A New Methodology for the Optimization of the Placement of Downhole Production-Monitoring Sensors
- G. Nævdal (RF-Rogaland Research) | E. Vefring (RF-Rogaland Research) | A. Berg (RF-Rogaland Research) | T. Mannseth (RF-Rogaland Research) | J.E. Nordtvedt (RF-Rogaland Research)
- Document ID
- Society of Petroleum Engineers
- SPE Journal
- Publication Date
- March 2001
- Document Type
- Journal Paper
- 108 - 116
- 2001. Society of Petroleum Engineers
- 5.5 Reservoir Simulation, 2.2.2 Perforating, 5.1 Reservoir Characterisation, 4.2 Pipelines, Flowlines and Risers
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A new methodology for designing the placement of production-well-monitoring sensors is presented. With a well-flow simulator, we estimate the inflow profile of a production well and solve the inverse problem associated with the mathematical model for fluid flow in the well. The accuracy in the estimated inflow profiles using different types and placements of sensors can be computed, and an efficient way to search for an instrumentation layout is presented.
Knowledge of the inflow profile is important for optimal control of a production well. It also gives useful information for reservoir characterization and thereby helps to increase the oil recovery. Information about the inflow profile can be obtained from measurements in the well. To keep the cost low, while still getting the maximum benefit from the measurements, the sensors must be optimally placed.
The use of downhole pressure and temperature sensors is increasing, and the technology for making other measurements is rapidly advancing. New technology also increases the opportunity for the engineers to control the production by shutting off water-producing zones.
With the methodology we have developed, we can estimate the inflow profile of a production well. An analysis for comparing how well an inflow profile can be estimated with different instrumentation layout is presented. Moreover, a search for an efficient design of the instrumentation layout can be done to get low error bounds on the estimated inflow profile. Cost constraints on the well instrumentation can be taken into account, and use of redundant sensors can be avoided. With the methodology presented, it is possible to obtain guidelines for the design of optimal placement of monitoring instrumentation in existing and future wells.
Through a series of examples, we show that by selecting the correct instrumentation layout, one can obtain great improvements in the accuracy of the estimated inflow profile. We also include an example on estimating the inflow profile.
A schematic picture of an instrumented well is shown in Fig. 1.
Because we do not have any direct access to the inflow profile of the well, an indirect approach is needed to determine the inflow profile. For a given inflow profile, a well-flow simulator can compute the values that different instruments located at different positions in the well will sense. This makes it possible to compare the measured data with simulated data for different inflow profiles and to search for profiles that will reconcile the measured data.
The Well-Flow Simulator.
Based on recent developments in the modeling of two-phase flow in both horizontal1 and inclined2 wells, we have developed and implemented a well-flow simulator. The calculation of fluid flow in the well is based on conservation of mass, momentum, and energy. We use a steady-state formulation. The conservation of mass is given by the following system of equations for oil, gas, and water, respectively.
A set of equations describing conservation of momentum (Eqs. A-1 through A-3) and a combined energy equation (A-4) are shown in the Appendix. We want to determine the space-dependent quantities of the source terms uo, uw, and ug, representing the inflow of oil, water, and gas to the well.
In the formulation of the equations for mass conservation, we use the black-oil model.3 Based on pressure/volume/temperature (PVT) input data, the superficial velocities are calculated at all locations in the well. This will define the flow regime at all locations. Then, from conservation of momentum, the pressure drop can be calculated. Thus, measurable quantities such as pressure drop, phase velocities, and phase fractions may be calculated. Conservation of energy yields the temperature distribution.4
Estimation of Inflow Profiles.
The inflow profile can be estimated with our well-flow simulator and measurements of physical quantities in the well. The well-flow simulator can, given an inflow profile, compute simulated values of the observables. The estimation of the inflow profile is done by searching for inflow profiles that reconcile the measured data.
To estimate the inflow profile, we make the simplifying assumption that the inflow rates for each of the three phases are constant in n specified zones of the well. This means that the inflow profile can be expressed by a vector containing 3n parameters. Hence, the simulated values are functions of the same parameters. The estimation of the inflow profile is done by finding the vector such that
is minimized. In the expression above, yi,obs=the value obtained at sensor i,fi( )=the simulated value for sensor i with inflow given by the parameter vector , and si=the standard deviation of sensor i.
To solve this weighted-least-squares problem, the Levenberg-Marquardt method is used.5 The existence of different flow regimes in the modeling of the well flow gives, in many cases, rise to local minima of the least-squares problem. The Levenberg-Marquardt algorithm efficiently computes an inflow profile that is a local minimum of the weighted-least-squares problem, but the estimated inflow profile might depend on the choice of initial value in the algorithm. This problem is overcome by running the algorithm several times with different initial values. A heuristic approach is used to find reasonable start values. The final estimate of the inflow profile is the profile that minimizes the least-squares expression.
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