Interconversion of Petroleum Distillation Curves

Inter novelty of Petroleum Distillation CurvesThe crops recommended by API 1a for the interconversion of ASTM D 86 and TBP (True Boiling Point) distillment folds are transposed into Mathcad computation platform. Two Mathcad versions are presented for each of direct, ASTM to TBP, and the backward, TBP to ASTM, cut offs conversions correspond to the API procedure. The first version, simpler, but with fewer possibilities of use, was presented in the first part 1a. This second part comprises the relations of the API procedure written as locks in the Mathcad worksheet. The procedure wreaks potentiometer be placed in a separate eye socket of the worksheet, range which may be then(prenominal) collapsed, locked and hidden. Alternatively, the dies can be stored in a circumstantial Mathcad file, which can be afterwards inserted and employed in the main worksheet with fictitious character pretermit. Other possibilities of Mathcad environment for interconnection of worksheets (fi les), such as use of Mathconnex or universe of Mathcad E-books, are briefly menti 1d, too. Utilization of Mathcad procedures is illustrated through some(prenominal) pillow slips. The Mathcad worksheets comprising the API procedures are thus providing a convenient computer tool for fast prediction of one of ASTM and TBP distillment foreshorten starting signal from the other one.Key words ASTM D 86, TBP, distillation, interconversion, Mathcad, petroleumIntroductionThe goal of the present work is to offer a general, easy-to-use Mathcad versions of the API (American Petroleum Institute) procedures for the ASTM D 86 and TBP distillation curves interconversion. A simpler Mathcad version of the API procedures was given in the first part 1a. However the simpler Mathcad version has limited possibilities of use, or even no receipts in some applications, such as those of iterative tasks comm only if solved with programming modules. Furtherto a greater extent, numerical information as signements needed to be placed in the worksheet earlier the methods expressions (case of worksheet setting of Automatic calculation as default, that is turned on allhow, if turned off, most of the present discussion becomes meaningless). In this second part we are divergence to deliver Mathcad written procedures which are more concise and have extended extend of application.The relations needed for distillation curves interconversion originating from describeence 2 and adapted by the importr for temperatures in degrees centigrade have been given explicitly in the first part 1a.Since the API procedure for ASTM TBP distillation curves interconversion was described in segmentation 1 1a, the reader is urged to refer to that part or to the original API fiber 2 for a better comprehension and details on both the API method procedure and Mathcad version herein presented. numerical checks against examples taken from literature 2 3 7 and made in order to verify our Mathcad versio ns of the API procedure, are also shown.Mathcad implementation of API procedures for ASTM TBP distillation curves interconversion. Using functionsThe main part of the Mathcad worksheet with the API method for friendship of TBP curve from ASTM distillation curve is reproduced in Fig. 1. Assignments of parameters value being identical with those already given in Fig. 1a of the first part 1a, the beginning area of the Mathcad worksheet containing these assignments is no more shown in the present Fig. 1. In the same area omitted from Fig. 1, there are also definitions of range unsettleds ip and id, which again are identical with those in fork 1, that is ip = 0,1..6 and id=0,1..5, needed for indexing current points of the distillation curve (corresponding to 0, 10, 30, 50, 70, 90 and 100 % vol.) and differences ( amidst temperatures), honourively. Thus, the distillation curve is assumed to be represented in the same format as in Part 1, i.e. 7 rows 2 newspaper columns matrix, wher e the first column elements are volume percentages (0, 10, 30, 50, 70, 90 and 100) of distillate and the second column elements are the corresponding six temperatures (oC) on the (ASTM or TBP) distillation curve.The task of the function dt_DC (where dt and DC in notation stand for difference of temperatures and distillation curve) as define by relation (1) in Fig. 1 is to pick up all pairs of consecutive temperatures on the given ASTM curve, to compute the difference between the both temperatures, and to give the result as a 6 elements array, which elements are the temperature differences. One of the two arguments of the function dt_DC in Fig. 1 needs to be the range unsettled id. Otherwise, a definition analogous(a)would issue an delusion message (Illegal context and expression (a) written in Mathcad turning into red) because, as expected, a range variable is not allowed as parameter within the function definition, or, being more specific, within the expression assigned to a function.Another definition but more lengthy, which can be used to obtain the same numerical result as dt_DC function in relation (1) of Fig. 1, i.e. the six temperature differences, is the next one (b)Fig. 1. distribute of the Mathcad worksheet with functions definitions to be used for API procedure for TBP curve prediction from the ASTM D86 distillation curve (continued with applications in Figures 2 and 3)Even if the numerical values produced with both definitions, (1) in Fig.1 or higher up (b), are same, it is worth of mention that the two outputs have different meanings in Mathcad. Thus, while the latter definition (b) produces a six-element vector, the first definition, which is used in relation (1) of Fig. 1, produces an array (which may be also called table) with also 6 values, but which has not the quality of a vector in Mathcad. Consequently, neither several operations typical for vectors, such as transposition (operator T as superscript) or vectorize (operator denoted by an arrow above an expression containing a vector) can be applied to the output of the twoargument function dt_DC. This behavior may be probably better understood if a function definition like that in relation (1) of Fig.1 for dt_DC is regarded as six one-variable functions simultaneously defined. Difference between the outputs of the two functions, dt_DC and dt_DCb is similar to that between a true vector and a range variable such as ip or id which is used for indexing.When desired, a workaround able to lead to a vector output is thus provided by the above definition of dt_DCb in (b). Moreover, this definition can be rewritten in a more concise form within a Mathcad worksheet employ programming modules (see Part 3 1b).In step 2 (Fig. 1), temperature for 50%vol. on TBP curve is estimated with the function denoted t_50%TBP, from temperature for 50% vol. of ASTM, as in API procedure described in Part 1 1a. According correlations of the same procedure (that is relations (3) given i n Part 1), differences between temperatures on TBP curve are then calculated in step 3 establish onFig. 2. Part of the worksheet containing an example using the Mathcad version of API procedure for ASTM-to-TBP distillation curves conversion (Mathcad version of the procedure given in Fig. 1 ASTM data and experimental TBP from 2)temperature differences of ASTM curve. This is done employing again a function with two arguments, of which the first is the range variable id (function named dt_TBP). Finally, TBP temperatures are determined in the quaternary and last step with function t_DC by subtracting or adding to priorly determined t50%TBP the appropriate temperature gaps found in step 3 (Fig. 1).An example using the Mathcad version of the API procedure described above is given in the portion of the Mathcad worksheet shown in Fig. 2. As antecedently explained, since the output of the function dt_DC in step 1 or of the function dt_TBP in step 3 (Fig. 2) is an array (table) and not a vec tor, presence of the index id at vector-variables tASTM1 or tTBP1, respectively, is imperative for a correct assignment of values computed by functions (dt_DC or dt_TBP) to the elements of mentioned vectors. Otherwise, the aforementioned error message (Illegal context) would be issued and corresponding expressions turned into red.Fig. 3. Part of the worksheet with another(prenominal) example using the Mathcad version of API procedure for ASTM-to-TBP distillation curves conversion (Mathcad version of the API procedure given in Fig. 1 ASTM data and corresponding TBP estimated by EdmisterOkamoto procedure taken from 3)Even if it can be right away noticed from both Fig. 1 and example in Fig. 2, we emphasize that in the present Mathcad version of API procedure (Fig. 1) it is possible to write the expressions of the procedure as a standalone cortege, independent on the 7 2 matrix with distillation curve data, due to use of functions. On the contrary, for the simpler Mathcad version gi ven in Part 1 1a, it was necessary to provide the distillation curve matrix in the Mathcad worksheet before the relations of the API procedure. Thus, presentation of simpler Mathcad procedure in 1a was actually possible only using a numerical example. However, it can be mentioned that even in the case of simpler version in Part 1 a workaround for the infringement of normal order, that is with data in the begining of the worksheet, may be provided by the use of a global definition (available in Mathcad).ASTM distillation data for example in Fig. 2 was taken from API Technical Data Book 2. The TBP curve determined in Fig. 2 is identical with that computed in 2 from the same ASTM distillation data and with same API procedure. For comparaison, experimental TBP (vector TBPexp) retrieved from the mentioned reference 2 is also given in Fig. 2.Fig. 4. Area of worksheet with the Mathcad version of the reversed API procedure, for conversion of the TBP curve into ASTM distillation curveThe use of the same Mathcad version of the API procedure is illustrated with another example in the part of the worksheet reproduced in Fig. 3. ASTM data (7 2 matrix ASTM2) in Fig. 3 and corresponding TBP values (matrix TBP2_EO) estimated with Edmister and Okamoto method 4 are quoted from reference 3.The suite of definitions shown in Fig. 1 as well as the two examples (Fig. 2 and 3) have been actually written in the same Mathcad worksheet.The Mathcad version of the reversed API procedure, for TBP curve conversion to ASTM distillation curve, is illustrated in Fig. 4. In step 1 the temperature differences between two consecutive temperatures amongst those of selected points on TBP curve can be computed with the same function dt_DC given in Fig. 1. Since the Mathcad versions of both direct and reversed API procedures have been written in same worksheet, there was no more need for another function definition for step 1 in Fig. 4.Coefficients in the expression of the function t_50%ASTM in rela tion (6) (Fig. 4), needed for the prediction of the 50% temperature on ASTM curve based on 50% temperature on TBP curve, are taken from Part 1 1a and they are coming from the same API procedure 2. As shown in Fig. 4, the temperature for 50% on ASTM curve can also be determined with the function tr_50%ASTM, which is the inverse of function t_50%PRF defined previously in the worksheet (with relation (2) in Fig. 1). The inverse function, tr_50%ASTM, is defined using the Mathcad built-in function beginning. First argument of root is the expression of whose root is wanted, the second argument indicates the variable with respect to which the equation defined by the expression has to be solved, and the 3rd and 4th arguments specify the interval where the desired root is lying.Fig. 5. Portion of Mathcad worksheet with example of TBP curve conversion intoASTM D86 distillation curve (API procedure 2)Presence of last two arguments is optional when these are included, Ridder or Brent algorithm is used internally by root to determine the reply otherwise Mueller-secant algorithm is employed. The accuracy of the computed root is determined by parameter TOL (tolerance) whose value can be set (for the entire worksheet) from Mathcad menu. For details on the Mathcad root function or on the mentioned algorithms, references 5-6, 9 may be consulted. Notations used in relation (6r) of Fig. 4 show that equation t_50%TBP()t=0 is (numerically) solved with respect to variable (that is unknown ) and the desired root (ASTM temperature for 50% vol.) is within interval (0, 1000) ( oC ) for all possible values of parameter t (temperature for 50% vol. on TBP curve).Differences between temperatures on ASTM curve are computed in step 3 based on temperature differences on TBP curve determined in step 1. Being previously defined in the worksheet (Fig. 1), coefficients AAPIC and BAPI in relations (7) are known. Finally, in step 4 temperatures on the ASTM curve are calculated using the same func tion t_DC already defined in a proceeding zone (Fig. 1) of the worksheet.We recall that for features of Mathcad employed herein or other capabilities reader can find of import and detailed information with good examples in Mathcad help 5a and particularly in the Resource Center 5b accompanying Mathcad platform.The use of the Mathcad version for the reversed API procedure, that is for TBP curve to ASTM curve conversion, is illustrated with the example in the part of Mathcad worksheet reproduced by Fig. 5.Other possibilities of utilization of Mathcad written proceduresTwo of these possibilities are illustrated below, one using an inserted area and the other the Reference command provided by the Mathcad environment.An area can be readily inserted in a worksheet, using the commands from Insert menu. In our case (Fig. 6), after inserting a new area (a blank area initially) in the worksheet, we have merely copied ( Copy/Paste ) the area given in Fig. 1 and pasted it in the inserted blank area. The area thus inserted contains also the assignments of values to parameters Aid and Bid needed in the procedure (parameters which values are given in Tab. 1 of 1a and are named AAPIC BAPI in Figures 1a,b and 2 in the same reference 1a and which are no more shown in Fig.1 of the present part). Obviously, in such a case one has to provide a sufficient size of the inserted area. Its enlargement can be made by selecting one (usually the lower) of the crosshairs corresponding to the boundaries of inserted area and dragging it, or by clicking indoors area and typing Enter one or several times, as needed to accommodate the whole pasted part. The inserted area may be then easily collapsed (Fig. 6), as indicated by instructions in the dialog box which appears with a mouse right-button click. After collapsing, the inserted region can be locked and protected by a password and then provided with a time stamp. Always after collapsing, presence of the inserted region may be even made inv isible (hidden) 5b. on the whole content of Fig. 6 was actually written in a new Mathcad file (worksheet), different from those illustrated in previous figures.Fig. 6. Mathcad worksheet with inserted area collapsed and an example of ASTM curve conversion into TBP curveFig. 7. Mathcad worksheet with Reference to the Mathcad file (named here ASTMTBP interconvAPI simple functions.mcd) containing the API procedure for the two distillation curves interconversionThe Reference command (Fig. 7) allows all variables or functions definitions from another worksheet ( pen worksheet or referenced Mathcad file) to be made available in the current (parent) worksheet. Thus the current worksheet will behave as if one should have inserted into it the actual regions from the referenced worksheet. The Reference containing line is merely introduced by a first mouse click in the main (parent) worksheet in the place where the referenced file is desired, then reservation the insert from the Reference com mand accessible in menu (Insert Reference), followed by pointing to referenced file location (as asked by dialog box). An icon (right headed arrow inside a square) will mark the place from which the referenced worksheet will take effect within the parent worksheet. (R) after the file name (ASTM-TBP interconvAPI simple functions.mcd in occurrence, Fig. 7) means that the relative path was chosen in the present case in order to locate the referenced file. Even if the referenced Mathcad file itself cannot be seen in the current (parent) worksheet, it may be opened with a double click on its Reference icon and then accessed and even modified.Like for any other computational environment or programming language, it is strongly advisable to use systematic and mnemonic notations for various variables, functions,, both in main and inserted worksheet (collapsed or not, or with Reference), in order to avoid errors. As already mentioned in 1a, errors in computed results may appear in case of no tations overlap, even without any error message highlighted by Mathcad (without any expression turned into red).In the case of long worksheets, more complicated structures of linked (concatenated) worksheets can be thus envisaged. For example a worksheet with an inserted area can be referenced from another worksheet. Again, in order to reduce the possibility of errors and for an acceptable readability, it is however advisable to limit to only a few the worksheets thus interconnected. If this is not possible, there are alternatives offered by Mathcad platform, such as use of Mathconnex environment or creation of a Mathcad electronic book. Both alternatives are easy to use and well documented in Mathcad help, for example the latter in the Authors reference item within Help menu. Moreover, new-made versions of Mathcad, i.e. starting with 2001i, offer the possibility to save worksheets under XML or HTML format.ConclusionIn the Mathcad version of API procedure for ASTM-TBP distillation curves interconversion presented in this part, use of functions allows to write the expressions of the procedure as a standalone suite, independent on the 7 2 matrix comprising distillation data. Utilization of some Mathcad features, such as functions with two arguments one of which being a range variable, vector-valued functions, definition of an inverse of a function using built-in root function, or area insertion in a Mathcad worksheet, are illustrated through examples. Interconnection of Mathcad worksheets (files) through the ,Reference command is also exemplified. Such features of Mathcad platform can provide added readability and broader generality to worksheets. Other capabilities of Mathcad, like utilization of Mathconnex or creation of Mathcad E-books are briefly envisaged. The Mathcad worksheets comprising the API procedures are thus providing a convenient tool for fast prediction of an ASTM or TBP distillation curve starting from the other one.