Determination of the Main Production Factors and Production Predictions of Test Wells in the Offshore Tight Oil Reservoirs in the L Formation of the Beibu Basin Using Multivariate Statistical Methods

Abstract

This study addresses the challenge of rapidly and accurately predicting the production of test wells in offshore tight oil reservoirs, specifically within the L Formation of the Beibu Basin. This challenge is particularly pronounced in situations where drill stem tests are limited and evaluating each untested well layer is difficult. To achieve this objective, we analyzed fifteen typical test wells in the L Formation, taking into account both geological and engineering factors. Initially, Pearson correlation analysis, partial correlation analysis, and grey relational analysis were used to identify the main production factors. Based on these analyses, two types of production prediction models were developed: one employing the comprehensive production index method and the other utilizing the production coefficient method. The research identified effective permeability, porosity, oil saturation, and shale content as the main production factors for the test wells in the study area. The model verification results showed that the comprehensive production index model performs effectively for the L Formation, with an average prediction error of 20.40% compared to the actual production values. This research is significant for optimizing and stabilizing production in tight oil reservoirs.

1. Introduction

The focus of exploration is shifting from conventional to unconventional resources, from shallow to deep reservoirs, and from terrestrial to marine environments [1,2,3,4,5]. Previous studies indicate that formations deeper than 3000 m contain substantial resource reserves and offer a significant potential for exploration [1,4]. As a result, offshore deep tight reservoirs have emerged as a key area of research in unconventional resources [1,6,7]. These reservoirs are typically located in high-temperature and high-pressure environments [8] and exhibit notable heterogeneity, complex pore structures, limited pore connectivity, and intricate fluid occurrence and distribution compared to conventional reservoirs [9,10]. Oil production is a critical factor in evaluating the potential of geological resources [11], and economic viability hinges on ensuring that production exceeds extraction costs, highlighting the need for accurate predictions of oil production.

Numerous researchers have employed statistical methodologies, including information theory, univariate analysis, and grey theory, to investigate principal production factors [12,13,14]. The principal production factors within the study area encompass both geological and engineering factors. Researchers such as Hu et al. have concentrated on tight oil reservoirs, developing a numerical model to evaluate production factors [15,16,17,18]. The findings suggest that the initial pressure gradient, permeability, reservoir pressure, and stress sensitivity are the primary geological factors impacting production. Furthermore, the length of the horizontal well section emerges as a pivotal engineering factor affecting production. The principal production factors in tight oil reservoirs can be classified as follows: geological factors, comprising porosity, permeability, reservoir thickness, the initial pressure gradient, and natural fractures [12,13,14,15,16,18,19,20]. The fluid properties include the viscosity and relative density of the crude oil [15,21,22,23]. Additionally, engineering factors such as the oil well radius [15,17,18] are considered.

The main production prediction methods in tight oil reservoirs are the well test method [24], the logging method [25,26], the analytical method, the numerical simulation method [15,16,17,18], and the machine learning method [27,28]. In actuality, it is challenging to consider all these factors comprehensively. Therefore, it becomes essential to identify and prioritize the main production factors. While analyzing production factors, the focus is often on discussing the production variations resulting from various factors rather than comparing the varying degrees of influence caused by the different factors. The number of drill stem test assessments conducted in offshore tight oil reservoirs is limited, making it challenging to assess the production of untested sections. Due to the complexities involved in obtaining crucial factors for offshore reservoirs and the intricate nature of tight oil reservoirs, the commonly employed production prediction methods also exhibit limitations.

The primary objective of this research is to construct two rapid-production prediction models for test wells in the L Formation of the Beibu Basin. The paper is structured as follows (Figure 1): The comprehensive production index method begins with a Pearson correlation analysis and partial correlation analysis to identify the main production factors: effective permeability, porosity, and oil saturation. Subsequently, a detailed analysis of each individual production factor is performed to determine the correlation coefficient between each factor and the specific oil production index. The corresponding weight coefficients are then calculated based on these correlation coefficients. Using these weight coefficients, a comprehensive production index model is constructed, which is then used to develop a production prediction model. The production coefficient method starts with a grey relational analysis to identify the key production factors: effective permeability, shale content, and porosity. These three factors are then combined to compute the production coefficient. Finally, the production coefficient and the specific oil production index are analyzed and fitted, leading to the development of a production prediction model in the form of a power function. Finally, the effectiveness and feasibility of the two proposed methods are validated using actual oil production data.

2. Selection of Production Factors

2.1. Calculation of Specific Oil Production

After the drill stem test, the specific oil production index served as a crucial metric for the production analysis [29].

The production index [30,31] is given as follows:

$$J_o={\displaystyle \frac{q_o}{\Delta p}}={\displaystyle \frac{q_o}{p_R-p_{wf}}}$$

(1)

where J_o is the production index, m³/d/MPa; q_o is the oil production rate, m³/d; Δp is the pressure differential, MPa; p_R is the original formation pressure; MPa; and p_wf is the well bottom pressure, MPa.

The specific oil production index [30,31] is given as follows:

$$J_{os}={\displaystyle \frac{J_o}{h}}={\displaystyle \frac{q_o}{\Delta ph}}={\displaystyle \frac{q_o}{\left(p_R-p_{wf}\right)h}}$$

(2)

where J_os is the specific oil production index, m³/d/MPa; and h is the effective thickness, m.

Typically, the pressure differential and oil flow under stable well-bottom flow conditions conform to the plane radial flow production formula [29,31,32]:

$$J_{os}={\displaystyle \frac{q_o}{\Delta ph}}={\displaystyle \frac{C{K}_{o}h}{B_o{\mu }_o\lg \left(\frac{r_e}{r_w}+S\right)}}\Delta p$$

(3)

where C is the unit conversion coefficient, constant; K_o is the effective permeability, mD; B_o is the oil volume factor, m³/m³; μ_o is the viscosity, MPa/s; r_e is the supply oil radius, m; r_w is the well radius, m; and S is the skin coefficient, dimensionless.

We collected fifteen layers of drill stem test data from fifteen wells in the L Formation of the Beibu Basin. Using Formulas (1) and (2), we calculated the production index and the specific oil production index for each well (

Table 1. The production index and the specific oil production index for fifteen wells in the L Formation of the Beibu Basin.

Well	Test	Depth	Formation	Jo	Jos
No.	No.	m		m3/d/MPa	m3/d/MPa
W-1	DST 1	3127.0–3169.5	L3	19.601	0.513
W-2	DST 1	3070.7–3094.6	L3	1.109	0.087
W-3	DST 1	3181.8–3225.0	L3	0.294	0.020
W-4	DST 1	3125.8–3179.7	L3	4.845	0.697
W-5	DST 1	3031.0–3049.0	L2	1.370	0.469
W-6	DST 1	3288.6–3354.7	L3	1.238	0.073
W-7	DST 1	3104.0–3270.0	L3	1.134	0.030
W-8	DST 1	2971.0–3031.0	L3	0.220	0.009
W-9	DST 1	3161.0–3180.0	L1	0.235	0.017
W-10	DST 1	2968.0–2980.0	L1	1.309	0.113
W-11	DST 1	3111.0–3365.5	L1	2.294	0.203
W-12	DST 1	2880.0–2897.0	L1	16.759	1.180
W-13	DST 1	2211.0–2221.5	L3	11.088	2.704
W-14	DST 1	2043.0–2064.0	L2	65.781	8.121
W-15	DST 1	3314.0–3323.0	L2	0.224	0.051

).

2.2. Determination of Production Factors

Reservoir production is intricately linked to reservoir properties, oil characteristics, supply oil radius, and various other factors (Formula (3)). Based on the formula of the specific oil production index (Formula (3)), eight production factors were identified (

Table 2. The production factors in the L Formation of the Beibu Basin.

Well	PR	Ko	φ	μo	SH	So	S	rw	Jos
No.	MPa	mD	%	MPa/s	%	%	f	m	m3/d/MPa
W-1	38.836	27.200	14.060	2.520	12.700	64.250	0.448	0.0785	0.513
W-2	38.045	5.260	15.660	2.520	8.800	62.930	0.230	0.0785	0.087
W-3	38.051	1.750	16.000	3.616	11.000	45.700	0.604	0.108	0.020
W-4	45.025	14.830	19.000	1.000	19.900	56.700	−0.970	0.108	0.697
W-5	47.270	0.960	12.710	1.000	18.900	42.900	−0.970	0.108	0.469
W-6	33.908	20.900	12.000	0.300	5.100	45.000	−0.990	0.0785	0.073
W-7	33.224	18.300	12.000	0.300	13.600	45.000	−0.990	0.0785	0.030
W-8	32.585	0.047	12.100	0.301	6.300	44.150	−0.993	0.0785	0.009
W-9	49.210	0.063	11.380	0.585	14.200	61.060	−1.990	0.0785	0.017
W-10	28.758	2.360	12.500	0.828	5.400	36.400	3.080	0.0785	0.113
W-11	50.930	4.100	13.270	1.195	10.700	55.670	1.580	0.108	0.203
W-12	28.620	78.700	14.300	2.161	10.200	57.690	1.740	0.11025	1.180
W-13	21.150	78.200	18.460	1.267	18.800	58.550	0.127	0.07856	2.704
W-14	21.146	140.000	21.360	0.526	19.000	73.710	3.750	0.07856	8.121
W-15	55.665	4.100	18.600	1.184	19.500	67.300	5.500	0.0785	0.051

). The shale content was obtained from logging data; the original formation pressure, porosity, viscosity, oil saturation, and well radius were obtained from reservoir physical property data and oil test data; and the effective permeability and skin coefficient were determined through well test interpretation.

3. Construction of Comprehensive Production Index Model

The process for constructing the comprehensive production index model can be summarized in five steps: (a) Determination of main production factors; (b) Data normalization; (c) Calculation of weight coefficients; (d) Construction of comprehensive index model; and (e) Verification (Figure 2).

3.1. Analysis of Main Production Factors

Using a Pearson correlation analysis and a partial correlation analysis, we identified three main production factors, which were then used to construct the comprehensive production index model. A single-factor analysis was performed on these three main production factors to obtain the correlation coefficients associated with production.

3.1.1. Pearson Correlation Analysis

The Pearson correlation analysis is a widely used method for evaluating single factors and can be employed to assess the linear correlation between variables [28,33]. The calculation formula for the Pearson correlation coefficient is as follows [34]:

$$p_{xy}={\displaystyle \frac{\mathrm{cov}\left(x,y\right)}{\sqrt{\mathrm{var}\left(x\right)}\sqrt{\mathrm{var}\left(y\right)}}}$$

(4)

where p_xy is the Pearson correlation coefficient, p_xy ∈ [–1, 1]. If p_xy < 0, the two variables are negatively correlated, while if p_xy = 0, the two variables are not correlated, and if p_xy > 0, the two variables are positively correlated. Additionally, cov (x, y) is the covariance of x and y, var (x) is the variance of x, and var (y) is the variance of y.

Based on the Formula (4), we calculated the Pearson correlation coefficient between the production factors and specific oil production index by using the data in Table 2, and the results of this analysis are depicted in Figure 3.

We identified four main production factors: effective permeability (0.91), porosity (0.67), original formation pressure (0.56), and oil saturation (0.54) (Figure 3a). In contrast, viscosity (−0.17), shale content (−0.43), skin coefficient (−0.37) and well radius (0.15) were found to have no significant linear relationship with production (Figure 3a).

3.1.2. Partial Correlation Analysis

The correlation coefficient measures whether there is a linear relationship between the variables x and y and quantifies the strength of this relationship. However, if a third variable z is numerically related to both x and y, it may lead to misleading results [35]. Therefore, calculating the partial correlation coefficient is essential to account for and eliminate the influence of the control variable z.

The partial correlation coefficient is based on the Pearson correlation coefficient, which is defined as follows [34,35]:

$$p_{xy\left|z\right.}=cor\left(\widehat{\epsilon },\widehat{\zeta }\right)={\displaystyle \frac{\mathrm{cov}\left(\widehat{\epsilon },\widehat{\zeta }\right)}{\sqrt{\mathrm{var}\left(\widehat{\epsilon }\right)}\sqrt{\mathrm{var}\left(\widehat{\zeta }\right)}}}$$

(5)

where p_xy|z is the partial correlation coefficient, p_xy|z ∈ [−1, 1]. If p_xy|z < 0, the two variables are negatively correlated; if p_xy|z = 0, the two variables are not correlated; and if p_xy|z > 0, the two variables are positively correlated. Additionally, $\mathrm{cov}\left(\widehat{\epsilon },\widehat{\zeta }\right)$ is the covariance of $\widehat{\epsilon }$ and $\widehat{\zeta }$; $\mathrm{var}\left(\widehat{\epsilon }\right)$ is the variance of $\widehat{\epsilon }$; and $\mathrm{var}\left(\widehat{\zeta }\right)$ is the variance of $\widehat{\zeta }$.

The process for calculating the partial correlation coefficient is as follows. First, a regression model was constructed.

The regression model of x is as follows:

$$x=z\alpha +\epsilon$$

(6)

The regression model of y is as follows:

$$y=z\beta +\zeta$$

(7)

Then, using ordinary least squares, we calculated the regression coefficients.

The regression coefficients of x are as follows:

$$\widehat{\alpha }={\left(z^{T}z\right)}^{-1}zx$$

(8)

The regression coefficients of y are as follows:

$$\widehat{\beta }={\left(z^{T}z\right)}^{-1}zy$$

(9)

According to the regression coefficients, we can obtain the following residuals.

The residual of x is as follows:

$$\widehat{\epsilon }=x-z\widehat{\alpha }$$

(10)

The residual of y is as follows:

$$\widehat{\zeta }=y-z\widehat{\beta }$$

(11)

By substituting Formulas (10) and (11) into Formula (5), the partial correlation coefficient can be obtained.

Based on the Formula (5), with the original formation pressure as the control variable, we calculated the partial correlation coefficient between the production factors and the specific oil production index by using the data in Table 2, and the results of this analysis are depicted in Figure 4.

As shown in Figure 4b, after accounting for the influence of the original formation pressure on the other production factors, the correlations between the porosity, oil saturation, and production improve significantly. We identified three main production factors: effective permeability (0.87), oil saturation (0.71), and porosity (0.70) (Figure 4a). In contrast, the shale content (−0.48), skin coefficient (−0.43), viscosity (−0.16), and well radius (0.025) did not exhibit a significant linear relationship with production (Figure 4a). The results from the partial correlation analysis are largely consistent with those obtained from the Pearson correlation analysis.

3.1.3. Analysis of Single-Production Factor

For the results of the Pearson correlation analysis and the partial correlation analysis, the three main production factors were effective permeability, porosity, and oil saturation (Figure 3 and Figure 4). These production factors were analyzed through a single-factor analysis, and their detailed impacts on production were discussed.

(I)

Analysis of effective permeability and production

Tight reservoirs exhibit characteristics such as low-permeability, porous media, capillary effects, and significant stress sensitivity [36,37]. For Figure 5a, the reservoir in the L Formation of the Beibu Basin predominantly features low permeability, with an effective permeability range from 0.0472 mD to 140 mD and an average of 26.451 mD. The reservoir shows strong heterogeneity and poor seepage performance. The linear curve indicates a robust correlation (0.827) between the effective permeability and the specific oil production index (

Table 3. The relationship model and correlation coefficient between the production factors and the specific oil production index in the L Formation of the Beibu Basin.

No.	Production Factor	Relationship Model	R2
1	Effective permeability	Jos = 0.047Ko − 0.2917	0.827
2	Porosity	Jos = 0.4504φ − 5.7557	0.451
3	Oil saturation	Jos = 0.1066So − 4.8521	0.293

).

(II)

Analysis of porosity and production

Porosity is one of the key factors of the physical properties of reservoirs, as it is directly related to the quality of the storage performance of the reservoir and has a certain impact on the oil well production. For Figure 5b, the porosity in the L Formation of the Beibu Basin is low, with a porosity range from 11.4% to 21.4%, and an average of 14.9%, indicating that the reservoir performance is not good. The linear curve indicates a general correlation (0.451) between the porosity and the specific production index (Table 3).

(III)

Analysis of oil saturation and production

The permeability and porosity only reflect the quality of its physical properties or the size of the liquid production and cannot reflect the fluid properties contained in the reservoir. Oil saturation is a very important factor in the reserve calculation, production evaluation and development plan design. Under the same conditions of reservoir permeability and porosity, the higher the oil saturation, the greater the oil content and oil production. For Figure 5c, the oil saturation range is from 36.4% to 73.7%, and has an average of 54.4%, indicating that the oil reserves in the Beibu Basin are generally poor. The linear curve indicates a poor correlation (0.293) between the oil saturation and the specific oil production index (Table 3).

3.2. Data Normalization

Based on the results of our single-factor analysis, the correlation coefficients among the effective permeability (0.827), porosity (0.451), and oil saturation (0.2931) are highest between the specific oil production index (Figure 5). These variables can be used as the independent variables to construct the comprehensive production index model. Due to the different dimensions of these production factors, each one was first normalized between 0 and 1 (Formulas (12)–(15)), as seen in (

Table 4. Normalization of main production factors.

No.	Well	Test	Ko’	φ’	So’
	No.	No.	f	f	f
1	W-1	DST 1	0.194	0.269	0.746
2	W-2	DST 1	0.037	0.429	0.711
3	W-3	DST 1	0.012	0.463	0.249
4	W-4	DST 1	0.106	0.764	0.544
5	W-5	DST 1	0.007	0.133	0.174
6	W-6	DST 1	0.149	0.062	0.231
7	W-7	DST 1	0.130	0.062	0.231
8	W-8	DST 1	0.000	0.072	0.208
9	W-9	DST 1	0.000	0.000	0.661
10	W-10	DST 1	0.017	0.112	0.000
11	W-11	DST 1	0.029	0.189	0.516
12	W-12	DST 1	0.562	0.293	0.571
13	W-13	DST 1	0.558	0.709	0.594
14	W-14	DST 1	1.000	1.000	1.000
15	W-15	DST 1	0.029	0.723	0.828

). The formulas are as follows:

$$x^{\prime }={\displaystyle \frac{x-x_{\min }}{x_{\max }-x_{\min }}}$$

(12)

where $x^{\prime }$ is the normalization of the production factors, dimensionless; x is the production factors; $x_{\min }$ is the minimum value of x; and $x_{\max }$ is the maximum value of x.

Normalization of effective permeability is given as follows:

$$K_o^{\prime }={\displaystyle \frac{K_o-K_{o\min }}{K_{o\max }-K_{o\min }}}$$

(13)

Normalization of porosity is given as follows:

$${\varphi }^{\prime }={\displaystyle \frac{\varphi -{\varphi }_{\min }}{{\varphi }_{\max }-{\varphi }_{\min }}}$$

(14)

Normalization of oil saturation is given as follows:

$$S_o^{\prime }={\displaystyle \frac{S_o-S_{o\min }}{S_{o\max }-S_{o\min }}}$$

(15)

3.3. Calculation of Weight Coefficient

For the Formula (16), the greater the correlation coefficient, the higher the corresponding weight coefficient, ensuring that the sum of each factor’s weight coefficients equals 1.

Table 5. The weight coefficients of the main production factors in the L Formation of the Beibu Basin.

No.	Production Factor	R2	The Sum of R2	a	The Sum of a
1	Effective permeability	0.827	1.571	0.526	1.000
2	Porosity	0.451		0.287
3	Oil saturation	0.293		0.187

illustrates the weight coefficients of the main production factors in the L Formation of the Beibu Basin.

$$a=a_i/{\displaystyle \sum _{i=1}^n{a}_i}$$

(16)

3.4. Calculation of Comprehensive Production Index

According to the main production factors and their corresponding weights, the comprehensive production index was obtained. The formula is as follows:

$$F_o=0.526\times K_o^{\prime }+0.287\times {\varphi }^{\prime }+0.187\times S_o^{\prime }$$

(17)

For Figure 6, a strong correlation exists between the comprehensive production index and the specific oil production index, indicated by a correlation coefficient of 0.793. Therefore, this model can accurately predict the production of the test wells in the L Formation of the Beibu Basin. The fitting formula is as follows:

$$J_{os}=7.3017\times F_o-1.171$$

(18)

Taking Formula (17) into Formula (18), the production prediction model of the test wells in the L Formation of the Beibu Basin can be obtained as follows:

$$J_{os}=7.3017\times \left(0.526\times K_o^{\prime }+0.287\times {\varphi }^{\prime }+0.187\times S_o^{\prime }\right)-1.171$$

(19)

For Figure 6, the production prediction model constructed using the comprehensive production index method shows further improvement compared to the correlations observed in the single-factor analysis. Therefore, it provides a more accurate prediction of oil production in the test wells in the L Formation of the Beibu Basin.

4. Construction Production Coefficient Model

The process for constructing the production coefficient model can be summarized in three steps: (a) Determination of the main production factors by a grey relational analysis; (b) Construction of the production coefficient model; and (c) Verification.

4.1. Grey Relational Analysis of Main Production Factors

The grey relational analysis is a statistical method used to assess the degree of correlation between factors based on the similarities and differences in their development trends [38,39].

Firstly, based on Table 2, the reference sequence is the specific oil production index [38]:

$$x_0=\left\{x_0\left(k\right)|k=1,2,3,\cdots ,n\right\}$$

(20)

where x₀ is the reference sequence; k is the number of samples; and n is the total number of samples.

The comparison sequence is the original formation pressure, effective permeability, porosity, viscosity, shale content, oil saturation, skin coefficient, and well radius [38]:

$$x_i=\left\{x_i\left(k\right)|k=1,2,3,\cdots ,n\right\}$$

(21)

where x_i is the comparison sequence; i is the production factor index, i = 1, 2, 3, ……, m; and m is the total number of the production factors index.

The production factors were averaged to eliminate the influence of dimensions between the data:

$$x_i\left(k\right)={\displaystyle \frac{x_i\left(k\right)}{ave\left(x_i\right)}}$$

(22)

where $ave\left(x_i\right)$ is the average of x_i.

The grey incidence coefficient is as follows [38]:

$${\zeta }_i\left(k\right)={\displaystyle \frac{{\min }_i {\min }_k {\Delta }_i\left(k\right)+\rho {\max }_i {\max }_k {\Delta }_i\left(k\right)}{{\Delta }_i\left(k\right)+\rho {\max }_i {\max }_k {\Delta }_i\left(k\right)}}$$

(23)

where ${\zeta }_i\left(k\right)$ is the grey incidence coefficient; min_i is the minimum value of i; min_k is the minimum value of k; ${\Delta }_i\left(k\right)$ is the difference sequences, ${\Delta }_i\left(k\right)=\left|x_0\left(k\right)-x_i\left(k\right)\right|$; ρ is the resolution coefficient, ρ = 0.5; max_i is the maximum value of i; and max_k is the maximum value of k.

The grey correlation degree is as follows [38]:

$$r_i={\displaystyle \frac{1}{n}}{\displaystyle \sum _k^n{\zeta }_i\left(k\right)}$$

(24)

where r_i is the grey correlation degree.

Based on Formulas (20)–(24), the grey correlation coefficient was calculated, and the production factors were ranked according to the grey correlation degree. The results are as follows (

Table 6. Ranking of production factors based on grey relational analysis.

Production Factor	Grey Correlation Degree	Rank
Effective permeability	0.908	1
Shale content	0.815	2
Porosity	0.814	3
Viscosity	0.813	4
Oil saturation	0.812	5
Well radius	0.806	6
Original formation pressure	0.784	7
Skin coefficient	0.684	8

).

According to Table 6, for the eight production factors, the correlation between the production and the effective permeability is the highest (0.908), followed by the shale content (0.815) and the porosity (0.814).

4.2. Calculation of Production Coefficient

Based on the results of the grey relational analysis, the effective permeability, shale content, and porosity were optimized to construct the production coefficient:

$$F_p=K_o\times SH\times \varphi$$

(25)

where F_p is the production coefficient.

Based on Formula (25), the result of the production coefficient in the L Formation of the Beibu Basin is shown as

Table 7. The result of the production coefficient in the L Formation of the Beibu Basin.

Well	Test	Formation	Ko	φ	SH	Fp	Jos
No.	No.		mD	%	%		m3/d/MPa
W-1	DST 1	L3	27.200	14.060	12.700	4856.886	0.513
W-2	DST 1	L3	5.260	15.660	8.800	724.870	0.087
W-3	DST 1	L3	1.750	16.000	11.000	308.000	0.020
W-4	DST 1	L3	14.830	19.000	19.900	5607.223	0.697
W-5	DST 1	L2	0.960	12.710	18.900	230.610	0.469
W-6	DST 1	L3	20.900	12.000	5.100	1279.080	0.073
W-7	DST 1	L3	18.300	12.000	13.600	2986.560	0.030
W-8	DST 1	L3	0.047	12.100	6.300	3.598	0.009
W-9	DST 1	L1	0.063	11.380	14.200	10.229	0.017
W-10	DST 1	L1	2.360	12.500	5.400	159.300	0.113
W-11	DST 1	L1	4.100	13.270	10.700	582.155	0.203
W-12	DST 1	L1	78.700	14.300	10.200	11,479.182	1.180
W-13	DST 1	L3	78.200	18.460	18.800	27,139.154	2.704
W-14	DST 1	L2	140.000	21.360	19.000	56,817.600	8.121
W-15	DST 1	L2	4.100	18.600	19.500	1487.070	0.051

.

Using the production coefficient calculated in Table 7, we performed a regression analysis to examine the relationship between the production coefficient and the specific oil production index (0.876), as shown in Figure 7. The formula is as follows:

$$J_{os}=0.0028F_p^{0.6007}$$

(26)

Taking Formula (25) into Formula (26), the production coefficient model of the test wells in the offshore tight oil reservoirs can be obtained as follows:

$$J_{os}=0.0028\times {\left(K_o\times SH\times \varphi \right)}^{0.6007}$$

(27)

5. Verification

According to the comprehensive production index model and the production coefficient model, data from two new oil test wells were introduced for verification (

Table 8. The main production factors for two verification wells in the L Formation of the Beibu Basin.

No.	Well	Test	Formation	Ko	φ	So	SH	Jos
	No.	No.		mD	%	%	%	m3/d/MPa
1	Y-1	DST 1	L2	2.160	16.840	59.782	18.200	0.673
2	Y-2	DST 1	L3	50.04	20.340	58.270	20.800	2.654

).

The production prediction results of the comprehensive production index model are detailed in

Table 9. The production prediction results of the comprehensive production index model for two verification wells in the L Formation of the Beibu Basin.

Well	Ko’	φ’	So’	Fo	Prediction Jos	Actual Jos	Relative Error
No.	f	f	f	f	m3/d/MPa	m3/d/MPa	%
Y-1	0.015	0.547	0.627	0.282	0.889	0.673	32.200
Y-2	0.357	0.898	0.586	0.555	2.883	2.654	8.600

and illustrated in Figure 8. The relative error between the actual and predicted production values falls within 35%, with an average error of 20.40%. This model effectively predicts production for test wells in the offshore tight oil reservoirs in the L Formation of the Beibu Basin.

The production prediction results of the production coefficient model are detailed in

Table 10. The production prediction results of the production coefficient model for two verification wells in the L Formation of the Beibu Basin.

Well	Ko	φ	SH	Fp	Prediction Jos	Actual Jos	Relative Error
No.	mD	%	%	f	m3/d/MPa	m3/d/MPa	%
Y-1	2.16	16.84	18.2	662.014	0.139	0.673	79.410
Y-2	50.04	20.34	20.8	21,170.523	1.111	2.654	58.147

and illustrated in Figure 8. The relative error between the actual and predicted production values falls within 80%, with an average error of 68.78%.

6. Conclusions

To accurately evaluate and predict the production of test wells in the offshore tight oil reservoirs within the L Formation of the Beibu Basin, this paper presents two production prediction methods: the comprehensive production index method and the production coefficient method. The model verification results indicate that the comprehensive production index model performs well when applied to the L Formation of the Beibu Basin, with an average error of 20.40% between the predicted and actual production values. The main conclusions are as follows:

(1)

According to the results of the Pearson correlation analysis, partial correlation analysis, and grey relational analysis, the main production factors involved in the test well in the research area are effective permeability, porosity, oil saturation, and shale content. Effective permeability is the most critical main production factor, and effective permeability has a great influence on production in the L Formation of the Beibu Basin.

(2)

According to the verification results achieved using the comprehensive production index method, the average error between the actual and predicted production values is 20.40%. The predicted production under this model is higher than the actual production. The model has shown a strong performance in applications within the L Formation of the Beibu Basin, providing more accurate production predictions.

(3)

According to the verification results achieved using the production coefficient method, the average error between the actual and predicted production values is 68.78%. The predicted production under this model is lower than the actual production. The model has been poorly applied to the L Formation of the Beibu Basin.

(4)

This method can be employed to rapidly predict the production of test wells and offer valuable insights for their further development.