A New Method for Determining the Specific Gravity of Paraffin
Abstract Generated abstract
This paper addresses the practical difficulty of determining the specific gravity of paraffin, whose density is typically lower than that of water and therefore cannot be measured by ordinary hydrostatic weighing. It proposes a simplified method that attaches a sinker to the paraffin sample, measures the sinker alone and the sinker with paraffin in water or another liquid, and uses the resulting buoyancy difference to calculate the sample volume and specific gravity. The method is presented as less accurate than matching the paraffin density with a water and alcohol mixture, but potentially useful when alcohol is unavailable, especially in applications such as rock porosity determination.
Full Text
A NEW METHOD FOR DETERMINING THE SPECIFIC GRAVITY OF PARAFFIN
L. A. Pukhlyakov
(Submitted by the Department of Fossil Fuels)
In determining the specific gravity of rocks, first, the weight of the body in air \((P_1)\) is found; second, its weight in water \((P_2)\); third, the specific gravity of water \((\gamma_{\mathrm{w}})\) is determined, and the calculation is carried out by the formula
\[ \gamma_{\mathrm{t}}=\frac{P_1\cdot \gamma_{\mathrm{w}}}{P_1-P_2}. \tag{1} \]
The specific gravity of paraffin, as a rule, lies within the range from \(0.88\ \mathrm{g/cm^3}\) to \(0.915\ \mathrm{g/cm^3}\). Therefore it is not possible to determine its weight in water, and in cases when it is necessary to know accurately the specific gravity of one or another grade of paraffin, this is done by obtaining a mixture of water and alcohol of the same specific gravity as the given paraffin sample [1]. This method has rather high accuracy; however, very often, because of the absence of alcohol, it is impossible to apply it. Meanwhile, sometimes—for example, in determining the porosity of rocks—the need for this is very acute. Here a new method is proposed for determining the specific gravity of paraffin, based on the same principles as in determining the specific gravity of rocks that sink in water. This method does not have the accuracy of the method using alcohol; nevertheless, under certain conditions it will find application.
To derive the formula of the new method, let us assume that a piece of paraffin with a volume of \(1\ \mathrm{cm^3}\) has a weight in air of \(0.89\ \mathrm{g}\) and that it is submerged in a liquid with a specific gravity of \(1.0\ \mathrm{g/cm^3}\). Obviously, a buoyant force of \(1\ \mathrm{g}\) will act on it, and \(89\%\) of this force will be compensated by the proper weight of the paraffin sample, while \(11\%\) will create an excess. An analogous ratio of forces will also occur in those cases when the volume of the paraffin sample is not equal to \(1\ \mathrm{cm^3}\). From what has been said it follows that, in order to determine the volume of this sample, it is sufficient to find its weight in air \((P_1)\) and add this weight to the excess buoyant force in a liquid whose density is \(1.0\ \mathrm{g/cm^3}\). This excess, in turn, can be determined in the following way: attach a sinker to the paraffin piece under study and find its weight with the sinker in water \((P_4)\), then find the weight of this sinker in water without the paraffin \((P_3)\), and subtract one from the other. Thus, the volume of the sample will be determined by the relation
\[ V_{\text{p}} = P_1 + (P_3 - P_4), \tag{2} \]
or, if the specific gravity of the liquid is not equal to \(1.0\ \text{g}/\text{cm}^3\), by the relation
\[ V_{\text{p}} = \frac{P_1 + (P_3 - P_4)}{\gamma_{\text{l}}}. \tag{3} \]
Hence, the specific gravity of paraffin is determined by the relation
\[ \gamma_{\text{p}} = \frac{P_1 \cdot \gamma_{\text{l}}}{P_1 + (P_3 - P_4)}. \tag{4} \]
Literature
- F. I. Kotyakhov. Fundamentals of the Physics of the Oil Reservoir. Gostoptekhizdat, 1956.