feed * dry %H₂S_feed * (100 - %H₂O_feed ) * 0.008455; or

= 1,000 std. cu ft/hr feed * wet %H₂S_feed* 0.008455 (H₂S concentration from a feed-gas analyzer may be on a wet basis.)

Step 4: For each feed stream, convert dry (%) values of feed components to wet basis. Inputs: dry % concentrations for H₂S, hydrocarbons, and NH₃, % water in feed stream. The dry-to-wet basis conversion use the following:

% component (wet) = % component (dry) * (100 - %H₂O_feed)/100

Step 5: Add all feed rates (amine acid gas, sour-water stripper [SWS] gas, tail-gas unit recycle, acid gas and/or fuel to reheaters) to obtain a total combined feed (F).

Determine the percentage of each component (H₂S, NH₃, water, and hydrocarbons) on a wet basis in the total feed stream. Following are suggested default values for various ambient and feed data parameters:

Ambient pressure (barometric) = 29.92 in. Hg

Ambient air temperature = 75° F.

Relative humidity = 50%

Amine acid-gas temperature = 95° F.

Acid-gas pressure = 12 psig

Acid gas H₂S (dry) content = 85%

(These should result in an amine acid-gas water vapor content of 3.04%.)

SWS-gas temperature = 190° F.

SWS-gas pressure = 12 psig

SWS-gas H₂S (dry) content = 53%

SWS-gas NH₃ content = 44%

(These should result in a SWS-gas water vapor content of 34.75%.)

Calculation No. 2

This calculation accounts for the mixture of different aliphatic hydrocarbons present in the feed streams. This is required to ensure accurate calculation of combustion air. It is assumed that there are no olefinic or aromatic compounds in the feeds.

The weighted hydrocarbon chain length (k) is calculated as the sum of the concentration of each component times the number of carbon atoms in that compound divided by the total concentration of (unweighted) hydrocarbons.

As an example, k is calculated for the following feed-gas hydrocarbon mixture:

CH₄ 2.40% 2.40 * 1 = 2.40

C₂H₆ 1.10% 1.10 * 2 = 2.20

C₃H₈ 0.65% 0.65 * 3 = 1.95

C₄H₁₀ 0.22% 0.22 * 4 = 0.88

Total %HC = 4.37%

Total = 7.43.

Weighted chain length ("k") = 7.43/4.37 = 1.720.

These two values, total percent hydrocarbons and k, are for the total combined feed and will be used in later calculations. Following are suggested default values for hydrocarbon data: hydrocarbon in feed (%HC) = 1.1% (dry); weighted chain length (k) = 2.0.

Calculation No. 3

Step 1: Calculate sulfur vapor pressure at the tail-gas stream temperature. ^{2 3} Inputs: tail-gas stream temperature (T in °R.). Sulfur vapor pressure is calculated with the following equation:

log (Vp_sulfur) = a + bT + c/T + d/T²

where:

a = 1.068652

b = 0.0030138

c = -2594.192

d = -7157435

with "Vp_sulfur" in psi and "T" in degrees Rankine [°R. = °F. + 459.7]).

Step 2: Calculate sulfur vapor concentration (as S₁) in the tail-gas stream. Inputs: tail-gas stream pressure (psig), barometric pressure (in Hg). Sulfur vapor concentration (%) in the tail-gas stream is calculated with the following equation:

%S_vapor = 100 * Vp_sulfur/(tail-gas stream pressure + ambient pressure) * 7.96

Calculation No. 4

Calculate combustion air and tail-gas flow rates with the following equations. Values for wet concentrations for H ₂S and SO ₂ are taken from the tail-gas stream analyzer, and historical or default values are used for H ₂, CO, COS, CS ₂, and S _L.

Let the following quantities be defined:

M = %H₂S_feed + %HC * (3 * k + 1) + %NH₃ * 3/2 (%s in total feed)

P = % H₂ + %CO + %COS + 2 * %CS₂ - %H₂S_TGas + %SO₂ * 2 (%s in tail gas)

B = %SO₂ + %S_v + %S_L (%s in tail gas)

N= 100 + %HC * 2 * k (%NH₃)

Q = f + %H₂O_air/100.

The ratio of air to oxygen (roughly 5 to 1) = D = 1/(20.946 * (100 - %H₂O_air)/10,000); where 20.946 is the average oxygen (%) in dry air.

The wet fraction of non-O₂ air components = f = (N₂ + CO₂ + Ar + trace inerts)/air; or, f = 0.7905 * (100 - %H₂O_air)/100; where 0.7905 is the fraction of non-O₂ components in dry air.

Following are the final equations describing the tail gas and combustion air flow rates:

T = (F * N/100 + Q * F * D * M/200)/(1 - B/100 + Q * D * P/200)

A = F * D/200 * M - T * D/200 * P.

These results are in lb-mole/hr. To convert to 1,000 std. cu ft/hr, divide each result by 2.637.

The value for entrained liquid sulfur in the tail gas is entered as wet percent and typically ranges between zero and 0.2%. Following are suggested default values (wet%) for various components in the tail gas:

Hydrogen (H₂) = 1.50%

Carbon monoxide (CO) = 0.50%

Carbonyl sulfide (COS) = 0.10%

Carbon disulfide (CS₂) = 0.08%

Entrained liquid sulfur (S_L) = 0.07%.

Final sulfur condenser conditions:

Temperature = 280° F.

Pressure = 1.0 psig (without tail-gas unit) = 2.5 psig (with tail-gas unit)

(These data, with P = 1.0 psig, should yield an S₁ (vapor) concentration of 0.0955%.)

From these default values and tail-gas values for H₂S and SO₂ of 0.6% and 0.3%, respectively, and acid gas and sour-water stripper (SWS) gas flows of 100 and 40 lb-mole/hr, respectively, the final calculated tail-gas rate should be 378.6 lb-mole/hr, and the combustion-air flow rate should equal 277.1 lb-mole/hr. Total feed sulfur would be 96.2 lb-mole/hr.

Calculation No. 5

The total sulfur in the tail-gas stream is easily calculated by multiplying the wet concentrations of tail-gas sulfur species by the total tail-gas flow rate and converting to weight basis.

The following equation is used for this calculation: W (lb/hr) = {% H₂S _TGas + % SO₂ + %COS + % CS₂ * 2 + %Sv + %SL} * T/100 * 32.064

Operating recovery efficiency (R) is calculated with this formula: R = (inlet sulfur - tail-gas sulfur)/inlet sulfur * 100 + L; or, (S - W)/S * 100 + L.

If necessary, the recovery offset factor (L) can be used to improve matching of these calculated results with those of external testing. Plant emissions can be calculated by multiplying the total inlet sulfur by the final recovery efficiency: sulfur emission (lb/hr) = % recovery * inlet sulfur/100; or, R * S/100

With all the default values, the calculated conversion should equal 95.44%, the recovery 94.79%, and the emitted sulfur 4.55 long tons/day (as sulfur).

Error analysis; exceptions

Brimstone Engineering Services has conducted a sensitivity study to estimate the magnitude of errors associated with nonideal input data. These results are shown in Table 1 [94,357 bytes].

For each of the input variables, deviations from base-case input values were introduced, and the magnitude of the resulting relative error for percentage recovery, tail-gas flow rate, and SO₂ emissions were calculated.

The base case chosen for the sensitivity study was a three-stage plant with amine acid gas, sour-water stripper, and tail-gas unit recycle gas feeds.

The plant was operating at a low H₂S/SO₂ ratio and had typical amounts of hydrocarbons in the feeds and a moderate amount of entrained liquid sulfur in the tail-gas stream. It operated at 95.0% recovery and had a tail-gas flow rate of 600 lb-mole/hr.

The results of this sensitivity study offer a sense of the magnitude of errors resulting from inaccuracies in each input variable. As expected, the calculated efficiencies are most sensitive to sulfur concentrations in the tail-gas stream.

It is strongly recommended that each user develop a sensitivity study based on his or her own plant to ensure that the most reliable results are achieved.

This algorithm should provide accurate results for all standard Claus plants with the following exceptions: oxygen enrichment, sub-dew point, and (lean) feed bypass sulfur-recovery units.

The calculation can be easily modified to accommodate feed bypass plants by considering the bypassed hydrocarbons as inert nitrogen in the tail-gas stream. The algorithm fails with sub-dew point plants only because the tail-gas analyzers are normally located upstream, rather than downstream of, the final catalytic stage.

References

1. Dean, John A., Lange's Handbook of Chemistry, 13th edition, McGraw-Hill Book Co., 1985, pp. 10-26.
2. Meyer, Beat., "Elemental Sulfur," Chemical Reviews, 1976, Vol. 76, No. 3, p. 374.
3. West, William A., and Menzies, Alan W., "The Vapor Pressure of Sulfur Between 100° and 550° C.," J. Physical Chemistry, Vol. 33, 1929, pp. 1880-1892.
4. TSweet, version 96.0, Bryan Research & Engineering Inc., Bryan, Tex.