Improved analogue computer particularly for the analysis of liquid-vapour phase equilibria

摘要

772,085. Electric analogue calculating systems. COMPAGNIE FRANCAISE DE RAFFINAGE. June 11, 1953 [June 21, 1952], No. 16161/53. Class 37. An analogue computer solving a. number of equations of the form (l.x i + αk i x i =N i ) wherein a is a function of x i , comprises for each equation a set of potontiometers consisting of a first group of two potentiometers representing terms and x i , a second group of three potentiometers representing terms a, k i and x i , and a third group consisting of a single potentiometer representing N i ; the multiple potentiometers being cascaded and each group being energized from a reference voltage source so that the slider voltages representing corresponding equation terms l.x i and αk i x i are each connected over one of a first bank of identical totalizing resistances to one side of a null indicator and the single potentiometer is similarly energized so that its slider voltage representing N i is connected over one of a second bank of identical totalizing resistances to the other side of the null indicator, from which a second resistance of the second bank is connected to a point of zero potential; whereby the potentiometers representing l, k i and N i may be set to known values thereof, the potentiometer representing a may be set to an assigned approximation thereto, and the potentiometer representing x i may be set to zeroize the null indicator at an approximate solution value of x i for the assigned value of α, from which is determined a more accurate value for a to which the corresponding potentiometer is reset so that a more accurate solution for x i is obtained as before, and the process is iteratively repeated until successive values of x i are identical at the accurate solution. Theory.-It is shown mathematically for a mixture of m different volatile constituents l to m containing N 1 to N m moles. of each constituent respectively, of which n 1 l to n m l are in the liquid phase and n 1 v to n m v are in the vapour phase, then at phase equilibrium of the system, (1) for any value of i from l to m where k i is the liquid/vapour equilibrium constant for the particular constant i. L is the total number of moles. in the liquid phase, V is the total number of moles. in the vapour phase and that the several values of nil for the various liquid constituents of the mixture when denoted as xi, are given by (2) and for the required value of (3) so that iteration is convergent. For solution, a is given an arbitrary value from which a first set of values is calculated for xi, and # xi is then determined, whereby a calculated value of α is found and compared with the arbitrary value, to derive a more accurate value of a from which a more accurate set of values for xi and E xi is obtained and wherefrom a further more accurate value of a is obtained; the process being iteratively repeated until two successive identical values of α are obtained allowing an accurate solution for x i . Construction,.-Figs. 4A, 4B, 6 and (5 not shown) illustrate apparatus for solving a set of seven equations of the form l.x i + αk i x i =N i wherein plural potentiometers and their controls are arranged in ten horizontal lines 1 to 9 and X and in fifteen vertical columns 1 to 15. Lines 1 to 7 comprise each a potentiometer 1 disposed respectively in odd numbered columns 1, 3, 5 ... 13, a potentiometer a disposed in even numbered columns 2, 4, 6 ... 14, and potentiometers N 1 , N 2 ...N 7 in column 15; line 8 comprises potentiometers k 1 , k 2 ... k 7 in the even numbered columns 2, 4, 6 ... 14 and line 9 comprises potentiometers 1 1 , 1 2 , , 1 3 ... 1 7 in odd numbered columns 1, 3, 5 ... 13; while in column 15, line 8 comprises potentiometer #kx and line 9 comprises potentiometer #n incorporating a 2 position switch 30 whose control is designated " Zero or #n." The ultimate line X contains seven pairs of ganged potentiometers x 1 , x 2 ... x 7 arranged in columns 1,2; 3, 4; 5, 6; ... 13, 14, and each controlled by a single knob located between each respective pair of columns, while there is also provided in line 9 a potentiometer designated " l 8 and (1 + α) " and in line X a potentiometer Ex, both situated between columns 14 and 15. A twoposition 2-way switch 31 designated -1 is also provided in line X at column 15. There are also provided on the control panel a line selector SL having ten operative positions 1 to 9 and 1 + α; an operation selector SO having operative " reading " positions X, N, k, and α, and a sixth "resolution" position; a 15- position column selector switch SC; and the thousands, hundreds, tens and units control switches m, c, d, u of a decade resistance box; together with the screen of a null indicating a cathode-ray tube TC whose x-plates are energized from an oscillator 0, and the y plates from amplifier A and input transformer T connected over single-pole 2-way switches S 1 , S 2 controlled by operation selector SO to the common connections of banks of totalizing resistances R 1 , R 9 and R 10 , R 24 in the "resolution " position of operation selector SO, and in its " reading " positions connected between the output slider of the decade resistance box and also to the moving arm of multi-way switch S 3 actuated by operation selector SO to traverse contacts corresponding to the five " reading " positions thereof. Supply bus-bars 20, 21 are provided. and energized from oscillator 0 for each of lines 1 to 9 over normally open switches S10 to S90 operated by line selector SL; the lower end of each potentiometer being permanently connected to its appropriate bar 20 while the upper ends of potentiometers N 1 to N 7 , #kx and En in column 15 and l 1 to l 8 in line 9 are per-- manently connected to their appropriate lines 21. The upper ends of potentiometers 1, a, and K 1 to K 7 are switchably connected to their appropriate bar 21, while the lower ends of potentiometers x 1 to x 7 and Ex in line X are connected to a common bus-bar 22, which is switchably connected to oscillator 0 by normally closed switch Sxo operated by line selector SL. Any selected line of potentiometers may be energized from the oscillator while in the " resolution " position of operation selector SO, the bar 20 of lines 8, 9 and the bar 22 of line X are switchably connected to the oscillator, and with the line selector SL set to line 8 or 9 all the bars 20 in lines 1 to 7 are similarly connected. Switches S11, S23, S35, S47, S59, S611, S713, energizing the l-potentiometers from the respective bars 21 are closed by the operation selector SO in its " reading " position 1, and its " resolution " position while switches S12, S24, S36, S48, S510, S612, S714 energizing the a potentiometers are similarly closed in the " reading a " and " resolution " positions. Switches S82, S84, S86, S88, S810, S812, S814 connect the upper ends of the potentiometers k 1 to k 7 to the appropriate bar 21 in the " reading k " position of the operation selector and also in the " line 8 " position of the line selector SL, while the potentiometers are similarly connected for energization to the sliders of the corresponding a-potentiometers in the " resolution " position of the operation selector SO and with the line selector SL set to any of lines 1 to 7. Threeway switches SX1, SX2, SX3, SX4, SX5, SX6; SX7, SX8; SX9, SX10; SX12, SX13; SX14, SX14A; are arranged to connect the upper ends of the x potentiometers to bar 21 in line 9 in the " reading x " position of the operation selector; while in the " resolution " position of the operation selector with the line selector set to any of lines 1 to 7; and in the " reading " 1, a, and k positions of the operation selector, the upper end of each x-potentiometer in oddnumbered columns is connected to the slider of the l-potentiometer corresponding therewith, the upper end of each x-potentiometer in even-numbered columns is connected to the slider of the corresponding k-potentiometer. In the " resolution " position of the operation selector, with the line selector in position 8, the upper ends of the even-numbered column x-potentiometers are left connected to the sliders of the corresponding k-potentiometers, while in the position 9 of the line selector, the upper ends of such x-potentiometers are disconnected while those of the oddnumbered column x-potentiometers are connected to the sliders of potentiometers L 1 to L 8 in line 9 and corresponding columns. In the " reading l " position of the operation selector, the sliders of the " l-potentiometers " in lines 1 to 7 are connected by corresponding switches SS11, SS23, SS35, SS36, SS47,SS59, SS611, SS713 to respective fixed contacts of a multiway switch S4 whose moving contact is connected to contact 1 of multiway switch S3 operated by the operation selector. Similar connections are made for the sliders of the apotentiometers in lines 1 to 7 to respective contacts of switch S5 whose moving contact is connected to contact a of the switch S3 in the " reading α " position of the operation selector ; for the sliders of the k-potentiometers in line 8 to respective contacts of switch S6 whose moving contact is connected to contact k of switch S3 in the " reading k " position ; for the sliders of potentiometers l 1 to l 8 in line 9 to respective contacts of switch S7 whose moving contact is connected to a further contact (not shown) of switch S3 in the appropriate " reading " position ; for the sliders of potentiometers x in odd-numbered columns of line X to respective contacts of switch S9 whose moving contact is connected to contact x of switch S3 in the " reading X " position. The sliders of the N- potentiometers in lines 1 to 7 are connected to the moving contacts of 3-way switches SS115, SS215, SS315, SS415, SS615, SS715, ganged to the operation selector so that in the " reading N " position thereo