Condensate gas reservoir is a special kind of reservoir between an oil reservoir and a gas reservoir. Under the condition of high temperature and pressure in deep formation, condensate gas reservoir exists in the form of a single gas phase. In the development process, with the continuous reduction of formation pressure and temperature, the heavy hydrocarbon components in the gas phase will change in phase state, precipitate from the gas phase and condense into liquid condensate to form gas–liquid two-phase (Orangi et al., 2011; Panja et al., 2019; Tang et al., 2021). By the end of 2020, the total recoverable resources of conventional condensate in the world were 534.9 × 10⁸ t, and the cumulative output was 55.4 × 10⁸ t, accounting for 10.4% and indicating that the discovered condensate oil and gas resources still have great development potential. The recoverable resources to be discovered are 241.8.9 × 10⁸ t, accounting for 45.2% and indicating that the condensate oil and gas resources still have great exploration potential (Tong et al., 2014; Tong et al., 2018; Wang et al., 2021). The newly discovered condensate oil and gas fields in China are mainly located in the Tarim Basin and Bohai Bay Basin (Hu et al., 2020; Yang et al., 2020; He et al., 2021). There are many transition types of fluids in the condensate gas reservoir, which have the characteristics of complex phase behavior and hydrocarbon components. These reservoir characteristics lead to a large deviation between the prediction result and the actual situation in the condensate gas reservoir, which seriously affects the implementation of potential tapping and well stimulation. So, accurate identification of hydrocarbon types is the key issue to improve the development efficiency of the condensate gas reservoir. The main methods to identification condensate gas include phase behavior research methods such as oil and gas reservoir temperature–pressure phase diagram and empirical statistical methods based on the content of methane (C1), ethane (C2), propane (C3), butane (C4), and pentane (C5), formation fluid density, component average molecular weight, and production gas oil ratio Among them, the identification result of phase state research method is more accurate, but it needs a large number of field sampling and experimental data. Empirical statistical methods need less data, but the reliability of the identification results will be reduced. In recent years, some researchers have tried to use logging information to quantitatively distinguish complex hydrocarbon types; for example, Gao et al. (2003) proposed a quantitative calculation of the gas–oil ratio method using the logging information to identify condensate gas reservoirs. Zhao et al. (2006) introduced the genetic algorithm into optimization of logging data processing due to the characteristics of global optimization in genetic algorithm. On this basis, they calculated the surface gas–oil ratio and achieved the purpose of identifying condensate gas reservoirs. Feng et al. (2020) used the logging information to calculate the relative content of CO₂ and apparent porosity to identify CO₂ gas reservoirs comprehensively. These attempts provide the ideas and methods for simple, rapid, and accurate identification of complex hydrocarbon types in reservoirs.

Because the condensate gas reservoir exists in the form of a single gas phase under the conditions of formation temperature and pressure, its geophysical logging response characteristics are similar to the conventional gas reservoirs, which leads to the unreliable discrimination results of the condensate gas reservoirs through only conventional logging information. Compared with conventional logging data, gas logging can directly obtain the relative content of C1–C5 components of the hydrocarbon reservoir and can more intuitively reflect the characteristics of reservoir fluid properties. So, the gas logging information is also widely used in complex hydrocarbon discrimination. For example, Liu et al. (2017) used the interpretation chart of gas logging to qualitatively identify condensate gas reservoir and light oil reservoir. Xu et al. (2019) proposed a method for identifying buried-hill condensate gas reservoirs in BZ 19-6 structure based on the statistical analysis of the geochemical logging data. Wei and Li (2020) applied similar conventional logging and mud logging comprehensive identification technology to the western South China Sea and achieved good application results in the identification of condensate gas layers and volatile oil reservoirs. Taking advantage of the advantages of the gas logging information in complex hydrocarbon identification, and based on the above research, we propose a gas–oil ratio calculation method which introduces gas logging data and uses the quantitative calculation results of the gas–oil ratio to distinguish the condensate gas reservoir.

For the condensate gas reservoirs, the formation components mainly include immovable oil, movable oil, movable water, natural gas, shale, and various skeletal minerals of rocks (Gao et al., 1995; Li et al., 2020; Zhao et al., 2020). The relative contents of these components in the formation are defined as x _or ,x _om ,x _fw ,x _gas ,x _sh ,x _ma , and the formation component volume model of the condensate gas reservoirs is as shown in Eq. 1: x o r + x o m + x f w + x g a s + x s h + x m a = 1 . (1)

According to the formation component volume model, we can get the general response equation as Eq. 2 for various of logging instruments: ∑ j = 1 n A i j x j = B i   ( i = 1 ,   2 ,   ⋯ , m ) , (2) where A _ij is the response value of the ith logging instrument to the jth component; m is the number of logging types, and B is the response value of the logging instruments to the formation.

The equation set of the model can be written as: { m i n f ( x → ) , f ( x → ) = ∑ i = 1 m ( ∑ j = 1 n A i j x j − B i ) 2 c o n s t r a i n t   R : ∑ j = 1 n x j = c 0 ≤ x j ≤ x m a x j ( i = 1,2, ⋯ ,m;j = 1,2, ⋯ ,n ) , , (3) where c, x _maxj are both constants. In the formation component analysis program, c = 1,x _maxj is the maximum relative volume of the j-th component. By solving Eq. 3, which consists of m equations, the relative contents of all of components in the formation can be obtained.

According to the ideal gas state equation, the relationship between the adiabatic bulk modulus, density, temperature, and pressure, as well as compressibility coefficient of gases, can be derived (Batzle and Wang 1992; Li, 2006): V = Z R T a P , (4) where p is the pressure, MPa; V is the molar volume, the value between 0 and 1; R is the gas constant, dimensionless; T _a is the absolute temperature, K; and Z is the gas compression factor.

The volume of the natural gas under the surface condition V _gs can be obtained from the volume of the natural gas under the formation condition V _gf from Eq. 4: V g s = T s P g f V g f z f T f P g s , (5) where T _s is the surface temperature, K; P _gf is the formation pressure, which is the pressure acting on the fluid in the rock pores, MPa; T _f is the formation temperature, which is converted from the surface temperature and the ground temperature gradient, K; Z _f is the compression factor of the natural gas at the well bottom, zero dimension; and P _gs is the surface pressure, MPa.

ROG is the ratio of the normal gas volume (V _gs ) and the movable oil volume (V _om ) under ground conditions: R O G = V g s V o m . (6)

The volume of movable oil on the ground is approximately equal to that under the ground. Assuming that the rock volume is V _rock , then V _gf = x _gas V _rock , V _om = x _om V _rock . Bringing Eq. 5 into Eq. 6, we get the calculation formula of the gas–oil ratio as follows: R O G = x g a s x o m T s P g f z f T f P g s . (7) where x _gas is the relative content of natural gas in the formation, and x _om is the relative content of movable oil in the formation.

The solution of the optimization mathematical model is to obtain x _gas and x _om by solving Eq. 3 and then bring them into the gas–oil ratio calculation formula, namely Eq. 7. In this way, we can quantitatively calculate the gas–oil ratio parameters. The specific solving process is as follows:

Select a point x → ( 0 ) in R, then the linear approximation function of f ( x → ) at x → ( 0 ) is f L ( x → ) = f ( x → ( 0 ) ) + [ ∇ f ( x → ( 0 ) ) ] ( x → − x → ( 0 ) ) . (12)

In the above equation, ∇ f ( x → ( 0 ) ) = [ ∂ f ( x → ( 0 ) ) ∂ x 1 , ∂ f ( x → ( 0 ) ) ∂ x 2 , ⋯ , ∂ f ( x → ( 0 ) ) ∂ x n ] . Obviously, solving the optimal solution of linear programming problem min f L ( x → ) is equivalent to solving the optimal solution of linear programming problem min [ ∇ f ( x → ( 0 ) ] T x → . Let x F L ( 0 ) be the optimal solution of Eq. 12, ∂ f ( x → ( 0 ) ) ∂ x k = min [ ∂ f ( x → ( 0 ) ) ∂ x 1 , ∂ f ( x → ( 0 ) ) ∂ x 2 , ⋯ , ∂ f ( x → ( 0 ) ) ∂ x n ] . It is known from the nature of linear programming that x → F L ( 0 ) must be a vertex of R, and therefore, x F L j ( 0 ) = { 0 ( j ≠ k ) x max j ( j = k ) ( j = 1,2 , … , n ) . (13)

1) When [ ∇ f ( x → ( 0 ) ] T ( x → F L ( 0 ) − x → ( 0 ) ) = 0 , x → F L ( 0 ) is the solution of the linear programming problem, and the iteration stops.

For the optimal solution λ₀, there must be 0 ≤ λ 0 ≤ 1 .

Let x → ( 1 ) = x → ( 0 ) + λ 0 ( x → F L ( 0 ) − x → ( 0 ) ) , take x → ( 1 ) as x → ( 0 ) , continue to linearly approximate the objective function f ( x → ) with the above method, and repeat the above steps until the accuracy is satisfied. Then, it is possible to obtain the solution of the linear overdetermined equation set with constraint in Eq. 3.

Using the method proposed in this article, we quantitatively calculate the gas–oil ratio parameters of the target layer of well O-A2 in O oilfield and identify the different hydrocarbon types.

Figure 6 shows the logging interpretation results of the interval from 2005 to 2052 m in well O-A1. The production gas–oil ratios of the No. 2 interpretation layer (2010–2019 m) and No. 4 interpretation layer (2040–2049.5 m) in this well are 5800 m³/m³ and 35 m³/m³, respectively. According to the production data, they are identified as condensate gas reservoir and conventional oil reservoir. The sixth track in Figure 6 is the parameter curve of the gas–oil ratio, quantitatively calculated by using the optimization mathematical model. The calculated gas–oil ratio of No. 2 interpretation layer (2010–2019 m) and No. 4 interpretation layer (2040–2049.5 m) is 8921 m³/m³ and 89 m³/m³, respectively. The interpretation and identification results are condensate gas reservoir and conventional oil reservoir, respectively, which are consistent with the production situation of the reservoirs.

Figure 7 shows the logging interpretation results of 2090–2052 m in well O-A1, in which M2RX means deep investigation induction logging curve, other logging curves are the same as Figure 6. The Modular Formation Dynamics Test (MDT) was performed at this well, and the MDT sampling gas–oil ratio of 2105–2106 m is 3794.4 m³/m³. According to the formation testing results, this layer was identified to be a condensate gas reservoir. The sixth track in Figure 7 is the parameter curve of the calculated gas–oil ratio. The calculated gas–oil ratio of No. 2 interpretation layer (2100.3–2112 m) is 3788 m³/m³, which is close to the MDT testing gas–oil ratio. According to the calculation results of gas-oil ratio, this layer is determined as a condensate gas layer.

Because the gas logging–derived parameters, H _heavy and H _light , show different response characteristics to the condensate gas reservoir, volatile oil reservoir, and conventional oil reservoir, the calculated gas–oil ratio can also discriminate the volatile oil reservoir effectively. There are some volatile oil layers in the W oilfield near the O oilfield, and we applied the quantitative calculation method of gas–oil ratio into the W oilfield. Figure 8 shows the logging interpretation results in the interval 2680–2713 m of well W-3-1. In this figure, AO20-AO90 means the array induction resistivity curve, other logging curves are the same as in Figure 6. The gas–oil ratio from the drill-stem test (DST) in the interval 2690–2701 m is 644 m³/m³. The conventional logging and gas logging response characteristics are between the condensate gas reservoir and the conventional oil reservoir. According to the DST testing results, this layer was identified to be a volatile oil reservoir. In the sixth track of Figure 8, the calculated gas–oil ratios of No. 1 interpretation layer (2690.2–2696.5 m) and No. 2 interpretation layer (2697.5–2703.4 m) are 605.3 m³/m³ and 676.58 m³/m³, respectively, which are close to the gas–oil ration from the DST. The interpretation and discrimination results are volatile oil reservoirs, which are consistent with the DST testing conclusions.

In this article, we propose a method to identify condensate gas reservoirs using gas–oil ratio parameters calculated by the optimization mathematical model. Through the analysis of gas logging data, we found that gas logging response character of the light hydrocarbon and heavy hydrocarbon components have obvious differences in condensate gas, volatile oil, and conventional oil reservoirs, and there is a clear correlation between the production gas–oil ratio and Tg/C1. Based on this cognition, we convert the fitting relationship between the gas logging derived parameters, H _heavy and H _light , and the production gas–oil ratio to the general form of the response equation of the logging instruments, then introduce it into the process for calculating the gas–oil ratio parameters. We apply the proposed theoretical method in the article to the condensate gas reservoirs in the O oilfield. The application results show that the quantitative calculation method of the gas–oil ratio can calculate the gas–oil ratio parameters more accurately, and the calculation results are consistent with the conclusions of the formation testing data. In addition, we also apply the above theoretical methods to the volatile oil reservoirs in the W oilfield and achieve good results in identifying the volatile oil reservoirs.