The Automatic Liquid Level Monitor digitally measures and records the depth to the liquid, the time of the measurement, and the casing pressure of a well at preselected time intervals. These data are used to calculate the bottom-hole pressure to obtain the buildup and drawdown characteristics of a pumping well. Introduction Pressure measurements in producing wells have been Pressure measurements in producing wells have been performed since the early 1920's. Since that time, much performed since the early 1920's. Since that time, much has been published on the importance of pressure tests and methods of analysis in oil and gas wells. Detailed analyses of pressure buildup and drawdown tests are used primarily to determine pump efficiency, formation primarily to determine pump efficiency, formation permeability, reservoir pressure, productivity index, and permeability, reservoir pressure, productivity index, and skin factor. The bottom-hole pressure in flowing wells is relatively easy to obtain with the use of a wireline bottom-hole pressure gauge. However, it is much more difficult to obtain accurate bottom-hole pressure data on pumping wells because of the production tubing and pumping wells because of the production tubing and pump in the well. In an attempt to overcome this pump in the well. In an attempt to overcome this problem, pressure gauges have been developed that mount on problem, pressure gauges have been developed that mount on the bottom of the production tubing. The pressure then is recorded on the surface by means of a cable that is clamped to the tubing. These gauges yield accurate data, but their expense for obtaining information on only one well at a time has limited their use. Some effort also has been made to lower a wireline bottom-hole pressure gauge through the casing annulus, but this, too, generally has proved to be impractical Acoustic well sounding of the liquid level in producing wells has received wide acceptance in the field and can be used to calculate the actual bottom-hole pressure. Several different types of manually operated well sounders presently are available. Each of these devices requires the presently are available. Each of these devices requires the operator to initiate the acoustic pulse into the well casing and to interpret a resultant strip chart, which records the reflections from the tubing collars and the liquid interface. The distances between the collar reflections are measured and are used to determine the depth to the liquid level. To define the shape of a buildup curve, it is necessary to obtain a large number of soundings over a long period of time. Because of the excessive operator time period of time. Because of the excessive operator time required to obtain these readings, the manually operated sounder seldom is used in this way. The Automatic Liquid Level Monitor, developed by Mobil Research and Development Corp., overcomes this difficulty so that the liquid level during buildup and drawdown tests can be measured automatically often enough and long enough to provide an accurate measure of the shape of the bottom-hole pressure curves. This is a digital system that prints out not only the actual depth to the liquid level in feet, but also the time of the sounding and the casing pressure, These measurements are made automatically on a preselected schedule without having an operator in attendance. Description of the Automatic Liquid Level Monitor The Automatic Liquid Level Monitor uses the same method of acoustic well sounding as do the manually operated devices. However, instead of determining the liquid depth by counting tubing collars, the travel time of the acoustic pulse is measured accurately by counting the number of pulses from a very precise 1-MHz crystal-controlled oscillator. This system yields a high degree of sensitivity to the liquid movement in a well with a precision limited only by the initial calibration of the monitor and the stability of the oscillator. JPT P. 1019
A novel technique for estimating the asymptotic stability region of nonlinear autonomous polynomial systems is established. The key idea consists of examining the optimal Lyapunov function (LF) level set that is fully included in a region satisfying the negative definiteness of its time derivative. The minor bound of the biggest achievable region, denoted as Largest Estimation Domain of Attraction (LEDA), can be calculated through a Generalised Eigenvalue Problem (GEVP) as a quasi-convex Linear Inequality Matrix (LMI) optimising approach. An iterative procedure is developed to attain the optimal volume or attraction region. Furthermore, a Chaotic Particular Swarm Optimisation (CPSO) efficient technique is suggested to compute the LF coefficients. The implementation of the established scheme was performed using the Matlab software environment. The synthesised methodology is evaluated throughout several benchmark examples and assessed with other results of peer technique in the literature.
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