## 6 Examples
### Example 1--Design of Cyclic Steam Stimulation Process  
Cyclic steam stimulation (\(CSS\)) has enjoyed great success as an enhanced oil recovery (EOR) process in its broad applications in heavy oil reservoirs. It is widely implemented for its attractive economic efficacy and rapid project response [8]. A typical \(CSS\) project consists of multiple repetitive cycles of (\(i\)) steam injection period, (\(ii\)) soaking period, and (\(iii\)) production period. During each of these three phases of the \(CSS\) process, only one well that serves as an injector and producer is utilized. During the injection stage, superheated steam is injected through the well. The injection period may last 2 to 10 days. Then, the well will be shut in (typically for 5 to 7 days). During this soaking period, the purpose is to create an opportunity for the injected steam to spread itself throughout the reservoir evenly and decrease the viscosity of the heavy and viscous oil. In the third phase of the process, the same well is put on production (typically from several weeks to several months) so that the heated oil with the reduced viscosity can flow more easily towards the wellbore. These three stages of injection, soaking, and production periods will be repeated in a cyclic manner if production rates at the end of each cycle are economical. From this short discussion, it should be clear that in the design of the process it will be important for the design engineer to plan the duration of each stage of the process and the total volume of the steam to be injected. It is not good practice to design a CSS project with fixed time periods of injection, soaking, and production stages. The disadvantage of such a pre-fixed time schedule is that the oil production rate may drop to an extremely low value  
Figure 7: Suggested protocol for finding an optimized ANN architecture.  
when the cycle switches because the energy introduced to the reservoir is not enough to sustain such a long production period as designed, or conversely, the timing of the cycle switching could prove to be premature since the oil production rate is still high. This highly nonlinear behavior of the system makes it more challenging for the expert system to learn. To address this issue [PERSON] and [PERSON] suggest the development of a supervisory ANN, which can be used as a classification tool based on the number of cycles [7]. In other words, a catalogue of sub-ANN models is developed for a fixed number of cycles to predict the oil production rate profiles for projects with different numbers of CSS cycles. At the first phase of the design process, the supervisory ANN will predict the number of cycles that will be necessary for the specific reservoir being studied. Based on the predicted number of cycles, the corresponding sub-ANN will be used to study and understand the performance of the same reservoir. The general workflow of the expert system is defined in Figure 8.  
The supervisory ANN is a fully connected three-layer model with its 78, 83, and 68 neurons on the first, second, and third intermediate layers, respectively. On the input layer with the help of 30 neurons, input parameters involving spatial properties, initial conditions, fluid properties, relative permeability coefficients, and project design parameters including steam quality, steam injection rate, steam temperature, production well bottom hole pressure, well drainage radius, injection duration, soaking duration, and cycle switching rate are provided to the network. As explained above, the output layer with one neuron, simply predicts the number of cycles. Once the number of cycles is learned from the supervisory ANN, the corresponding sub-ANN developed for that specific number of cycles predicts the oil production rate as shown in Figure 9.  
Figure 8: Division of work between the supervisory ANN and sub-ANN models of the CSS process [7].