3.1. Heat Transfer Simulation
According to the Darcy seepage mode extended by Brinkman-Forchheimer [
18,
19], nitrogen is conserved in mass, momentum and energy through the heat conduction process of fractures to oil shale. The calculation parameters of related oil shale reservoirs and fractures are listed in
Table 6.
Considering the pyrolysis temperature range of organic matter obtained from thermogravimetric experiments in Fuyu oil shale and the thermophysical parameters under different temperature conditions, when the temperature is 500 °C, the pyrolysis rate of organic matter tends to peak, and the porosity of oil shale is 10.89%. Therefore, set 500 °C as the injection temperature for oil shale in-situ pyrolysis simulation. The temperature control equation of the fluid in the formation fissure is,
where
T0 is the initial temperature of oil shale formation, °C;
T is the gas temperature in the well, °C;
ke is the reservoir equivalent permeability, mD;
Q is the gas flow rate, m
3/min;
f(t) is the loss of heat in time when the heat capacity is considered in the process of steady state heat transfer.
where
rh is the outer radius of cement ring in gas injection well, i.e., 385 mm,
ae is the thermal diffusivity of the oil shale reservoir,
ω is the ratio of the formation to the heat capacity of the wellbore, i.e., 1, and
τ is the micro pore average diameter, i.e., 1000 nm.
When the nitrogen temperature is 500 °C and the pressure is up to 9.5 MPa, the output pressure of the well increases gradually with the increase in injection time, as shown in
Figure 3. In the microscopic pore and fissure of oil shale, the transport of nitrogen satisfies Hagen–Poiseuille equation of porous media [
20].
where
u is the nitrogen flow velocity, m/s;
ε is the porosity of oil shale;
C is the oil page rock layer ratio heat capacity, J/(kg·K);
CP is the nitrogen constant pressure specific heat capacity, J/(kg∙K);
λ is the coefficient of oil shale thermal conductivity, W/(m·K); and
F is the force of the porous medium on the nitrogen.
where
β is the average thermal expansion coefficient,
T0 is the oil shale initial temperature, i.e., 288 K, and
dp is the particle mean diameter, mm.
When the injection flow rate is 11 m
3/min, during the pyrolysis of oil shale, the heat is transferred from the wellbore along the fissure to the stratum and the temperature of the oil shale reservoir increases with the heating time. As shown in
Figure 3, with the extension of heating time, it can be seen from the temperature cloud chart that the temperature of the oil shale reservoir around the fracture first increased. After heating for 200 days, the temperature of the whole surrounding fracture reaches the temperature of oil shale pyrolysis. With the extension of the heating time and the progress of the pyrolysis process, the extent of pyrolysis gradually expanded from fractures to oil shale formations on both sides.
In the late heating stage, the formation temperature increased obviously with the prolongation of the injection heat time, but the temperature influence range did not increase further. This is because the oil shale formation near the fissure is first heated, the kerogen is pyrolyzed and the oil and gas products are released. The high temperature oil and gas products are displaced by high pressure gas to FK-2 well and then to surface equipment. Therefore, part of the heat is carried out, which affects the diffusion of heat to oil shale and the effective heat transfer distance. In addition, the injected heat fluid also enters the porous medium under the action of Darcy flow. As the temperature of the formation rises, an increasing number of oil and gas products are generated, and the resistance of thermal fluid into the porous medium is increased; therefore, the range of heat conduction is limited. After 700 days of heating, the oil shale in the fracture extension is basically pyrolyzed.
In addition, as shown in
Figure 4, with the extension of heating time, the pyrolysis zone of the oil shale gradually expanded. The heat transfer of hot nitrogen to oil shale formation gradually reached equilibrium. This is because when the injected heat stays the same, the hot nitrogen gas conducts heat to oil shale formation while maintaining the temperature needed for pyrolysis of kerogen in the pyrolysis zone. Moreover, the oil and gas products produced by pyrolysis of kerogen will be replaced by high-temperature gas to produce wells and take part of the heat. Therefore, with the increase in heat transfer area, the heat loss also increases, which leads to the gradual balance of heat transfer.
3.2. Influence Range of Pressure
Based on the X and Y directions in the oil shale layer, a pressure loss model of gas in a single fracture is proposed based on Beskok and Karniadakis [
21].
where
μ is the injection gas viscosity, Pa∙s;
L0 is the fracture length of FK1 well, mm;
b is the slip coefficient;
α is the equivalent width of fracture, mm;
L1 is the fracture length of FK2 well, mm;
δ is the equivalent thickness of fracture, mm;
R is the gas constant, J/(mol∙K);
T is the temperature, K;
P is the pressure, MPa;
M is the Mole mass of gas, g/mol;
f(ε) is a factor related to the shape, because the effective width of the fracture is only 5 mm, the length of the fracture is 15 m–25 m, the length and width ratio is more than 3000, the value of the fracture is more than 3000, the value of
f(ε) is 0.994 and
b = 0 in the state without slip.
The relationship between displacement flow and differential pressure in main fractures is given by,
where
Pw is the flow pressure, MPa;
α is the main fracture width, mm;
xf is the main fracture half length, i.e., 7.5 m, and
h is the reservoir thickness, m.
In the early stage of heating, under the action of high-pressure displacement, the fluid mainly flows out from the direction of the oil shale bedding. At this time, the oil shale formation is not completely heated, and the porosity of the primary strata is low. The fluid flows through the mining well along the fracture. Only a few fluids flow out from the primary pores of the oil shale under Darcy seepage, the resistance is high along the way and the outlet pressure is small. As shown in
Figure 5, with the increase in oil shale formation temperature, especially the fissure temperature, the porosity increases and the resistance decreases. However, porosity from the fracture to the boundary decreases. Therefore, the seepage field becomes more and more complicated owing to the seepage behavior from fractures in the oil shale. The seepage behavior proceeds from the center of the fracture to the boundary and the outlet of the well. When the oil shale formation is completely thermally pyrolyzed, the porosity of the whole oil shale reservoir increases to 10.89%. The pressure gradient of the seepage field in the whole area becomes uniform, the flow direction is stable and the resistance along the flow further decreases. The pressure field between the high-pressure heat injection well to the low-pressure mining well decreases, and the output pressure of the well is increased; therefore, the displacement effect is enhanced. The pressure gradient between the high-pressure water injection well and low-pressure production well becomes smaller, the pressure field becomes uniform and the output pressure of the well increases, which improves the displacement effect.