New sensors have been developed for measuring in-situ fluid density that are based on the natural vibration of a structural member in contact with fluids being sampled using a wireline pumpout formation tester. Typically, a fluid-conveying tube is driven to its natural frequency and the frequency changes with fluid density. This design has the potential to greatly enhance the downhole fluid density measurement capability. However, the physical characterization and subsequent calibration of the sensor had to be proven for the harsher downhole environment. Although the principle for the vibrating density sensor is simple, a long list of factors, such as temperature, pressure, and tension, directly or indirectly affect the response of the sensor.
Experimental correlations are typically used to calibrate this type of sensor. However, in this paper, we systemically study all of these factors and derive a differential equation that fully describes the physics of the vibrating tube densitometer based entirely on first principles. This is followed by the solution of the equation and its subsequent application to laboratory test results as part of the sensor calibration process. Comparisons between theoretically predicted density values for various fluids and their known fluid density values show this method to be more robust than previous correlations methods. An accuracy of better than +/- 0.002 gm/cm3 over the pressure range of 0 to 20,000 psi and a temperature range of 75 to 350° F under controlled conditions is achievable. The resolution of the sensor can also be better than 0.001 gm/cm3. Experimental results and field examples are presented to demonstrate the accuracy and resolution of the sensor.
Introduction
A pumpout wireline formation tester (PWFT) is a tool routinely used by operators to collect pressure, volume, and temperature (PVT) reservoir fluid samples. Among the long list of sensors included in the PWFT, the in-situ fluid density sensor plays crucial roles because an accurate determination of the formation fluid density under reservoir conditions is one of the fundamental objectives of formation evaluation. The importance of accurate density is reflected in the number of applications in which in-situ density is essential, such as pressure gradient analysis, fluid contacts, zonal compartmentalization analysis, delineation of oil-water transition zones, contamination analysis during sampling, and fluid identification analysis for immiscible fluids.
Pressure gradient analysis based on PWFT pressure surveys has long been a fundamental method of determining fluid types because the in-situ moveable fluid density is directly related to the fluid type. However, there are well-known inherent uncertainties associated with errors in the gradient as a result of inaccuracy in the depth and pressure measurement (Collins et al. 2007). Furthermore, complications in the wellbore environment, such as invasion, supercharging, depletion, formation wettability, and capillary pressure effects (Desbrandes et al. 1988 and Carneigie 2007) combine to introduce additional errors. Therefore, although the practice of using pressure gradient has been one of the primary methods of determining fluid density since its introduction in the 1970s (Pelisser-Combescure et al. 1979), a direct in-situ measurement of fluid density that can overcome these complications is still highly desirable.
Various methods have been adapted for density measurement (Godefroy et al. 2008). There are currently two types of sensors for in-situ downhole fluid density measurement; both are based on the principle of measuring the resonance frequency of a vibrating member in contact with fluid. One type has one or more vibrating elements submerged in the flow line (O'Keefe et al. 2007). The disadvantage of this type of sensor is its limited volume of investigation. Although the sensor is fully immersed in the fluid stream, it is sensitive only to a boundary layer in the immediate vicinity of the vibrating sensing element. Thus, it may inherently have problems in measuring multiphase liquids (Webster 1999).
