Introduction

Worldwide, most mid- and large-scale oil and gas reservoirs were formed in the late hydrocarbon accumulation stage (Klemme and Ulmishek 1991; MacGregor 1996; Jia et al. 2006). As exploration proceeded, more and more reservoirs were observed in deep basins; these reservoirs have become important exploration targets (Burruss 1993; Kutcherov 2008; Pang 2010). Although some hydrocarbons in the late-formed reservoirs were formed from adjusted or reformed previous reservoirs, most are from carbonate source rocks in deep basins (e.g., the Williston Basin in North America and the Tarim Basin in China). However, most deep carbonate source rocks have reached high or very high mature stage, such as the source rocks in the Tarim Basin. According to the classic model of hydrocarbon generation from kerogen thermo-decomposition, a large amount of hydrocarbons have already been generated during the mature stage. Therefore, a question regarding the amount of hydrocarbon that can be generated during high and very high mature stage arises. The answer is quite important for exploration of hydrocarbon in late-formed or deep reservoirs. Many petroleum geologists have paid close attention to this problem. To answer the question, we need to determine the mature period at which carbonate source rocks will no longer generate hydrocarbons, i.e., we need to determine the upper limit of maturity for hydrocarbon generation (ULMHG) or the limit for hydrocarbon generation. The ULMHG is the maturity at which the hydrocarbon generation potential of the organic matter decreases to a minimum value.

Tissot and Welte (1984) reported that different types of kerogen in the deep formations of different areas have similar characteristics. As depth increases, the hydrocarbon generation potential initially increases and then decreases until it reaches a minimum value. The maturity at the minimum point is the ULMHG. The maturity can be ascertained using several parameters such as vitrinite reflectance (VR), maximum temperature (T max) from Rock-Eval pyrolysis, time–temperature index (TTI), spore coloration, and ratio of hydrogen and carbon atoms in kerogen (H/C); however, the most useful and effective parameter is VR (Carr and Williamson 1990; Huang 1996). VR is considered to be a function of temperature and time (Hunt 1979; Waples 1980; Tissot and Welte 1984; Ritter 1984), but the temperature has a greater effect on VR (Ritter 1984). The Cambrian and Ordovician carbonate source rocks in the Tarim Basin formed at an early time and are deeply buried. They have experienced a long thermal evolution history and their paleo-temperature is relatively high. Most of the source rocks have reached high or very high mature stage. Study of the ULMHG will provide more information about hydrocarbon generation and accumulation mechanisms, and will aid in the evaluation of deep hydrocarbon resources, determination of potential exploration areas, and design of drilling plans in the deep formations.

Many studies have been conducted on the factors affecting ULMHG. However, these studies have their own limitations. Some studies employed methods, such as thermal simulation experiments or hydrocarbon generation dynamics, which are too simple and limited (Cramer et al. 2001; Xie et al. 2002; Zhang et al. 2002; Su et al. 2012). Some studies conducted only qualitative analysis rather than quantitative calculations of the ULMHG (Qin et al. 2000; Xie et al. 2002; Wang et al. 2005). Other studies were conducted on mudstone, shale, and coal rather than carbonate source rocks (Hu et al. 2006; Chen et al. 2007). This study focuses on the Cambrian and Ordovician carbonate source rocks in the Tarim Basin Platform (TBP), is based on the mechanisms of hydrocarbon generation, retention, and expulsion, and combines many quantitative methods for studying ULMHG. The aim of this study is to understand the ULMHG under real geological condition in the TBP.

Geological setting

The Tarim Basin is the largest petroliferous sedimentary basin in Xinjiang Province, China, with an area of 56 × 104 m2. As shown in Fig. 1a, the TBP mainly contains Paleozoic marine formations. The area includes the Tabei uplift, the northern depression (including the Awaiti sag in the west and the Manjiaer sag in the east), the middle uplift (including, form west to east, the Bachu uplift, the Tazhong uplift, and the Tadong low uplift), and several other tectonic zones. By the end of 2010, 26 oil and gas fields were discovered, and 36 petroliferous structures were identified, with proven oil reserves of 12.06 × 108 t, representing 65 % of those of the entire basin. Concurrently, the total gas proven in this area was 3,940.1 × 1012 m3, which forms 35 % of those of the entire basin. Thus, the TBP is a major area for accumulation of marine oil and gas.

Fig. 1
figure 1

Geological setting of the Tarim Basin Platform: a Location and tectonic areas. b formations

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Paleozoic, Mesozoic, and Cenozoic formations are all well developed in the TBP (Fig. 1b). Manjiaer sag is the center of sedimentation, with a rapid depositional rate at a great depth. The Tarim Basin is a typical superimposed basin that experienced several stages of tectonic evolution and was exposed to two intense periods of magmatic activity and volcanic eruptions in the early Caledonian and late Hercynian times, which in turn, controlled the thermal evolution of the basin (Wang et al. 1995a, b; Li et al. 2000, 2005). The paleo-temperature of the Tarim Basin has been declining since the Paleozoic, indicating a transition from a hot to a cold basin (Li et al. 2000). The paleo-thermal gradient from the Cambrian to the early Ordovician period was 32–35 °C/km, whereas the present paleo-thermal gradient is 20 °C/km (Li et al. 2005). The present heat flow is 30–72.3 mW/m2, with an average of 44.05 mW/m2 (Wang et al. 1995a). The heat flow increases from the edge to the center of the basin, and the largest heat flow occurs in the Tazhong uplift.

The main source rocks in the TBP are of early Paleozoic (Cambrian and Ordovician) age, and consist of two types of rock: mudstone and carbonate rocks. The carbonate source rocks consist of Cambrian to Lower Ordovician and Middle to Upper Ordovician formations. The source rocks of lower and middle Cambrian are better than those of the upper Cambrian to Lower Ordovician in the former source rocks in the TBP (Zhang et al. 2004). The source rocks of middle and Lower Cambrian are mainly observed in the eastern undercompensated basin and western evaporative lagoonal facies. They contain type I kerogen, with total organic carbon (TOC) content of 0.10–5.52 wt% and VR of 1.64–3.61 wt%. Therefore, they are in high and very high mature and gas generation stages. The Middle-Upper Ordovician source rocks are mainly located in the central Tarim Basin and in platform-edge to slope lime-mud mound facies in the western Majiaer Depression. These rocks mainly contain type I kerogen with a combination of type II2 and type III, and have TOC levels of 0.10–5.40 wt% and VR of 0.81–1.30 wt%. So, they are in the mature and oil generation stages (Liang et al. 2000; Gao et al. 2006).

Methods for studying ULMHG

To perform a good-quality quantitative study, we use VR to define the ULMHG, which corresponds to the point at which the potential amount of further hydrocarbon generation is less than 1 % of the total potential amount of hydrocarbon generation in a source rock. The reasons for choosing 1 % as the critical condition are mainly as follows: (1) at the post-mature stage, the source rocks are saturated with residual hydrocarbons; therefore, small amount of hydrocarbons generated can be expelled and can contribute to reservoirs; (2) with the advancement of exploitation techniques and decrease of its cost, even the hydrocarbons generated by source rocks with low generation potential may form industrial reservoirs, which have production values (e.g., shale gas); (3) for previous studies (Hu et al. 2006; Chen et al. 2007), the ULMHG decided by 30 or 10 % of the remaining hydrocarbon generation may be smaller than actual value. Therefore, choosing 1 % as the critical value is reasonable herein. Actually, the ULMHG is a relative concept, because the ULMHG will also change if the critical values vary.

Generally, the ULMHG values are similar for source rocks with the same lithology and organic matter type. Most of the Cambrian and Ordovician carbonate source rocks in the TBP contain type I kerogen, which assists in the choice of source rock samples and parameters and determination of the ULMHG in the two target formations. Taking the carbonate source rocks in the TBP as an example, this study discusses the principles, processes, and results of all types of methods for determining the ULMHG. Some methods such as variation in hydrocarbon generation potential, optimum simulation of organic materials based on material balance, variation in hydrocarbon retention amount, and variation in hydrocarbon expulsion amount are being employed for the first time in the study of ULMHG. Because only a few VR values have actually been measured, most VR values are obtained from the relationship between VR and depth.

Reduction in atomic ratio for organic elements

Hydrocarbon generation from organic materials is primarily a process of deoxidation, dehydrogenation, carbon-enrichment, and condensation of aromatic nuclei. During the main stage of oil and gas generation, the H and O contents of organic materials decrease, which results in the decline of kerogen atomic H/C and O/C rations (Tissot et al. 1974; Tissot and Welte 1984; Huang et al. 1984; Baskin 1997). When H/C and O/C decrease to their minimum values, hydrocarbons cannot be generated from the organic materials. The maturity at this point is the ULMHG. In this study, data on the organic elements of carbonate source rocks in the TBP are shown in Table 1, in which most data are collected from oil fields. This study lists only representative data due to lack of space.

Table 1 Some representative data of organic elements of carbonate source rocks in the TBP
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Reduction in atomic H/C

As organic material experiences thermal evolution and generates more hydrocarbons, the reduction amount of atomic H/C of organic materials decreases. Figure 2 reflects on the variation in H/C corresponding to changes in VR of the Cambrian and Ordovician source rocks in the TBP. Figure 2a is the scatter plot of the relationship between H/C and VR. Figure 2b is the variation in the average value of H/C with VR, specifically, the H/C average value is the average of the total H/C values for every 0.2 % change in VR; the curve in the figure is drawn manually taking into account the reduction trend in the H/C average value. Figure 2c shows the curve fitted between the average value of H/C and VR; the formula in this figure is fitted between these two factors, (these three figures will be used in the rest of the study; each has been drawn by a similar method and has a similar meaning, and they will not be discussed later). Theoretically, when hydrocarbon generation is completed, H/C is reduced to a minimum value and will be stable thereafter. Previous studies have shown that, once H/C value has reached 0.1, roughly the same value as that of graphite, it will not change (Lorant and Behar 2002; Chen et al. 2007). This study takes 0.1 as the ultimate minimum value for H/C. The H/C value corresponding to a VR of 0.5 % of hydrocarbon generation threshold is regarded as the maximum value of H/C (this can be obtained using the fitted formula in Fig. 2c). In this manner, the ULMHG of carbonate source rocks in the TBP can be determined (Fig. 3). The fitted formulas between H/C and VR can be expressed as follows:

Fig. 2
figure 2

Decrease in H/C of the Cambrian and Ordovician carbonate source rocks in the TBP: a measured value of H/C. b average value of H/C. c fitted curve of decrease in H/C

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Fig. 3
figure 3

Principle of determining the ULMHG using method of decrease in H/C

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$$ \mathrm{H}/\mathrm{C}\left(\mathrm{VR}\right)={2.1364}^{-0.698\mathrm{VR}} $$
(1)
$$ \mathrm{VR}\left(\mathrm{H}/\mathrm{C}\right)=1.428 \ln \left(\mathrm{H}/\mathrm{C}\right)+1.0908 $$
(2)

According to the definition of ULMHG, the ULMHG can be expressed as the VR value, after which the change in H/C is less than 1 % of the total variation (Rx in Fig. 3). In this manner, formula 3 can be established.

$$ \frac{\mathrm{H}/\mathrm{C}\left({R}_{\mathrm{x}}\right)-0.1}{\mathrm{H}/\mathrm{C}(0.5)-0.1}=0.01 $$
(3)

where H/C is the ratio of hydrogen and carbon atoms in kerogen (dimensionless), VR is the vitrinite reflectance (%), and Rx is the VR value corresponding to the ULMHG (%).

From formulas (1), (2), and (3), the ULMHG is 4.19 % when H/C is 0.11.

Reduction in atomic O/C

Similarly, as organic material experiences thermal evolution and generates more hydrocarbons, the reduction amount of atomic O/C in the organic materials decreases. Figure 4 reflects the variation in H/C corresponding to the VR values of Cambrian and Ordovician source rocks in the TBP. Theoretically, at the ULMHG, O/C is at its minimum value and will remain steadily. Previous studies shown that, when the O/C value reaches 0.02, it will remain at this value (Hunt 1979; Zhang et al. 1999). Therefore, we consider 0.02 as the ultimate minimum value of O/C, and the value corresponding to a VR of 0.5 % is regarded as the maximum value of O/C. The principle of determining the ULMHG of carbonate source rocks in the TBP is shown in Fig. 5. The fitted formulas between O/C and VR can be expressed as follows:

Fig. 4
figure 4

Decrease in O/C of the Cambrian and Ordovician carbonate source rocks in the TBP: a measured value of O/C. b average value of O/C. c fitted curve of decrease in O/C

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Fig. 5
figure 5

Principle of determining the ULMHG using method of decrease in O/C

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$$ \mathrm{O}/\mathrm{C}\left(\mathrm{VR}\right)=0{.1566}^{-0.49\mathrm{VR}} $$
(4)
$$ \mathrm{VR}\left(\mathrm{O}/\mathrm{C}\right)=-2.038 \ln \left(\mathrm{O}/\mathrm{C}\right)-3.775 $$
(5)

Similarly, the ULMHG can be expressed as the VR, after which the change in O/C is less than 1 % of the total variation. In this manner, formula 6 can be established.

$$ \frac{\mathrm{O}/\mathrm{C}\left({R}_{\mathrm{x}}\right)-0.1}{\mathrm{O}/\mathrm{C}(0.5)-0.1}=0.01 $$
(6)

where O/C is the ratio of oxygen and carbon atoms in kerogen (dimensionless), VR is the vitrinite reflectance (%), and R x is the VR value corresponding to the ULMHG (%).

From formulas (4), (5), and (6), the ULMHG is 4.10 % when O/C is 0.021.

Variation in hydrocarbon generation potential

The Rock-Eval pyrolysis parameters S 1 and S 2 represent the free and pyrolysis hydrocarbons, respectively. S 1 + S 2 express the hydrocarbon generation potential. (S 1 + S 2)/TOC is the index of current hydrocarbon generation potential. In this study, some typical pyrolysis data of hydrocarbon generation potential of carbonate source rocks in the TBP are shown in Table 2, for which some data were obtained by our own pyrolysis experiments. Previous studies have shown that (S 1 + S 2)/TOC initially increases and then decreases with increasing of depth or VR (Zhou and Pang 2002; Pang et al. 2004). (S 1 + S 2)/TOC increases because organic matter undergoes deoxidation during diagenesis. CO2 is generated and the amount of TOC decreases during this time. Later, (S 1 + S 2)/TOC decreases because hydrocarbons are discharged from the source rocks. When the hydrocarbon generation potential decreases to a minimum value and remain steady, hydrocarbon generation within the source rocks ceases. To have a better understanding of the ULMHG, Cambrian and Lower Ordovician source rocks with high maturity were used as our research objects. Figure 6 shows the variations in (S 1 + S 2)/TOC with VR for the Cambrian and Lower Ordovician source rocks in the TBP. A VR value of 0.90 % is set as the boundary in this study. (S 1 + S 2)/TOC increases with increasing VR when VR is less than or equal to 0.90 %, but decreases with increasing VR when VR is greater than 0.90 %. To perform quantitative analysis, we divided the (S 1 + S 2)/ TOC variations into two parts, shown in Fig. 6c.

Table 2 Some representative pyrolysis data of hydrocarbon generation potential of carbonate source rocks in the TBP
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Fig. 6
figure 6

Variation in (S 1 + S 2)/TOC of the Cambrian and Ordovician carbonate source rocks in the TBP: a measured value of (S 1 + S 2)/TOC. b average value of (S 1 + S 2)/TOC. c fitted curve of variation in (S 1 + S 2)/TOC

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When the amount of final hydrocarbon generation A3 is equal to 1 % of the total hydrocarbon generation, the VR at this point is defined as the ULMHG in this study. The area under the curve of (S 1 + S 2)/TOC and VR represents the amount of hydrocarbon. The area can be calculated using integral. The calculation is divided into two parts: VR values of 0.5–0.9 % (A1) and VR values of 0.9–6.0 % (A2). A VR of 0.5 % is the hydrocarbon generation threshold, and the (S 1 + S 2)/TOC value at this point is the start point of the study. To study the proportion of the final amount of hydrocarbon, the minimum hydrocarbon generation potential must be determined. From previous studies, the ULMHG is normally less than 6.0 % (Tissot and Welte 1984; Wang et al. 2005; Chen et al. 2007). Therefore, we use 6.0 % as the final point of the study (Fig. 7). The fitted formulas for (S 1 + S 2)/TOC and VR can be expressed as follows:

Fig. 7
figure 7

Principle of determining the ULMHG using method of variation in (S 1 + S 2)/TOC

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  • for VR ≤ 0.90 %,

    $$ \left({S}_1+{S}_2\right)/\mathrm{TOC}{\left(\mathrm{VR}\right)}_1=41.66{e}^{2.518\mathrm{VR}} $$
    (7)
    $$ A1={\displaystyle {\int}_{0.5}^{0.9}\left({S}_1+{S}_2\right)/\mathrm{TOC}{\left(\mathrm{VR}\right)}_1}d\mathrm{VR} $$
    (8)

  • for VR > 0.90 %,

    $$ \left({S}_1+{S}_2\right)/\mathrm{TOC}{\left(\mathrm{VR}\right)}_2=1459.8{e}^{-1.035\mathrm{VR}} $$
    (9)
    $$ A2={\displaystyle {\int}_{0.9}^6\left({S}_1+{S}_2\right)/\mathrm{TOC}{\left(\mathrm{VR}\right)}_2}d\mathrm{VR} $$
    (10)
    $$ \frac{A3}{A1+A2}=0.01 $$
    (11)

where (S 1 + S 2 )/TOC is the index of hydrocarbon generation potential for the source rock (mg/g), VR is the vitrinite reflectance (%), A1 is the hydrocarbon generation amount as (S 1 + S 2 )/TOC increases (mg/g), A2 is the hydrocarbon generation amount as (S 1 + S 2 )/TOC decreases to a minimum (mg/g), and A3 is the hydrocarbon generation amount in the VR range from the ULMHG to 6.0 % (mg/g).

From formulas (8), (10), and (11), the ULMHG is 4.83 % when A3 is 6.6 mg/g.

Optimum modeling of organic materials based on the material balance principle

Organic materials mainly consist of five elements: C, H, O, N, and S, which comprise more than 99.5 % of total organic materials. Based on the principle of material balance, products from organic materials will also be composed of these five elements. Thus, the loss of these five elements should be equal to the amount of hydrocarbons generated. The five elements mainly form ten products: CH4, C2H6, C3H8, C4H10, CO2, H2S, N2, H2, H2O, and oil. As a result, a quantitative model for five elements and products can be established (Pang and Zhou 1995). In fact, the principle of material balance is applicable during the process of hydrocarbon generation; additionally, there are restrictions from geological and geochemical conditions. These conditions include the following: (1) the ratio of the amount of heavy hydrocarbon gases (such as ethane, propane, and butane) to the amount of methane gas generated at a certain stage is a constant; (2) the relative rates of CO2 and H2O generation are limited by the relative abundance of radicals and radical functional groups in the organic matrix structure; (3) the relative quantity of generated H2 does not exceed the maximum amount seen in natural gas reservoirs and source rock formations; and (4) the relative rate of generation of liquid hydrocarbons is consistent with that obtained from pyrolysis simulation experiments. In addition, the output of the ten products gained cannot be negative. According to the foregoing four conditions, when the difference between the quantity of the ten products and the total loss of organic matrices is a minimum value, a quantitative model for the hydrocarbon generation can be established. The formulas can be expressed as follows:

$$ \min \left(\delta \right)= Abs\left(\varDelta M-{\displaystyle \sum_{i=1}^{10}{X}_i}\right) $$
(12)

where ΔM is the total loss of organic matter (g or kg), ∑ X i is the output of ten products (g or kg), δ is the difference between ΔM, and ∑ X i (g or kg).

The final product obtained from formula (12) is the optimum answer. Thus, if the accumulative amounts and percentages of different products corresponding to different VR values can be acquired, it will be possible to determine the ULMHG.

By the optimum modeling of organic materials based on the material balance principle, the instantaneous and cumulative amounts of ten products generated from a unit mass TOC in carbonate source rocks in the Tarim Basin were obtained for the VR range 0.5–5.0 %. The results are shown in Fig. 8. The cumulative amount of hydrocarbons corresponding to a VR of 5.0 % is regarded as the total amount of hydrocarbons generated. The VR value corresponding to 99 % of the total amount of hydrocarbon is referred to as the ULMHG. From this method, the maximum gas generation potential for carbonate source rocks is 0.436 m3/g TOC, and its ULMHG is 4.44 %. The amount of gas generated with a VR of 5 % might be a little less than the total gas generated, and the ULMHG obtained might be less. However, the amount of gas generated after a VR of 5.0 % is very small, and thus it can cause only a small error. As a result, the ULMHG determined using this method is reliable.

Fig. 8
figure 8

Results of optimum modeling based on material balance principle of per mass TOC of carbonate source rocks in Tarim Basin

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Thermal simulation experiment

Thermal simulation experiments are important methods for determination of the ULMHG. From the time–temperature compensation theory, the VR value corresponding to the end of hydrocarbon generation can be obtained from measurements of the hydrocarbon generation rate during thermal simulation and the VR values for different temperatures. Thermal simulation experiments include both anhydrous and hydrous experiments, and the results of the latter are a better model for natural evolution (Lewan et al. 1979; Lewan 1983). Although the conditions in thermal simulation experiments greatly differ from real geological conditions in sedimentary basins and cannot reveal the real hydrocarbon generation of source rocks, the ULMHG obtained by this method can be used as an important reference. There have been many previous studies of the ULMHG using hydrous thermal simulation experiments (Cramer et al. 2001; Zhang et al. 2002; Xie et al. 2002).

Hu et al. (2006) and Chen et al. (2007) conducted studies of the ULMHG of coal and marine mudstone source rocks in the TBP. However, their ULMHG values were qualitatively estimated and have relatively large errors. On the strength of the quantitative definition of ULMHG, we restudied the ULMHG using thermal simulation experiments. On an open system, Hu (2005) simulated the rate of gas generation of marl source rocks in Well Tazhong 201 in the Tarim Basin, with a TOC of 1.38 wt%, a VR of 1.1 %, and organic material type of II1. To better reflect the ULMHG, we use the experiment data of Hu (2005). When the VR is 3.1 %, the cumulative rate of gas generation is 61.8 m3/t TOC. From the trend of the rate of gas generation, the estimated maximum cumulative rate of gas generation is 65 m3/t TOC, which corresponds to a VR of 5.0 % (Fig. 9). Taking into account the last 1 % of gas generation (0.65 m3/t TOC), the ULMHG is 4.30 %.

Fig. 9
figure 9

Gas generation rate and its predicted value of Tazhong 201 well by thermal simulation experiments

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Variation in hydrocarbon retention amount

The amount of chloroform bitumen “A” or S 1 reflects the amount of residual hydrocarbons in source rocks. We use the amount of hydrocarbon retention per unit of organic carbon (S 1/TOC or “A”/TOC) to define the hydrocarbon retention ability of source rocks. Previous studies have shown that because of the influence of the organic matter maturity, pressure, temperature, porosity of the source rocks, and oil–gas solubility in water, the S 1/TOC or “A”/TOC first increases and then decreases with increasing depth or VR (Pang 1995; Pang et al. 2004; Hao et al. 1996). This is because some hydrocarbons are residual in source rocks as a result of adsorption and dissolution. Hydrocarbons are only discharged when a sufficient quantity has been retained in source rocks, that is, when the critical saturation of residual hydrocarbon has been reached (Dickey 1975; Magara 1978; Durand 1988). This critical saturation of residual hydrocarbon initially increases and then decreases with depth (Pang 1995). When S 1/TOC or “A”/TOC decreases to a minimum value, hydrocarbon generation and expulsion cease, or the amount of hydrocarbon generated is equal to the amount expelled and this amount is so small that it can be ignored. The VR at this point is defined as the ULMHG. The principle for hydrocarbon retention of studies of the ULMHG is similar to that for the method of hydrocarbon generation potential. Representative data for “A” and S 1 is shown in Tables 2 and 3.

Table 3 Some representative data of Chloroform bitumen "A" of carbonate source rocks in the TBP
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Variation in S 1/TOC

The data used for this method are the TOC values and the pyrolysis parameters (S 1) of the Cambrian and Ordovician carbonate source rocks in the TBP. As shown in Fig. 10, the VR of the turning point is 0.94 %. The principle for use of S 1/TOC in the study of the ULMHG is shown in Fig. 11. When the amount of final residual hydrocarbon A3 is equal to 1 % of the total residual hydrocarbon, the VR value at this point is the ULMHG. Furthermore, the area under the curve of residual hydrocarbon S 1/TOC and VR represents the amount of residual hydrocarbon. The calculation is divided into two parts: for VR of 0.5–0.94 % (A1) and for VR of 0.94–6 % (A2). The S 1/TOC value for a VR of 0.5 % is the starting point of the study. Similarly, we use the S 1/TOC value corresponding to a VR of 6.0 % as the end point of the study (Fig. 11). The fitted formulas for S 1/TOC and VR can be expressed as follows:

Fig. 10
figure 10

Variation in S 1/TOC of the Cambrian and Ordovician carbonate source rocks in the TBP: a measured value of S 1/TOC. b average value of S 1/TOC. c fitted curve of variation in S 1/TOC

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Fig. 11
figure 11

Principle of determining the ULMHG using method of variation in S 1 /TOC

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  • for VR ≥ 0.94 %,

    $$ {S}_1/\mathrm{TOC}{\left(\mathrm{VR}\right)}_1=14.762{e}^{2.9494\mathrm{VR}} $$
    (13)
    $$ A1={\displaystyle {\int}_{0.5}^{0.94}{S}_1/\mathrm{TOC}{\left(\mathrm{VR}\right)}_1}d\mathrm{VR} $$
    (14)

  • for VR < 0.94 %,

    $$ {S}_1/ TOC{(VR)}_2=789.44{e}^{-1.1\mathrm{VR}} $$
    (15)
    $$ A2={\displaystyle {\int}_{0.94}^6{S}_1/\mathrm{TOC}{\left(\mathrm{VR}\right)}_2}d\mathrm{VR} $$
    (16)

where S 1/TOC is the index of hydrocarbon retention of source rock (mg/g), VR is the vitrinite reflectance (%), A1 is the hydrocarbon retention amount as S 1/TOC increases (mg/g), A2 is the hydrocarbon retention amount as S 1/TOC decreases to a minimum (mg/g), and A3 is the hydrocarbon retention amount in the VR range from the ULMHG to 6.0 % (mg/g).

From formulas (11), (14), and (16), the ULMHG is 4.65 % when A3 is 3.32 mg/g.

Variation in “A”/TOC

The data required for this method are the levels of TOC and chloroform bitumen “A” of the Cambrian and Ordovician carbonate source rocks in the TBP. As shown in Fig. 12, the turning point of VR is 1.1 %. The principle of the “A”/TOC method for the study of the ULMHG is shown in Fig. 13. The calculation is divided into two parts: for VR range 0.5–1.1 % (A1) and for VR range 1.1–6.0 % (A2). The fitted formulas for “A”/TOC and VR can be expressed as follows:

Fig. 12
figure 12

Variation in “A”/TOC of the Cambrian and Ordovician carbonate source rocks in the TBP: a measured value of “A”/TOC. b average value of “A”/TOC. c fitted curve of variation in “A”/TOC

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Fig. 13
figure 13

Principle of determining the ULMHG using method of variation in “A”/TOC

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  • for VR ≤ 1.1 %,

    $$ ^{\prime \prime}\mathrm{A}^{\prime \prime }/\mathrm{TOC}{\left(\mathrm{VR}\right)}_1=3.2649{e}^{1.9397\mathrm{VR}} $$
    (17)
    $$ A1={\displaystyle {\int}_{0.5}^{1.1\prime\prime}\mathrm{A}^{\prime \prime }/\mathrm{TOC}{\left(\mathrm{VR}\right)}_1}d\mathrm{VR} $$
    (18)

  • for VR > 1.1 %,

    $$ ^{\prime \prime}\mathrm{A}^{\prime \prime }/\mathrm{TOC}{\left(\mathrm{VR}\right)}_2=105.87{e}^{-1.085\mathrm{VR}} $$
    (19)
    $$ A2 = \int {_{{1.1}}^{6}{{{\prime \prime {\rm{A}}\prime \prime }} \left/ {{{\rm{TOC}}{{{\left( {{\rm{VR}}} \right)}}_{2}}d{\rm{VR}}}} \right.}} $$
    (20)

where “A”/TOC is the index of hydrocarbon retention of the source rock (mg/g), VR is the vitrinite reflectance (%), A1 is the hydrocarbon retention amount as “A”/TOC increases (mg/g), A2 is the hydrocarbon retention amount as “A”/TOC decreases to a minimum (mg/g), and A3 is the hydrocarbon retention amount in the VR range from the ULMHG to 6.0 % (mg/g).

From the formulas (11), (18), and (20),the ULMHG is 4.78 % when A3 is 0.4 mg/g.

Variation in hydrocarbon expulsion amount

The amount of hydrocarbon expulsion first increases and then decrease with increasing VR (Tissot and Welte 1984; Pang 1995) under the influence of hydrocarbon generation and residual hydrocarbon. Decrease of the expulsion to zero or a minimum amount indicates the end of the hydrocarbon expulsion, and further suggests that hydrocarbon generation has ceased. The VR value corresponding to the minimum amount of hydrocarbon expulsion is defined as the ULMHG. When the expulsion is zero, the expulsion velocity is reduced to zero and the expulsion efficiency is increased to a maximum of nearly 100 %. The expulsion velocity and efficiency at that point can be used to determine the ULMHG. The method of hydrocarbon generation potential, based on the hydrocarbon expulsion threshold theory, is an effective method for calculating hydrocarbon the expulsion velocity and efficiency (Zhou and Pang 2002; Ma et al. 2009) (Fig. 14).

Fig. 14
figure 14

Mode of calculating hydrocarbon expulsion velocity and efficiency using method of hydrocarbon generation potential

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Variation in expulsion velocity

The same method as for obtaining the hydrocarbon generation potential is employed to calculate the expulsion velocity (V e ) of the Cambrian and Lower Ordovician source rocks in the Tazhong area (Fig. 15). When the VR is 1.16 %, the expulsion velocity increases to a maximum value, which is the peak of hydrocarbon expulsion. The area under the V e and VR curve represents the amount of hydrocarbon expulsion. The principle of determining the ULMHG from the expulsion velocity is shown in Fig. 16. When the amount of final hydrocarbon expulsion A3 is equal to 1 % of the total amount of hydrocarbons expelled, the VR at this point is the ULMHG. The calculation is divided into two parts: for VR values of 1.06–1.16 % (A1) and for VR values of 1.16–6.0 % (A2). A VR value of 1.16 % is the turning point. The fitted formulas for V e and VR can be expressed as follows:

Fig. 15
figure 15

Variation in hydrocarbon expulsion velocity of the Cambrian and Ordovician carbonate source rocks in the Tazhong area: a calculating value of hydrocarbon expulsion velocity. b fitted curve of variation in hydrocarbon expulsion velocity

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Fig. 16
figure 16

Principle of determining the ULMHG using method of variation in hydrocarbon expulsion velocity

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  • for VR ≤ 1.06 %,

    $$ {V}_{\mathrm{e}}{\left(\mathrm{VR}\right)}_1=-1634.8{\mathrm{VR}}^2+3829.6\mathrm{VR}-2220.7 $$
    (21)
    $$ A1={\displaystyle {\int}_{1.06}^{1.16}{V}_{\mathrm{e}}}{\left(\mathrm{VR}\right)}_1d\mathrm{VR} $$
    (22)

  • for VR > 1.16 %,

    $$ {V}_{\mathrm{e}}{\left(\mathrm{VR}\right)}_2=60.081{e}^{-1.12\mathrm{VR}} $$
    (23)
    $$ A2={\displaystyle {\int}_{1.16}^6{V}_{\mathrm{e}}}{\left(\mathrm{VR}\right)}_2d\mathrm{VR} $$
    (24)

where V e is the hydrocarbon expulsion velocity of the source rock (kg/(t∙102 m)), VR is the vitrinite reflectance (%), A1 is the amount of hydrocarbon expelled as V e increases (kg/t or mg/g), A2 is the amount of hydrocarbon expulsion as V e decreases to zero (kg/t or mg/g), and A3 is the hydrocarbon expulsion amount in the VR range from the ULMHG to 6.0 % (kg/t or mg/g).

From formulas (11), (22), and (24),the ULMHG is 4.83 % when A3 is 0.17 mg/g.

Increasing in expulsion efficiency

The same method as for hydrocarbon generation potential can also be employed to calculate the expulsion efficiency (F e) of the Cambrian and Lower Ordovician source rocks in the Tazhong area. To have a better understanding of trends in F e variation and for the purpose of quantitative analysis, we select the larger value of F e in the latter part to be used in a quantitative fitted formula (Fig. 17). Based on the definition of the ULMHG, and assuming F e can increase to 100 %, the VR value corresponding to F e = 99 % is the ULMHG. The fitted formula for Fe and VR can be expressed as follows:

Fig. 17
figure 17

Hydrocarbon expulsion efficiency of the Cambrian and Lower Ordovician carbonate source rocks in the Tazhong area: a Select fitted value of hydrocarbon expulsion efficiency. b Fitted curve of hydrocarbon expulsion efficiency

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$$ \mathrm{VR}\left({F}_{\mathrm{e}}\right)=0.0036{F}_{\mathrm{e}}^2-0.496{F}_{\mathrm{e}}+18.73 $$
(25)

where VR is the vitrinite reflectance (%), and F e is the hydrocarbon expulsion efficiency (%).

From the formula (25), the ULMHG is 4.84 % when F e is 99 %.

Results and discussion

Comprehensive determination and evaluation of the ULMHG

This study employs six methods for investigating the ULMHG of carbonate source rocks in the TBP (Table 4). It shows some differences between the results generated using different methods, but the differences are small. The ULMHG varies from a VR of 4.10 % to a VR of 4.84 %.

Table 4 Comparison of the ULMHG determined using different methods
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Study of the ULMHG in this paper is based on the mechanisms of hydrocarbon generation, retention, and expulsion, and the principles used herein are clear. Data on the organic elements, pyrolysis parameters, and chloroform bitumen “A” can be obtained from experiments or from the oilfield database, and thus, the implementation process is simple and feasible. The ULMHG values, which range from 4.10 to 4.84 %, show only small differences, indicating that our study may be reliable. However, these methods also have some drawbacks. Except for the thermal simulation experiments on hydrocarbon generation, other methods require statistical results to a greater or lesser degree. Differences in the data and data reliability may affect the final result. Therefore, it is important to select and screen the data so as to be able to use similar data obtained from the same formation, lithology, and sedimentary facies. Hydrocarbon expulsion efficiency cannot reach 100 %; therefore, the ULMHG determined using the expulsion efficiency is the maximum possible value. For methods of variation in hydrocarbon generation potential and hydrocarbon retention, the VR of the hydrocarbon generation threshold is determined as 0.5 %, but this ignores the fact that some hydrocarbons might have been generated and then remained as a residue when VR was less than 0.5 %. Therefore, the ULMHG determined using these two methods is higher than the real value. Optimum simulation of organic materials based on the principle of material balance regards hydrocarbons as being generated only when VR is 0.5–5 %; therefore, the ULMHG from this method is lower than the real value. Considering the pros and cons of the various methods, the ULMHG values of marine carbonate source rocks obtained from some methods are higher and those from other methods are lower. We consider the average VR of 4.55 % as a reliable value for the ULMHG.

Comparison with previous studies of the ULMHG

Mostly, the ULMHG is studied in terms of natural gas. Some research on the main gas generation period and the ULMHG of different source rocks has been conducted. During thermal evolution of organic matters, the amounts of gas generated during different phases of thermal evolution are different. Large amounts of gas are generated at a particular stage of thermal evolution. This stage is called the main gas generation period, and a majority of the gas (generally 60–80 %) is generated during this time (Zhao et al. 2005; Wang et al. 2005; Chen et al. 2007; Su et al. 2012). VR is used to represent the main gas generation period. The VR of types I and II kerogen during the main gas generation period is 0.96–3.0 %, and that of crude cracked gas is 1.5–3.5 %. Under geological conditions, source rocks resemble a closed system (Behar et al. 1995). Natural gas generation processes mainly involve the generation of gas pyrolysis and crude cracking; therefore, the ULMHG of carbonate source rocks should be greater than 3.5 %.

Different studies of the ULMHG have yielded different results. Tissot and Welte (1984) argued that source rocks enter the metamorphic stage when VR is greater than 4.0 %. Part of the residual kerogen is converted to graphite. Furthermore, methane is destroyed at that time, and the source rocks enter the ULMHG. For marine organic matter, from the study of hydrocarbon generation dynamics, Wang et al. (2005) argued that the ULMHG of type I kerogen is approximately 3.5 %, the VR for type II kerogen is 4.4–4.5 %, and the VR for marine oil is approximately 4.6 %. Su et al. (2012) argued that the ULMHG of type II kerogen is 4.38 %. Through qualitative analysis using several methods including pyrolysis, the elements present in kerogen, high-temperature pyrolysis gas chromatography, and thermal simulation experiments in gold tubes, Chen et al. (2007) showed that the ULMHG for types I and II kerogen of the Cambrian and Ordovician marine source rocks in the Tarim Basin is 3.0 %. This value is clearly too small. We used several quantitative calculation methods to investigate the ULMHG and determined the VR of type I kerogen to be 4.10–4.84 %, with an average value of 4.55 %. The results from different methods are very similar. Previous studies have shown that the ULMHG of kerogen and crude oil can be 4.4–4.6 % (Wang et al. 2005; Chen et al. 2007). Therefore, the ULMHG values determined in this study are in agreement with the characteristics of hydrocarbon generation under actual geological conditions.

Residual hydrocarbon generation potential of carbonate source rocks in TBP

From the ULMHG values of the carbonate source rocks in the TBP and the actual measured VR value of these source rocks, we can discern whether the source rocks have reached the ULMHG and their residual hydrocarbon generation potential (Table 5). On the basis of actual measured VR values, the Cambrian and Ordovician source rocks have reached the maturity stage. The VR values of the Tazhong uplift, the Bachu uplift, and the Tabei uplift are 0.81–2.25, 1.15–2.34, and 0.64–2.21 %, respectively. The source rocks of these areas have not reached the ULMHG, and are still in the oil generation and wet gas generation stages. Their residual hydrocarbon generation potential is large according to the classic theory of the hydrocarbon generation from thermo-decomposition of kerogen (Tissot and Welte 1984). In the Tadong area, the VR is 0.87–4.90 %, indicating that some of the source rocks have reached the ULMHG and others have entered the middle or late dry gas generation stages. The residual hydrocarbon generation potential is small. The source rocks in the Manjiaer sag have greater depth and higher maturity and may have ceased to generate oil and gas. For source rocks of different formations, the VR values of the Cambrian source rocks is 1.21–4.90 % and the amount of further hydrocarbon generation is small. The residual hydrocarbon generation potential of the Ordovician source rocks with VR values of 0.64–3.57 % is large. To summarize, the carbonate source rocks in the TBP have generated a large amount of hydrocarbons but they still have good potential for hydrocarbon generation. Large reservoirs could form, and therefore, the exploration prospects in the deep TBP are favorable. The Cambrian dolomite deep reservoir detected by well Zhongshen 1 in 2012 is a very good example of this.

Table 5 Evaluation of residual potential of hydrocarbon generation in different areas or formations in the TBP
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Conclusions

The upper limit of maturity for hydrocarbon generation (ULMHG) is the maturity at which the hydrocarbon generation potential of the organic matter decreases to a minimum value. It is represented by the vitrinite reflectance (VR), where the VR reaches the point at which the amount of further hydrocarbon generation is less than 1 % of the total hydrocarbon generation. Studying the ULMHG can help us understand the mechanism of hydrocarbon generation and accumulation and evaluate the deep hydrocarbon resource potential in the Tarim Basin. Furthermore, it has great importance and practical significance for predicting potential favorable exploration areas and designing deep reservoir drilling.

From the mechanism of hydrocarbon generation, retention, and expulsion, the ULMHG of the carbonate source rocks in the TBP was systematically and quantitatively studied using six separate methods. These methods are as follows: reduction in atomic ratio for organic elements, variation in hydrocarbon generation potential, optimum modeling of organic materials based on material balance principle, thermal simulation experiments, variation in hydrocarbon retention amount, and variation in hydrocarbon expulsion amount. This study shows that the VR values corresponding to the ULMHG determined using the different methods range from 4.10 to 4.84 % with an average value of 4.55 %, which is in agreement with the actual geological conditions of hydrocarbon generation.

The Cambrian and Ordovician carbonate source rocks in the Tazhong uplift, the Bachu uplift, and the Tabei uplift have not yet reached the ULMHG. They are still in the oil generation and wet gas generation stages, and the residual hydrocarbon generation potential is relatively large. In the Tadong area, some source rocks have reached the ULMHG. They have entered the middle or late dry gas generation stages and the amount of further hydrocarbon generation is small. The source rocks in the Manjiaer sag may have ceased oil and gas generation. The hydrocarbon generation potential of the Ordovician source rocks is still large, but that of the Cambrian source rocks is relatively small. In summary, large-scale reservoirs can form and there are good exploration prospects in the deep TBP.