P-V Diagram Simulation: A New Approach To Modeling Reciprocating Compressor Performance
Authors: Bishop Lewis E. 
Published: December 2007

Bishop Jr., Lewis E., SPE, Exxon Co. USA

Summary
A calculation routine for simulating the pressure-volume (P-V) relationships within individual compressor cylinders and predicting horsepower independently of gas throughput has been developed at Exxon's King Ranch Gas Plant, which operates 27 integral engine/compressors totaling 49,000 hp [36 600 kW]. The supporting study, which is based on digital engine/compressor analyzer tests, provides new information about the expected value of the polytropic exponent of compression, n. A computer program based on this routine generates compressor loading tables that permit operating personnel to load engines confidently at rated capacity for personnel to load engines confidently at rated capacity for best fuel efficiency and maximum gas throughput. Previously, the low confidence placed in available loading curves caused load factors to average only 90% of capacity. A Hewlett-Packard 41-CV calculator program listing is included to assist the practicing engineer in using this procedure.

Introduction
The King Ranch Gas Plant, located 50 miles [80 km] southwest of Corpus Christi, TX, processes about 700 million cu ft/D [19.8 × 10(6) m3/d] of gas from fields in Kleberg and surrounding counties. Two large compressor installations at the plant provide boost service for much of the incoming gas. The Engine Room 1 houses nine 2,000-hp [1490-kW] Cooper-Bessemer GMWA-8 integral compressors and six 1,350-hp [1,000-kW] GMVA-10 units, totaling 26,100 hp [19,400 kW]. The Engine Room 2 consists of 12 Clark integral engine/compressors totaling 23,000 hp [17,200 kW]. The Clark units include models designated TCV-10, TLA-8, TRA-8, and HBA-6T. These engine/compressors are tested several times annually by company technicians using electronic engine/compressor analyzer (E/CA) equipment. This practice, which is cost effective on the basis of reduced maintenance expense through early detection of worn or damaged parts, also verifies actual compressor load. When new cylinders were installed on nine 2,000-hp [1,500-kW] units in 1977, discrepancies of more than 20% were seen between values from the manufacturer's load curves and the engine analyzer results. Table 1 shows that significant differences were not limited to a narrow range of Operation. Ref. 2 also reports problems of insufficient accuracy in the manufacturer's compressor loading data. In this plant, it was mandatory that the operators be furnished with loading data because the suction pressure often varied by 50 psi [0.34 MPa] owing to gas-demand fluctuations. Further, the average suction pressure was declining by about 15 psi [0.103 MPa] per month as a result of reservoir depletion. Typewritten loading tables were prepared on the basis of manufacturer's data adjusted for E/CA results. After operating the system for 3 years, most of the questions about loading accuracy remained unanswered. Every suite of engine analyzer tests precipitated load revisions of 5 to 10%. In early 1982, work was begun to develop a more precise method of predicting engine loads. Our goal was to develop a horsepower calculation method that matched E/CA test results within2% over a wide range of operating pressures and cylinder clearances. A rough approximation of horsepower expended in inactive cylinder ends also was desired. Accuracy with regard to calculated gas throughput was not considered important because maximum throughput is achieved as the load on the compressors is maximized. All previously used formulas and curves were eliminated as a fresh approach was sought.
P-V Simulation: The Method and its Advantages P-V Simulation: The Method and its Advantages Because the emphasis was on matching the horsepower indication of engine analyzers, the first question to be addressed was, how does an analyzer determine horsepower? The electronic analyzer simulates the indicated mean effective pressure (IMEP), and applies appropriate multipliers for speed and cylinder swept volume to model the horsepower. One type of analyzer simulates piston velocity, and thus volume, with voltage generators. Another type of analyzer uses a digital computing device to calculate a table of volume increments as a function of crankshaft rotation. Both types of analyzers obtain pressure data by using strain-gauge type transducers. It was beyond the scope of this study to provide a rigorous assessment of electronic engine analyzer accuracy; however, Table 2 shows excellent deadweight pressure indications that were recorded during a routine test using the digital type analyzer and a "factory-calibrated" pressure transducer. pressure transducer. Simply stated, the analyzer monitors the pressure and relates it to volume by tracking the crankshaft motion.
JPT
p. 881