Method and system for determining vapor pressure of liquid compositions

Abstract: The vapor pressure of a multi-component liquid composition is measured by providing an eductor 10 through which the liquid composition is caused to flow at selected inlet pressures to provide incrementally changing pressure differentials across the eductor. The pressure differen­ tial is read for each incremental change across the eductor and the suction port pressure is read at each incremental pressure differential until the suction port pressure as a function of the pressure differential indicates a change in slope or point of inflection along the so-called dead fluid curve indicating the bubble point or true vapor pressure of the liquid composition. A motorized pressure regulator valve may be interposed in the liquid composition flow conduit upstream of the eductor for incrementally changing the pressure differen­ tial. The point of inflection may be obtained by determining the mathematical relationship using the cubic spline fit technique and calculating the second derivative of the function of the suction port pressure versus the pressure differential across the eductor until the second derivative equals zero.

Description: The present invention pertains to a method for determining the vapor pressure of a multi-component liquid, such as crude oil, using an eductor and associated equipment for determining the change in the slope of a curve which represents the change in the suction port pressure of the eductor as a function of the pressure differential across the eductor. Measurement of the vapor pressure of a multi-component liquid is difficult in that the various components of the liquid typically have different vapor pressures at a particular temperature. Conventional vapor pressure measurement techniques and systems perform operations to reduce the pressure acting on a sample of liquid in a controlled environment until the pressure remains substantially constant, indicating that the vapor pressure of the liquid has been reached. However, as certain components of a multi-component fluid vaporize, the vapor pressure of the remaining liquid changes to a different value. This phenomenon complicates conventional vapor pressure measurement techniques and results in inaccurate determinations of the true vapor pressure (otherwise referred to as "bubble point pressure") of a particular liquid composition. The aforementioned deficiencies in conventional vapor pressure measurement techniques may be of particular concern when attempting to measure the vapor pressure of liquids such as crude petroleum which have various hydrocarbon components mixed therein. The handling and transport of such a liquid should usually be controlled to prevent unwanted vaporization of the lower molecular weight components during the transport and storage processes. One relatively uncomplicated device for measuring vapor pressure of a liquid utilizes an eductor. Conventional eductor-type vapor pressure measurement devices operate to provide a liquid flow rate through the eductor such that a relatively large pressure drop across the eductor is assured whereby measurement of the flow stream pressure at the so-called suction port of the eductor provides for measurement of a vapor pressure condition of at least one component of a multi-component liquid. However, use of an eductor type system may not be accurate if the liquid to be measured is made up of various liquid components, if only one flow condition is observed or if the pressure measurements are taken under the wrong range of flow conditions. US Patent 4733557 describes a method and system for measuring the vapor pressure of a multi-component liquid such as crude oil utilizing an eductor device. The system and method described therein assumes that if a sufficiently large pressure differential is caused to occur across the eductor, it can be assumed that the suction pressure is being measured at a point above the region of variable vapor pressure of the liquid and where the vapor pressure remains substantially constant with change in the differential pressure, and that the pressure measured at the so-called suction port under such conditions will be representative of the vapor pressure of the liquid. The patent also proposes a technique for estimating the bubble point pressure of a multi-component liquid. However, the technique involves plotting the suction port pressure at a number of different pressure differentials in the region of the variable vapor pressure condition of the multi-component liquid and then projecting the curve so obtained backwards to find the intercept thereof with the portion of the curve representing a so-called dead liquid. The point of intercept is taken to be an approximate indication of the bubble point pressure of the multi-component liquid. In other words, the procedure described in the patent involves measuring the so-called suction port pressure at a plurality of pressure differentials above that at which the so-called suction port pressure will provide an indication of the bubble point pressure and projecting the curve so-obtained backwards to obtain an estimate of the bubble point pressure. However, for many multi-component liquids, this approach to measuring vapor pressure can introduce a degree of error which may not be acceptable in certain operating conditions or when attempting to accurately measure the true vapor pressure of a particular fluid composition. For example if the process is begun with a pressure differential across the eductor which is too large and only a small amount of a volatile liquid component is present, perhaps only a momentary and not easily measured pressure will occur at the suction port as the most volatile liquid vaporizes. Accordingly, such a measurement process is inaccurate and the true bubble point will not be determined. The present invention provides a method and system for overcoming the above-mentioned deficiencies of the prior art vapor pressure measurement systems utilizing so-called eductor devices. The present invention provides an improved method and system for measuring the true vapor pressure (bubble point pressure) of a multi-component liquid utilizing an eductor-type or similar flow device through which the liquid is caused to flow while various pressure measurements are taken, preferably at a constant liquid temperature during the measurement process. According to the present invention, there is provided a method for determining the bubble point pressure of a multi-component liquid composition which typically exhibits, at a constant temperature, different vapor pressures due to the vaporization of components of different molecular weight in the liquid, whereby the bubble point pressure is determined by passing a sample of liquid through an eductor having an inlet port, a suction port and an outlet port, while a pressure differential between said inlet port and said outlet port and a pressure at said suction port is measured, the method is characterised by: increasing said pressure differential from an essentially zero pressure differential to a pressure differential which lies in a pressure differential range where relatively small changes in the suction port pressure occur for relatively large changes in the pressure differential and measuring the corresponding suction port pressures, establishing a curve where the ordinate of the curve is given by said pressure differentials and the abscissa by said suction port pressures, and determining the point of inflection of said curve. The point of inflection in the curve generated by plotting suction port pressure against pressure differential as the latter is increased indicates the onset of vaporization of the component of the liquid composition having the highest vapor pressure and is thus representative of the true vapor pressure (bubble point pressure) of the liquid composition. A preferred embodiment of the procedure includes the step of increasing the pressure differential between the inlet port and the outlet port of said eductor substantially beyond the pressure differential and the suction port pressure values which provide the point of inflection to confirm that the point of inflection represents the bubble point pressure of the liquid composition. Preferably, increasing the pressure differential between the inlet port and the outlet port of said eductor is carried out by increasing the pressure of the liquid flowing to said inlet port. It is also preferred that the step of increasing the pressure differential between said inlet port and said outlet port is carried out at a substantially constant temperature of said liquid composition. In accordance with one aspect of the invention, the procedure involves calculating the second derivative of the relationship between suction port pressure and pressure differential to determine when the change in slope of the function has a zero value. This point in the change in slope of the suction port pressure-pressure differential function indicates the onset of vaporization of the liquid and thus the true vapor pressure of that liquid. Accordingly, the true vapor pressure of a multi-component liquid may be defined as the highest pressure at which vaporisation of any of the components of the liquid begins. For practical purposes in the handling and transport of a multi-component liquid, it is important to know the onset of vaporization of any component of that liquid, particularly for volatile compositions included in crude oils and other hydrocarbon fluids. The invention also provides apparatus for determining the bubble point pressure of a multi-component liquid composition which typically exhibits, at a constant temperature, different vapor pressures due to the vaporization of components of different molecular weight in the liquid, said apparatus comprises: an eductor including an inlet port, a throat portion, a suction port downstream of said throat portion and an outlet port downstream of said suction port in the direction of flow of liquid through said eductor, conduit means connected to said inlet port and said outlet port for conducting said liquid composition through said eductor; means for measuring a pressure differential between said inlet port and said outlet port, means for measuring the pressure at said suction port, pump means for causing liquid composition to flow through said eductor, characterised by means for increasing said pressure differential from an essentially zero pressure differential to a pressure differential which lies in a pressure differential range where relatively small changes in the suction port pressure occur for relatively large changes in the pressure differential, means for establishing a curve where the ordinate of the curve is given by said pressure differentials and the abscissa by said suction port pressures, and for determining the point of inflection of said curve. Preferably, the apparatus also includes enclosure means for enclosing said eductor, said enclosure means providing a space adapted in operation to be filled with a liquid at a substantially constant temperature for stabilizing the temperature of said eductor and said liquid composition flowing through said eductor during a process of measuring the bubble point pressure of said liquid composition. The means for increasing the pressure differential suitably includes pressure regulator valve means disposed in said conduit means connected to said inlet port for controlling the pressure of said liquid composition flowing to said inlet port to be at a predetermined value for providing a predetermined pressure differential between said inlet port and said outlet port; and means associated with said regulator valve means for changing the regulated pressure in said conduit means between said eductor and said regulator valve. The invention will now be described in more detail with reference to preferred embodiments thereof and with the aid of the accompanying drawings in which Figure 1 is a schematic diagram of an eductor of a type which is particularly suitable for use in measuring the vapor pressure of multi-component liquids in accordance with the present invention; Figure 2 is a diagram showing the suction port pressure as a function of the pressure differential across an eductor-type measurement device for a multi-component liquid; and Figure 3 is a schematic diagram of a vapor pressure measurement system in accordance with the present invention. In the description which follows, like parts are marked throughout the specification and drawing with the same reference numerals, respectively. The drawing figures are in schematic or diagrammatic form in the interest of clarity and conciseness. Referring to Figure 1, the system and method of the present invention utilizes a device commonly known as an eductor and generally designated by the numeral 10. The eductor 10 has an inlet passage or port 12 which is reduced in diameter to a smaller diameter or throat portion 14 which opens into a larger diameter chamber 16. The chamber 16 may also be referred to herein as the "suction port" of the eductor 10. Slightly downstream, in the normal direction of flow of fluid through the eductor 10, is a somewhat larger diameter outlet port 18 which has a greater cross-sectional flow area than the throat 14. The port 18 typically opens into a larger passage 19. In the operation of the eductor 10 for performing vapor pressure measurements in accordance with the present invention, the pressure drop across the eductor is measured between pressure measuring devices comprising transducers or gauges 20 and 22. The so-called suction pressure of the eductor 10 or what is actually the point of measurement of the vapor pressure of the liquid flowing through the eductor is measured at the gauge 24. The pressure at the gauge 20 may be designated as P in , the pressure at the gauge 22 may be designated as P out and the pressure at the gauge 24 measuring from the port or chamber 16 may also be designated as P suction . When a liquid is caused to flow through the eductor 10, the flow rate of the liquid may be increased such as to transcend from so-called pipe flow conditions to a condition wherein the pressure in the chamber or port 16 is reduced significantly. The eductor may, in fact, be utilized as a vacuum pump or what is sometimes known as an ejector. In any case, the pressure in the chamber or port 16 may be reduced to the point wherein the liquid will vaporize as it passes from the throat 14 to the outlet port 18 and the pressure measured at the gauge 24 will represent the vapor pressure of the liquid composition flowing through the eductor 10. As the flow rate through the eductor 10 is increased from a point at which the pressure differential P in minus P out is nil, the onset of vaporization of the lower molecular weight compositions in the fluid will cause a change in the slope of the curve representing the vapor pressure or P suction pressure as a function of the pressure differential across the eductor (P in minus P out ). Referring now to Figure 2, there is illustrated a diagram indicating the vapor pressure characteristic of a pure or single composition liquid and the vapor pressure characteristic of a multi-component liquid such as crude oil including lighter or lower molecular weight fluids such as natural gasoline liquids mixed therein, for example. The smooth line curve 30 shows the characteristic of a so-called dead or pure liquid with respect to the measurement of the eductor suction pressure at the gauge 24 as a function of increasing pressure differential measured between the gauges 20 and 22 of the eductor 10. If the liquid did not change state under any pressure condition or was a truly "dead" liquid, the curve 30 would intercept the abscissa at approximately 689 kPa (100 PSI) differential pressure, for example. On the other hand, if the liquid was a pure liquid that had a specific vapor pressure at the temperature that the liquid was being caused to flow through the eductor, the suction pressure as a function of increasing differential pressure would reach a certain minimum or the vapor pressure point, as indicated by the line 32. With increasing differential pressure (P in - P out ), the liquid would continue to vaporize and the pressure at the gauge 24 would remain constant with increasing differential pressure as indicated. However, a multi-component liquid will not exhibit a constant vapor pressure with increasing pressure differential across the eductor throat since the lower molecular weight liquids will typically begin to vaporize at a higher pressure and, when these liquids have vaporized, the suction port pressure will decrease to the vapor pressure of the heavier molecular weight liquids. Accordingly, the selection of a flow condition through the eductor 10 wherein an arbitrarily large pressure differential is created and then decreased to find changes in vapor pressure as indicated by the line 34, as proposed in US-A-4 733 557, will provide an intercept 31 with the curve 30 but very likely not an accurate measure of the actual onset of vaporization or the "bubble point" pressure of the liquid composition in question. For purposes of this discussion, the so-called bubble point pressure or the initial vapor pressure of a liquid composition will be characterized as the true vapor pressure. Certainly for some liquid handling and transport processes, it is necessary to know the "bubble point" pressure or the highest pressure at which onset of vaporization of at least some component of the liquid composition occurs. In Figure 2, the heavy line curve 36 represents the actual vapor pressure characteristic of a multi-component liquid caused to flow through an eductor while increasing the pressure differential across the eductor throat, in accordance with the present invention, to determine the initial or true vapor pressure of the liquid. As indicated by the curve 36 it generally follows the curve 30 to an inflection point 38 wherein the slope of the curve decreases and with incrementally increasing differential pressure (P in minus P out ) the slope continues to decrease. This point 38 is indicative of the value of the true vapor pressure of the fluid being measured. One technique for determining the point 38 in accordance with the present invention is to calculate the second derivative of the function of the suction pressure with respect to the pressure differential across the eductor 10. When the second derivative equals zero, this characteristic marks the point of inflection 38 of the curve 36 and yields the value of true vapor pressure of the fluid composition in question. Determination of the point 38 on the curve 36 by conducting vapor pressure measurements with an improved system in accordance with the present invention will now be described in further detail. The method is carried out by increasing the fluid pressure drop across the eductor 10 incrementally while monitoring the pressure drop versus the pressure at the suction port or chamber 16. The incremental change in the suction pressure for each incremental change in pressure drop or differential pressure across the eductor is compared with the previous value of suction pressure as a function of differential pressure across the eductor and when the slope of the curve changes such that the second derivative of the function which represents the curve 36 equals zero, it is indicated that the point 38 has been reached, which corresponds to the true vapor pressure. In order to be sure that the vapor pressure of the fluid being measured has been reached, further incremental increases in the pressure differential (P in minus P out ) are obtained and the suction pressure at the port 16 measured to be sure that the slope of the curve 36 has continued at the significantly decreased or changed value for a change in the differential pressure across the eductor. In this way, minor variations in the relationship between the eductor suction port pressure and the pressure differential across the eductor, such as indicated at 37 in Figure 2, are detected and ignored. One preferred way of determining the inflection point 38 is to use a curve fitting technique known as a cubic spline fit. The mathematical technique known as a cubic spline fit may be carried out on a digital computer using a program basically of the type described in a publication entitled "Numerical Recipes: The Art of Scientific Computing", by W. H. Press et al, Cambridge University Press. Referring now to Figure 3, there is illustrated in schematic form a diagram of a preferred system for measuring the vapor pressure of a multi-component liquid at in accordance with the invention a particular temperature condition. The system illustrated in Figure 3 is generally designated by the numeral 50 and is shown connected to a fluid transmission pipeline 52 for sampling liquid flowing therethrough to determine its vapor pressure from time to time. The system 50 includes a liquid inlet conduit 54 connected to the pipeline 52 for withdrawing liquid therefrom. Preferably, a general purpose liquid filter 56 is interposed in the conduit 54 upstream of a motorized pressure regulating valve generally designated by the numeral 58. The pressure regulating valve 58 is of a general type which is operable to maintain, at a selected valve operating condition, a predetermined pressure in the conduit 55 downstream of the valve in the direction of flow as indicated by the arrows in Figure 3. Accordingly, for a particular setting of the valve 58, the valve will modulate the flow of liquid through the conduit 54 to maintain the predetermined pressure setting in the conduit on the downstream side of the valve or in the conduit segment indicated by the numeral 55. The conduit segment 55 is connected to the eductor 10 which is disposed in a suitable enclosure 60. The enclosure 60 is preferably fluid tight and adapted to be filled with a heat exchange fluid 63 such as water maintained at a constant temperature so that the temperature of the liquid flowing through the eductor 10 is maintained at a predetermined value while the vapor pressure is being sampled. The enclosure 60 is preferably adapted to be fitted with a liquid level sensor 62 and a heating element 64 which is automatically controlled to maintain the liquid in the enclosure at a predetermined temperature. The sensor 62 is operable to shut off the heating element 64 in the event of a leak or loss of liquid from the enclosure 60. The eductor 10 is connected on its downstream side to a pump 66 by way of an eductor outlet conduit 68. A suitable temperature sensor 70 is also interposed in the outlet conduit 68 for monitoring the temperature of the liquid sample. The pump 66 is connected by way of a discharge conduit 71 to the pipeline 52 for returning the liquid sample being analyzed back to the pipeline flow stream. A suitable flow control switch 72 is interposed in the conduit 71 for monitoring flow of liquid through the system and operating the system to shut down if a continuous flow of liquid sample is not being conducted through the conduits 54, 55, 68 and 71. The operation of the system 50 may be automatically controlled by a digital computer 74 operating through an interface module 76 which is adapted to convert analog data to digital data and vice versa for reading the pressure gauges 20, 22 and 24 and the temperature gauge 70, for controlling the motorized pressure regulator valve 58 and the pump 66 and for controlling the temperature of the heat exchange liquid in the enclosure 60. In the operation of the system 50, the pump 66 is controlled to operate at a volume flow rate which will assure a significant pressure drop across the eductor 10 when the motorized pressure regulator valve is set to maintain a relatively high pressure in the conduit 55 and the inlet port to the eductor 10. In this way a significant pressure drop across the eductor 10 is assured. The computer 74 and the digital/analog interface module 76 are adapted to be operable, when carrying out a vapor pressure measurement routine, to set the pressure regulator valve 58 initially at a relatively low pressure setting for the pressure in the conduit 55 and sufficiently low to provide essentially zero pressure drop (P in minus P out equals zero) condition across the eductor. This is the starting point of the curve 36 at the ordinate of the diagram of Figure 2. The regulator valve 58 is then operated to increase the pressure in the conduit 55 so that incremental changes in the pressure drop across the eductor 10 in increments of, for example, 6.9 kPa (one psi) are recorded. For each reading of pressure drop across the eductor, the suction pressure or pressure at the port 16 is read and recorded. These readings are repeated until the pressure drop across the eductor 10 is well into a region which will be known to produce a vapor pressure reading at the pressure transducer or gauge 24. The data set obtained for each operating cycle is then stored in the computer 74 and utilized to perform a curve fitting function using the cubic spline method to develop the curve 36. By taking the second derivative of the function which defines the curve 36 at each reading, the point 38 may be observed when the second derivative is equal to zero. This reading is noted by the system operating program as the true vapor pressure of the sample being analyzed. Accordingly by measuring the pressure differential across an eductor beginning with a flow condition in the so-called pipe flow regime wherein there is virtually no pressure drop across the eductor throat and increasing the flow to obtain progressively greater pressure differentials across the eductor while recording the pressure in the suction port of the eductor for each pressure differential condition, the onset of vaporization of the highest vapor pressure component of a multi-component liquid, which is the true vapor pressure of that liquid, is more accurately and easily determined than in accordance with prior art processes. Moreover, the unique system for performing this method is effective yet relatively uncomplicated in that the eductor apparatus itself is inherently mechanically simple and reliable. Moreover, by providing a pressure regulator valve which is capable of being set at selected pressure conditions, a set of data points representing the suction port pressure of the eductor for a given pressure differential across the eductor may be easily obtained. Those skilled in the art will recognize that vapor pressure measurements may be taken using the method and system of the present invention for a multi-component as well as single component or pure liquid composition However, the method and system of the present invention is particularly advantageous for making true vapor pressure measurements of various hydrocarbon liquid mixtures including crude oils and certain refined hydrocarbon liquid mixtures.

Claims: A method for determining the bubble point pressure of a multi-component liquid composition which typically exhibits, at a constant temperature, different vapor pressures due to the vaporization of components of different molecular weight in the liquid, whereby the bubble point pressure is determined by passing a sample of liquid through an eductor having an inlet port, a suction port and an outlet port, while a pressure differential between said inlet port and said outlet port and a pressure at said suction port is measured, the method is characterised by: increasing said pressure differential from an essentially zero pressure differential to a pressure differential which lies in a pressure differential range where relatively small changes in the suction port pressure occur for relatively large changes in the pressure differential and measuring the corresponding suction port pressures, establishing a curve where the ordinate of the curve is given by said pressure differentials and the abscissa by said suction port pressures, and determining the point of inflection of said curve. The method set forth in Claim 1 including the step of: increasing the pressure differential between the inlet port and the outlet port of said eductor substantially beyond the pressure differential and the suction port pressure values which provide the point of inflection to confirm that the point of inflection represents the bubble point pressure of the liquid composition. The method set forth in Claim 1 or Claim 2 wherein: increasing the pressure differential between the inlet port and the outlet port of said eductor is carried out by increasing the pressure of the liquid flowing to said inlet port. The method set forth in Claim 1 including the step of: calculating the second derivative of the function of the pressure at the suction port of said eductor and said pressure differential to determine where said second derivative equals zero as an indication of the value of suction port pressure corresponding to the bubble point pressure of said liquid composition. The method set forth in claim 1 wherein: the step of increasing the pressure differential between said inlet port and said outlet port is carried out at a substantially constant temperature of said liquid composition. Apparatus for determining the bubble point pressure of a multi-component liquid composition which typically exhibits, at a constant temperature, different vapor pressures due to the vaporization of components of different molecular weight in the liquid, said apparatus comprises: an eductor (10) including an inlet port (12), a throat portion (14), a suction port (16) downstream of said throat portion and an outlet port (18) downstream of said suction port in the direction of flow of liquid through said eductor, conduit means (55, 68) connected to said inlet port and said outlet port for conducting said liquid composition through said eductor; means (20, 22) for measuring a pressure differential between said inlet port and said outlet port, means (24) for measuring the pressure at said suction port, pump means (66) for causing liquid composition to flow through said eductor, characterised by means (58) for increasing said pressure differential from an essentially zero pressure differential to a pressure differential which lies in a pressure differential range where relatively small changes in the suction port pressure occur for relatively large changes in the pressure differential, means (74) for establishing a curve where the ordinate of the curve is given by said pressure differentials and the abscissa by said suction port pressures, and for determining the point of inflection of said curve. Apparatus as claimed in Claim 6 including: enclosure means (60) for enclosing said eductor (10), said enclosure means providing a space adapted in operation to be filled with a liquid (63) at a substantially constant temperature for stabilizing the temperature of said eductor and said liquid composition flowing through said eductor during a process of measuring the bubble point pressure of said liquid composition. Apparatus as claimed in claim 6 or claim 7 wherein: said means for increasing the pressure differential includes pressure regulator valve means (58) disposed in said conduit means (55) connected to said inlet port (12) for controlling the pressure of said liquid composition flowing to said inlet port to be at a predetermined value for providing a predetermined pressure differential between said inlet port and said outlet port (18); and means (74) associated with said regulator valve means for changing the regulated pressure in said conduit means between said eductor and said regulator valve.

Inventors: REED DONALD B, REED, DONALD B.
Applicants: ATLANTIC RICHFIELD CO, ATLANTIC RICHFIELD COMPANY
Application year: 1990
Main classification: G01N7
IPC codes: G01L13, G01N7