Abstract
Cyclic steam stimulation (CSS) is one efficient technology for enhancing heavy-oil recovery. However, after multiple cycles, steam channeling severely limits the thermal recovery because high-temperature steam preferentially breaks through to the producers. To solve the issues of steam breakthrough, it is essentially important and necessary to recognize steam channeling. In this work, a machine-learning-assisted identification model, based on a random-forest ensemble algorithm, is developed to predict the occurrence of steam channeling during steam huff-and-puff processes. The set of feature attributes is constructed based on the permeability ratio, steam quality, and steam-injection speed, which provides the reference for the construction of the training-sample set, steam-channeling reconstruction set, and prediction set. Based on the realistic data, the Pearson correlation coefficient is implemented to confirm the linear correlation among different characteristics; thus, the dimension reduction of the characteristic parameters is achieved. The random oversampling method is adopted to treat the unbalanced training-sample set. Our results show that this model can accurately describe the current state of steam channeling and predict steam propagation in the following cycles.
1. Introduction
Thermal enhanced recovery via steam injection has been proven to be an efficient technology for heavy-oil reservoirs [1–3]. The well-known mechanism for thermal recovery is decreasing the viscosity, thus increasing the mobility of heavy oil [4–6]. Cyclic steam injection is one of the most important ways to improve heavy-oil recovery. The steam is injected into the oil layer continuously at a high speed in a relatively short time. After shutting the well, the injected steam gradually permeates the formation by heating the oil for several days. Finally, the well is reopened to produce the low-viscosity heavy oil [7, 8].
The main challenge associated with cyclic steam injection is the occurrence of early steam breakthrough or steam channeling at the production well due to the formation heterogeneity and mobility difference between injected steam and heavy oil [9–11]. The injected steam usually prefers to override the upper layer or direct channels through high-permeability streaks. In either case, injected high-temperature steam bypasses the unswept region of the reservoir, resulting in inefficient use of injected heat and a reduction in the ultimate steam flood oil recovery. In addition, high-velocity vapor entering the wellbore cuts downhole tubulars and leads to severe sanding and other production problems [12, 13].
In this context, some investigations on improving the performance of cyclic steam injection are carried out [14–16]. A novel means of mitigating steam channeling and premature steam breakthrough in steam flooding is to add a high-temperature gel [9, 10, 17, 18]. Gel additives can reduce steam channeling and steam gravity override in mature thermal projects by diverting steam from preexisting steam channels. Therefore, the areal steam sweep efficiency is improved significantly [12, 19, 20]. Another possible way to increase the sweep efficiency of the steam-soak processes is to develop a steam-foam system [21, 22]. The mobility of steam is reduced considerably (e.g., ) due to the presence of foam; thus, the pressure gradient in the steam-swept region increases in a greater order [23–25]. In turn, the increment of pressure gradient can displace the heated oil better and divert steam to the unheated interval [26]. Recently, some innovative techniques, e.g., nanothermal insulation and ultrasonic vibration, have been developed to reduce the energy loss during steam injection [27–29].
Although these methods industrially solve the steam-channeling problems and increase heavy-oil recovery, the expenses, like steam generation, additives, and environmental problems, are relatively high because steam channeling is unpredictable, and a large amount of steam and additives is required [30]. In order to reduce the cost, we need to try to predict the occurrence of steam breakthrough and select effective treatment projects. Many types of reservoir models and data are available for steam-channeling prediction, but the conventional reservoir simulation cannot solely handle such complicated problems. Machining learning, combined with reservoir simulation, has gradually attracted more attention due to its powerful capability and extensibility [31].
The machine-learning technique has been widely used in various applications related to improving heavy-oil recovery [32–34]. The combination of the state-of-art machine-learning method with the advanced reservoir simulator containing the partial differential equations of reservoir fluid flow is a new direction in current reservoir management [35]. It can provide long-term predictive capacity and low computational cost. A simulation-augmented data-driven approach for cyclic steam development is proposed to include field data analysis and integration and mechanistic modeling of the field in interest, thus generating a machine-learning model to evaluate various scenarios, optimize injection job parameters, and assess uncertainties [36]. In addition, machine-learning-assisted field applications, e.g., field surveillance for steam floods, predicting heavy-oil combustion kinetics, and optimization of steam-injection plan in a real field, also verify its ability in multiple petroleum-related projects [37–39].
In this work, we extend the machine-learning technique into predicting the occurrence of steam channeling during cyclic steam injection in heavy-oil reservoirs based on real data from an oil industry. A machine-learning-assisted identification model, based on a random-forest ensemble algorithm, is developed. Three sets, e.g., the training-sample set, steam-channeling reconstruction set, and prediction set, are constructed according to the permeability ratio, steam quality, and steam-injection speed. Considering the realistic data with some uncertainties, a dimension reduction of the characteristic parameters is performed to clean the data. In addition, a random oversampling method is adopted to treat the unbalanced training-sample set.
This work is structured as follows. First, we briefly analyze the steam-channeling mechanisms during steam injection and confirm the dominant parameters which affect the degree of steam breakthrough. Next, we show the criteria for the evaluation of steam channeling and the detailed procedure to construct the machine-learning identification model [40]. Based on this machine-learning model, we then test the feasibility and accuracy of our model in a realistic reservoir. We conclude the paper by summarizing the main conclusions.
2. Analysis of Steam-Channeling Mechanisms
2.1. Model Setup and Parameters
To build the identification model, one needs to figure out the factors which impact steam channeling. Thus, a conceptual model is generated to investigate the key features during the steam huff-and-puff process. Once all factors are confirmed, we can classify them based on the importance evaluation. The model parameters are listed in Table 1. The dimensions of the model are with a fixed block size of . The block size in the direction varies depending on the formation properties. is 0.5 m for the interlayer, while it is 1.3 m for the sandstone formation. The wells are located in the middle of the direction and in the side of the direction. The initial reference pressure is set as 2.4 MPa.
In addition, the viscosity of oil and density (degassed) of heavy oil applied in this work were 16,200 mPa·s at 32°C. According to the composition of the oil sample, the proportions of different components in comprehensive SARA (Saturates, Aromatics, Resins, and Asphaltenes) are 22.0%, 42.5%, 25.0%, and 10.5%, respectively.
2.2. Influence Factors of Steam Channeling
The high-temperature steam preferentially breaks through into the channels with high permeability and porosity. With continuous steam injection, the rock near the well is damaged, leading to the dissolution of clay minerals and the rock skeleton. Further, the rock particles can be divided into an immovable rock skeleton and movable rock particles. Thus, the original porosity and permeability change. In this work, the kinetic reaction model in the CMG-STARS module is used to simulate the variation of permeability due to the steam injection. Taking into account movable rock particles in fluid migration, the kinetic reaction incorporates the removal of movable rock particles from the original rock site. The movable particles are set in the oil phase fluid. In addition, the viscosity linear-interpolation formula is used to calculate the viscosity of the oil phase characterized by movable rock particles.
Figure 1(a) shows the variation of permeability after 4th-cycle steam injection. The channel between two wells forms; therefore, the injected steam floods into the channel and carries the sands moving to the producers. The channel permeability changes from 4000 mD to 4300 mD. However, the region where steam or hot water cannot sweep keeps the same permeability. Figure 1(b) displays the well bottom-hole temperature (BHT) variation with time. As shown, at around 1100 days when PRO1 is injecting steam, the BHT of PRO2 increases abruptly, indicating that the high-temperature steam has arrived there. Once the channel forms, the injected steam of the following cycles can easily penetrate into the neighboring wells if the schedules of the two wells are asynchronous. This time can be used to demonstrate steam breakthrough between two wells.
(a) Permeability variation
(b) Temperature variation (P2)
Except for the change of reservoir permeability and BHT, there are numerous factors affecting the process of steam channeling, including reservoir static properties (e.g., well distance, average permeability, and oil viscosity) and dynamic parameters (e.g., steam-injection pressure, steam quality, and steam temperature). To figure out the underlying influence of different factors, an orthogonal experiment is carried out to confirm the different roles of each factor in steam-channeling formation. For reservoir static properties, we choose the average permeability, oil viscosity, permeability ratio, shale content, and well distance as the main factors. As for dynamic parameters, steam quality, steam-injection speed, soak time, and injection/production ratio play a more important role. The selected values for the orthogonal design are listed in Table 2. After the orthogonal design, 18 experiments are performed to investigate the temperature variation.
Figures 2 and 3 show the temperature distribution when steam channeling forms with the reservoir static parameter and dynamic parameters, respectively. As shown, with different parameters, the shape of channels is distinct. It indicates that these parameters have different impacts on steam channeling. Figure 4 displays the range comparison among various parameters. Regarding reservoir static parameters, the permeability ratio between layers is the critical factor affecting the steam breakthrough. In practice, the injected steam flows along the high-permeability channel, causing a short breakthrough time. The oil viscosity is one important factor but can be relaxed during the construction of the machine-learning model. In terms of dynamic parameters, the injected steam quality plays a vital role in the steam-channeling time. Thus, it should be taken into account in the machine-learning model. The ratio of injection and production rate can be ignored due to their less importance. In principle, the orthogonal experiments confirm the importance of different factors. Based on the real data, we need to relax some criteria.
(a)
(b)
(c)
(a)
(b)
(c)
(a) Static
(b) Dynamic
3. Machine-Learning-Assisted Identification Procedure
3.1. Description of Target Reservoir
The target reservoir consists of 50 wells, and most wells suffer from severe steam breakthrough during steam injection. After multiple cycles of steam injection, the efficiency of steam flooding gets worse due to the limited sweep area and heat loss. Figure 5 displays the current steam channels in the target reservoir. The strong heterogeneity causes a nonuniform distribution of those channels. In addition, there are some bidirectional steam channels; i.e., in two wells, each one injects steam, and another well acting as a sink well produces a lot of steam or hot water.
3.2. Criteria for the Evaluation of Steam Channeling
During the cycles of steam huff-and-puff processes, each well experiences three stages: steam injection, soak, and production. Due to the asynchronous performance of different wells, the possibility of steam channeling among neighbor wells is increased. This process is significantly affected by the current state of the neighboring wells. As shown in the five-spot well pattern in Figure 6, when the central well continuously injects high-temperature steam, it has the potential to break through to the surrounding wells in the corner. In addition, the peripheral wells and the central wells in the neighboring well pattern can be the steam-channeling well pairs, depending on the geological parameters. After a series selection, these static and dynamic indexes are the basic sample set for steam-channeling prediction.
In this work, we select four typical criteria: well distance, well state, well location, and formation properties. Based on these criteria, the possibility of steam-channeling wells is limited to a relatively small range during the steam-injection process. To simplify the problems of interest, three target wells, which satisfy all the criteria, are selected as the potential neighboring wells. The universal attribute set, listed in Table 3, is used to evaluate the possibility of steam channeling. Given that most of the selected data is related to time series with a high dimension and noise, it is necessary to clean the data, thus allowing the model to accurately achieve the prediction.
3.2.1. Transformation of Reservoir Data
There are 50 wells with a 30-year production history (1990–2020) in the target field. During steam huff-and-puff processes, some attributes, such as the steam-injection rate, injection pressure, injection temperature, and steam quality, change with time randomly due to the real-time operation. To make the model more accurate, we transform the raw data and injection and production data of 50 wells in 30 years into around 1000 cycles, which means that each cycle of each well is a standalone sample. Therefore, the sample can deliver more valuable information with a smaller data dimension. The factors affecting steam channeling are preliminarily selected and reduced into a relatively small dimension. The static properties (e.g., permeability and porosity), however, vary with time during the cyclic steam injection. A reconstruction of these properties is crucial to reflect the dynamic change during the development of heavy-oil reservoirs.
The formation porosity and permeability in the near-well region increase after steam injection because high-temperature steam and hot water can dissolve the rock and bring the small particles to a far area. The fluid mobility, thus, is improved, which changes the near-well formation properties. In this work, an empirical correlation is adopted to describe the variation of permeability with steam injection, where is the permeability variation ratio of one layer and and are the certain cycle in the steam huff-and-puff process and the cumulative steam injection of one layer, respectively. The porosity is determined based on the Carmon-Kozeny relation, where and are the permeability at the current state and initial state, respectively. and are the porosity at the current state and initial state, respectively. is a coefficient with a range of . Based on these correlations, the variations of steam injectivity in different layers can be accurately represented after multiple cycles.
In addition, due to the complicated geological characteristics among different layers, one may need to modify the well location in the process of steam injection. To effectively reflect the invisible relation between steam channeling and the change of production layers, it is required to involve layer information in the attribute set. However, this kind of data is discrete and cannot be numerically expressed; thus, the one-hot-encoding technique is implemented to map the layer information in the Euler space [41]. This treatment speeds up the calculation of distance between different features. In this work, the target reservoir contains 7 layers with unique features. For a single well, if it penetrates the layer, the characteristic value is 1; otherwise, the value is 0. The array , for instance, means that at a certain time, the perforations are located in the second and third layers.
3.2.2. Tag Construction of Steam Channeling
The steam-channeling speed is one key factor to express the extent of steam breakthrough during the steam huff-and-puff process, where is the steam-channeling speed, is the well distance between injectors and producers, and is the steam-channeling time. From the history data, and can be confirmed. To simplify the model, the extent of steam channeling in the target area is normalized into a range of .
Aside from the steam-channeling speed, the direction of steam channeling is another key factor that needs to be taken into account. In this work, the steam-channeling radian is introduced to quantitatively express the position of the steam breakthrough. The reference direction is the north, where the injector is located, and the included angle between the injector and producer is the azimuth. The advantage of this treatment is to avoid the model deviation due to the huge order-of-magnitude difference. The range of the steam-channeling radian is , and the tag is −1 if there is no steam breakthrough. Finally, a two-dimension array, , is built to describe the development of steam channeling. and are the normalized speed and the direction of steam channeling, respectively.
Once the tags of all attributes are constructed, we need to reduce the data dimensions because the similar attributes of the input data can cause some unexpected deviations. In this work, a Pearson correlation coefficient is selected to express the explicit or implicit linear relationship among different attributes [42], where is the correlation coefficient between and , is the covariance of and , is the standard deviation of , and is the mathematical expectation of . For a system with attributes, we randomly select and calculate the correlation coefficient between and the rest of the attributes. If the coefficient is greater than 0.8, one of the attributes can be ignored without any significant influence on the final results. Following this criterion, some attributes in Table 3, for instance, steam temperature and porosity, are deleted.
After similarity analysis, there are still too many attributes, which can increase the complexity of the model, especially for the case with a small number of samples. Therefore, further dimension reduction is required to obtain an optimal attribute set. In this work, the tree-based embedded (TBE) approach is implemented to acquire the contribution of each feature. This approach can get the weight coefficients of all attributes based on the training models, and these coefficients represent the importance of each attribute on the contribution to the model construction. The irrelevant and indistinguishable features, thus, are not taken into account. Figure 7 shows the final ranking score with a threshold 0.02 and the attributes selected based on the TBE approach.
In this work, we adopt the method of Table 4 in constructing the steam channeling, which is divided into the baseline data set, reconstruction data set, and prediction data set. The baseline data set is the key to building, training, and validating the machine-learning model. The reconstruction data set uses the trained machine-learning model and obtains the relative steam channel of the whole region. The prediction data set is the assumed periodic data, and the machine-learning model will predict future steam channeling.
3.3. Construction of Machine-Learning Model
The data from the oilfield is not complete, and some reports are missing, which make the construction of the model difficult. In this work, the total samples are divided into base sets, reconstruction sets, and prediction sets. The baseline data set is the key to building, training, and validating the machine-learning model. The reconstruction data set uses the trained machine-learning model and obtains the relative steam channel of the whole region. The prediction data set is the assumed periodic data, and the machine-learning model will predict future steam channeling. The detailed procedure to construct the steam-channeling sample is shown in Table 5.
The random-forest ensemble algorithm, based on the decision tree and the CART (i.e., classification and regression tree), is implemented to construct the steam-channeling identification model. The base classifier of the random-forest algorithm is a decision tree (tree model) that is not pruned, including the root node, middle node, and leaf node. It is a nonparametric supervised-learning method. The root node in the decision tree has only an edge, which represents the attribute of the object. In the prediction of steam channeling, it represents the attributes, e.g., the permeability, formation coefficient, steam quality, and cyclic number of the huff-and-puff process. The middle node has both inlet and outlet edges, and it is also represented as an attribute of the object. The child node has only the inlet side and no outlet side, which represents the label of steam channeling, i.e., the degree and azimuth of steam channeling.
The CART method, taking information entropy as the criterion of splitting, is used in this work to regress the degree and azimuth of steam channeling. Assuming that and are input and output variables, respectively, is an ordinal continuous variable in the steam-channeling-prediction problem. Given the training data set ,
Square difference is adopted in CART to express the prediction error of this regression tree for the training set. The optimal of all in a unit is the average output value with the corresponding :
The variable and the value are selected randomly as the tangent point and tangent variable; thus, two regions, e.g., and , are defined. Then, the optimal tangent point and tangent variable can be confirmed by
All variables are traversed to find the optimal tangent variable , and the input space is divided into two regions. Then, this process is repeated for each region to generate the final CART tree, i.e., the least-square regression tree.
The random-forest algorithm is a statistical-learning theory. It mainly uses bagging sampling technology (with putting back and without weight sampling) to extract subsample sets (/ is about 2/3) from the original sample set . The samples in each sample set may be duplicated. This is precise to prevent the random forest from generating local optimal solutions. Then, decision trees are built based on the above sample sets. Finally, the results of the whole random forest are determined by the classification/regression results of each decision subtree.
In the process of splitting the random forest, attributes are randomly selected from all attributes, according to a certain probability distribution, to split (). The regression accuracy, thus, is improved. The random-forest algorithm first groups the input random variables and then uses the CART algorithm to generate a subtree for each group of variables, so that it can fully grow without pruning. On each node, the random grouping is repeated, and the CART algorithm is recursively used until all nodes are leaf nodes. The construction process is shown in Figure 8, and the model parameters are listed in Table 6.
(a) Forest generation
(b) Decision tree
4. Application of Machine-Learning Model in History Regression and Prediction
4.1. Regression of History Data
Based on the machine-learning model and history data, we carry out the training test. Figure 9 shows the training and validation results based on the random-forest regression model. In terms of steam-channeling degree and direction, both the training model and the prediction model show satisfying accuracy with 95.28% training precision and 92.30% verification precision. In principle, the accuracy can be improved further by implementing other advanced algorithms or adding more parameters to the model; these strategies are beyond the scope of this work. In addition, the random-forest regression model shows good performance in the prediction of the steam-channeling direction due to the repeatability and periodicity of steam channeling; i.e., the random-forest regression model can easily learn and find the intrinsic features of the steam-channeling direction.
(a) Steam-channeling degree
(b) Steam-channeling direction
Figure 10 shows the prediction results of the reconstruction set with 128 samples using the random-forest model. Most samples lie in the bottom-left corner with a value of ; i.e., the high-temperature steam does not break through to the neighboring wells at this moment. In addition, the severity and steam-channeling azimuth are also different. With a similar degree, the azimuth can vary in a large range, which indicates that the formation parameters (e.g., permeability and porosity) and fluid properties (e.g., steam-injection rate and injection pressure) can impact the flow direction of steam in the desired well pattern. The prediction results of the reconstruction set are used to build the steam-channeling field of the whole reservoir with the historical steam-channeling reported data.
4.2. Application of Prediction Model
After the construction of the random-forest prediction model, we can accurately describe the steam channeling in the subsurface and reconstruct the historical degree of steam breakthrough. To quantitatively evaluate the degree of steam channeling, it is normalized into a range of . In particular, for those wells with a high frequency of steam channeling, the amount of cyclic steam injection is integrated into a single curve based on the weighted average value. Figure 11 illustrates the degree of steam channeling in the current well pattern. There are some wells, for instance, well 3511 and well 3612, which suffer from bidirectional steam channeling; i.e., one injector (e.g., well 3511) injects steam, and another producer (e.g., well 3612) produces high-temperature steam, and vice versa. The number of steam channeling in Figure 11 is far less than that of all samples, indicating that there are a large number of repeated channels. In addition, for those wells with long distances, it is hard for steam to break through, but the pressure can propagate, e.g., well 3711 and well 3709. In the bottom-left and upper-right regions, the density of steam channeling is greater due to the short well distance and good formation features. Overall, with multiple cycles of the steam huff-and-puff process, steam channeling exists in most wells to a different degree. These channels severely affect the efficiency of steam injection.
5. Conclusions
In this work, we develop a machine-learning identification model to predict the steam channeling during the cyclic steam-injection process. A conceptual model is constructed to confirm the key factors affecting steam breakthrough. Based on the real data, the machine-learning model is built to regress the steam-channeling history and predict the occurrence in the following cycles. The following conclusions can be made: (i)Some factors may affect steam breakthrough, but can be neglected considering their relatively low importance(ii)The random-forest regression model shows good performance in the prediction of the steam-channeling direction even though some features are missing during the regression(iii)Steam channeling is one complicated process, and it can occur repeatedly. To accurately predict this phenomenon, more factors should be taken into account during the construction of the machine-learning model
Data Availability
No underlying data was collected or produced in this study.
Conflicts of Interest
The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.
Acknowledgments
We thank Mr. Ma for his help and guidance in this work. We also thank the Science Foundation of China University of Petroleum, Beijing (no. 2462022BJRC003) and National Natural Science Foundation of China Joint Fund Project (no. U20B6003) for their finical support.