Introduction

The expulsion of hydrocarbons from hydrocarbon source rocks is also called the primary migration of oil and gas and typically refers to the process by which oil and gas are discharged from low-permeability source rocks into high-permeability reservoirs (Hunt 1979; Tissot and Welte 1984). The expulsion of hydrocarbons from source rocks is one of the weakest points in oil and gas geochemical studies but is very important for predicting oil and gas resources in oil and gas basins (Chen et al. 2014). The hydrocarbon expulsion efficiency is the key parameter for predicting conventional oil and gas resources; therefore, since the 1960s, many geochemists have exerted significant effort to explore the mechanisms and efficiency of hydrocarbon expulsion from hydrocarbon source rocks.

The hydrocarbon expulsion efficiency is very closely related to the single-layer thickness of the hydrocarbon source rocks. Many experts and scholars have thoroughly investigated this relationship. Tissot and Welte (1984) found that hydrocarbon source rocks have higher contents of hydrocarbons, colloids and asphaltenes, which are from the farthest reservoir, indicating that these hydrocarbons can only be expelled from the reservoirs and hydrocarbon source rocks within a certain distance. Magara (1978) and Dieckmann et al. (2002) reported similar observations, finding that hydrocarbons cannot be entirely expelled due to large sedimentary thicknesses, low permeability and brief windows of hydrocarbon expulsion power. The hydrocarbons in hydrocarbon source rocks can be entirely expelled within the effective thickness of hydrocarbon expulsion. Zhao et al. (2006) found that thin-layer source rocks and the rocks within several meters of the edge of thick-layer source rocks have high hydrocarbon expulsion efficiency, whereas thick-layer hydrocarbon source rocks do not favor hydrocarbon expulsion. Moreover, the hydrocarbon expulsion efficiency in the middle of a thick layer of hydrocarbon source rocks is low. Wilhelms et al. (1990), Jarvie et al. (2007) and Li et al. (2015a) observed that the hydrocarbon expulsion efficiency is not high overall and that considerable quantities of hydrocarbons remain stranded in shales. Because of the complex mechanisms of hydrocarbon expulsion, no appropriate model or formula exists to explain the hydrocarbon expulsion process. In this paper, we examine the type II1 source rocks in the Dongying Sag as an example and subject them to pyrolysis experiments to investigate the influence of the thicknesses of single-layer source rocks. Additionally, we establish a geological model of the oil expulsion efficiency to more accurately reflect the geological conditions affecting the oil discharge efficiency.

Samples and methods

Sampling

The mudstone samples used here were collected from the Oligocene Sha He Street Group in the Dongying Sag. The organic carbon content exceeded 2%, and the hydrogen index exceeded 500 mg/g, which is typical of type II1 high-quality hydrocarbon source rocks. The vitrinite reflectance was less than 0.5%, corresponding to immature source rocks. Thus, these samples were ideal for this work (Abrakasa et al. 2016; Ramachandran et al. 2013; Blanc and Connan 1992; Espitalie 1985; Hang et al. 2015; El Nady 2013; Pepper and Corvi 1995; Tissot et al. 1987; Ayyildiz 2006; Li et al. 2015b).

Pyrolysis experiments on hydrocarbon generation and expulsion to confirm the theoretical maximum oil expulsion efficiency

The instrument used here was a high-temperature and high-pressure oil-and-gas-formation simulation system, which primarily consists of a pressure vessel, a temperature and pressure automatic control instrument, and a product collection system. To better represent the geological conditions affecting oil expulsion, we used block samples rather than powder samples. We cut the cores into several small cylindrical bodies with diameters and heights of approximately 2 cm, and we used the cumulative simulation method. Each sample simulated a temperature point, and a total of 10 temperature points were investigated (Table 1). The oil-phase product was collected after the reaction, and the retained oil was extracted by chloroform, collected and quantitatively analyzed. We were able to simulate the whole thermal evolution process in the experiment and determine the oil incidence factor, oil expulsion factor and oil expulsion efficiency (Table 1 and Fig. 1).

Table 1 The oil generation and expulsion pyrolysis experimentation data of type II1 hydrocarbon source rocks
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Fig. 1
figure 1

The oil generation and expulsion model of type II1 source rocks

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From the experimental results, we observe that, in general, the oil incidence factor, oil expulsion factor and oil expulsion efficiency initially increased and then decreased as the thermal evolution degree increased. The retained oil peaked at Ro = 0.8% and contained approximately 165 mg/g total organic carbon (TOC). The oil incidence factor peaked at Ro = 0.9%, and the peak value was approximately 340 mg/g TOC. The peak of the oil expulsion factor occurred later than that of the oil incidence factor, i.e., at Ro = 1.0%, and the peak value was approximately 240 mg/g TOC. The oil expulsion efficiency initially increased as the Ro increased, peaking at Ro = 1.0% and then plateaued. The largest oil expulsion efficiency was approximately 80%, but the oil expulsion efficiency was lowest when Ro = 0.8% and retained oil was at its peak. This model of oil generation and expulsion demonstrates that the whole evolution process can be divided into the following stages:

  1. (1)

    Low-maturity stage (Ro = 0.5–0.7%): The oil incidence factor, oil expulsion factor and oil expulsion efficiency increase slowly, and the oil expulsion efficiency is very low (approximately 40%).

  2. (2)

    Mature stage (Ro = 0.7–1.0%): The oil incidence factor, oil expulsion factor and oil expulsion efficiency increase rapidly. The oil incidence factor and oil expulsion factor reach their peaks, and the oil expulsion efficiency increases rapidly from 40 to 80%.

  3. (3)

    High-maturity stage (Ro = 1.0–1.3%): The oil incidence factor, oil expulsion factor and oil expulsion efficiency begin to decrease, the oil incidence factor and oil expulsion factor are relatively high, and the oil expulsion efficiency remains high and changes little.

  4. (4)

    Overly mature stage (Ro = 1.3–2.0%): The oil incidence factor, oil expulsion factor and oil expulsion efficiency decrease rapidly, and the liquid hydrocarbon content decreases. Thus, the hydrocarbons have entered the gas generation phase because of the high degree of thermal evolution, and the oil expulsion efficiency cannot be assessed.

Overall, Ro changes from 0.8 to 1.3% during the main phase of oil generation and expulsion. The simulation experiment temperatures are higher than the actual temperatures under the geological conditions experienced by hydrocarbon source rocks during the evolution process. Furthermore, because the experimental samples are small, the hydrocarbon expulsion path is short. These conditions facilitate oil and gas expulsion. Thus, the experimental expulsion efficiency is likely higher than the realistic natural expulsion efficiency (Lewan 1997) and is consequently referred to as the theoretical maximum oil expulsion efficiency (Ko).

Establishing a geological oil expulsion model based on the efficient oil expulsion thickness

The thickness of the source rocks significantly influences the oil expulsion effect (El Nady 2013). Oil and gas are not completely discharged from hydrocarbon source rocks after generation (Lewan 1997). However, discharge can only occur to reservoir facies within a certain distance of the source rock. In other words, the effective thickness of hydrocarbon expulsion is critical. Under actual geological conditions, hydrocarbon source rocks can generate abundant oil, but this oil cannot be discharged everywhere, and in many cases, it cannot be discharged smoothly. Furthermore, some rocks are not capable of discharging any oil at all. The true oil expulsion mode is more complicated than that in the simulation experiment, and the true oil expulsion efficiency is lower than that in the experimental data. Therefore, the lag oil belt, which does not contribute to the oil discharge quantity, should be considered when calculating the amount of oil expulsion. Three ideal, efficient oil expulsion modes based on different source rock thicknesses are described below (Fig. 2):

  1. (1)

    Full expulsion mode

    In this mode, the thickness of an individual source rock is typically less than 10 m, and the porosity and pressure are in equilibrium, indicating that the source rocks can fully expel hydrocarbons. The complete set of oil layers can be divided into upper and lower full oil expulsion belts, and the total oil expulsion efficiency approximates Ko.

  2. (2)

    Full and transition expulsion mode

    In this mode, a single layer of source rock is typically thicker than 10 m but thinner than 20 m. The source rock can be divided into upper and lower oil expulsion belts, which can be further divided into four total parts according to the oil discharge degree: upper and lower full oil expulsion belts and upper and lower transitional oil expulsion belts.

  3. (3)

    Full and transition and retention expulsion mode

    In this mode, a single layer of source rock is typically thicker than 20 m. The fluid located in the middle of a mudstone cannot be easily expelled because of the low degree of permeability of the mudstone, and a lag oil belt develops in the single layer of mudstone. A complete set of source rocks can contain a lag oil belt via the full and transition expulsion mode.

Fig. 2
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The effective oil expulsion patterns of single-layer hydrocarbon source rocks

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These modes are based on the following assumptions. (1) The oil expulsion process in a single layer of mudstone is uniform and gradual, is mainly driven by the pressure difference between the source rocks and the reservoir rocks and is little influenced by geological structures. (2) Several source rock parameters, such as TOC, Ro, organic matter type, lithology and porosity, are considered to be homogeneous. (3) In the upper and lower full oil expulsion belts, the hydrocarbon can be fully expelled, and the hydrocarbon expulsion efficiency (K) is approximately equal to Ko. The oil expulsion efficiencies of the upper and lower transitional oil belts decrease from Ko to 0, indicating that the reduction in oil expulsion efficiency is a function of the thickness. The oil expulsion efficiencies in the lag oil belts are approximately 0.

The correction formula for oil expulsion based on the single-layer thickness of the hydrocarbon source rock

Given the assumptions and simplified conditions described above, we use the weighted average method to correct the oil expulsion efficiency. The formula is as follows:

$$K = \left( {h_{1} \times K_{1} + \, h_{2} \times K_{2} + h_{3} \times K_{3} + h_{4} \times K_{4} + h_{5} \times K_{5} } \right)/h\; = \;\left[ {\left( {h_{1} + \;h_{2} } \right) + \left( {h_{3} + h_{4} } \right)/2} \right] \times {\text{Ko}}/h$$
(1)

where K is the oil expulsion efficiency of the single-layer hydrocarbon source rock, (h 1 + h 2) is the thickness of the full oil expulsion belt, (h 3 + h 4) is the thickness of the transitional oil expulsion belt, h is the thickness of the single-layer source rock, and Ko is the theoretical maximum oil expulsion efficiency; K 1, K 2, K 3, K 4 and K 5 represent the oil expulsion efficiencies of each belt.

To control the value of K, we must use appropriate thicknesses for the full oil expulsion belts and the transitional oil expulsion belts. Previous researchers have stated that a hydrocarbon source rock mudstone less than 10 m in thickness can fully expel oil; thus, the maximum of (h 1 + h 2) is 10 m. The effective oil expulsion thickness is the sum of (h 1 + h 2) and (h 3 + h 4); therefore, the thickness of the transitional oil expulsion belt can be calculated if the effective oil expulsion thickness is known. Chen and Zha (2011) produced an empirical formula for the thickness of effective hydrocarbon expulsion by studying the hydrocarbon expulsion mechanism of hydrocarbon source rocks in a rift lake basin:

$$y = \left\{ {\begin{array}{*{20}l} x \hfill & {(x \le 20)} \hfill \\ {0.4x + 10} \hfill & {(20 < x \le 50)} \hfill \\ {30} \hfill & {(x > 50)} \hfill \\ \end{array} } \right.$$
(2)

In this formula, y is the thickness of effective hydrocarbon expulsion and x is the thickness of the single-layer hydrocarbon source rock.

The formula to compute the oil expulsion efficiency of y for a single-layer hydrocarbon source rock can be obtained by synthesizing the above formula and conditions:

$$k = \left\{ {\begin{array}{*{20}l} {k_{0} } \hfill & {(h \le 10)} \hfill \\ {\left( {\frac{1}{2} + \frac{5}{h}} \right)k_{0} } \hfill & {(10 < h \le 20)} \hfill \\ {\left( {\frac{1}{5} + \frac{{10}}{h}} \right)k_{0} } \hfill & {(20 < h \le 50)} \hfill \\ {\frac{{20k_{0} }}{h}} \hfill & {(h > 50)} \hfill \\ \end{array} } \right.$$
(3)

In this formula, K is the oil expulsion efficiency of the single-layer hydrocarbon source rock after correction, h is the thickness of the single-layer hydrocarbon rock, and K 0 is the theoretical maximum oil expulsion efficiency.

For a geologic section comprising multiple single-layer hydrocarbon source rock layers, the TOC value is assumed to be uniform, the organic matter type is assumed to be the same, and the maturity is assumed to be similar; therefore, the comprehensive oil expulsion efficiency can be calculated based on the weighted average of each layer:

$$k_{c} = \sum\nolimits_{i = 0}^{n} {\frac{{k_{i} h_{i} }}{H}}$$
(4)

where K c is the comprehensive oil expulsion efficiency in the section and K i is corrective oil expulsion efficiency. Based on formula 3, h i is the thickness of each single-layer source rock, and H is the total thickness of the geologic section.

The oil expulsion efficiencies were calculated according to formula 3, and the values are influenced by both the thickness of the single-layer hydrocarbon source rocks and the maturity of type II1 hydrocarbon source rocks (Fig. 3). The oil expulsion efficiency increases as the maturity increases. In low-maturity stages, the maximum oil expulsion efficiency is 30%, whereas in high-maturity stages, it is 80%. When the maturity is constant, the oil expulsion efficiency decreases as the thickness of the single-layer source rocks increases. When the thickness reaches a certain value, regardless of the maturity, the oil expulsion efficiency is low (less than 10%).

Fig. 3
figure 3

The relationship between the oil expulsion efficiency and the single-layer hydrocarbon source rock thickness of type II1 rocks with different maturities

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Credibility

To test the accuracy of the oil expulsion efficiency correction formula, we selected samples of hydrocarbon source rocks of different thicknesses and maturity levels from the Dongying Sag and used the rock pyrolysis material balance method (Chen et al. 2014) to calculate the oil expulsion efficiency. We then compared the experimental efficiencies to those determined using the oil expulsion efficiency correction formula. We found that the calculated oil expulsion efficiencies were in good agreement with the experimental efficiencies and appeared to be highly reliable (Table 2).

Table 2 Calculation coincidence rate of oil expulsion efficiencies
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Results and discussion

We divided hydrocarbon source rocks into four categories according to their thicknesses: thin layers (h ≤ 10 m), intermediate layers (10 < h ≤ 20 m), thick layers (20 < h ≤ 50 m) and super-thick layers (h > 50 m). To research the trend of the oil expulsion efficiency, we sampled the Sha He Street Formation from a well in the Dongying Sag as an example (Fig. 4). In this section, the thicknesses of the single-layer source rocks varied widely among the 4 types mentioned above. Additionally, their TOC values ranged between 0.5 and 1.5%, and the organic matter type was mainly type II1. The total thickness was not large; thus, the maturity of the entire section can be assumed to be the same. Furthermore, the oil expulsion efficiency of each layer and the comprehensive oil expulsion efficiency were calculated using formulas 3 and 4. The results are shown in Table 3.

Fig. 4
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Single-well bar chart of the Sha He Street Formation in well A in the Dongying Sag

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Table 3 Oil expulsion efficiencies of the Sha He Street Formation in well A in the Dongying Sag
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As shown in Table 3, the comprehensive oil expulsion efficiency increases from 18 to 44% as Ro increases. In the low-maturity stages, the thickness of a single-layer hydrocarbon source rock results in insignificant differences in the expulsion efficiencies, and the oil expulsion efficiency is low (between 10 and 30%). In contrast, in the high-maturity phases, the oil expulsion efficiencies exhibit significant differences. Furthermore, the oil expulsion efficiencies of the thin-layer hydrocarbon source rocks are high, exceeding 70%, whereas those of the thick and super-thick layer types are only approximately 30%. Thus, the thickness of a single-layer hydrocarbon source rock exerts considerable influence on the oil expulsion efficiency, particularly during the oil-generating and expulsion peak stages.

Conclusions

The method of calculating the oil expulsion efficiency is based on hydrocarbon generation/expulsion pyrolysis experiments and a geological model, thereby avoiding the need to research the complex oil expulsion mechanisms while accurately characterizing the oil expulsion efficiency under actual geological conditions. This method is also concise and can be applied to modeling oil and gas resources.

The single-layer thickness of a hydrocarbon source rock strongly influences the oil expulsion efficiency, particularly during the raw oil generation and peak discharge stages. The oil expulsion efficiency decreases as the single-layer thickness increases. From the super-thick layer to the thin-layer classes, the oil expulsion efficiency changes substantially, increasing from approximately 10% to approximately 75%.