Evaluation of Steam Channeling Severity Between Cyclic Steam Simulation Wells in Offshore Heavy Oil Reservoirs Based on Cloud Model and Improved AHP-CRITIC Method

Abstract

Steam channeling significantly affects the production performance of cyclic steam stimulation (CSS) wells in offshore heavy oil reservoirs. However, there remains a lack of effective methods for evaluating the steam channeling severity between CSS wells in offshore heavy oil reservoirs. This study develops a novel evaluation model to quantitatively evaluate the steam channeling severity between CSS wells in offshore heavy oil reservoirs via the improved AHP-CRITIC (IAHP-CRITIC) method and the cloud model. The results indicated that, compared with the reservoir survey results for the three typical reservoirs, the accuracies of the results obtained by the AHP, CRITIC, AHP-CRITIC, and IAHP-CRITIC methods were 88%, 52%, 92%, and 100%, respectively. Therefore, the IAHP-CRITIC method was more reliable than the other methods in terms of calculating the indicator weights and evaluating the steam channeling severity between the CSS wells. The Lw7 and Lw12 in the L reservoir and Rw2, Rw3, and Rw6 in the R reservoir exhibited strong steam channeling. It is necessary to control the steam channeling of these CSS wells. This is the first study to report the evaluation of steam channeling severity between CSS wells in offshore heavy oil reservoirs. This study provides an effective model to quantitatively evaluate the steam channeling severity between CSS wells and offers valuable insights for the selection of effective strategies to control the steam channeling between CSS wells and enhance offshore heavy oil recovery.

1. Introduction

The ongoing global pandemic, economic downturn, and sustained low oil prices have driven increased demand for hydrocarbon resources worldwide [1]. With the progressive depletion of conventional onshore oil reserves, significant attention has shifted toward exploiting heavy oil reserves in offshore reservoirs [2,3]. Notably, China’s Bohai Bay contains proven heavy oil reserves exceeding 4 billion metric tons [4]. Cyclic steam stimulation (CSS) has emerged as a predominant thermal method for heavy oil reserves and has been successfully implemented in multiple offshore heavy oilfields within Bohai Bay. Despite its popularity and success, CSS is not devoid of limitations or inherent inefficiencies. During the early cycles of the CSS process, thermal energy effectively mobilizes heavy oil near the CSS wells, yielding satisfactory performance (Figure 1a). However, as the number of CSS cycles increases, reservoir thermodynamic conditions change and increase the possibility of steam channeling between CSS wells [5,6]. This phenomenon occurs when steam preferentially flows through high-permeability zones or overrides the oil layers, which reduces the thermal efficiency and substantially impairs the production performance of the surrounding CSS wells (Figure 1b).

Many factors affect the steam channeling between CSS wells, including reservoir heterogeneity, fluid saturation distribution, well spacing, etc. [7]. Therefore, the steam channeling severity varies among different CSS wells, making it difficult to conduct a quantitative evaluation. This significantly hinders the selection of effective strategies to control steam channeling between CSS wells and enhance offshore heavy oil recovery.

The multi-well CSS process is a complex system, and steam channeling emerges from the coupled interaction of multiple factors rather than any single variable. In previous studies, either only the influence of a single indicator on steam channeling severity was considered or the relative importance relationships between evaluation indicators were neglected, resulting in poor evaluation accuracy. For instance, Li et al. [8] calculated the temperature variation in surrounding CSS wells via reservoir simulations to determine the steam channeling severity during the CSS process. Zheng et al. [9] identified steam channeling wells according to the water cut and temperature during steam flooding processes. Zheng et al. [10] assessed the steam channeling severity during steam flooding processes on the basis of the increased liquid production rate, water cut, and temperature. To our knowledge, there is a lack of effective methods for evaluating the steam channeling severity between CSS wells in offshore heavy oil reservoirs.

The cloud model, which is grounded in probability theory and fuzzy set theory [11], has proven to be an effective evaluation method in diverse engineering applications. Its successful implementations include the evaluation of pedestrian—vehicle conflicts, straddle-type monorail systems, and medical equipment. Chen et al. [12] integrated the entropy method, gray relational analysis, and analytic hierarchy process (AHP) to determine the weights of the indicators and used the cloud model to evaluate the pedestrian–vehicle conflict. Similarly, Wen et al. [13] developed a safety assessment model for monorail systems by combining a CRITIC (criteria importance through intercriteria correlation) method with the cloud model. In the medical domain, Zhang et al. [14] established a comprehensive evaluation system incorporating operational status, utilization efficiency, and service quality metrics, where the subjective and objective weights were derived through the AHP and entropy weight methods, respectively.

The aforementioned literature demonstrates that the cloud model has the potential to evaluate the steam channeling severity between CSS wells and involves a critical process of calculating the indicator weights.

Currently, the subjective calculation methods for indicator weights include the AHP [15], fuzzy comprehensive evaluation [16], gray correlational analysis, etc. Among these methods, the AHP is the predominant approach for calculating indicator weights [17]. It decomposes a complex problem into interconnected factors organized in a hierarchical structure and determines the indicator weights through expert scoring. However, the AHP also presents several limitations, such as high subjectivity that may compromise reliability, a requirement for consistency verification in each calculation that increases the computational burden, and particular challenges when handling systems with numerous indicators [18].

In addition, objective calculation methods, including the entropy method [19], factor analysis, and CRITIC, are widely used for indicator weight determination [20]. Among these, CRITIC demonstrates particular effectiveness in handling interdependent indicators [21]. However, conventional CRITIC approaches exhibit limitations when applied to multidimensional indicators with nonlinear distribution patterns [22]. Such indicators often present significant dispersion characteristics [23], which conventional CRITIC methods fail to account for during computation, potentially compromising weight calculation accuracy.

This study develops a novel evaluation model to quantitatively evaluate the steam channeling severity between CSS wells in offshore heavy oil reservoirs via the improved AHP-CRITIC (IAHP-CRITIC) method and the cloud model. First, an indicator system for the steam channeling severity on the basis of monitoring and production data was established. To integrate the advantages of both objective and subjective weights and overcome the limitations of the conventional AHP and CRITIC methods, the IAHP-CRITIC method was subsequently proposed to calculate the combined weights. To the best of our knowledge, there is no report in the literature about the use of the IAHP-CRITIC method in the cloud model. Finally, the proposed model was used to evaluate the steam channeling severity between cyclic steam stimulation (CSS) wells in three typical offshore heavy oil reservoirs. This is the first study to report the evaluation of steam channeling severity between CSS wells in offshore heavy oil reservoirs. This study provides an effective model to quantitatively evaluate the steam channeling severity between CSS wells and offers valuable insights for the selection of effective strategies to control the steam channeling between CSS wells and enhance offshore heavy oil recovery.

2. Methodology

The workflow for evaluating the steam channeling severity between CSS wells is illustrated in Figure 2, which comprises three key steps: (1) construction of the indicator system, (2) calculation of combined weights, and (3) evaluation of steam channeling severity between CSS wells.

2.1. Construction of the Indicator System

When steam channeling occurs between CSS wells, the monitoring data and production data of the surrounding CSS wells significantly change, such as an increase in water cut, temperature, and cumulative water production in each cycle, etc. On the basis of the aforementioned characteristics of steam channeling between CSS wells, a two-layer indicator system was established. The first layer includes two basic parameters: the monitoring data and production data. The second layer contains 6 indicators: the water cut increment, steam breakthrough time, temperature increment, cumulative liquid production in each cycle, cumulative water production in each cycle, and cumulative oil production in each cycle (Figure 3).

2.2. Calculation of Combined Weights

2.2.1. Improved AHP (IAHP) Method

The conventional AHP, originally developed by Saaty [24] in the 1970s, is a hierarchical decision-making framework based on network system theory [25]. Because of its strong subjectivity, it is widely used for subjective weight determination. However, the conventional AHP presents two notable limitations: significant subjectivity in expert judgments and computationally intensive consistency verification requirements for each calculation [26]. These limitations become particularly pronounced when systems with numerous indicators are used. In this study, we implemented an IAHP method to determine subjective weights, with the procedure detailed below [27].

(1)

Construction of a judgment matrix A:

$$A={\left(a_{ij}\right)}_{n\times n}(i, j=1,2,3,\dots ,n)$$

(1)

where a_ij represents the relative importance of the i-th indicator compared to the j-th indicator. Its reciprocal a_ji represents the inverse relationship. n is the indicator number.

The following equations are satisfied [28]:

a_ij = 1/a_ji,  a_ij > 0,  a_ii = 0

(2)

The proportional relative formula (W_i/W_j) is used to determine the a_ij values. W_i and W_j represent the relative distributions of the i-th and j-th indicators, respectively, and W_i + W_j = 1 is satisfied.

(2)

Construction of an antisymmetric matrix

Let b_ij = lg a_ij; the antisymmetric matrix B is obtained, where $B={\left(b_{ij}\right)}_{n\times n}$ and b_ij = −b_ji is satisfied.

(3)

Construction of the optimal transfer matrix

The c_ij is determined based on b_ij:

$$c_{ij}={\displaystyle \frac{1}{n}}{\displaystyle \sum _{k=1}^n(b_{ik}-b_{jk})}(k=1,2,\dots ,n)$$

(3)

where b_ik is the value in the i-th row and k-th column of matrix B and b_jk is the value in the j-th row and k-th column of matrix B. When ${\displaystyle {\sum }_{i=1}^n{\displaystyle {\sum }_{j=1}^n{(c_{ij}-b_{ij})}^2}}$ is minimized, the optimal transfer matrix C satisfies $C={\left(c_{ij}\right)}_{n\times n}$.

(4)

Construction of the optimization matrix:

$$A*={\left(a_{ij}^{*}\right)}_{n\times n}$$

(4)

where $a_{ij}^{*}={10}^{C_{ij}}$.

(5)

Determination of the subjective weight of the i-th indicator ω_i:

$${\omega }_i={\displaystyle \frac{{\displaystyle \sum _{j=1}^n\frac{a_{ij}^{*}}{{\displaystyle {\sum }_{i=1}^n{a}_{ij}^{*}}}}}{{\displaystyle \sum _{i=1}^n{\displaystyle \sum _{j=1}^n\frac{a_{ij}^{*}}{{\displaystyle {\sum }_{i=1}^n{a}_{ij}^{*}}}}}}}$$

(5)

2.2.2. Improved CRITIC (ICRITIC) Method

The conventional CRITIC method demonstrates superior performance over the entropy method for determining objective weights, primarily through its consideration of both indicator conflict and contrast intensity [29]. However, this approach fails to account for data dispersion characteristics. To address this limitation, we incorporated information entropy into the CRITIC method [30]. This enhancement enables simultaneous evaluation of interindicator conflicts, contrast intensity, and data dispersion patterns. The procedure for this ICRITIC method is detailed below.

(1)

Normalization of the dimensional heterogeneity among indicators

The original indicator data were standardized to obtain $G={\left(g_{ij}\right)}_{n\times m}$, where m is the number of CSS wells in an offshore heavy oil reservoir.

(2) Calculation of the information entropy δ_i for the i-th indicator g_i:

$${\delta }_i=-{\displaystyle \frac{1}{\ln m}}{\displaystyle \sum _{l=1}^m\frac{g_{il}}{{\displaystyle {\sum }_{l=1}^m{g}_{il}}}}\ln {\displaystyle \frac{g_{il}}{{\displaystyle {\sum }_{l=1}^m{g}_{il}}}}(i=1,2,\dots ,n;l=1,2,\dots ,m)$$

(6)

where g_il represents the value of g_i of the l-th CSS well in matrix G.

(3)

Calculation of the standard deviation σ_i of indicator g_i and the correlation coefficient $r_{ij}$ between indicators g_i and g_j.

$${\overline{g}}_i={\displaystyle \frac{1}{m}}{\displaystyle \sum _{l=1}^m{g}_{il}}$$

(7)

$${\sigma }_i=\sqrt{{\displaystyle \frac{{\displaystyle \sum _{l=1}^m}{\left(g_{il}-{\overline{g}}_i\right)}^2}{m-1}}}$$

(8)

$$r_{ij}={\displaystyle \frac{{\displaystyle \sum _{l=1}^m\left(g_{il}-{\overline{g}}_i\right)\left(g_{jl}-{\overline{g}}_j\right)}}{\sqrt{{\displaystyle \sum _{l=1}^m{\left(g_{il}-{\overline{g}}_i\right)}^2}}\sqrt{{\displaystyle \sum _{l=1}^m{\left(g_{jl}-{\overline{g}}_j\right)}^2}}}}$$

(9)

where ${\overline{g}}_i$ and ${\overline{g}}_j$ are the average values of indicators g_i and g_j, respectively, and σ_i denotes the standard deviation of indicator g_i.

(4)

Calculation of the information content C_i for indicator g_i:

$$C_i=({\sigma }_i+{\delta }_i){\displaystyle \sum _{j=1}^n}\left(1-\left|r_{ij}\right|\right)$$

(10)

(5)

Calculation of the objective weight of indicator g_i (${\xi }_i$) as follows:

$${\xi }_i={\displaystyle \frac{C_i}{{\displaystyle {\sum }_{i=1}^n{C}_i}}}={\displaystyle \frac{({\sigma }_i+{\delta }_i){\displaystyle \sum _{\mathrm{j}=1}^n}\left(1-\left|r_{ij}\right|\right)}{{\displaystyle {\sum }_{i=1}^n({\sigma }_i+{\delta }_i){\displaystyle \sum _{\mathrm{j}=1}^n}\left(1-\left|r_{ij}\right|\right)}}}$$

(11)

2.2.3. Combined Weights

In this study, the IAHP method was used to determine the subjective weights on the basis of the subjective experience of the experts from offshore heavy oil oilfields, whereas the ICRITIC method was used to calculate the objective weights on the basis of the data from the CSS wells. The combined weights were subsequently calculated on the basis of the subjective and objective weights. This method makes use of both subjective experience and the dependability of objective data [31]. The calculation method for the combined weights w_i is described as follows:

$$w_i=\phi {\omega }_i+(1-\phi ){\xi }_i$$

(12)

where φ is a constant, which is 0.8 in this study.

2.3. Construction of the Cloud Model

2.3.1. Cloud Model

(1)

Concept of the cloud model

The cloud model is a sophisticated approach for uncertainty evaluation, grounded in the principles of probability theory and fuzzy set theory [32]. Consider a qualitative domain denoted as U, with C representing the corresponding qualitative concept defined over U. Assume that x is a random variable that adheres to a normal distribution, where x ∈ U, and the membership degree of x to C is a random variable characterized by a stable tendency that satisfies specific probabilistic conditions. In this framework, x and its distribution are defined as cloud droplets and clouds, respectively.

The uncertainty associated with x is articulated by cloud parameters: Ex signifies the mathematical expectation of cloud droplets in their spatial distribution, thereby reflecting the central position of the cloud. En, termed entropy, quantifies the dispersion of cloud droplets, dictating the permissible degree of certainty for cloud droplets within the spatial distribution, and is influenced by both qualitative concepts and inherent randomness. He, known as hyper entropy, acts as a metric of uncertainty to represent entropy, capturing the thickness or density of cloud droplets. The values of these cloud parameters can be computed as follows:

$$\left\{\begin{array}{l}Ex={\displaystyle \frac{1}{m}}{\displaystyle \sum _{i=1}^m{x}_i}\\ En={\displaystyle \frac{{\displaystyle \sum _{i=1}^m{(x_i-\overline{x_i})}^2}}{m-1}}\\ He=y\end{array}\right.$$

(13)

where x_i represents the indicator data of the i-th CSS well; y is equal to 0.005 in this study.

(2)

Cloud generator

Cloud generators are utilized primarily to facilitate the interchange between qualitative concepts and quantitative data, encompassing both forward and backward cloud generators, as depicted in Figure 4. The forward cloud generator (CG) serves to transform cloud parameters into cloud maps, thereby enabling the intuitive visualization of numerical ranges and their associated distribution patterns. In contrast, the backward cloud generator (CG⁻¹) operates as the inverse process of the forward cloud generator, converting cloud maps back into accurate cloud parameters.

2.3.2. Standard Evaluation Cloud (SEC)

According to the production experiences of CSS wells, the steam channeling severity is divided into five levels, “No steam channeling”, “weak steam channeling”, “moderate steam channeling”, “strong steam channeling”, and “extremely strong steam channeling”, which are labeled as levels 1–5, respectively. These five levels were scored between 0 and 1, and the golden ratio was used to determine the value ranges of each level in the cloud model in

Table 1. The calculated cloud parameters of the standard evaluation cloud.

Severity Levels	Value Ranges	Exs	Ens	Hes	Instructions
1	[0, 0.2]	0.1	0.033	0.005	No steam channeling
2	(0.2, 0.45]	0.325	0.042	0.005	Weak steam channeling
3	(0.45, 0.55]	0.5	0.016	0.005	Moderate steam channeling
4	(0.55, 0.8]	0.675	0.042	0.005	Strong steam channeling
5	(0.8, 0.1]	0.9	0.033	0.005	Extremely strong steam channeling

. A higher value indicates that more severe steam channeling occurs between the CSS wells.

By referencing the value ranges specified for each level in Table 1, the values of the three cloud parameters for the SEC were calculated via the following equations:

$$\left\{\begin{array}{l}E{x}_s=(c+d)/2\\ E{n}_s=(d-c)/6\\ H{e}_s=y\end{array}\right.$$

(14)

where c and d are the left and right boundaries of the value ranges for Level s, respectively, as shown in Table 1. Ex_s, En_s, and He_s represent the mathematical expectation, entropy, and hyper entropy of the SEC for Level s, respectively. The calculated values of Ex_s, En_s, and He_s are shown in Table 1.

The calculated values of Ex_s, En_s, and He_s were input into the forward cloud model, generating a SEC map to depict the severity of steam channeling between the CSS wells, as illustrated in Figure 5. The SEC map corresponds to five different levels of steam channeling severity between the CSS wells.

2.3.3. Comprehensive Evaluation Cloud (CEC)

On the basis of the evaluation criteria for the steam channeling severity between the CSS wells outlined in

Table 2. Evaluation criteria for determining the steam channeling severity between CSS wells.

Indicators	Value Ranges
	No Steam Channeling	Weak Steam Channeling	Moderate Steam Channeling	Strong Steam Channeling	Extremely Strong Steam Channeling
F1/%	0 ≤ F1 < 0.1	0.1 ≤ F1 < 0.2	0.2 ≤ F1 < 0.3	0.3 ≤ F1 < 0.6	F1 ≥ 0.6
F2/day	100 > F2 ≥ 60	60 > F2 ≥ 30	30 > F2 ≥ 10	10 > F2 ≥ 5	5 > F2 ≥ 0
F3/°C	0 ≤ F3 < 10	10 ≤ F3 < 20	20 ≤ F3 < 30	30 ≤ F3 < 55	55 ≤ F3 < 200
F4/×104 m3	0 < F4 < 2.5	2.5 ≤ F4 < 3	3 ≤ F4 < 3.5	3.5 ≤ F4 < 4	4 ≤ F4 < 8
F5/×104 m3	0 < F5 < 1	1 ≤ F5 < 1.5	1.5 ≤ F5 < 2	2 ≤ F5 < 3	3 ≤ F5 < 8
F6/×104 m3	2.5 > F6 ≥ 1.5	1.5 > F6 ≥ 1.4	1.4 > F6 ≥ 1.3	1.1 > F6 ≥ 1	1 > F6 ≥ 0

, the cloud parameters (Ex_i, En_i, and He_i) of the evaluation cloud for the i-th indicator are computed via Equations (15) and (16):

$$H_{il}={\displaystyle \frac{(h_{il}-a)}{b-a}}\times (d-c)+c$$

(15)

$$\left\{\begin{array}{l}E{x}_i=H_{il}\\ E{n}_i={\displaystyle \frac{{\displaystyle \sum _{l=1}^m{(H_{il}-\overline{H_i})}^2}}{m-1}}\\ \\ H{e}_i=y\end{array}\right.$$

(16)

where h_il and H_il are the values of the i-th indicator for the l-th CSS well before and after cloud transformation, respectively; a and b represent the left and right boundaries of the value ranges of each indicator, respectively (Table 2); Ex_i, En_i, and He_i are the expectation, entropy, and hyper entropy of the evaluation cloud for the i-th indicator after cloud transformation, respectively; and $\overline{H_i}$ is the average value of the i-th indicator for all the CSS wells after cloud transformation.

On the basis of Equation (17), the cloud parameters (Ex, En, and He) of the CEC are calculated to evaluate the steam channeling severity between the CSS wells as follows:

$$\left\{\begin{array}{l}Ex={\displaystyle \sum _{i=1}^n\left(E{x}_i\cdot w_i\right)}\\ En={\displaystyle \sum _{i=1}^n\left(E{n}_i\cdot \frac{w_i^2}{w_1^2+w_2^2+\cdots +w_n^2}\right)}\\ He={\displaystyle \sum _{i=1}^n\left(H{e}_i\cdot \frac{w_i^2}{w_1^2+w_2^2+\cdots +w_n^2}\right)}\end{array}\right.$$

(17)

To quantify the similarity between the CEC and SEC, a determination method was proposed as follows:

$$E_s={\mathrm{e}}^{(-{(x_{\mathrm{p}}-E{x}_s)}^2/(2E{n_s^{\prime }}^2\left)\right)}$$

(18)

$$T_s={\displaystyle \frac{{\displaystyle {\sum }_{t=1}^T{E}_s}}{T}}$$

(19)

where E_s and T_s are the preliminary similarity and final similarity between the CEC and SEC for level s, respectively; T is the repeated number of normal random numbers; and x_p, Zx, and $E{n}_s^{\prime }$ are the normal random numbers determined by the cloud parameters of the CEC and SEC for level s, which satisfy the following equations:

$$\begin{array}{l}{x}_p~N(Ex,Zx)\\ Zx~N(En,He)\\ E{n}_s^{\prime }~N(E{n}_s,H{e}_s^2)\end{array}$$

(20)

The level with the highest T_s is the corresponding level of steam channeling severity between the CSS wells.

3. Case Study

3.1. Data Collection

The reservoirs L, R, and T are typical offshore heavy oil reservoirs developed by large-scale CSS processes and are located in Bohai Bay, China. The reservoirs commenced production in April 2022. The cumulative oil production surpassed 500,000 tons by March 2024. However, as the CSS process continued, steam channeling occurred between the CSS wells, significantly affecting their production performance. Therefore, to propose corresponding schemes for controlling steam channeling between CSS wells and then enhancing offshore heavy oil recovery, evaluating the steam channeling severity between these CSS wells is imperative.

The monitoring and production data of the CSS wells in the three reservoirs are presented in

Table 3. Indicator data of the CSS wells in the three reservoirs.

Reservoir Names	Well Names	F1/%	F2/Day	F3/°C	F4/×104 m3	F5/×104 m3	F6/×104 m3
L	Lw1	0	100	0	2.63	1.46	1.17
	Lw2	20	10	35	3.49	2.38	1.11
	Lw3	3	100	0	6.24	5.45	0.78
	Lw4	2	21	40	3.62	2.76	0.85
	Lw5	3	30	20	8.19	5.86	2.32
	Lw6	2	7	50	4.9	2.64	2.26
	Lw7	60	6	40	2.93	0.9	2.02
	Lw8	3	100	0	8.52	4.29	4.23
	Lw9	3	100	0	4.34	3.01	1.33
	Lw10	15	100	0	1.98	0.94	1.04
	Lw11	20	4	0	1.74	0.64	1.09
	Lw12	30	6	0	2.95	1.13	1.81
	Lw13	3	100	0	3.48	2.2	1.28
R	Rw1	24	14	28	5.65	4.4	1.25
	Rw2	34	8	36	6.06	4.58	1.48
	Rw3	55	5	49	7.82	5.87	1.95
	Rw4	11	25	12	3.5	2.47	1.03
	Rw5	12	20	16	4.05	2.65	1.4
	Rw6	37	6	39	6.42	4.72	1.7
T	Tw1	0	100	0	2.54	1.51	1.03
	Tw2	31	14	28	5.96	4.41	1.55
	Tw3	12	25	13	3.9	2.55	1.35
	Tw4	15	19	16	4.61	3.34	1.27
	Tw5	16	18	23	4.74	3.49	1.25
	Tw6	10	26	11	3.35	1.73	1.62

. On the basis of the monitoring and production data shown in Table 3, an indicator system for evaluating the steam channeling severity between the CSS wells in the three reservoirs was constructed.

3.2. Calculation of Indicator Weights

The subjective weights of all the indicators were determined via the IAHP method and are shown in Figure 6. The calculated process parameters, including A, B, C, and A*, are as follows:

$$\begin{array}{l}A=\left[\begin{array}{cccccc}0.5& 0.65/0.35& 0.55/0.45& 0.8/0.2& 0.7/0.3& 0.85/0.15\\ 0.35/0.65& 0.5& 0.4/0.6& 0.65/0.35& 0.55/0.45& 0.7/0.3\\ 0.45/0.55& 0.6/0.4& 0.5& 0.75/0.25& 0.65/0.35& 0.8/0.2\\ 0.2/0.8& 0.35/0.65& 0.25/0.75& 0.5& 0.45/0.55& 0.55/0.45\\ 0.3/0.7& 0.45/0.55& 0.35/0.65& 0.55/0.45& 0.5& 0.65/0.35\\ 0.15/0.85& 0.3/0.7& 0.2/0.8& 0.45/0.55& 0.35/0.65& 0.5\end{array}\right]\\ B=\left[\begin{array}{cccccc}0.6931& 0.6190& 0.2007& 1.3863& 0.8473& 1.7346\\ -0.6190& 0.6931& -0.4055& 0.6190& 0.2007& 0.8473\\ -0.2007& 0.4055& 0.6931& 1.0986& -0.6190& 1.3863\\ -1.3863& -0.6190& -1.0986& 0.6931& -0.2007& 0.2007\\ -0.8473& -0.2007& -0.6190& 0.2007& 0.6931& 0.6190\\ -1.7346& -0.8473& -1.3863& -0.2007& -0.6190& 0.6931\end{array}\right]\\ C=\left[\begin{array}{cccccc}0& 0.6909& 0.2465& 1.3153& 0.9392& 1.5960\\ -0.6909& 0& -0.4444& 0.6244& 0.2483& 0.9051\\ -0.2465& 0.4444& 0& 1.0688& 0.6927& 1.3494\\ -1.3153& -0.6244& -1.0688& 0& -0.3761& 0.2807\\ -0.9392& -0.2483& -0.6927& 0.3761& 0& 0.6568\\ -1.5960& -0.9051& -1.3494& -0.2807& -0.6568& 0\end{array}\right]\end{array}$$

$$A*=\left[\begin{array}{cccccc}1& 4.9079& 1.7641& 20.6685& 8.6936& 39.4428\\ 0.2038& 1& 0.3594& 4.2112& 1.7713& 8.0365\\ 0.5669& 2.7821& 1& 11.7160& 4.9280& 22.3584\\ 0.0484& 0.2375& 0.0054& 1& 0.4206& 1.9084\\ 0.1150& 0.5645& 0.0209& 2.3774& 1& 4.5370\\ 0.0254& 0.1244& 0.0447& 0.5240& 0.2204& 1\end{array}\right]$$

The objective weights of all the indicators were calculated through the ICRITIC method, which is also shown in Figure 6. The process parameters, including, ${\delta }_j$, ${\sigma }_j$, and $C_j$, are shown in

Table 4. Process parameters calculated via the ICRITIC method.

Indicators	${\mathit{\delta }}_{\mathit{j}}$	${\mathit{\sigma }}_{\mathit{j}}$	${\mathit{C}}_{\mathit{j}}$
F1	1.884	0.2850	7.0207
F2	2.4458	0.2945	9.6559
F3	1.5714	0.3955	8.1033
F4	2.2115	0.3221	7.2606
F5	2.1909	0.3271	7.6908
F6	2.0966	0.2710	9.2392

.

The combined weights of the indicators were calculated via Equation (12) and are shown in Figure 6. As shown in Figure 6, the ranking of the indicators used to determine steam channeling severity between CSS wells is as follows: the water cut increment > temperature increment > steam breakthrough time > cumulative liquid production in each cycle > cumulative water production in each cycle > cumulative oil production in each cycle.

To verify the viability of the IAHP-CRITIC method introduced in this study, a comparison was conducted among the IAHP, ICRITIC, and IAHP-CRITIC methods (Figure 7). Figure 7 shows that the weights determined by the IAHP method have obvious differences between the indicators, indicating that the IAHP method is subjective and overlooks the objective effects linked to the indicator data. The results are consistent with the results of Shi et al., who also found that the weights determined by the IAHP method have obvious differences between the indicators [33]. The weights calculated by the ICRITIC method have a relatively uniform distribution. The weights calculated by the IAHP-CRITIC method fall within the range of those determined by the IAHP method and the ICRITIC method individually. This observation suggests that the IAHP-CRITIC method can integrate the influences of both subjective and objective factors. Therefore, the proposed IAHP-CRITIC method results in a more reasonable weight distribution.

3.3. Evaluation of the Steam Channeling Severity Between CSS Wells

In this section, the 25 CSS wells in the three reservoirs are systematically evaluated via the developed IAHP-CRITIC method and cloud model. First, the cloud parameters for both the SEC and CEC of the 25 CSS wells were calculated. The aforementioned model was then programmed into a program via MATLAB R2021a program and used to calculate the SEC and CEC maps. Finally, the final similarities between the SEC and CEC maps were calculated to determine the levels of the steam channeling severity between the CSS wells.

3.3.1. Evaluation Cloud Maps of the Indicators

Taking Lw7 as an example, the cloud parameters for all the indicators were calculated via Equations (15) and (16) on the basis of the indicator data of Lw7 in Table 3, which are presented in

Table 5. Cloud parameters for all the indicators of Lw7.

Indicators	Exi	Eni	Hei
F1	0.8	0.0812	0.005
F2	0.75	0.0867	0.005
F3	0.63	0.1564	0.005
F4	0.41	0.1038	0.005
F5	0.1	0.107	0.005
F6	0.55	0.0735	0.005

. Through the forward cloud generator, the evaluation cloud maps for all the indicators are generated, as shown in Figure 8.

3.3.2. Comprehensive Evaluation Cloud Maps

On the basis of the combined weights and cloud parameters of all the indicators (Table 5), the cloud parameters of the CEC map were determined via Equation (17) (

Table 6. Cloud parameters of the CEC maps, T_s, and evaluation results.

Reservoir Names	Well Names	Cloud Parameters			Ts					The Severity Levels
		Ex	En	He	Level 1	Level 2	Level 3	Level 4	Level 5
L	Lw1	0.06	0.1005	0.005	2.2 × 10−1	1.6 × 10−2	4.6 × 10−138	1.1 × 10−12	1.5 × 10−54	1
	Lw2	0.51	0.1005	0.005	4.3 × 10−5	9.0 × 10−2	1.9 × 10−1	1.5 × 10−1	4.9 × 10−4	3
	Lw3	0.10	0.1005	0.005	3.2 × 10−1	3.6 × 10−2	3.4 × 10−6	1.6 × 10−8	2.6 × 10−40	1
	Lw4	0.32	0.1005	0.005	4.6 × 10−2	3.6 × 10−1	3.6 × 10−2	1.6 × 10−3	6.3 × 10−15	2
	Lw5	0.30	0.1005	0.005	3.6 × 10−2	4.2 × 10−1	2.8 × 10−2	2.4 × 10−4	7.5 × 10−24	2
	Lw6	0.39	0.1005	0.005	7.1 × 10−3	3.8 × 10−1	8.3 × 10−2	2.3 × 10−2	1.6 × 10−10	2
	Lw7	0.66	0.1005	0.005	6.9 × 10−11	2.5 × 10−3	4.3 × 10−2	3.8 × 10−1	3.0 × 10−2	4
	Lw8	0.13	0.1005	0.005	1.8 × 10−1	8.4 × 10−2	1.2 × 10−5	6.4 × 10−10	3.0 × 10−42	1
	Lw9	0.12	0.1005	0.005	2.4 × 10−1	7.0 × 10−2	1.4 × 10−5	9.8 × 10−10	6.7 × 10−32	1
	Lw10	0.16	0.1005	0.005	3.1 × 10−1	1.4 × 10−1	1.1 × 10−3	5.3 × 10−7	2.7 × 10−31	1
	Lw11	0.46	0.1005	0.005	8.4 × 10−4	1.8 × 10−1	1.3 × 10−1	3.3 × 10−2	1.4 × 10−5	2
	Lw12	0.57	0.1005	0.005	4.1 × 10−11	3.0 × 10−2	4.4 × 10−2	1.8 × 10−1	4.3 × 10−3	4
	Lw13	0.09	0.1005	0.005	3.1 × 10−1	3.7 × 10−2	4.2 × 10−14	2.0 × 10−9	3.1 × 10−25	1
R	Rw1	0.53	0.0385	0.005	1.2 × 10−24	2.9 × 10−4	3.1 × 10−1	6.2 × 10−2	3.7 × 10−11	3
	Rw2	0.61	0.0385	0.005	6.1 × 10−21	1.6 × 10−7	4.0 × 10−3	4.5 × 10−1	1.2 × 10−8	4
	Rw3	0.74	0.0385	0.005	1.8 × 10−74	1.0 × 10−18	3.9 × 10−23	3.5 × 10−1	5.9 × 10−3	4
	Rw4	0.31	0.0385	0.005	6.3 × 10−4	7.2 × 10−1	9.1 × 10−8	9.9 × 10−12	7.6 × 10−78	2
	Rw5	0.38	0.0385	0.005	7.4 × 10−9	4.9 × 10−1	8.9 × 10−3	2.4 × 10−8	1.1 × 10−46	2
	Rw6	0.64	0.0385	0.005	4.8 × 10−28	2.9 × 10−8	3.4 × 10−3	5.8 × 10−1	1.5 × 10−10	4
T	Tw1	0.06	0.0349	0.005	3.6 × 10−1	7.7 × 10−10	4.0 × 10−272	4.3 × 10−40	1.9 × 10−165	1
	Tw2	0.57	0.0349	0.005	1.2 × 10−35	1.0 × 10−5	8.3 × 10−2	7.2 × 10−2	4.2 × 10−9	3
	Tw3	0.35	0.0349	0.005	3.8 × 10−8	6.1 × 10−1	4.0 × 10−4	4.7 × 10−9	6.0 × 10−76	2
	Tw4	0.41	0.0349	0.005	1.4 × 10−15	1.8 × 10−1	4.0 × 10−2	5.5 × 10−6	3.0 × 10−32	2
	Tw5	0.46	0.0349	0.005	7.1 × 10−15	3.4 × 10−2	1.5 × 10−1	1.1 × 10−3	1.7 × 10−25	3
	Tw6	0.29	0.0349	0.005	9.9 × 10−5	5.1 × 10−1	3.6 × 10−13	6.6 × 10−15	2.4 × 10−50	2

). Through the forward cloud generator, the CEC maps for the 25 CSS wells are generated and overlaid with the SEC maps, providing a visual evaluation of the steam channeling severity between the CSS wells, as shown in Figure 9. According to Equations (18) and (19), the T_s values between the CEC maps and the SEC maps are calculated and shown in Table 6.

According to the comparisons in Figure 9 and the evaluation results shown in Table 6, the steam channeling severities of Lw7, Lw12, Rw2, Rw3, and Rw6 are level 4, indicating that these CSS wells exhibit strong steam channeling during the CSS process. The steam channeling severities of Lw2, Rw1, Tw2, and Tw5 are Level 3, indicating that these CSS wells exhibit moderate steam channeling during the CSS process. The steam channeling severities of Lw4, Lw5, Lw6, Lw11, Rw4, Rw5, Tw3, and Tw6 are Level 2, indicating that these CSS wells exhibit weak steam channeling during the CSS process. The steam channeling severities of Lw1, Lw3, Lw8, Lw9, Lw10, Lw13, and Tw1 are Level 1, indicating that these CSS wells have no steam channeling during the CSS process. In addition, the cloud maps’ half-widths reflect significant uncertainty in quantifying the steam channeling severity between CSS wells. High uncertainty is also a characteristic of the steam channeling phenomena [34]. To address this high uncertainty, it is necessary to determine the steam channeling severity between CSS wells by the calculated T_s shown in Table 6, which can quantify the similarity between the CEC and SEC instead of directly observing the similarity between the CEC and SEC shown in Figure 9. In conclusion, steam channeling is severe in the three reservoirs, and it is necessary to control steam channeling between CSS wells via relevant measures, such as the injection of chemical blocking agents, the optimization of injection parameters of CSS wells, and the implementation of combined CSS processes.

3.4. Validation of the Evaluation Results

The relative errors between the Ex_s of the SEC and the Ex of the CEC determined by the IAHP-CRITIC, AHP-CRITIC, AHP, and CRITIC methods are compared to verify the accuracy of the model and are shown in

Table 7. Relative errors between Ex_s and E_x determined by different methods.

Reservoir Names	Well Names	Ex				Exs	Relative Errors/%
		AHP	CRITIC	AHP-CRITIC	IAHP-CRITIC		AHP	CRITIC	AHP-CRITIC	IAHP-CRITIC
L	Lw1	0.079	0.157	0.059	0.061	0.1	21.50	57.40	41.20	39.30
	Lw2	0.520	0.519	0.520	0.511	0.5	3.90	3.88	3.90	2.14
	Lw3	0.137	0.260	0.106	0.100	0.1	36.50	159.70	5.70	0.40
	Lw4	0.362	0.439	0.343	0.319	0.325	11.48	35.14	5.54	1.75
	Lw5	0.345	0.482	0.311	0.299	0.325	6.12	48.25	4.40	7.87
	Lw6	0.445	0.566	0.415	0.394	0.325	36.89	74.28	27.54	21.38
	Lw7	0.636	0.540	0.660	0.664	0.675	5.81	19.96	2.27	1.58
	Lw8	0.166	0.339	0.122	0.130	0.1	65.50	238.80	22.10	30.41
	Lw9	0.157	0.315	0.117	0.119	0.1	56.80	214.50	17.40	18.71
	Lw10	0.146	0.114	0.154	0.164	0.1	45.70	14.30	53.60	64.15
	Lw11	0.443	0.351	0.466	0.457	0.325	36.28	7.85	43.38	40.65
	Lw12	0.561	0.522	0.570	0.567	0.675	16.96	22.71	15.53	16.05
	Lw13	0.119	0.239	0.089	0.091	0.1	18.70	139.20	11.40	9.40
R	Rw1	0.54	0.58	0.55	0.53	0.5	8.24	15.48	9.69	6.97
	Rw2	0.62	0.64	0.60	0.61	0.675	8.30	5.48	11.11	9.12
	Rw3	0.74	0.72	0.74	0.74	0.675	10.14	5.98	9.30	9.46
	Rw4	0.32	0.40	0.34	0.31	0.325	1.58	22.28	3.20	3.84
	Rw5	0.38	0.50	0.41	0.38	0.325	18.02	52.80	24.97	16.18
	Rw6	0.65	0.67	0.65	0.64	0.675	3.55	1.33	3.11	4.47
T	Tw1	0.06	0.14	0.07	0.06	0.10	43.89	44.53	26.20	43.35
	Tw2	0.57	0.60	0.58	0.57	0.5	14.54	20.84	15.80	14.04
	Tw3	0.35	0.46	0.38	0.35	0.325	8.81	42.37	15.52	7.45
	Tw4	0.42	0.51	0.44	0.41	0.325	29.12	58.24	34.95	27.27
	Tw5	0.47	0.54	0.48	0.46	0.5	6.56	8.76	3.49	8.21
	Tw6	0.29	0.39	0.31	0.29	0.325	9.58	18.47	3.97	10.18
Average relative errors/%	/						20.98	53.30	16.61	16.57

. In addition, the evaluation results were compared with the reservoir survey results of the three reservoirs and are shown in

Table 8. The severity levels of CSS wells were determined by different methods.

Reservoir Names	Well Names	AHP	CRITIC	AHP-CRITIC	IAHP-CRITIC	Reservoir Survey Results
L	Lw1	1	1	1	1	1
	Lw2	4	3	4	3	3
	Lw3	1	2	1	1	1
	Lw4	2	2	2	2	2
	Lw5	2	3	2	2	2
	Lw6	2	4	2	2	2
	Lw7	4	4	4	4	4
	Lw8	1	2	1	1	1
	Lw9	1	2	1	1	1
	Lw10	1	1	1	1	1
	Lw11	3	2	2	2	2
	Lw12	4	3	4	4	4
	Lw13	1	2	1	1	1
R	Rw1	3	3	3	3	3
	Rw2	4	4	4	4	4
	Rw3	4	4	4	4	4
	Rw4	2	3	2	2	2
	Rw5	2	3	3	2	2
	Rw6	3	4	4	4	4
T	Tw1	1	1	1	1	1
	Tw2	3	3	3	3	3
	Tw3	2	3	2	2	2
	Tw4	2	3	2	2	2
	Tw5	3	3	3	3	3
	Tw6	2	3	2	2	2
Accuracy/%	/	88	52	92	100	/

.

Table 7 shows that the relative errors between Ex_s and Ex determined by the IAHP-CRITIC, AHP-CRITIC, AHP, and CRITIC methods are 16.57%, 16.61%, 20.98%, and 53.30%, respectively. The results indicate that the IAHP-CRITIC method results in the most concentrated distributions and the smallest fluctuations in the number of cloud droplets in the CEC map of the steam channeling severity. In other words, for the CEC maps of the 25 CSS wells determined by the IAHP-CRITIC method, the majority of the cloud droplets can fall within the range of the correct level, and only a few cloud droplets are distributed in the ranges of the wrong levels.

In addition, compared with the reservoir survey results for the three reservoirs (Table 8), the accuracies of the results obtained via the AHP, CRITIC, AHP-CRITIC, and IAHP-CRITIC methods are 88%, 52%, 92%, and 100%, respectively. Therefore, compared with other methods, the IAHP-CRITIC method has greater reliability in terms of calculating indicator weights and evaluating the steam channeling severity between CSS wells. The results provide compelling evidence for the model’s accuracy in determining the indicator weights and evaluating the steam channeling severity between CSS wells. This study can be used as a reference for practical applications of this novel method in other offshore heavy oil reservoirs. The reason is that the IAHP-CRITIC method effectively considers the influences of both subjective and objective factors on individual indicator weights. It is noted that the results are consistent with the results of Ali et al., who also found that the AHP-CRITIC method has greater reliability in terms of calculating indicator weights than the AHP and CRITIC method [35].

However, the accuracy of the model was verified only in three offshore heavy oil reservoirs. The indicator system and SEC were developed on the basis of the data from offshore heavy oil, and the generalizability of the model is still limited. In addition, the model validation relied solely on the reservoir survey. More methods are needed to further verify the accuracy of the model. Therefore, more research, including verifying the accuracy of the model with more reservoir data and independent sources (distributed acoustic sensing and distributed temperature sensing measurements, tracer tests, or 4D seismic), will be required in the future.

To prove the accuracy of the combinations of indicators in this study, an alternative combination of indicators was used to determine the steam channeling severity between CSS wells. Due to the limited monitoring data and production data for offshore heavy oil reservoirs, the water cut (F₁₁) and temperature (F₃₃) were used to replace the water cut increment and temperature increment (the indicators shown in Figure 3) in the initial combinations of indicators.

Indicator data of the CSS wells in the three reservoirs are presented in

Table 9. Indicator data of the CSS wells in the three reservoirs (the alternative combinations of indicators).

Reservoir Names	Well Names	F11/%	F2/Day	F33/°C	F4/×104 m3	F5/×104 m3	F6/×104 m3
L	Lw1	90	100	55	2.63	1.46	1.17
	Lw2	61	10	90	3.49	2.38	1.11
	Lw3	52	100	61	6.24	5.45	0.78
	Lw4	45	21	100	3.62	2.76	0.85
	Lw5	53	30	86	8.19	5.86	2.32
	Lw6	50	7	112	4.90	2.64	2.26
	Lw7	95	6	100	2.93	0.90	2.02
	Lw8	46	100	60	8.52	4.29	4.23
	Lw9	49	100	65	4.34	3.01	1.33
	Lw10	52	100	60	1.98	0.94	1.04
	Lw11	71	4	60	1.74	0.64	1.09
	Lw12	78	6	60	2.95	1.13	1.81
	Lw13	42	100	60	3.48	2.20	1.28
R	Rw1	65	14	80	5.65	4.4	1.25
	Rw2	77	8	88	6.06	4.58	1.48
	Rw3	79	5	130	7.82	5.87	1.95
	Rw4	50	25	80	3.5	2.47	1.03
	Rw5	55	20	84	4.05	2.65	1.4
	Rw6	67	6	101	6.42	4.72	1.7
T	Tw1	55	100	60	2.54	1.51	1.03
	Tw2	71	14	90	5.96	4.41	1.55
	Tw3	63	25	82	3.9	2.55	1.35
	Tw4	66	19	79	4.61	3.34	1.27
	Tw5	65	18	94	4.74	3.49	1.25
	Tw6	68	26	82	3.35	1.73	1.62

. The evaluation criteria for determining the steam channeling severity between CSS wells are shown in

Table 10. Evaluation criteria for determining the steam channeling severity between CSS wells (the alternative combinations of indicators).

Indicators	Value Ranges
	No Steam Channeling	Weak Steam Channeling	Moderate Steam Channeling	Strong Steam Channeling	Extremely Strong Steam Channeling
F11/%	0 ≤ F11 < 30	30 ≤ F11 < 50	50 ≤ F11 < 70	70 ≤ F11 < 90	90 ≤ F11 < 1
F2/day	100 > F2 ≥ 60	60 > F2 ≥ 30	30 > F2 ≥ 10	10 > F2 ≥ 5	5 > F2 ≥ 0
F33/°C	0 ≤ F33 < 60	60 ≤ F33 < 80	80 ≤ F33 < 100	100 ≤ F33 < 120	120 ≤ F33 < 200
F4/×104m3	0 < F4 < 2.5	2.5 ≤ F4 < 3	3 ≤ F4 < 3.5	3.5 ≤ F4 < 4	4 ≤ F4 < 8
F5/×104m3	0 < F5 < 1	1 ≤ F5 < 1.5	1.5 ≤ F5 < 2	2 ≤ F5 < 3	3 ≤ F5 < 8
F6/×104m3	2.5 > F6 ≥ 1.5	1.5 > F6 ≥ 1.4	1.4 > F6 ≥ 1.3	1.1 > F6 ≥ 1	1 > F6 ≥ 0

. A comparison of the evaluation results determined by the different combinations of indicators is shown in

Table 11. Cloud parameters of the CEC maps, T_s, and evaluation results calculated by the alternative combinations of indicators.

Reservoir Names	Well Names	Cloud Parameters			Ts					The Severity Levels
		Ex	En	He	Level 1	Level 2	Level 3	Level 4	Level 5
L	Lw1	0.49	0.042	0.005	3.3 × 10−25	1.2 × 10−2	1.1 × 10−1	1.1 × 10−3	3.8 × 10−23	3
	Lw2	0.51	0.042	0.005	2.5 × 10−27	1.1 × 10−4	1.5 × 10−1	3.5 × 10−3	7.9 × 10−41	3
	Lw3	0.36	0.042	0.005	2.0 × 10−8	6.7 × 10−1	4.9 × 10−6	9.9 × 10−12	3.7 × 10−52	2
	Lw4	0.47	0.042	0.005	1.9 × 10−22	1.7 × 10−2	5.0 × 10−1	4.2 × 10−4	3.7 × 10−38	3
	Lw5	0.51	0.042	0.005	1.6 × 10−28	1.8 × 10−3	7.0 × 10−1	1.0 × 10−2	2.5 × 10−19	3
	Lw6	0.59	0.042	0.005	6.9 × 10−30	3.4 × 10−7	6.4 × 10−3	2.2 × 10−1	4.5 × 10−10	4
	Lw7	0.71	0.042	0.005	1.1 × 10−51	1.7 × 10−12	3.0 × 10−6	5.6 × 10−1	3.2 × 10−4	4
	Lw8	0.36	0.042	0.005	1.2 × 10−10	6.5 × 10−1	2.8 × 10−4	7.9 × 10−9	7.8 × 10−70	2
	Lw9	0.38	0.042	0.005	8.8 × 10−8	4.8 × 10−1	4.3 × 10−5	4.8 × 10−7	1.6 × 10−40	2
	Lw10	0.28	0.042	0.005	4.7 × 10−4	4.9 × 10−1	8.5 × 10−42	2.9 × 10−14	2.5 × 10−85	2
	Lw11	0.41	0.042	0.005	1.7 × 10−14	2.1 × 10−1	6.5 × 10−3	1.3 × 10−5	4.5 × 10−25	2
	Lw12	0.50	0.042	0.005	6.6 × 10−32	5.3 × 10−3	5.7 × 10−1	4.1 × 10−3	6.9 × 10−17	3
	Lw13	0.30	0.042	0.005	2.0 × 10−5	7.8 × 10−1	6.8 × 10−15	7.4 × 10−14	2.4 × 10−49	2
R	Rw1	0.53	0.011	0.005	6.8 × 10−35	2.5 × 10−6	3.1 × 10−1	3.9 × 10−2	2.6 × 10−22	3
	Rw2	0.61	0.011	0.005	5.3 × 10−63	3.3 × 10−10	6.9 × 10−8	2.5 × 10−1	6.5 × 10−15	4
	Rw3	0.73	0.011	0.005	7.2 × 10−78	2.9 × 10−20	3.2 × 10−29	5.3 × 10−1	1.0 × 10−5	4
	Rw4	0.46	0.011	0.005	5.4 × 10−14	2.1 × 10−2	1.8 × 10−1	2.4 × 10−5	3.0 × 10−36	3
	Rw5	0.51	0.011	0.005	4.5 × 10−23	5.3 × 10−4	6.8 × 10−1	2.2 × 10−4	9.8 × 10−18	3
	Rw6	0.60	0.011	0.005	1.9 × 10−36	6.9 × 10−8	1.7 × 10−9	3.2 × 10−1	1.1 × 10−20	4
T	Tw1	0.32	0.007	0.005	3.6 × 10−10	9.7 × 10−1	8.2 × 10−15	2.4 × 10−14	1.1 × 10−49	2
	Tw2	0.56	0.007	0.005	3.1 × 10−26	1.8 × 10−6	1.2 × 10−8	2.7 × 10−2	1.5 × 10−29	4
	Tw3	0.51	0.007	0.005	4.2 × 10−22	2.0 × 10−5	7.8 × 10−1	2.3 × 10−3	4.3 × 10−25	3
	Tw4	0.53	0.007	0.005	1.1 × 10−33	2.2 × 10−4	5.3 × 10−1	1.0 × 10−3	2.9 × 10−36	3
	Tw5	0.55	0.007	0.005	1.3 × 10−50	4.8 × 10−7	7.9 × 10−2	1.5 × 10−2	2.6 × 10−13	3
	Tw6	0.50	0.007	0.005	1.3 × 10−21	6.3 × 10−5	8.9 × 10−1	6.4 × 10−4	1.6 × 10−18	3
accuracy/%	/									32

. As shown in Table 8 and Table 11, compared with the reservoir survey results for the three reservoirs, the accuracies of the results obtained via the initial and alternative combinations of indicators are 100% and 32%, respectively, indicating the accuracy of the initial combinations of indicators in this study. The results are attributed to the fact that a higher water cut increment and temperature increment can indicate more severe steam channeling between CSS wells. A higher water cut and temperature are normal phenomena that occur in the later stage of development for CSS wells. They do not necessarily indicate the occurrence of severe steam channeling.

According to Equation (13), the cloud parameters Ex and En are fixed values once the indicator data are determined. Therefore, a sensitivity analysis was conducted by changing the value of H_e in this study to prove the accuracy of the results. A comparison of the evaluation results determined by the different H_e values is shown in Table 8 and

Table 12. Cloud parameters of the CEC maps, T_s, and evaluation results by using the different H_e values.

Well Names	Cloud Parameters			Ts					The Severity Levels
	Ex	En	He	Level 1	Level 2	Level 3	Level 4	Level 5
Rw1	0.54	0.0385	0.001	5.47 × 10−34	6.77 × 10−6	2.56 × 10−1	2.05 × 10−3	7.46 × 10−28	3
			0.003	1.74 × 10−38	1.22 × 10−6	1.47 × 10−2	1.28 × 10−2	1.23 × 10−23	3
			0.005	1.27 × 10−24	2.97 × 10−4	3.05 × 10−1	6.22 × 10−2	3.73 × 10−11	3
			0.007	1.05 × 10−42	2.50 × 10−7	1.08 × 10−2	2.01 × 10−2	1.76 × 10−24	4
			0.01	8.93 × 10−39	8.62 × 10−7	1.54 × 10−2	1.72 × 10−2	2.03 × 10−24	4
Tw2	0.57	0.0349	0.001	8.49 × 10−38	3.62 × 10−7	7.64 × 10−3	1.48 × 10−2	1.86 × 10−26	4
			0.003	1.34 × 10−44	2.76 × 10−6	1.18 × 10−2	1.49 × 10−2	2.47 × 10−21	4
			0.005	1.19 × 10−35	1.01 × 10−5	8.33 × 10−2	7.17 × 10−2	4.24 × 10−9	3
			0.007	1.87 × 10−66	8.84 × 10−7	6.61 × 10−2	3.19 × 10−2	4.50 × 10−25	3
			0.01	8.45 × 10−54	1.43 × 10−5	2.50 × 10−2	1.75 × 10−2	1.03 × 10−16	3
Tw5	0.46	0.0349	0.001	4.31 × 10−26	1.06 × 10−2	2.76 × 10−2	1.18 × 10−6	3.29 × 10−39	3
			0.003	5.68 × 10−25	8.73 × 10−3	4.24 × 10−2	1.46 × 10−8	1.75 × 10−27	3
			0.005	7.16 × 10−15	3.44 × 10−2	1.53 × 10−1	1.12 × 10−3	1.78 × 10−25	3
			0.007	1.59 × 10−2	4.55 × 10−1	2.14 × 10−1	3.39 × 10−2	1.53 × 10−5	2
			0.01	5.84 × 10−39	8.93 × 10−2	3.57 × 10−3	4.74 × 10−7	2.84 × 10−28	2

. As shown in Table 8 and Table 12, when the H_e value is equal to 0.005, the evaluation results for the three wells are correct. H_e values that are too high or too low result in incorrect evaluation results for some CSS wells. Therefore, the H_e value of 0.005 used in this study is accurate. This is because He acts as a metric of uncertainty to represent entropy, capturing the thickness or density of cloud droplets. Either a too high or too low He value will lead to a decrease in T_s, thereby making it prone to result in incorrect evaluation results.

4. Conclusions and Discussion

This study developed a novel evaluation model to quantitatively evaluate the steam channeling severity between CSS wells in offshore heavy oil reservoirs via the improved AHP-CRITIC (IAHP-CRITIC) method and the cloud model. An indicator system for the steam channeling severity on the basis of monitoring and production data was established. The IAHP-CRITIC method was subsequently proposed to calculate the combined weights. The proposed model was used to evaluate the steam channeling severity between CSS wells in a typical offshore heavy oil reservoir. The results indicated that the constructed indicator system can be used to evaluate the steam channeling severity between CSS wells. The improved AHP-CRITIC method yielded a more reasonable weight distribution because it effectively considered the influences of both subjective and objective factors on individual indicator weights. Compared with the reservoir survey results for the L reservoir, the accuracies of the results obtained by the AHP, CRITIC, AHP-CRITIC, and IAHP-CRITIC methods were 88%, 52%, 92%, and 100%, respectively. Therefore, the IAHP-CRITIC method was more reliable than the other methods in terms of calculating the indicator weights and evaluating the steam channeling severity between the CSS wells. The Lw7 and Lw12 in the L reservoir, as well as Rw2, Rw3, and Rw6 in the R reservoir, exhibited strong steam channeling. It is necessary to control the steam channeling of these CSS wells. This is the first study to report the evaluation of steam channeling severity between CSS wells in offshore heavy oil reservoirs. This study provides an effective model to quantitatively evaluate the steam channeling severity between CSS wells and offers valuable insights for the selection of effective strategies to control the steam channeling between CSS wells and enhance offshore heavy oil recovery. However, it is noted that the model validation relied solely on the reservoir survey in three offshore heavy oil reservoirs. More research, including verifying the accuracy of the model by more reservoir data and independent sources (distributed acoustic sensing and distributed temperature sensing measurements, tracer tests, 4D seismic, etc.), will be required in the future.