## 4 Results and Analysis
### Exploration of the Transport and Settlement Laws of Proppant Based on Artificial Intelligence  
As mentioned above, the migration and settlement laws of backflow proppant after fracturing tight sandstone are affected by various factors such as construction factors and rock conditions. Currently, development mainly relies on the experience of engineering personnel. However, in the continuous construction of digital and green oilfields, improving quality and efficiency have become important goals for reservoir extraction. Therefore, it is particularly important to clarify the transport and settlement patterns of backflow proppants. In actual production, it is often difficult to establish an accurate mathematical model for backflow proppants to determine the optimal solution. This article considers introducing a multi-task learning network (MTLN), which has the capacity for multiple inputs and outputs and can adapt to the influence of multiple physical parameters on proppants. At the same time, through iterative learning of multiple hidden layers and continuous weight correction, it can effectively fit any mathematical mapping relationship, thus avoiding the problem of difficulty in establishing an accurate mathematical model for backflow proppants. The proposed MTLN algorithm process includes the following: (1) network topology determination. This article intends to select construction operation parameters (construction displacement, time, sand ratio, and total operation time), particle size, viscosity, and density of proppant as input layers, with a total of seven items as input layers. The input matrix is represented as \([i_{1},i_{2},i_{3},i_{4},i_{5},i_{6},i_{7}]\), the output layer is the settling velocity and equilibrium height of proppant particles, the output matrix is represented as \([o_{1},o_{2}]\), and the hidden layer can be determined by \(c=\sqrt{a+b}+q\mathbb{L}\). \(a\) and \(b\) represent the number of nodes in the output layer and the hidden layer, respectively, and \(q\) is an adjustable constant. (2) As mentioned earlier, the influencing factors of backflow proppant and settlement law indicators contain multiple physical parameter dimensions, and their numerical differences are significant. To prevent masking low-range data changes and resulting in poor training effectiveness, the maximum normalization method \(X_{norm}=\frac{X}{[X_{max}]}\) is used to map the data to the [\(-\)1,1] interval. (3) Taking the production data of a tight sandstone proppant as examples, model training was organized into 1000 sets of datasets, with 70 randomly selected as the training sets and the remaining 30% as the testing sets. Table 2 presents 20 sets of data, with the first 70% being the training sets and the rest being the testing sets. Figure 3 shows the training fitting effect of the proposed MTLN algorithm. It can be seen from the figure that the proposed model can fit the input-output relationship well, effectively supporting the study of proppant transport and settlement laws. Figure 2: Multi-dimensional factors affecting the transport and settlement patterns of proppants. The migration and settlement laws of backflow proppant after tight sandstone fracturing are important issues in unconventional oil and gas extraction, which is of great value for production planning and development plans. For a long time, the extraction of long-term gas reservoirs has mostly relied on the experience and judgment of engineering and technical personnel. The core of this method lies in the accumulation and effective judgment of technical personnel, which has significant engineering value in the development of conventional gas reservoirs. However, as oil and gas extraction gradually enters unconventional gas reservoirs, the engineering physical environment has undergone significant changes, and the drawbacks of this method, such as low accuracy in judgment and difficulty in replication and promotion, have gradually become apparent.