1. copyright (c) 2011 Stefan Rudbäck, Matematica,+46 708387910, mail@matematica.se, matematica.se sid 1 Date: 120101 Matematica/Abstracts Translation of scientific knowledge from text/mathematics to (computer) code without any compromises according; flow,energy,thermodynamics.

2. copyright (c) 2011 Stefan Rudbäck, Matematica,+46 708387910, mail@matematica.se, matematica.se sid 2 Date: 120101 Matematica/customers AGA; Measurement of gasflows (O2, N2, GNG…). Söderenergi; Calculation of energy production in powerplants. Siemens; Design of flow meters and calculations.

3. copyright (c) 2011 Stefan Rudbäck, Matematica,+46 708387910, mail@matematica.se, matematica.se sid 3 Date: 120101 Matematica/History Founded >25 years ago by Stefan Rudbäck, civ ing (m Sc). First customers;Johnson mek verkstads AB, production of standard flowmeters (ex orifice plates), and AGA (gas production).

4. copyright (c) 2011 Stefan Rudbäck, Matematica,+46 708387910, mail@matematica.se, matematica.se sid 4 Matematica dpns tech total system unc<0.4% Matematica hp tech sys unc<0.7% Fig showing Real unc of installed natural gas flow meters in Sverige

5. copyright (c) 2011 Stefan Rudbäck, Matematica,+46 708387910, mail@matematica.se, matematica.se sid 5 dp T Gas Chromatograph, GC Orifice plate 1. Complete Matematica hp system for natural gas in Nynäshamn P Gas flow Tube kg/h kg MW MWh

6. copyright (c) 2011 Stefan Rudbäck, Matematica,+46 708387910, mail@matematica.se, matematica.se sid 6 dp 4 temp transm, Temp_meas Gaschromatograph, GC measurement of molfractions of 6 gas components CH4,C2H6,C3H8,C4H10,CO2,N2 Orifice plate 1.1 Hardware/transmitters Matematica high precision system <0,7% unc for natural/Bio- gas flow and energy measurement in a tube P calculationTemp_cal Gas flowTube

7. copyright (c) 2011 Stefan Rudbäck, Matematica,+46 708387910, mail@matematica.se, matematica.se sid 7 1.2 Software/ Matematica high prec system for natural gas

8. copyright (c) 2011 Stefan Rudbäck, Matematica,+46 708387910, mail@matematica.se, matematica.se sid 8 1.3.1 ABB/CPU Matematica ABB dpns Energy/Flow computer

9. copyright (c) 2011 Stefan Rudbäck, Matematica,+46 708387910, mail@matematica.se, matematica.se sid 9 Matematica/Siemens dpns GNG Energy/Flow computer. 1.3.2 Siemens/CPU

10. copyright (c) 2011 Stefan Rudbäck, Matematica,+46 708387910, mail@matematica.se, matematica.se sid 10 Matematica/Siemens hp/dpns GNG Energy/Flow computer. 1.3.3 Siemens/CPU

11. copyright (c) 2011 Stefan Rudbäck, Matematica,+46 708387910, mail@matematica.se, matematica.se sid 11 dpns-technology statistical temp=31,75 mean value temp =31,74 live values from AGA’s plant in Nynäshamn 1.4 Example of Matematica double precision non stop (dpns) technology

12. copyright (c) 2011 Stefan Rudbäck, Matematica,+46 708387910, mail@matematica.se, matematica.se sid 12 Temp_meas= (most prob temp from 4 transmitters) Abs press= (Pöver+Patm) dprot= (sqrt calc dp from dp-transm) Mol parts from GC Mass flow Totalized Mass flow Energy flow Totalized Energy flow 2.Matematica natural gas. Connection btw transmitters and code with output

13. copyright (c) 2011 Stefan Rudbäck, Matematica,+46 708387910, mail@matematica.se, matematica.se sid 13 Date: 120101 3. Why Matematica.Lib? -General and precise code based on latest standards. -Measurement & calculation systems based on Matematica.Lib can be improved at need and afterwards with Matematica.Lib double precision non stop technology.

14. copyright (c) 2011 Stefan Rudbäck, Matematica,+46 708387910, mail@matematica.se, matematica.se sid 14 Date: 120101 4. Abstracts/1 4.1. Open design improves clarity=each parameter is calculated separate. 4.2. Open design improves error search.

15. copyright (c) 2011 Stefan Rudbäck, Matematica,+46 708387910, mail@matematica.se, matematica.se sid 15 Date: 120101 4. Abstracts/2 4.3. General & precise code for -Static precision & -Dynamic precision no additional errors from code at fast signal changes

16. copyright (c) 2011 Stefan Rudbäck, Matematica,+46 708387910, mail@matematica.se, matematica.se sid 16 Date: 120101 4. Abstracts/3 4.4. Stable code independent of external environment. 4.5. At ”impossible” signals=> totalization will be ”freezed”.

17. copyright (c) 2011 Stefan Rudbäck, Matematica,+46 708387910, mail@matematica.se, matematica.se sid 17 Date: 120101 5. Disadvantages CPU-time <=1 s (PCS7) Recommendation; Dedicated CPU for Matematica.Lib hp/dpns tech.

18. copyright (c) 2011 Stefan Rudbäck, Matematica,+46 708387910, mail@matematica.se, matematica.se sid 18 6. Details/1 Natural gas input

19. copyright (c) 2011 Stefan Rudbäck, Matematica,+46 708387910, mail@matematica.se, matematica.se sid 19 6. Details/2 Natural gas Output

20. copyright (c) 2011 Stefan Rudbäck, Matematica,+46 708387910, mail@matematica.se, matematica.se sid 20 6. Details/3 Temperature Naturgas_7 temp_ber block Input -measured temp i C -Flow in kg/s Output -Calc temp in C at upper pressure tapping of flowmeter (isolated tube) dp 4 pcs temp, Temp_meas orifice P calculationTemp_cal

21. copyright (c) 2011 Stefan Rudbäck, Matematica,+46 708387910, mail@matematica.se, matematica.se sid 21 dp linearization block 1=>linearization, 0=>output=input -Scaling of dp-transm=20mA=span -Sqrt-calculated output from dp-transm -Linearized dp from dp-transm Comment Why? Se next slide 6. Details/4 linearization of dp-signal

22. copyright (c) 2011 Stefan Rudbäck, Matematica,+46 708387910, mail@matematica.se, matematica.se sid 22 1.Linear output from dp-transm A/D-conversion unc= +-0.1% of span (16 mA) Sqrt Control system 10% flow = 1 % dp =4.16 mA 10% unc from A/D-conv 5% unc 2.Sqrt-calc output from dp-transm A/D-conversion unc=+-0.1% of span Control system 10% flow = 5.6 mA 1% unc from A/D-conv Figure 3 How A/D conv unc can be reduced from 5 to 1% with dp-sqrt-function

23. copyright (c) 2011 Stefan Rudbäck, Matematica,+46 708387910, mail@matematica.se, matematica.se sid 23 6. Details/5 Natural gas/density block Input -static pressure in PaA -static temp in C -measured mol% of 5 (up to 21) fractions in natural gas Output -density in kg/m3 -compressibility factor Z -number of iterations Comment 1 If all inputs are exact density will be calculated with 0,1% uncertainty. For this precision ~1400 statement code is needed. Comment 2 Only relation btw molar fractions are needed Measured with Gas Chromatograph. Sum of molar fractions can differ from 100% (or 1).

24. copyright (c) 2011 Stefan Rudbäck, Matematica,+46 708387910, mail@matematica.se, matematica.se sid 24 Date: 120101 6.Calculations Nynäshamn. If all hardware and software are according specification mass flow, energy flow totalized mass flow and energy flow will be calculated with a total unc<+-0,7% of actual flow.

25. copyright (c) 2011 Stefan Rudbäck, Matematica,+46 708387910, mail@matematica.se, matematica.se sid 25

26. copyright (c) 2011 Stefan Rudbäck, Matematica,+46 708387910, mail@matematica.se, matematica.se sid 26 6. Details/7 Mass Flow Natural Gas flow ISO5167 block Input -linearized dp i Pa -d=throat size in m -dp<dp_dropout flöde =>(normalflowmass)=0 =totalizations freezed Output normalflowmass =flow in kg/s reynerror=1 =standard limit violated Conversion from kg/s to kg/h

27. copyright (c) 2011 Stefan Rudbäck, Matematica,+46 708387910, mail@matematica.se, matematica.se sid 27 6. Details/8 Energy Cal_value Calc of Energy of natural gas at; temp before comb. 15C temp after comb. 15C +all vapour condensed after combustion

28. copyright (c) 2011 Stefan Rudbäck, Matematica,+46 708387910, mail@matematica.se, matematica.se sid 28 6. Details/9 Totalizations Comment To avoid underflow the Matematica.Lib Totalizer-block calculates with>100 numbers.underflow What¨s underflow? Example; Amount threw the pipe last year = 1234567 kg Amount threw the pipe last second = 1.234567 kg The sum of these 2 amounts will be 1234568 kg in a computer.234567 disappears in underflow>20%. Matematica.Lib totalizer can summarize for hundred years without underflow.

29. copyright (c) 2011 Stefan Rudbäck, Matematica,+46 708387910, mail@matematica.se, matematica.se sid 29 Date: 120101 7. System sensibility 7.1 (GC). Not very important! What happens with sys unc if GC molar fractions unc goes from 1 to 2%? Answer: 0,66=>0,67 Mass flow 0,67=>0,72 Energy flow

30. copyright (c) 2011 Stefan Rudbäck, Matematica,+46 708387910, mail@matematica.se, matematica.se sid 30

31. copyright (c) 2011 Stefan Rudbäck, Matematica,+46 708387910, mail@matematica.se, matematica.se sid 31 Date: 120101 8. Possible improvements 8.1 digital signal from dp-transm to control system ~0,7-0,6

32. copyright (c) 2011 Stefan Rudbäck, Matematica,+46 708387910, mail@matematica.se, matematica.se sid 32

33. copyright (c) 2011 Stefan Rudbäck, Matematica,+46 708387910, mail@matematica.se, matematica.se sid 33 Date: 120101 8. Possible improvements 8.2 two dp-transm =>0,7-0,6 minor improvement

34. copyright (c) 2011 Stefan Rudbäck, Matematica,+46 708387910, mail@matematica.se, matematica.se sid 34

35. copyright (c) 2011 Stefan Rudbäck, Matematica,+46 708387910, mail@matematica.se, matematica.se sid 35 Date: 120101 8. How far can You go? With Matematica software You can calculate the most cost effective improvement for a system. So far simple improvements can deliver 0,4% system unc. With Matematica.Lib dpns technology it¨s up to You to spec Your limit (You name it).

36. copyright (c) 2011 Stefan Rudbäck, Matematica,+46 708387910, mail@matematica.se, matematica.se sid 36 Date: 120101 9. More of Matematica/dpns-technology. Se following slides

37. copyright (c) 2011 Stefan Rudbäck, Matematica,+46 708387910, mail@matematica.se, matematica.se sid 37 T1T2T3 T4 T_most_probably Meausure of 4 temps in a tube Failure of transmitter 4 = no problem (compare with simple calc (1+2+3+10)/4=4>>2.146) Double precision non stop technology. Ex 2; Dpns statistical calc of most probably value Signal unlikely value

38. copyright (c) 2011 Stefan Rudbäck, Matematica,+46 708387910, mail@matematica.se, matematica.se sid 38 Example; Improvement of a GNG massflow/energyflow calc system with Matematica.Lib function block double precision non stop (dpns) Note simplified graphics dpns temp_meas Temp_meas_1 P_abs Matematica.Lib GNG flow/energy double precision non stop technology calculation system <0,4% sys unc dpns flow Flow orifice dp-cell 1 Temp_meas_2 Temp_meas_3 Temp_meas_4 Temp cal Flow orifice dp 2 Flow ISA nozzle dp 1 Flow ISA nozzle dp 2 GC gaskromatograf

39. copyright (c) 2011 Stefan Rudbäck, Matematica,+46 708387910, mail@matematica.se, matematica.se sid 39 Contact; Matematica Stefan Rudbäck, civ ing mail@matematica.se www.matematica.se +46(0)708387910 skype; stefan.rudback (On the following pages more about Matematica if You are interested)

40. copyright (c) 2011 Stefan Rudbäck, Matematica,+46 708387910, mail@matematica.se, matematica.se sid 40

41. copyright (c) 2011 Stefan Rudbäck, Matematica,+46 708387910, mail@matematica.se, matematica.se sid 41 Strypfläns/corner/fläns/D&D/2 tappings med yttre rörledning som medelvärdesbildare. (=Triple-T, rekommenderas framför ringkammare). Symmetriska (impuls)rör + resp - tryckanslutning dp-cell Mitt på = medelvärdesbildning av medelvärdesbildningen rörledning

42. copyright (c) 2011 Stefan Rudbäck, Matematica,+46 708387910, mail@matematica.se, matematica.se sid 42 Date: 110506 2.1 Matematica.Lib. The function library that uses scientific state of the art knowledge without compromises. Ex: Power/energy calc with Matematica.Lib can reduce the calc error from typical 5% to <0.3%

43. copyright (c) 2011 Stefan Rudbäck, Matematica,+46 708387910, mail@matematica.se, matematica.se sid 43 Power/energy calc with Matematica.Lib general function blocks

44. copyright (c) 2011 Stefan Rudbäck, Matematica,+46 708387910, mail@matematica.se, matematica.se sid 44 Part_1

45. copyright (c) 2011 Stefan Rudbäck, Matematica,+46 708387910, mail@matematica.se, matematica.se sid 45 Part_2

46. copyright (c) 2011 Stefan Rudbäck, Matematica,+46 708387910, mail@matematica.se, matematica.se sid 46 Date: 110506 2.2 Matematica.Lib/dpns (Double precision non stop technology) Specify your demands for; Production reliability and Production precision and Matematica.Lib will meet those demands (Ex; see below)

47. copyright (c) 2011 Stefan Rudbäck, Matematica,+46 708387910, mail@matematica.se, matematica.se sid 47 Flow signal from one dim flowmeter like US/mag Flow profile corrected ignal 100-66.206, difference=34%! For this case Example of FLOW PROFILES HANDLED BY Matematica dp_flow Date: 110506 Double precision non stop technology. Ex 1; Dp_flow.

48. copyright (c) 2011 Stefan Rudbäck, Matematica,+46 708387910, mail@matematica.se, matematica.se sid 48 Let T4_stat_proc_value control the wheight factor wf4 (T4_proc=wf4*T4_stat_proc and so on for 1,2,3) =(1+2+3)/3

49. copyright (c) 2011 Stefan Rudbäck, Matematica,+46 708387910, mail@matematica.se, matematica.se sid 49 Matematica.Lib.dpns block under normal conditions T1T2T3T4 T_avg

50. copyright (c) 2011 Stefan Rudbäck, Matematica,+46 708387910, mail@matematica.se, matematica.se sid 50 With Matematica double precision non stop technology the following is possible; -The measurement uncertainty can be reduced to a limit defined by the user (to a certain limit). -The reliability can be improved to a limit defined by the user. (transmitter failure will be non-stop handled by the dpns-system) -Transmitters can be simplified. Failures will be non-stop handled. -Safety system operating parallell with the production system can be eliminated. Failures will be non-stop handled. -Real transmitter errors will be calculated.

51. copyright (c) 2011 Stefan Rudbäck, Matematica,+46 708387910, mail@matematica.se, matematica.se sid 51 Exemple of Matematica.Lib funktion blocks

52. copyright (c) 2011 Stefan Rudbäck, Matematica,+46 708387910, mail@matematica.se, matematica.se sid 52 Example of Matematica.Lib function blocks

53. copyright (c) 2011 Stefan Rudbäck, Matematica,+46 708387910, mail@matematica.se, matematica.se sid 53 Matematica.Lib in list form

54. copyright (c) 2011 Stefan Rudbäck, Matematica,+46 708387910, mail@matematica.se, matematica.se sid 54 Matematica.Lib in list form 2

55. copyright (c) 2011 Stefan Rudbäck, Matematica,+46 708387910, mail@matematica.se, matematica.se sid 55 Matematica.Lib steam MMI

56. copyright (c) 2011 Stefan Rudbäck, Matematica,+46 708387910, mail@matematica.se, matematica.se sid 56 Soft package Matematica calculation system for GNG delivery of kg and energy amount at Nynäs/Sweden MWh kg

57. copyright (c) 2011 Stefan Rudbäck, Matematica,+46 708387910, mail@matematica.se, matematica.se sid 57 Matematica:Lib Natural Gas GNG density calculation Code based on ISO 12213 <0.1% uncertainty >1400 statements of code in naturgasdens function block Siemens PCS 7 /ABB CB General and precise

58. copyright (c) 2011 Stefan Rudbäck, Matematica,+46 708387910, mail@matematica.se, matematica.se sid 58 Soft package Matematica calculation system for GNG delivery of kg and energy amount at Nynäs/Sweden

59. copyright (c) 2011 Stefan Rudbäck, Matematica,+46 708387910, mail@matematica.se, matematica.se sid 59 Matematica:Lib Naturgas GNG flow calculation Code based on ISO 5167 = 0.5% uncertainty >450 statements of code in ISO_5167 function block (orifice plates, venturis and nozzles) Siemens PCS 7/ABB CB General and precise

60. copyright (c) 2011 Stefan Rudbäck, Matematica,+46 708387910, mail@matematica.se, matematica.se sid 60 Soft package Matematica calculation system for GNG delivery of kg and energy amount at Nynäs/Sweden

61. copyright (c) 2011 Stefan Rudbäck, Matematica,+46 708387910, mail@matematica.se, matematica.se sid 61 Matematica:Lib Naturgas GNG totalization of power to energy with function block Totalizer_3. Code developed by Matematica with 84 digits without underflow. May summarize in 100 years with 1 ms sampling <0.0001% underflow. Totalizer_3 function block appr. 800 statements of code Siemens PCS 7/ABB CB General and precise

62. copyright (c) 2011 Stefan Rudbäck, Matematica,+46 708387910, mail@matematica.se, matematica.se sid 62 Date: 110506 Matematica How can Your organisation and Matematica cooperate in the future? There are (at least) 4 possibilities;

63. copyright (c) 2011 Stefan Rudbäck, Matematica,+46 708387910, mail@matematica.se, matematica.se sid 63 Date: 110506 Matematica-Your organisation coop 1. Start point; Consult basis. Matematica designes/calculates/generates control system code with Processline.

64. copyright (c) 2011 Stefan Rudbäck, Matematica,+46 708387910, mail@matematica.se, matematica.se sid 64 Date: 110506 Matematica-Your organisation coop 2. Developed coop; Licens agreement for Processline.

65. copyright (c) 2011 Stefan Rudbäck, Matematica,+46 708387910, mail@matematica.se, matematica.se sid 65 Date: 110506 Matematica-Your organisation coop 3. Developed coop; Simulation licens (Windows) for Matematica.Lib.

66. copyright (c) 2011 Stefan Rudbäck, Matematica,+46 708387910, mail@matematica.se, matematica.se sid 66 Date: 110506 Matematica-Your organisation coop 4. Developed coop; Simulation and online- license (Windows and Siemens/ABB) for Matematica.Lib.

67. copyright (c) 2011 Stefan Rudbäck, Matematica,+46 708387910, mail@matematica.se, matematica.se sid 67 Date: 110506 At last; I hope some of my soft or hard packages can help Your organisation to better business in the future. Do not hesitate to contact me for a discussion of the first step in a future cooperation. Regards Stefan Rudbäck, Man dir, civ ing, M Sc