#### 3.1. Temperature Extrapolation

The temperature data were measured at various depth from well to well, but 2000 m was the depth where a mass of measurements were concentrated. As the temperature measured at depths greater than 3 km is scattered and uneven, extrapolation of the temperature in a vertical direction is essential for investigation of deep geothermal resources. If the basic parameters (thermal conductivity and radiogenic heat production of different strata) were sufficient, the one-dimensional thermal conductive approaches could be used for extrapolating the temperature to greater depths [

27,

28]. Unfortunately, the Daqing Oilfield does not have enough thermal–physical parameters for this calculation. Besides, the geothermal gradient is depth-dependent in the Songliao basin [

8]. Thus, the deep temperature cannot simply be extrapolated according to the geothermal gradient measured in the shallow wells.

Temperature gradient in the boreholes with continuous temperature log or more than two DST data points was calculated using linear least squares regression [

29]. When only one DST data point was obtained, the gradient was calculated by:

The

T_{0} is given by 0.8–5 °C, the

Z_{0} is given by 30 m [

17].

Above 2000 m, the temperature gradients in the shallow wells (depth less than 500 m) were obviously gentler than those in the deep wells (average depth greater than 1500 m). In general, the temperature gradient steepened when the depths increased to 2000 m (

Figure 3). The difference can be considered as a systematic deviation of temperature gradient calculated from the measurements in shallow wells. The temperature gradients then were multiplied by a correction factor, which is determined by the ratio of average gradient of deep oil wells to average gradient of the water wells, to correct the gradients of water wells at the depth of 2000 m. It is notable that points with values higher than 45 °C/km mainly represent the gradients calculated from DST data, which reflect true condition of the strata more accurately. The effect of local climate on shallow water wells is another potential factor responsible for the discrepancy between gradients.

Beneath 2000 m, the temperature gradients were extrapolated using steady-state heat conduction equation. In the simple situation of steady-state (the radiogenic heat production was ignored) heat flow in the layer

i and

j can be expressed as [

30]:

where

q,

G, and

K represent the conductive heat flow, thermal gradient, and thermal conductivity of layer

i and

j, respectively. In the sedimentary layers with thickness less than 5 km, the heat-flow contribution of the radiogenic heat production will be less than 8 mW·m

^{−2} [

15], which could be ignored when compared with the average surface heat-flow values of 79 mW·m

^{−2} in the Daqing Oilfield [

17]. This allows the heat-flow values at various depths of a well to be considered as a constant number. The reverse relationship between thermal gradient and thermal conductivity can be derived from the Equations (1) and (2):

Equation (4) means that the deep temperature gradient can be extrapolated just according to the thermal conductivity of various layers. Compared with the common 1-D steady-state heat conduction method, the radiogenic heat production was ignored. At the central depression zone, lateral variation of thermal conductivity is not as significant as it is in the vertical direction [

31,

32]. The thermal conductivity of different depth ranges was given according to Zhang et al. [

8] and Wu [

33].

Based on the calculated geothermal gradient, one-dimensional extrapolations were applied to estimate the temperature at 5 km depth in each well of the oilfield. Three scenarios were considered separately [

34]: (1) when the temperature was measured at a depth greater than 5 km, the temperature is determined by straight-line interpolation between the BHT and the surface temperature; (2) when the temperature’s measured depth was shallow than 5 km, the temperature of the upper layers was estimated according to (1) and the temperature at the lower layers was extrapolated from the bottom hole temperature with the equation:

where

Z and

Z_{1} are the depth of known and calculated temperature, respectively,

T_{z} and

T_{1} are the known and calculated temperature, and

G_{z} is the temperature gradient of the interval depth.

The calculation of deep temperature from the geothermal gradient values is different from common methods used by Blackwell et al. [

35], Wang et al. [

36], and other researchers. The computing process has not considered the radiogenic heat production within 5 km. The results might be slightly higher than actual values, but it is still acceptable since we have seriously considered the decreasing trend of temperature gradient and the actual measurements to corroborate the calculated values within the depths of 4 km, despite the fact that extrapolated depths are limited. The great benefit for this method is that relatively small amounts of data are required for calculation.

The temperature is obtained with the premise of a one-dimensional vertical steady-state, and it represents a steady-state temperature conduction field. Geological processes, including regional groundwater activities, rapid uplift, and erosion of the surface could make the temperature field deviate from the steady conduction dominated temperature field [

37]. Furthermore, one-dimensional calculations of deep temperatures cannot reflect the lateral heat transfer in the rock contact zone with different heat conduction rates (uplift and depression contact zone) [

38]. The above two factors may cause a significant difference between the calculated temperature and the real temperature, especially in the shallow depth. Thus, in the process of calculation, the convection-dominated temperature logs were excluded. The dense and even distribution of temperature measurements facilitates a detailed and precise estimation of the lateral temperature variations.

#### 3.2. Volumetric Method

The volumetric method is widely used on assessment of geothermal resources in oil and gas reservoirs. It refers to the calculation of thermal energy in the rock and the fluid that could be extracted based on specified reservoir volume, reservoir temperature, and reference or final temperature. However, it was found that the existing volumetric method tends to overestimate the geothermal reserves in oil and gas reservoirs. Thus the effects of oil and gas saturations on the estimation of geothermal reserve in oil and gas reservoirs are necessarily considered [

39].

The heat in situ consists of the heat stored both in the rock skeletons and in the fluid of pores (either water or oil). If the porosity and permeability are extremely low, the heat stored in the fluid in pores is ignorable, the heat will just be stored in HDR, which can be exploited with EGS. The geothermal resource base is actually the heat content of the targeted medium calculated by Equation (6) [

40,

41]:

where ρ represents rock density,

Cp represents rock specific heat,

V is rock volume,

T is rock temperature at a specific depth, and

Tc refers to the average surface temperature or specific reference temperature. To calculate the heat in situ, the continental area of China was divided into 1 km × 1 km cells on the horizontal plane and 100 m slices in the vertical direction. The computational units can be considered as 1 km × 1 km × 0.1 km cuboids. For each cell, the parameters were given by the mean value. The total thermal energy

Q for all systems (that is, the total mean identified accessible resource base) is simply the sum of the mean thermal energies of the individual systems. All the parameters are listed in the

Table 1.

The volumetric method has been widely used in the HDR geothermal resource assessment due to its simplicity and availability. Utilization of the method in the oil and gas reserve need to be modified [

42]. For the HDR resource from 3 to 5 km, because of the large resource base and relative low porosity, the effects of oil and gas saturation on the geothermal resource can be ignored.