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5.4 CHAPTER FIVE DISCHARGE VOLUME ACTUAL CYLINDER DISCHARGE PRESSURE DISCHARGE DIFFERENTIAL (INDICATED POWER(DIPd)) 32 1 4 Pd Ps TOP DEAD CENTER RE-EXPANSION SUCTION INTAKE VOLUME COMPRESSION SUCTION DIFFERENTIAL INDICATED POWER (DIPs) BOTTOM DEAD CENTER ACTUAL CYLINDER SUCTION PRESSURE SWEPT VOLUME OR PISTON DISPLACEMENT (Pd) TOTAL CYLINDER VOLUME (INCLUDING POCKETS) VOLUME EVs = (SUCT. INTAKE VOL.)/Pd EVd = (DISCH. VOL.)/Pd PRESSURE CLEARANCE VOLUME (INCLUDING POCKETS) FIGURE 5.1 Near ideal PV diagram. decreases as the piston moves towards TDC, raising the pressure inside the cylinder. The shape of the compression line (Line 1-2) is determined by the molecular weight of the gas or compression exponent. For an ideal gas (adiabatic-process—no flow of heat to or from the gas being compressed), the compression exponent is the isentropic (constant entropy) exponent that is equal to the ratio of specific heat of the gas being compressed. Line 2-3: At point 2, the pressure inside the cylinder has become slightly greater than discharge line pressure. The resulting differential pressure across the discharge valve causes the valve to open, allowing gas to flow out of the cylinder. The volume continues to decrease toward point 3, maintaining a sufficient pressure differential across the discharge valve to hold it open. Line 3-4: At point 3, the piston reaches TDC and reverses direction. At TDC, as the piston comes to a complete stop prior to reversing direction, the differential pressure across the valve becomes equal. This allows the discharge valve to close. The volume increases, resulting in a corresponding drop in pressure in the cylinder. The gas trapped in the cylinder expands as the volume increases toward point 4. At point 4, the gas pressure inside the cylinder becomes less than suction line pressure, creating a differential pressure that opens the suction valves. The cycle then starts over again. The shape of the re-expansion line (Line 3-4) is dependent on the same compression exponent that determines the shape of the compression line. 5.6.2 Suction Valve Leak Figure 5.2 illustrates the PV diagram of a typical compressor cylinder with suction valve leakage. The difference between the theoretical PV diagram and the actual COMPRESSOR ANALYSIS 5.5 THEORETICAL DIAGRAM 2 2A3B 3 3A ACTUAL P-V DIAGRAM 4A 4 1 FIGURE 5.2 PV diagram illustrating the effects of suction valve leakage. PV diagram will depend on the severity of leakage through the suction valves. The following is a step-by-step analysis of the PV diagram in Figure 5.2. Line 1-2A: During compression, gas leaks out through the suction valve(s). Since gas is being pushed out of the cylinder during the compression stroke, the piston must travel further to reach the discharge valve opening pressure. If the leak is severe enough, the pressure within the cylinder will not reach discharge pressure. The cylinder volume at point 2A is less than point 2, resulting in a shorter effective discharge stroke or a loss in discharge volumetric efficiency (DVE). Line 2A-3B: During the discharge stroke, gas is exiting through both suction and discharge valves. Should the leak be severe enough, the discharge valve will close prematurely at 3B instead of point 3. Line 3B-3A: With the discharge valve prematurely closed, the piston is still moving towards TDC as gas continues to leak out of the cylinder through the suction valve. The internal cylinder pressure at point 3A is less than discharge line pressure at point 3. This effect may not be noticeable unless severe leakage is present. Line 3A-4A: The cylinder’s re-expansion slope occurs more quickly than normal due to the continuing gas leakage through the suction valve(s), thus causing the suction valve to open at point 4A. Line 4A-l: The early opening of the suction valves causes the actual suction volumetric efficiency (SVE) to be greater than the theoretical SVE. Symptoms: 1. Inlet temperature rises because of the re-circulation of the gas. 2. Leaking suction valve cap temperature will increase. Other valve cap tempera- tures may increase, but not as significantly. 3. Actual discharge temperature will increase (actual discharge temperature com- pared to theoretical discharge temperature). 4. Indicated horsepower may be lower than normal. 5. Compression ratio may decrease. 5.6 CHAPTER FIVE 2 2A ACTUAL P-V DIAGRAM 1A 1 1B4A 4 THEORETICAL P-V DIAGRAM 3 FIGURE 5.3 PV diagram illustrating the effects of dis- charge valve leakage. 6. The calculated capacity based on the SVE will be higher than the calculated capacity based on the DVE, resulting in a capacity ratio greater than 1.0. 7. The compression and re-expansion lines will not match the theoretical PV curve. 5.6.3 Discharge Valve Leak Figure 5.3 illustrates the PV diagram of a typical compressor cylinder which is experiencing discharge valve leakage. The difference between the actual PV dia- gram and the theoretical PV diagram will depend on the severity of leakage through the discharge valves. The following is a step-by-step analysis. Line 3-4A: During re-expansion, the trapped gas in the cylinder is expanded as gas leaks through the discharge valve(s) into the cylinder increasing internal cyl- inder pressure. This increase in pressure causes the piston to move further down the stroke, re-expanding gas as it enters the cylinder through the discharge valve until it reaches a point where pressure is reduced, allowing the suction valves to open at point 4A. The result is a smaller effective suction stroke, thus reducing suction volumetric efficiency. If the discharge leak is severe enough, the internal cylinder pressure will not reach suction pressure. Line 4A-1B: During the suction portion of the cycle, gas is entering the cylinder through the open suction valve and leaking discharge valves. The cylinder pressure can rise to a point causing premature closure of the suction valves at point IB. Line 1B-1A: The suction valve has closed, cylinder volume is increasing, and the internal cylinder pressure is rising, which results in a higher pressure at point 1A than suction line pressure at point 1. Line 1A-2A: The actual compression line will not match the theoretical com- pression line since the pressure at 1A is not the same as the pressure at 1, and gas continues leaking into the cylinder through the discharge valves during the com- pression stroke. The discharge valve opens when cylinder pressure rises above discharge line pressure. COMPRESSOR ANALYSIS 5.7 3 3B 2A 2 THEORETICAL P-V DIAGRAM 1A 1 1B 4 4A ACTUAL P-V DIAGRAM 3A FIGURE 5.4 PV diagram illustrating the effects of ring leakage. Symptoms: 1. The actual discharge temperature will be higher than the discharge temperature observed in normal operation, or as compared to the theoretical discharge tem- perature. 2. The measured cylinder capacity will be less than the design cylinder capacity. 3. Capacity calculations based on DVE will be greater than capacity calculations based on SVE, resulting in a capacity ratio of less than 1.0. 4. Indicated horsepower may be lower than normal. 5. The actual compression and re-expansion lines will differ from a theoretical PV curve. 5.6.4 Piston Ring Leakage Figure 5.4 illustrates the PV diagram of a typical HE compressor cylinder which is experiencing piston ling leakage. The shape of the actual PV diagram will depend on the severity of the leakage. Line lA-2A: As the piston travels from point 1A to 2A, gas is initially leaking from the HE side of the piston into the CE, as would happen with a leaking discharge valve. Line 2A-3B: Gas is exiting through the discharge valve and continues to leak past the rings. Should the leakage be severe enough, premature closing of the discharge valve could occur at point 3B. Line 3B-3A: As the piston slows, and continues toward TDC, gas continues to leak past the ring, resulting in internal cylinder pressure drop to point 3A. This pressure at point 3A is lower than application pressure (point 3). Line 3A-4A: During the re-expansion stroke, gas continues to leak past the rings, resulting in a much quicker drop to suction pressure until pressure equalizes on both sides, just like a leaking suction valve. After pressure equalizes fairly far down the stroke, pressure is now higher on the crank-end side of the cylinder, and gas 5.8 CHAPTER FIVE Pd Ps FIGURE 5.5 Operational and design problems. starts leaking into the head-end side, again looking like a leaking discharge valve. Usually this happens so far down the stroke that it is not noticeable. Line 4A-1B: Gas is entering the cylinder through the suction valves and is leak- ing past the piston rings. This leakage results in premature closing of the suction valves at point 1B. Line 1B-1A: The suction valves have closed and the cylinder volume is increas- ing. Pressure in the cylinder increases due to continued piston ring leakage into the cylinder. The pressure at point 1A is higher than design pressure (point 1). Symptoms: 1. Measured capacity might be lower than the application capacity. 2. Discharge temperature will increase due to re-circ1uation of the gas. Compare actual discharge temperature to a normal value or theoretical discharge temper- ature. With severely leaking rings, discharge temperature may rise 80 ЊF or more (double acting cylinder). 3. Leaking rings usually show up as a capacity ratio of greater than 1. However, leaking rings can also show up as a capacity of less than 1. 4. The measured compression and re-expansion lines will not match theoretical compression and re-expansion lines. 5.6.5 General Operation Limits Generally, three common operational problems grouped together are: pulsation ef- fects, valve losses, and cylinder gas passage losses. Their effect on compressor performance should be minimized as much as possible in the cylinder design and taken into consideration in the stated compressor horsepower and capacity figures. Even though they are taken into account in the compressor design, they are some- times either underestimated or undefinable to the accuracy required and are re- sponsible for performance problems. Figure 5.5 illustrates the cylinder losses for a typical PV diagram. COMPRESSOR ANALYSIS 5.9 DISCHARGE RESTRICTION NORMAL TRACE Ps Pd FIGURE 5.6 Discharge passage too small PV. Another area of fault is that of restricted passages. Passageways may be blocked for a number of reasons. Some of these include: incorrect cylinder design or sizing bottle restrictions such as plugged screens or broken diffuser tubes, valve restric- tions such as plate lift decreased through improper machining processes or debris stuck in the valves. In the case of discharge, it may be plugged with melted piston ring debris. When passages are restricted, there may be excessive valve losses with the hump of the discharge line more pronounced towards the end of the stroke. If a sharp rise should occur just before the end of the stroke, valves may be partially covered by the piston. DVE will be smaller than before, but due to the added valve losses, hp may not necessarily be less. In fact, total hp may be higher than normal. These restrictions can also occur on the suction side for the same reasons, for the same type of action, but during the suction cycle. Suction terminal pressure may be less than the line pressure. Because enough gas cannot get into the cylinder, the slope of the compression line will be longer. This will mean less capacity and a lower than normal DVE. Horsepower may decrease somewhat and suction valve hp losses will be high. 5.6.6 Pulsation Effects While the suction and discharge valves are open, the acoustic pulsation present in the system is passed into the compressor cylinder. Should the pulsation levels be of sufficient amplitude, the valve opening and closing times can be affected. Also, the average inlet and/or discharge pressures of the cylinder may be different than the design pressures with the net result being horsepower and capacity values which are different than the design values. These values may be greater or smaller, de- pending on the pulsation characteristics. The change in horsepower and flow may be proportional, resulting in actual BHP/MMSCF figures that are the same as design. However, the predicted loading curves will no longer be accurate. 5.10 CHAPTER FIVE Pd Ps NORMAL TRACE SUCTION RESTRICTION FIGURE 5.7 Suction passage too small PV. 5.6.7 Valve and Cylinder Gas Passage Losses Valve horsepower loss is due to the pressure drop across the compressor valve. Cylinder gas passage loss is the pressure drop between the cylinder flange and the compressor valve. Should these losses exceed the cylinder design allowances, actual flow will be less than the design flow. (Note that these losses are also affected by gas pulsations.) A general rule of thumb is that valve and cylinder gas passage losses should not exceed 5% of the indicated horsepower for that cylinder end. 5.6.8 Excessively Strong Discharge Valve Springs Strong discharge valve springs will be evident when evaluating a PV curve, usually identified by a normal trace until the start of the discharge stroke. Pressure will have to rise higher than normal to open the valve. A single hump may appear and then taper off until the cylinder reaches the end of the discharge stroke. With extremely stiff springs, there may be oscillations above and below the discharge line throughout the discharge stroke. Pressure pulsations can also show a similar pattern. In this case, it is necessary to look at the bottle pressure trace for indications of pulsations. Horsepower may not increase much, but excessive valve hp losses will be evident. 5.6.9 Excessively Strong Suction Valve Springs The suction valve may have stiff valve springs as well. The same effects occur with suction springs as with discharge. For stiff springs, a single dip would appear at the beginning of the suction stroke. SVE will probably stay the same or a little less, but computed valve losses would be much higher. An easy way to determine the difference between excessive spring forces and valve chatter created by weak or broken springs, with either suction or discharge, is: COMPRESSOR ANALYSIS 5.11 EXCESSIVELY STIFF SPRINGS NORMAL TRACE Ps Pd FIGURE 5.8 Stiff discharge spring PV. Pd Ps EXCESSIVELY STIFF SPRINGS NORMAL TRACE FIGURE 5.9 Stiff suction spring PV. • If valve hp losses are high, then the most probable cause is excessively stiff springs. • If valve hp losses are low, then the most probable cause is weak or broken springs. 5.7 COMPRESSOR PRESSURE/TIME (PT) PATTERNS 5.7.1 Double Acting Compressor Cylinders A double acting cylinder moves gas on both sides of the piston simultaneously. The furthest end from the crankshaft is referred to as the head-end (HE), and the cylinder end closest to the crankshaft is the crank-end (CE). A double acting cyl- inder requires suction and discharge valves on both ends of the cylinder. 5.12 CHAPTER FIVE SUCTION DISCHARGE ROD CRANK SHAFT PACKING CE HE CYLINDER HEAD FIGURE 5.10 Double acting compressor cylinder. There are three possible pressure measurement points: • Suction nozzle/bottle • Discharge nozzle/bottle • Head and crank end cylinder measurements While HE and CE cylinder pressure measurements are the most common, nozzle pressures also have value in determining causes of excessive valve and passage losses, or pulsation. The analyst must decide what is to be done with information obtained when determining the necessity to collect the above pressure readings. TDC BDC TDC HEAD END TRACE CRANK END TRACE FIGURE 5.11 Double acting compressor cylinder PT. The above diagram represent typical HE & CE cylinder pressure traces with the suction and discharge pressure traces overlaid. 5.7.2 Suction Pressure Time Trace At line #1 (Fig. 5.12), suction line pressure, we see a line moving across the screen. Ideally, the line would be very steady. This represents the pressure, preferably at the suction inlet nozzle of the cylinder. The function of this line is to allow the analyst to evaluate the flow of gas entering into the compressor cylinder and its COMPRESSOR ANALYSIS 5.13 TDC O BDC 180 TDC 0 DISCHARGE PRESSURE SUCTION PRESSURE 2 D E 1 C B 3 A TBC BDC TBC DISCHARGE PRESSURE SUCTION PRESSURE C B A E D 4 C FIGURE 5.12 HE & CE with suction and discharge PT’s dis- played. effect on the internal cylinder pressures. The area below the suction pressure line within the PV curve is considered valve and passage horsepower loss. 5.7.3 Discharge Pressure Time Trace In a similar manner, the trace at the #2 position is that of the discharge line pressure collected from the discharge nozz1e leading into the discharge bottle. Ideally, this line should be very steady. As with the suction pressure trace, this aids in the determination of internal cylinder pressure characteristics. The area above the dis- charge pressure line within the PV curve is considered valve and passage horse- power loss. 5.7.4 Head-End Pressure Time Trace (Internal Cylinder Pressure) Trace #3 is a representation of the head-end pressure within the cylinder. Top dead center (TDC) starts at the far left of the pressure screen. At TDC, both the cylinder pressure and discharge line pressure should meet as the discharge valves close. Line A-B: The cylinder pressure quickly drops to just below suction line pres- sure, allowing the suction valve to open. [...]... calculation of rod load tension COMPRESSOR ANALYSIS 5.19 HE 2 040 2000 CE 1 940 DISCH 1733 1500 1000 SUC 700 CE 660 HE 600 500 -180 -120 -60 0 60 120 180 ANGLE (DEGREE) FIGURE 5.20 PT diagram for rod load Compression ϭ (3. 14 ϫ 2.31ˆ2 ϫ 2 040 ) Ϫ ((3. 14 ϫ 2.31ˆ2) Ϫ (3. 14 ϫ 1.25ˆ2)) ϫ 660 ϭ 2 642 7 lbs Tension ϭ (3. 14 x2.31ˆ2 ϫ 600) Ϫ ((3. 14 x2.31ˆ2) Ϫ (3. 14 ϫ 1.25ˆ2) ϫ 1 940 ϭ 12990 lbs The results indicate... in most compressor manuals Below is an example from real data gathered in the field on an actual unit Calculated rod loads using line pressures and then rod loading using internal pressures Line pressures of the cylinder were found to be: • • • • Suction ϭ 700 psi Discharge ϭ 1733 psi Piston diameter ϭ 4. 625؆ Rod diameter ϭ 2.500؆ Compression ϭ (3. 14 ϫ 2.31ˆ2 ϫ 1733) Ϫ ((3. 14 ϫ 2.31ˆ2) Ϫ (3. 14 ϫ 1.25ˆ2))... Defining The Overall Task The task of designing or analyzing a compressor and piping system includes: • • • • • • Piping acoustics (from compressor valve to acoustic termination) Piping mechanical dynamics (compressor manifold and external) Pressure drop analysis (efficiency considerations) Compressor valve dynamics (both performance and reliability) Compressor performance (cost efficiency) Piping mechanical... mass flow versus time waves that commonly occur at compressor valves Figure 6.2 illustrates the frequency content of the head end discharge flow pulse It is readily apparent that the frequency content of the pulsative flow is limited to compressor rpm and multiples of compressor RPM A single compressor end produces decreasing amplitudes moving from the first compressor order (rpm ϫ 1) to the higher multiples... Discharge ϭ 1733 psi Piston diameter ϭ 4. 625؆ Rod diameter ϭ 2.500؆ Compression ϭ (3. 14 ϫ 2.31ˆ2 ϫ 1733) Ϫ ((3. 14 ϫ 2.31ˆ2) Ϫ (3. 14 ϫ 1.25ˆ2)) ϫ 700 ϭ 20793 lbs Tension ϭ (3. 14 ϫ 2.31ˆ2 ϫ 700) Ϫ ((3. 14 ϫ 2.31ˆ2) Ϫ (3. 14 ϫ 1.25ˆ2)) ϫ 1733 ϭ 8 848 lbs The compression and tension loads differ Limits from the manufacturer may be different between each as well The limits for this rod might be something like 25000... SYSTEMATIC COMPRESSOR ANALYSIS The primary focus of a systematic analysis approach is to ensure a thorough compressor evaluation that consumes the least amount of time Utilizing a form such as in Fig 5. 34, to record all the pertinent information makes it less likely to waste time or overlook important analysis infomation Follow the analysis format by completing items 1-17 as shown in Fig 5. 34 Use a check... leaving the cylinder Valves are designed with losses in mind (Generally, the more efficient the valve COMPRESSOR ANALYSIS 5.31 is, the less durable it is Also a valve can be durable at the expense of high losses.) To measure actual compressor valve horsepower losses, collect a pressure trace from a tapped compressor valve cap and overlay on the PV curve Analysis of valve (system) losses—As a general rule,... Stroke 1 & 2 Cylinder Pressure Equalization H.E BDC 180° H.E TDC 0° H.E TDC 0° d D e a A E DISCHARGE PRESSURE VIBRATION ULTRASONIC TRACE 1 SUCTION PRESSURE 2 B FIGURE 5. 24 C b c Normal PT and VT illustration COMPRESSOR ANALYSIS 5.8 .4 5.23 Pressure Reversal An event that should not be seen as vibration, except in very low amplitude or in magnified resolution, is pressure reversal The pressure reversal... engines, compressors exhibit cross talk and echoing as described below 5.8.3 Compressor Cross Talk Cross talk is the effect of one valve, on one end of the cylinder, presenting itself in the vibration/ultrasonic waveform of other vibration traces collected around the entire cylinder body This is the reason that overlaying one pattern on top of another provides valuable information Figure 5. 24 indicates... end) and back (crank end) ends of the piston are used simultaneously, cancellation and reinforcement of compressor order occurs Most notably, the odd orders (1ϫ, 3ϫ, 5ϫ ) tend to be reduced due to cancellation of the two ends Reinforcement occurs on the even order (2ϫ, 4 , 6ϫ ) Therefore, double acting compressors cylinders produce strong pulsative flow at even orders This reinforcement and cancellation . load. Compression ϭ (3. 14 ϫ 2.31 ˆ 2 ϫ 2 040 ) Ϫ ((3. 14 ϫ 2.31 ˆ 2) Ϫ (3. 14 ϫ 1.25 ˆ 2)) ϫ 660 ϭ 2 642 7 lbs. Tension ϭ (3. 14 x2.31 ˆ 2 ϫ 600) Ϫ ((3. 14 x2.31 ˆ 2) Ϫ (3. 14 ϫ 1.25 ˆ 2) ϫ 1 940 ϭ 12990 lbs. The results. diameter ϭ 4. 625؆ • Rod diameter ϭ 2.500؆ Compression ϭ (3. 14 ϫ 2.31 ˆ 2 ϫ 1733) Ϫ ((3. 14 ϫ 2.31 ˆ 2) Ϫ (3. 14 ϫ 1.25 ˆ 2)) ϫ 700 ϭ 20793 lbs Tension ϭ (3. 14 ϫ 2.31 ˆ 2 ϫ 700) Ϫ ((3. 14 ϫ 2.31 ˆ 2). tension. COMPRESSOR ANALYSIS 5.19 HE 2 040 CE 1 940 DISCH 1733 SUC 700 CE 660 HE 600 2000 1500 1000 500 -180 -120 -60 0 60 120 180 ANGLE (DEGREE) FIGURE 5.20 PT diagram for rod load. Compression ϭ (3.14