| Abstract |
In this work we explored three alternative methods for optimizing injection schedules based on the concept of tracer transport kernels. The tracer kernel method (Juliusson and Horne, 2011) was extended to thermal transfer models, thus providing the ability to adjust the transport time from injector to producer as a function of the injection rates. This added flexibility of the objective function can add to the applicability of previous injection allocation methods such as those presented by Lovekin and Horne (1989). For the first optimization method we defined an objective function that computes the cumulative mass produced as a function of the injection schedule. It was assumed that by minimizing the mass produced over a given time interval, an injection configuration could be found that approximated the configuration that maximizes heat extraction. In this case, an equality constraint had to be applied to the total injection rate, such that the optimal solution would yield nonzero injection values. The second method was based on predictions of the thermal breakthrough. The objective in this case was to find the injection strategy that maximized the energy extracted from the reservoir over a given project life time. The results were similar to those obtained from the mass minimization method, for the relatively simple test case presented here. The potential advantage of using this method is that it can account for the variability in fracture apertures (or effective heat transfer areas), should that information be available. The final approach was based on the net present value (NPV) of production from the reservoir. In this case an empirical correlation was used to relate the injection and production temperature to the specific electrical power output. This, in conjunction with predictions for the future energy prices and interest rates, allowed the computation of the NPV. The results were interesting in that they suggested that the maximum total injection rate allowable should not necessarily be used. This is believed to be the most realistic model, although many of the parameters and assumptions required are rather hard to prescribe. The results from each of the three optimization method were tested and verified using data from discrete fracture reservoir simulations. The first two methods were tested only on a relatively simple model with two injectors and two producers. The third method (the NPV model) was tested also on a larger flow model which was based on data from the Soultz enhanced geothermal system in France. The results in all cases looked promising. |