Modeling and Simulation Studies of a Variable Speed Compressor

Modeling and Simulation Studies of a Variable Speed Compressor

Pavan Kumar Veldandi

Department of Chemical Engineering Osmania University College of Technology Hyderabad, India

Prof. V. Ramseh Kumar Prof. Chintha Sailu

Department of Chemical Engineering Osmania University College of Technology Hyderabad, Indiad

Abstract With the increasing need for optimizing the power consumption and to regulate emissions from any process plant, large number of manufacturers looking towards to operating compressors using variable speed drives. The performance of a gas compressor cab be described by the relationship of Actual Flow (Q), Isentropic Head (H), Isentropic Efficiency (), with the operating speed as a parameter (Reference 1). In this paper a computer model has been developed to simulate the variation of power, pressure with inlet flowrate of the compressor and rotation speed of the compressor. It is found that the head, power, pressure ratios can be related to inlet volumetric rate of the compressor using a quadratic expression. It is also found that this variable can be linearly fitted to the speed of the compressor. When multiple speed data curves are given a compressor performance can be predicted at an unknown speed

Keywords Variable speed compressor, Process Simulation and Modeling, Least square analysis.

1. INTRODUCTION

   Centrifugal compressors are the preferred mean of compressing the gas in a process system. Centrifugal compressors exhibit performance characteristics that depend on the operating point imposed on them by the process (Reference 3). It is thus, necessary for a process simulation model to determine the performance of the gas compressor depending on the head and flow requirement of the operating point, and subsequently, the performance of the compressor as a function of the speed and absorbed power .With the increasing need for optimizing the power consumption and to regulate emissions from any process plant, large number of manufacturers looking towards to operating compressors using variable speed drives (Reference 4). The performance of a gas compressor is described by the relationship of Actual Flow (Q), Isentropic Head (H), Isentropic Efficiency (), with the operating speed as a parameter. Typical manufacturer data includes a map containing this information, which looks as shown below (Refer to Fig. 1

2. ADVANTAGES

   The advantages of predicting the performance of a compressor at variable speeds are as follows

   • Multiple number of compressor performance curves can be generated

   • Extrapolation for speeds which fall beyond the data for which user has data

   • Head vs Flow data generation , when compressor operates on a fluid with a different MWt than for which user has data

   • Surge and stonewall prediction for various RPMs and MWts

3. PROCEDURE FOR PERFORMANCE CURVE FITTING

   When a user wants to simulate and find the compressor performance curve, itll be necessary for user to fit performance of the compressor to an equation.If the compressor performance data is Head vs flow then this data can be fitted to an equation say a polynomial of the order 2, which looks as follows.

   H=a*Q^2+b*Q+c —- (1)

   From the performance data H and Q are available. A computer program can be written to find the parameters a through e . A Sum of squares of errors method can be employed to find these parameters.

   (H-(a*Q^2+b*Q+c) )^2=0—- (2)

   Once these parameters are available, using the same equation

   (1) the performance of the compressor can be estimated any unknown flow rates. And when the values estimates from the generated parameters and plotted against the data available it should exactly overlap. Same method can be employed to predicted other performances of the compressor like Outlet pressure, Outlet Temperature and work vs Flowrate

   Generally compressor vendors provide the compressors performance data at 5 to 6 operating speeds, ranging from 80% to 105% of the normal operating speed (100%). So users will have data only at these operating speeds, but when user wants to predict the performance of a compressor at a speed for which data is not available following procedure need to be employed

   If RPM is the Speed of the Compressor and H is the Head developed at any given flow rate. As shown in the above diagram if user has the data at 11347 and 14184 RPMs and needs to predict the performance data at a speed of 12766 RPM following linear fitting can be used to generate Head data at various flow rates and once the data is available same can be fitted to equation (1) to predict the Head at an unknown flow rates.

   When the RPMx is in between RPM1 and RPM2, the Hx data generated using (3) data when plotted against the data user already has it should exactly fall in between as shown in Fig (2) .Above mentioned two techniques are very important in curve fitting in any commercial simulation.

4. RESULTS AND DISCUSSION

   1. To model multiple performance curves

      The first step in predicting the compressor performance is to be able to read the data for different speeds and be able to fit that data to equation (1). The data in table (1) is considered as input data and when the model is run following output is generated as shown in table (2) & table (3). From the figure 2 its clear that the input data and fitted curve data match properly without much deviation. Now same fitted curve can be used to predict head value at a given volumetric rate for input speeds. The purpose of this step is to make the view the compressor performance curves in graphical format only

   2. To compare the fitted data with output from program

      Now that the input data is fitted to equations, next step is to run the compressor model at the speed which is equal to input data. In this step the compressor model is run at a speed of 11347. A case study is run varying the inlet molar rate of the entering fluid and output adiabatic head is calculated (refer to table 4). The resulting adiabatic head is plot against the inlet volumetric rate. From fig. 4 it is clear that the compressor is running properly at the user supplied speed.

   3. To get the performance at unknown speed

      In step 3, the compressor input speed it changed from 11347 to 12000. Same case study as mentioned in step-2 is run and the compressor output data (table 5) of Adiabatic Head vs Volumetric Rate is plot. The compress output is shown in middle curve in fig 5. It falls exactly it between the two compressor performance curves without any overlapping.

   4. To get the performance for Output Pressure curves

      The procedure explained in section-1 can be extended to performance data of Outlet Pressure of the compressor vs Inlet volumetric rate. The compressor is operated at a speed of 12000 RPM which is the speed at which no performance data is available. Case study is run by varying the inlet molar rate and Outlet pressure output is generated. The data in tables 6,7 & 8 plot as Outlet pressure against Volumetric rate as shown in fig.6, The middle curve gives the output from compressor case study.

   5. To introduce the efficiency curves

      All the above steps from step-1 to step -4 are at a constant efficiency of 100%. But generally the compressor efficiency curves are provided by vendors at different RPMs. The same method as mentioned in section-1 which is used to predict the performance as Head vs Volumetric rate can be used to predict the efficiency values at different volumetric rates and Speeds. The efficiency cure fitting for tabular data is as shown below in tables 9,10 and 11. The same data is plot as shown in Fig 7.

   6. To get the performance for Pressure Ratio curves

      Similar to step-4, in which outlet pressure vs volumetric rate curves are generated, user can give performance curves in Pressure ratio vs Volumetric rate format also. When these curves along with multiple speed Efficiency curves are applied following results are obtained as shown in tables 12,13 &14. The same data is plot in Fig 8.

   7. Surge Points prediction

      The next step is the prediction of surge point. User needs to mention for each performance curve what is the surge point; only then percentage surge can be predicted. When the inlet flow goes too low the head developed by a compressor is very high and it may lead to reverse flow. When the inlet flow goes below surge point following warning is given to the user by calculating the inlet flowrate. The operating point is shown as in Fig 9.

      ** WARNING ** UNIT 1, 'C1' – Volumetric flow rate is at

      83.158 percent of SURGE.

   8. Stonewall Points prediction

   When the flowrate to the compressor is very high the inlet pressure and outlet pressure almost becomes the same. Following warning is given to the user to that effect. The operating point is shown as in Fig 10.

   ** WARNING ** UNIT 1, 'C1' – Volumetric flow rate is at

   102.73 percent of STONE WALL.

5. TABLES

   TABLE 1 GENERAL COMPRESSOR INPUT DATA

   Input Data @ RPM1 Volumetric Flowrate Adiabatic (m3/hr) Head(m)		Input Data @ RPM2 Volumetric Adiabatic Flowrate(m3/hr) Head(m)
   4919.2798	12654.7	5838.5698	16032.9
   5457.3999	12545.7	6264.5698	15996.6
   5995.52	12364.1	6600.8999	15923.9
   6354.2598	12146.1	7094.1699	15778.6
   6668.1602	11964.5	7475.3398	15597
   6982.0601	11710.2	7968.6099	15233.8
   7228.7002	11456	8372.2002	14834.2
   7542.6001	11056.4	8820.6299	14325.6
   8013.4502	10402.5	9067.2598	13998.7
   8372.2002	9821.35	9358.7402	13599.1
   8618.8301	9349.13	9650.2197	13126.9
   8820.6299	8876.9	10031.4	12364.1
   9156.9502	8077.75	10278	11782.9
   9291.4805	7714.5	10479.8	11238

   TABLE 2: COMPARISON OF INPUT PERFORMANCE DATA AND FITTED DATA AT

   Input Data		Fitted Data		Fitted Data
   m3/hr	Head (M)	m3/hr	Head (M)	m3/hr	Head (M)
   4919.28	12654.7	4919.28	12654.7	6793.72	11872.1
   5457.4	12545.7	5026.904	12638.7	6856.5	11821.2
   5995.52	12364.1	5134.528	12619.8	6919.28	11767.3
   6354.26	12146.1	5242.152	12598	6982.06	11710.2
   6668.16	11964.5	5349.776	12573.3	7031.39	11663.6
   6982.06	11710.2	5457.4	12545.7	7080.72	11614.8
   7228.7	11456	5565.024	12523.3	7130.04	11564
   7542.6	11056.4	5672.648	12494	7179.37	11511.1
   8013.45	10402.5	5780.272	12457.7	7228.7	11456
   8372.2	9821.35	5887.896	12414.4	7291.48	11378.4
   8618.83	9349.13	5995.52	12364.1	7354.26	11299.7
   8820.63	8876.9	6067.268	12319.6	7417.04	11219.7
   9156.95	8077.75	6139.016	12275.6	7479.82	11138.7
   9291.481	7714.5	6210.764	12232	7542.6	11056.4
   		6282.512	12188.8	7636.77	10935.5
   		6354.26	12146.1	7730.94	10809.7
   		6417.04	12115.6	7825.11	10678.9
   		6479.82	12082.2	7919.28	10543.2
   		6542.6	12045.9	8013.45	10402.5
   		6605.38	12006.6	8085.2	10296.3
   		6668.16	11964.5	8156.95	10185.1
   		6730.94	11919.8	8228.7	10068.9

   SPEED = 11347 RPM

   TABLE3: COMPARISON OF INPUT PERFORMANCE DATA AND FITTED DATA AT

   SPEED = 12766 RPM

   Data comparison @ Speed = 12766 RPM
   Input Data		Fitted Data		Fitted Data
   m3/hr	Head (M)	m3/hr	Head (M)	m3/hr	Head (M)
   5838.57	16032.9	5838.57	16032.9	7869.96	15317.5
   6264.57	15996.6	5923.77	16030.6	7968.61	15233.8
   6600.9	15923.9	6008.97	16025.9	8049.33	15158.3
   7094.17	15778.6	6094.17	16018.6	8130.05	15080.6
   7475.34	15597	6179.37	16008.9	8210.76	15000.7
   7968.61	15233.8	6264.57	15996.6	8291.48	14918.5
   8372.2	14834.2	6331.84	15983.8	8372.2	14834.2
   8820.63	14325.6	6399.1	15970.1	8461.89	14741.3
   9067.26	13998.7	6466.37	15955.6	8551.57	14644
   9358.74	13599.1	6533.63	15940.2	8641.26	14542.3
   9650.22	13126.9	6600.9	15923.9	8730.94	14436.2
   10031.4	12364.1	6699.55	15902.9	8820.63	14325.6
   10278	11782.9	6798.21	15877.9	8869.96	14261
   10479.8	11238	6896.86	15848.9	8919.28	14196.1
   10883.4	9748.7	6995.52	15815.8	8968.61	14130.7
   		7094.17	15778.6	9017.93	14064.9
   		7170.4	15749.2	9067.26	13998.7
   		7246.64	15716.3	9125.56	13924.6
   		7322.87	15680	9183.85	13847.6
   		7399.11	15640.2	9242.15	13767.7
   		7475.34	15597	9300.44	13684.8
   		7573.99	15535.4	9358.74	13599.1
   		7672.65	15468.3	9417.04	13512.4
   		7771.3	15395.6	9475.33	13421.8

   TABLE 4: COMPARISON OF FITTED DATA WITH COMPRESSOR OUTPUT DATA AT SPEED = 11347 RPM

   Compressor output data @ Speed = 11347 RPM
   m3/hr	Head, M	m3/hr	Head, M
   5454.3657	12550.812	7227.0347	11461.819
   5590.7251	12521.252	7363.394	11291.956
   5727.084	12480.771	7499.7529	11116.46
   5863.4434	12429.079	7636.1123	10940.108
   5999.8022	12365.663	7772.4712	10756.279
   6136.1616	12281.509	7908.8306	10562.079
   6272.5205	12198.968	8045.1895	10359.681
   6408.8799	12123.874	8181.5488	10149.267
   6545.2388	12048.396	8317.9082	9920.7471
   6681.5981	11959.294	8454.2666	9680.3398
   6817.957	11856.876	8590.626	9412.1992
   6954.3164	11739.811	8726.9854	9099.832
   7090.6758	11608.71

   TABLE5: COMPRESSOR OUTPUT PERFORMANCE DATA AT SPEED = 12000 RPM

   Compressor output @ speed = 12000 RPM
   m3/hr	Head, M	m3/hr	Head, M	m3/hr	Head, M
   5454.37	14146.3	6681.598	13778.6	7772.471	12893
   5590.73	14136.4	6817.957	13707.3	7908.831	12738
   5727.08	14117.6	6954.316	13624.6	8045.19	12572
   5863.44	14089.9	7090.676	13530.8	8181.549	12398
   5999.8	14052.9	7227.035	13426.3	8317.908	12210
   6136.16	14001.8	7363.394	13304.3	8454.267	12015
   6272.52	13948.5	7499.753	13174.1	8590.626	11802
   6408.88	13895.5	7636.112	13038.1	8726.985	11560
   6545.24	13840.6

   TABLE 6: COMPARISON OF INPUT PERFORMANCE DATA AND FITTED DATA AT

   SPEED = 11347 RPM

   Speed @ RPM = 11347
   Input Data		Fitted data
   m3/hr	K Pa	m3/hr	K Pa	m3/hr	K Pa
   5357.8	2276.8	5357.8	2276.8	6677	2236.8
   5996.8	2267.7	5485.6	2276.4	6786	2229.5
   6460.1	2249.4	5613.4	2275.3	6895	2221.5
   7003.2	2212.9	5741.2	2273.5	7003	2212.9
   7562.3	2158.2	5869	2270.9	7115	2204.5
   7993.6	2094.3	5996.8	2267.7	7227	2194.8
   8440.9	2030.4	6089.5	2265	7339	2183.9
   8872.2	1948.3	6182.1	2261.8	7450	2171.7
   9335.5	1847.9	6274.8	2258.2	7562	2158.2
   9782.8	1729.3	6367.4	2254	7649	2145.2
   10150	1619.8	6460.1	2249.4	7735	2132.4

   TABLE 7: COMPARISON OF INPUT PERFORMANCE DATA AND FITTED DATA AT

   TABLE 8: COMPRESSOR OUTPUT PERFORMANCE DATA AT SPEED = 12000 RPM

   Output data @ 12000 RPM
   m3/hr	Kpa	m3/hr	Kpa	m3/hr	Kpa
   5509.294	2388.66	7850.75	2255.6	10054.46	1823.55
   5647.027	2387.14	7988.48	2237.76	10192.2	1782.79
   5784.759	2384.96	8126.21	2220.41	10329.93	1739.75
   5922.492	2382.1	8263.94	2201.45	10467.66	1694.42
   6060.224	2378.65	8401.68	2180.81	10605.39	1646.81
   6197.957	2374.53	8539.41	2157.95	10743.13	1596.91
   6335.689	2369.64	8677.14	2133.28	10880.86	1544.73
   6473.421	2363.99	8814.87	2107.88	11018.59	1490.26
   6611.154	2357.86	8952.6	2082.16	11156.32	1433.5
   6748.886	2351.45	9090.34	2056.59	11294.05	1374.46
   6886.618	2343.91	9228.07	2029.51	11431.79	1313.13
   7024.351	2335.38	9365.8	2000.13	11569.52	1249.52
   7162.083	2326.23	9503.53	1968.39	11707.25	1183.62
   7299.815	2315.48	9641.27	1934.53	11844.98	1115.44
   7437.548	2303.27	9779	1898.94	11982.72	1044.97
   7575.28	2289.42	9916.73	1862.02	12120.45	972.213
   7713.013	2272.82			12120.45	897.172

   TABLE 9: COMPARISON OF INPUT EFFICIENCY DATA AND FITTED DATA AT

   Efficiendy data @ Speed RPM = 11347
   Input Data		Fitted Data @ RPM = 11347
   m3/hr	Eff %	m3/hr	Eff %	m3/hr	Eff %	m3/hr
   5357.8	84	5358	84	7734.8	86.1	8700
   5996.8	86	5486	84.6	7821.1	86.1	8786
   6460.1	86	5613	85.1	7907.3	86	8872
   7003.2	86	5741	85.5	7993.6	86	8965
   7562.3	86	5869	85.8	8083.1	85.9	9058
   7993.6	86	5997	86	8172.5	85.8	9150
   8440.9	86	6089	86	8262	85.7	9243
   8872.2	84	6182	86	8351.4	85.6	9335
   9335.5	81	6275	86	8440.9	85.5	9425
   9782.7	75	6367	86	8527.2	85.3	9514
   10150	71	6460	86	8613.4	85	9604

   SPEED = 11347 RPM

   SPEED = 12766 RPM

   Speed @ RPM = 12766
   Input Data		Fitted data
   m3/hr	K Pa	m3/hr	K Pa	m3/hr	K Pa
   5916.933	2514.07	5916.93	2514.07	7507.988	2450.876
   6571.885	2495.82	6047.92	2511.21	7629.394	2441.18
   7386.582	2459.32	6178.91	2507.96	7750.799	2430.229
   7993.611	2404.56	6309.9	2504.31	7872.205	2418.024
   8520.767	2331.56	6440.9	2500.26	7993.611	2404.563
   9000	2249.43	6571.89	2495.82	8099.042	2391.415
   9511.183	2158.18	6734.82	2491.91	8204.473	2377.541
   9862.62	2076.05	6897.76	2486.3	8309.904	2362.94
   10357.83	1939.16	7060.7	2479	8415.336	2347.613
   10996.81	1701.9	7223.64	2470.01	8520.767	2331.559

   TABLE 10: COMPARISON OF INPUT EFFICIENCY DATA AND FITTED DATA AT

   SPEED = 12766 RPM

   Efficiency Data @ RPM = 12766
   Input Data		Fitted Data @ RPM = 12766
   m3/hr	Eff %	m3/hr	Eff %	m3/hr	Eff %	m3/hr	Eff %
   5916.93	84	5916.93	84	8808.3	86.11	9862.62	83
   6571.89	86	6047.92	84.54	8904.2	86.07	9961.66	82.4
   7386.58	86	6178.91	85.01	9000	86	10060.7	81.6
   7993.61	86	6309.9	85.41	9102.2	85.8	10159.8	80.8
   8520.77	86	6440.9	85.74	9204.5	85.6	10258.8	80
   9000	86	6571.89	86	9306.7	85.4	10357.8	79
   9511.18	85	6734.82	86	9408.9	85.2	10485.6	77.7
   9862.62	83	6897.76	86	9511.2	85	10613.4	76.2
   10357.8	79	7060.7	86	9581.5	84.66	10741.2	74.6
   10996.8	71	7223.64	86	9651.8	84.28	10869	72.9
   		8616.61	86.07	9722	83.88	10996.8	71
   		8712.46	86.11	9792.3	83.46

   TABLE 11: COMPRESSOR OUTPUT EFFICIENCY DATA AT SPEED = 12000 RPM

   TABLE 12: COMPARISON OF INPUT PRESSURE RATIO DATA AND FITTED DATA AT SPEED = 11347 RPM

   Speed @ RPM = 11347
   Input Data		Fitted Data @ RPM = 11347.000000
   m3/hr	Pres Ratio	m3/hr	Pres Ratio	m3/hr	Pres Ratio
   5357.8	2.46	5357.8	2.465	6568.69	2.428365
   5996.8	2.45	5485.6	2.46454	6677.316	2.421047
   6460.1	2.43	5613.4	2.46333	6785.942	2.413048
   7003.2	2.4	5741.2	2.46135	6894.569	2.404365
   7562.3	2.34	5869	2.45858	7003.195	2.395
   7993.6	2.27	5996.8	2.455	7115.016	2.38595
   8440.9	2.2	6089.5	2.45204	7226.837	2.375525
   8872.2	2.11	6182.1	2.44856	7338.658	2.363725
   9335.5	2	6274.8	2.44456	7450.48	2.35055
   9782.7	1.87	6367.4	2.44004	7562.301	2.336
   10150	1.75	6460.1	2.435	7648.563	2.322007

   Speed @ RPM = 12766
   Input Data		Fitted Data @ RPM = 12766
   m3/hr	Pres Ratio	m3/hr	Pres Ratio	m3/hr	Pres Ratio
   5916.93	2.721	5916.93	2.721	7507.99	2.6529
   6571.89	2.702	6047.92	2.71814	7629.39	2.6425
   7386.58	2.662	6178.91	2.71481	7750.8	2.6307
   7993.61	2.603	6309.9	2.71101	7872.21	2.6175
   8520.77	2.524	6440.9	2.70674	7993.61	2.603
   9000	2.435	6571.89	2.702	8099.04	2.5888
   9511.18	2.336	6734.82	2.69759	8204.47	2.5738
   9862.62	2.247	6897.76	2.69139	8309.9	2.558
   10357.8	2.099	7060.7	2.68339	8415.34	2.5414
   10996.8	1.842	7223.64	2.67359	8520.77	2.524
   		7386.58	2.662	8616.61	2.5065

   TABLE 13: COMPARISON OF INPUT PRESSURE RATIO DATA AND FITTED DATA AT SPEED = 12766 RPM

   Efficiency Data @ RPM = 12000
   m3/hr	Eff %	m3/hr	Eff %	m3/hr	Eff %
   5509.29	83.38	7299.8	86	8814.9	85.1
   5647.03	84.03	7437.5	86	8952.6	84.8
   5784.76	84.57	7575.3	86	9090.3	84.4
   5922.49	85.03	7713	86.03	9228.1	83.8
   6060.22	85.35	7850.7	86.03	9365.8	82.8
   6197.96	85.58	7988.5	86	9503.5	81.6
   6335.69	85.76	8126.2	85.98	9641.3	80.3
   6473.42	85.91	8263.9	85.91	9779	79
   6611.15	86	8401.7	85.78	9916.7	77.7
   6748.89	86	8539.4	85.61	10054	76.4
   6886.62	86	8677.1	85.42	10192	75.2

   TABLE 14: COMPRESSOR OUTPUT PERFORMANCE DATA SPEED = 12000 RPM

   Compressor output Speed 12000 RPM
   m3/hr	Pres Ratio	m3/hr	Pres Ratio	m3/hr	Pres Ratio
   5509.294	2.58524	6886.62	2.537	8126.21	2.403628
   5647.027	2.58376	7024.35	2.5277	8263.942	2.383136
   5784.759	2.58153	7162.08	2.5178	8401.675	2.360808
   5922.492	2.57855	7299.82	2.5062	8539.406	2.336058
   6060.224	2.57489	7437.55	2.4931	8677.139	2.309332
   6197.957	2.57049	7575.28	2.4781	8814.871	2.281803
   6335.689	2.56523	7713.01	2.4602	8952.604	2.253863
   6473.421	2.55911	7850.75	2.4416	9090.336	2.226085
   6611.154	2.55237	7988.48	2.4224	9228.068	2.196699
   6748.886	2.54529			9365.801	2.164898

6. FIGURES

   Fig 1.Compressor Performance data fitting using SSE

   Fig 2.compressor performance

   Fig 3.Compressor data viewing in curve format

   Fig 4.Compressor performance matching with the data in curve format

   Fig 5.Compressor performance prediction at 12000 rpm

   Fig 6.Compressor performance prediction at 12000 rpm

   Fig 10 .Compressor stonewall point prediction at 12000 rpm

7. CONCLUSIONS

   Compressor Efficiency

   Curves

   Input Data @ RPM = 11347.000000

   Input Data @ RPM = 12766.000000

   From the above analysis its clear that a quadratic fit will be sufficient to model performance curves of a variable speed compressor

   The assumption of variation of heat developed by a compressor is linearly proportional to its speed can be verified

   Volumetric Flowrate (m3/hr)

   70

   4000 9000 14000

   90

   85

   80

   75

   Adiabatic Efficiency (%)

   FIG 7.Compressor efficiency prediction at 12000 rpm

   Fig 9 .Compressor surge point prediction at 12000 rpm

8. REFERENCES

1. Perry, R.H. and Green, D.W. (Editors) , Perrys Chemical Engineers

   Hand Book,8th Edition, McGraw-Hill, New York 2007

2. McCabe, W., Smith, J. and Harriott, P. Unit operations of chemical engineering, 7th Edition, McGraw-Hill, New York 2004

   Fitted Data @

   RPM = 11347.000000

3. Bruce A. Finlayson, Introduction to Chemical Engineering Computing, 2nd Edition, Wiley, Washington 2014

4. P.A. O'Neill, Industrial Compressors: Theory and Practice Hardcover

,1st Edition,Butterworth-Heinemann , Oxford 199