Multi-layer heavy oil reservoir steam injection directional well commingling production limit heating radius calculation method

Abstract

The invention discloses a multi-layer heavy oil reservoir steam injection directional well commingling production limit heating radius calculation method. The method comprises the steps that S1, seepage resistance of all oil layers of a multi-layer heavy oil reservoir is calculated; s2, the steam injection speed of each oil layer of the multi-layer heavy oil reservoir is calculated; s3, designing an orthogonal numerical experiment according to the heat efficiency influence factors; s4, establishing an interlayer heat absorption capacity proportion correlation formula; s5, calculating the corresponding production time when the heat loss amount tends to be stable; s6, iteratively updating the calculated value of the steam injection speed of each oil layer; s7, calculating the equivalent heating radius of the steam area; and S8, the commingling production limit heating radius of the multi-layer heavy oil reservoir steam injection directional well is calculated. The method can be used for rapidly evaluating the heating front edge sweep, guiding mine field well site deployment and recovery efficiency prediction, can effectively guide efficient development of heavy oil thermal recovery, and has important significance in guiding calculation of the heating radius of a heavy oil field and well site deployment.

Description

Technical Field

[0001] The invention belongs to the field of methods for determining a limiting heating radius, and in particular relates to a method for calculating a limiting heating radius of a multi-layer heavy oil reservoir in which a directional steam injection well is combined. Background Art

[0002] Steam injection thermal recovery is the main technology for heavy oil production in China. During the steam injection process, steam is both a displacement medium and a heat transfer medium for the oil layer. When steam enters the reservoir to displace crude oil, only a part of the heat is used to heat the oil layer, and the other part of the heat is lost to the top and bottom cap layers and interlayers, which reduces the utilization rate of the injected heat and directly affects the thermal recovery heating range and the final development effect. my country's heavy oil reservoirs are mostly thin interlayers with small thickness and high difficulty in production. During the steam injection process of thin-layer heavy oil reservoirs, the interlayer heat loss is serious. During development, there are large differences in steam absorption and utilization between layers, and it is often difficult to achieve a good development effect. The heating range of multi-layer combined production in directional wells is mainly affected by the heating radius. When the injected heat is constant, due to the influence of heat loss, the heating range has a maximum value, that is, there is a limit heating radius. The conventional method for calculating the limit heating radius is mainly based on the piston displacement model, which does not consider the steam overburden phenomenon and interlayer heat loss, as well as the influence of injected steam on reservoir permeability, and lacks a more accurate calculation method. Summary of the invention

[0003] The present invention is proposed to solve the shortcoming that the traditional method is difficult to quantitatively characterize the difference in heating range between multi-layer commingled production layers, and its purpose is to provide a method for calculating the maximum heating radius of commingled production of multi-layer heavy oil reservoirs with steam injection directional wells.

[0004] The present invention is achieved through the following technical solutions:

[0005] A method for calculating the limiting heating radius of a directional steam injection well in a multi-layer heavy oil reservoir comprises the following steps:

[0006] S1. Calculate the seepage resistance of each oil layer in a multi-layer heavy oil reservoir.

[0007] According to the principle of seepage mechanics, the seepage resistance of the oil layer is the sum of the internal plane radial flow, the middle hemispherical centrifugal flow, and the external plane radial flow. Prepare the viscosity of the injected steam in the production layer section of the target area, the thickness and average permeability of each oil layer, the total thickness of the oil layer, the skin coefficient, the wellbore radius, and the supply radius data, and use formulas (1) to (4) to calculate the seepage resistance of the i-th layer of the reservoir.

[0008]

[0009]

[0010] In the formula, C1 is the coefficient related to the unit, and its value is 11.574; K iis the average permeability of the i-th layer of the reservoir, mD; h i is the thickness of the i-th layer in the reservoir, m; R i is the seepage resistance of the i-th layer of the reservoir, MPa·d / m 3 ; are the internal, middle and external seepage resistance of the i-th layer of the reservoir, MPa·d / m 3 ;μ s is the steam viscosity, mPa·s; H is the total thickness of the oil layer, m; r w is the borehole radius, m; S is the skin factor, dimensionless; r e is the supply radius, m.

[0011] S2. Calculate the steam injection rate of each oil layer in a multi-layer heavy oil reservoir.

[0012] Based on the principle of hydropower similarity, the steam injection volume of each layer is split according to the seepage resistance when injecting steam. Prepare the total steam injection volume data of the production layer in the target area, combine the seepage resistance of each oil layer determined in the first step, and use formula (5) to calculate the steam injection rate of the i-th layer of the reservoir.

[0013]

[0014] In the formula, q s,t is the total steam injection rate, kg / d; q s,i is the steam injection rate of the i-th layer of the reservoir, kg / d; n is the number of oil layers in the reservoir, dimensionless.

[0015] S3. Design orthogonal numerical experiments based on the factors affecting thermal efficiency. Select 4 static parameters (oil layer / interlayer thickness ratio, number of interlayers, oil saturation, and permeability range) and 4 dynamic parameters (steam injection dryness, steam injection rate, cycle injection volume, and production-injection ratio) to conduct an 8-factor orthogonal design. Each factor contains 5 levels. Design L50 (5 8 ), a total of 50 numerical simulation schemes.

[0016] S4. Establish a correlation formula for the proportion of interlayer heat loss. CMG thermal recovery numerical simulation software was used to calculate the 50 simulation schemes designed in the third step. The three main control factors affecting thermal efficiency, namely, oil layer / interlayer thickness ratio, steam injection dryness, and steam injection rate, were used as variables. Heating efficiency was used as an evaluation index. Multiple linear regression was carried out to establish a correlation formula for the proportion of interlayer heat loss, as shown in formula (6). Combined with the target area oil layer / interlayer thickness ratio, steam injection dryness, steam injection rate, and reservoir pore volume multiples, the proportion of interlayer heat loss in the i-th layer of the reservoir can be calculated.

[0017] η i =a+bx+cv s,i +dr (6)

[0018] Where η i is the heat loss ratio of the i-th interlayer in the reservoir, decimal; x is the steam injection dryness, decimal; v s,i is the steam injection rate of the i-th layer of the reservoir, v s,i =q s,i / ρ w , m 3 / d; r is the ratio of oil layer / interlayer thickness, decimal; a, b, c, d are regression coefficients, which are the pore volume multiples PV of the i-th layer in the reservoir i A function of , dimensionless.

[0019] The pore volume multiple of the i-th layer of the reservoir is calculated using formula (7).

[0020]

[0021] In the formula, PV i is the multiple of the pore volume of the i-th layer of the reservoir, dimensionless; ρ w is the density of water, kg / m 3 ; φ is the porosity, a decimal; t is the production time, d.

[0022] The calculation formulas for a, b, c, and d are:

[0023] a=N1PV i +N2

[0024] b=N3PV i 2 +N4PV i +N5

[0025] c=N6PV i 2 +N7PV i +N8

[0026] d=N9PV i +N 10

[0027] That is, a, d and PV i There is a linear function relationship between them; b, c and PV i There is a binary linear function relationship between them; the coefficients N1 to N 10 It was obtained by multiple linear regression based on the orthogonal simulation scheme of eight factors and five levels;

[0028] S5. Calculate the production time corresponding to when the heat loss tends to be stable. According to the heat loss ratio of the insulation layer obtained in the fourth step, draw a curve of the change of the heat loss ratio of the insulation layer with the production time, and then apply formula (8) to obtain the heat loss change rate η′, and draw a curve of the change of the heat loss change rate with the production time. When the heat loss change rate is less than the given value ε′, it is approximately considered that the heat loss tends to be stable, and the injected heat and the heat loss are balanced. The corresponding heating radius at this time is the limit heating radius, and the corresponding production time t is calculated.

[0029]

[0030] Where Δη is the difference between the next time node and the previous time node, dimensionless; Δt is the time step, d.

[0031] S6. Iteratively update the calculated value of steam injection rate for each oil layer. With the continuous injection and flushing of steam, the reservoir permeability will change, which will cause the seepage resistance of each oil layer and the steam injection amount to change continuously.

[0032] Permeability correlation considering the permeability change caused by steam scouring:

[0033]

[0034] The relationship between the permeability change rate and the amount of injected steam:

[0035] r k,i =0.011ln(PV i ) (10)

[0036] In the formula, is the average permeability of the i-th layer of the reservoir at time t, mD; r k,i is the rate of change of permeability of the i-th layer in the reservoir at time t, dimensionless.

[0037] Apply formulas (7), (9) and (10), and combine with the production time t obtained in step 5, repeat the calculation process of steps 1 and 2 to calculate the steam injection volume q of each oil layer corresponding to time t s,i .q s,i Specific calculation steps: Given the initial time (t = 0) K i , calculate the time q s,i ; Calculate the Δt time Will Substitute into formulas (1) to (5) and iteratively update R i and q s,i value until the iteration reaches time t, at which time q s,i That is, the steam injection amount of each oil layer corresponding to time t.

[0038] S7. Calculate the equivalent heating radius of the steam zone. According to the energy conservation of the steam zone, consider the overburden effect, determine the bottom heating radius of the steam zone, and then determine the equivalent heating radius of the steam zone. Prepare the data of crude oil density, steam density, and effective steam permeability, and combine the steam injection volume q of the i-th layer of the reservoir at time t obtained in step 6 s,i , use formula (11) to calculate the steam overburden shape factor of the i-th layer of the reservoir at time t.

[0039]

[0040] In the formula, A rd,i is the steam overburden shape factor of the i-th layer of the reservoir at time t, dimensionless; C2 is a coefficient related to the unit, with a value of 1.157×10 7 ρ o is the density of crude oil, kg / m 3 ρ s is the steam density, kg / m 3 ; K s,i is the effective steam permeability of the i-th layer of the reservoir at time t (generally 1 / 4 of the average permeability of the oil layer), mD; g is the gravity acceleration, taken as 9.8m / s 2 .

[0041] The heating radius ratio of the top and bottom cap layers of the i-th steam zone in the reservoir at time t is calculated according to formula (12).

[0042]

[0043] In the formula, y i It is the ratio of the heating radii of the top and bottom cap layers of the i-th steam zone in the reservoir at time t, and is dimensionless.

[0044] Prepare the data of reservoir heat capacity, bottom hole steam temperature, reservoir initial temperature, and reservoir initial pressure. Combined with the interlayer heat loss ratio obtained in the fourth step, the bottom heating radius of the i-th steam zone in the reservoir at time t is obtained according to formulas (13) to (16).

[0045]

[0046] L v =273×(374.15-T b ) 0.38 (14)

[0047] T b =210×P i 0.21 -30 (15)

[0048] E l,s =q s,i xL v tη i(16)

[0049] Where: r sd,i is the bottom heating radius of the steam zone of the i-th layer of the reservoir at time t, in meters; q s,i is the steam injection rate of the i-th layer of the reservoir, in kg / d; x is the steam injection dryness, in decimal; t is the production time, in d; y i M is the ratio of the heating radius of the top and bottom cap layers of the i-th steam zone in the reservoir at time t, dimensionless; R is the reservoir heat capacity, in kJ / (m 3 ℃); T s is the bottom steam temperature, in °C; T i is the initial temperature of the reservoir, in °C; L v is the latent heat of vaporization, in kJ / kg; T b is the saturation temperature, in °C; P i is the initial reservoir pressure, in MPa; E l,s is the heat loss of the steam zone barrier, in kJ; η i is the proportion of heat loss in the i-th interlayer of the reservoir, decimal;

[0050] The equivalent heating radius of the steam zone in the i-th layer of the reservoir at time t is calculated according to formula (17).

[0051]

[0052] In the formula, r s,i is the equivalent heating radius of the steam zone in the i-th layer of the reservoir at time t, m.

[0053] S8. Calculate the limit heating radius of the combined production of steam injection directional wells in multi-layer heavy oil reservoirs. Assume that the heating radius of the hot water area in the i-th layer of the reservoir at time t is r hi Initial value, combined with the equivalent heating radius of the steam zone determined in step 7, the temperature distribution function T of the hot water zone of the i-th layer of the reservoir at time t under this condition is obtained by applying formula (18): h,i (r). h,i Substitute (r) into formula (19), combine formula (20) to (22), and iteratively solve the heating radius r of the hot water zone in the i-th layer of the reservoir at time t h,i , until the iteration error F(r h,i ) is less than the allowed accuracy ε, at which point r h,i It is the heating radius of the hot water zone in the i-th layer of the reservoir at time t, that is, the limit heating radius of the layer.

[0054]

[0055] Where, T h,i (r) is the temperature distribution function of the hot water area in the i-th layer of the reservoir at time t; T fis the front edge temperature of the hot water area, °C; r h,i is the heating radius of the hot water area in the i-th layer of the reservoir at time t, m; A and B are the fitting coefficients of the dimensionless temperature distribution correlation formula of the hot water area, dimensionless; r is the heating radius, m.

[0056]

[0057] h ws =1.08×(T b +17.78) 1.24 (20)

[0058] h wr =1.08×(T i +17.78) 1.24 (twenty one)

[0059] E l,h =q s,i (h ws -h wr )tη i (twenty two)

[0060] In the formula, F(r h,i ) is the iteration error, dimensionless; h ws is the enthalpy of saturated hot water, kJ / kg; h wr is the thermal enthalpy of water at the initial reservoir temperature, kJ / kg; E l,h is the heat loss of the hot water zone insulation, kJ.

[0061] The calculation principle of the present invention is:

[0062] Based on the principle of hydropower similarity, the seepage resistance of multi-layer commingled production was calculated, and the steam injection volume of each oil layer was split accordingly. The influence of steam injection volume on reservoir permeability was considered in the calculation process, and then a correlation formula for the proportion of interlayer heat loss was established, which achieved a quantitative description of interlayer heat loss in commingled production of multi-layer heavy oil reservoirs with steam injection and directional wells. The heating radius calculation method was corrected by introducing the steam overlay shape factor. On this basis, the heating range under typical geological reservoir parameters and injection and production parameters can be obtained, and then the relationship between heat loss and injected heat under any heating range conditions is calculated. When the two are equal, the corresponding heating radius is the limit heating radius.

[0063] The beneficial effects of the present invention are:

[0064] The present invention provides a method for calculating the ultimate heating radius of a multi-layer heavy oil reservoir combined production by a steam injection directional well, which can be used to quickly evaluate the influence of the heating front, guide the well site deployment and recovery rate prediction of a mine field, and effectively guide the efficient development of heavy oil thermal recovery. It is of great significance for guiding the calculation of the heating radius and the well site deployment of heavy oil fields. BRIEF DESCRIPTION OF THE DRAWINGS

[0065] Figure 1 is a flow chart of the method of the present invention;

[0066] Figure 2 It is a schematic diagram of the steam injection volume splitting method based on the hydropower similarity principle in the present invention (a is a schematic diagram of a multi-layer heavy oil reservoir model; b is a schematic diagram of the hydropower similarity principle);

[0067] Figure 3 is a curve diagram showing the ratio of heat loss of the insulation layer to production time in the present invention;

[0068] Figure 4 It is a curve diagram showing the change rate of heat loss versus production time in the present invention;

[0069] Figure 5 It is a schematic diagram of a longitudinal section of steam overburden of a multi-layer heavy oil reservoir in the present invention;

[0070] Figure 6 It is a schematic diagram of the development of the steam chamber for steam injection thermal recovery in the present invention.

[0071] For ordinary technicians in this field, other relevant drawings can be obtained based on the above drawings without any creative work. DETAILED DESCRIPTION

[0072] In order to enable those skilled in the art to better understand the technical solution of the present invention, the technical solution of the present invention is further described below with reference to the accompanying drawings and through specific implementation methods.

[0073] like Figure 1 As shown, a method for calculating the combined production limit heating radius of a multi-layer heavy oil reservoir directional steam injection well comprises the following steps:

[0074] S1. Calculate the seepage resistance of each oil layer in a multi-layer heavy oil reservoir.

[0075] According to the principle of seepage mechanics, the seepage resistance of the oil layer is the sum of the internal plane radial flow, the middle hemispherical centrifugal flow, and the external plane radial flow. Prepare the viscosity of the injected steam in the production layer section of the target area, the thickness and average permeability of each oil layer, the total thickness of the oil layer, the skin coefficient, the wellbore radius, and the supply radius data, and use formulas (1) to (4) to calculate the seepage resistance of the i-th layer of the reservoir.

[0076] R i =R i i +R i m +R i o (1)

[0077]

[0078] In the formula, C1 is the coefficient related to the unit, and its value is 11.574; K i is the average permeability of the i-th layer of the reservoir, mD; h i is the thickness of the i-th layer in the reservoir, m; R i is the seepage resistance of the i-th layer of the reservoir, MPa·d / m 3 ; R i i , R i m , R i o are the internal, middle and external seepage resistance of the i-th layer of the reservoir, MPa·d / m 3 ;μ s is the steam viscosity, mPa·s; H is the total thickness of the oil layer, m; r w is the borehole radius, m; S is the skin factor, dimensionless; r e is the supply radius, m.

[0079] by Figure 2 (a) Taking a three-layer reservoir as an example, the calculation method of the combined production limit heating radius of a multi-layer heavy oil reservoir with steam injection directional wells is described. The viscosity of the steam injected into the production layer of the target area μ s is 0.0176 mPa·s, the initial average permeabilities K1, K2, and K3 of the reservoir Ⅰ, Ⅱ, and Ⅲ layers are 783 mD, 620 mD, and 435 mD, respectively, the thicknesses of the reservoir Ⅰ, Ⅱ, and Ⅲ layers h1, h2, and h3 are 5.4 m, 8.7 m, and 17.5 m, respectively, the total thickness of the reservoir H is 31.6 m, the skin coefficient S is 0, and the wellbore radius r w is 0.1m, supply radius r e The initial seepage resistances R1, R2, and R3 of the reservoir Ⅰ, Ⅱ, and Ⅲ layers are 1.28×10 -5 , 1.32×10 -5 , 1.62×10 -5 MPa·d / m 3 .

[0080] S2. Calculate the steam injection rate of each oil layer in a multi-layer heavy oil reservoir.

[0081] Based on the hydropower similarity principle, the steam injection amount of each layer during general steam injection is split according to the seepage resistance, such as Figure 2 Prepare the total steam injection volume data of the target area production layer, combine the seepage resistance of each oil layer determined in the first step, and use formula (5) to calculate the steam injection rate of the i-th layer of the reservoir.

[0082]

[0083] In the formula, qs,t is the total steam injection rate, kg / d; q s,i is the steam injection rate of the i-th layer of the reservoir, kg / d; n is the number of oil layers in the reservoir, dimensionless.

[0084] Total steam injection rate q in the production layer of the target area s,t 2×10 5 kg / d, combined with the initial seepage resistance R1, R2, R3 of reservoir Ⅰ, Ⅱ, Ⅲ layers calculated in the first step, the daily steam injection rate of each layer of the general steam injection is split, and the steam injection rate q of reservoir Ⅰ, Ⅱ, Ⅲ layers at the initial time is calculated by formula (5): s,1 ,q s,2 ,q s,3 They are 7.26×10 4 ,7.02×10 4 , 5.72×10 4 kg / d.

[0085] S3. Design orthogonal numerical experiments based on the factors affecting thermal efficiency.

[0086] Four static parameters (oil layer / interlayer thickness ratio, number of interlayers, oil saturation, and permeability range) and four dynamic parameters (steam injection dryness, steam injection rate, cycle injection volume, and production-injection ratio) were selected to conduct an 8-factor orthogonal design, with each factor containing 5 levels. The L50 (5 8 ), a total of 50 numerical simulation schemes.

[0087] The static and dynamic parameter values ​​are shown in Table 1, and the 8-factor 5-level orthogonal simulation scheme is shown in Table 2.

[0088] Table 1 Static and dynamic parameter values

[0089] Table 2 8 factors and 5 levels orthogonal simulation scheme

[0090]

[0091]

[0092] S4. Establish a correlation formula for the proportion of insulation heat loss.

[0093] CMG thermal recovery numerical simulation software was used to calculate the 50 simulation schemes designed in the third step. The three main control factors affecting thermal efficiency, namely, oil layer / interlayer thickness ratio, steam injection dryness, and steam injection rate, were used as variables. Heating efficiency was used as the evaluation index to carry out multivariate linear regression and establish a correlation formula for the proportion of interlayer heat loss. As shown in formula (6), the proportion of interlayer heat loss in the i-th layer of the reservoir can be calculated by combining the target area oil layer / interlayer thickness ratio, steam injection dryness, steam injection rate, and reservoir pore volume multiples.

[0094] η i =a+bx+cv s,i +dr (6)

[0095] Where η i is the heat loss ratio of the i-th interlayer in the reservoir, decimal; x is the steam injection dryness, decimal; v s,i is the steam injection rate of the i-th layer of the reservoir, v s,i =q s,i / ρ w , m 3 / d; r is the ratio of oil layer / interlayer thickness, decimal; a, b, c, d are regression coefficients, which are the pore volume multiples PV of the i-th layer in the reservoir i A function of , dimensionless.

[0096] The pore volume multiple of the i-th layer of the reservoir is calculated using formula (7).

[0097]

[0098] In the formula, PV i is the multiple of the pore volume of the i-th layer of the reservoir, dimensionless; ρ w is the density of water, kg / m 3 ; φ is the porosity, a decimal; t is the production time, d.

[0099] For the 50 simulation schemes designed in Table 2, multivariate linear regression was carried out to establish a correlation formula for the proportion of heat loss in the insulation layer as shown in formula (6), where the regression coefficient calculation formula is shown in Table 3.

[0100] Table 3 Calculation formula of correlation regression coefficient of insulation heat loss ratio

[0101] Regression coefficient Correlation regression coefficient calculation formula a <![CDATA[a=0.0343PV i +0.0853]]> b <![CDATA[b=0.0003PV i 2 -0.0015PV i -0.0017]]> c <![CDATA[c=-2.3×10 -5 PV i 2 +1.71×10 -4 PV i +3.2×10 -4 <!-- 8 -->]]> d <![CDATA[d=-4×10 -5 PV i +5×10 -7 ]]>

[0102] The porosity of the target area is φ28.5%, and the density of water is ρ w 1000kg / m 3 , we can get the pore volume multiple PV of the i-th layer of the reservoir at time t i The steam mass injection rate q of the reservoir Ⅰ, Ⅱ, and Ⅲ layers at the initial moment obtained in the second step is s,1 ,q s,2 ,qs,3 and the density of water ρ w , we can get the steam volume injection rate v of reservoir Ⅰ, Ⅱ, Ⅲ layers at the initial time s,1 、v s,2 、v s,3 72.6, 70.2, 57.2m 3 / d, given that the oil layer / interlayer thickness ratio r is 1.6 and the steam injection dryness x is 0.4, the curve of the heat loss ratio of the interlayers of the reservoir Ⅰ, Ⅱ, and Ⅲ as a function of production time can be obtained by applying formula (6) Figure 3 ).

[0103] S5. Calculate the production time corresponding to when the heat loss tends to be stable.

[0104] According to the heat loss ratio of the insulation layer obtained in the fourth step, a curve of the heat loss ratio of the insulation layer changing with the production time is plotted. Then, the heat loss change rate η′ is calculated using formula (8), and a curve of the heat loss change rate changing with the production time is plotted. When the heat loss change rate is less than the given value ε′, it is approximately considered that the heat loss tends to be stable, and the injected heat and the heat loss reach a balance. At this time, the corresponding heating radius is the limit heating radius, and the corresponding production time t is calculated.

[0105]

[0106] Where Δη is the difference between the next time node and the previous time node, dimensionless; Δt is the time step, d.

[0107] According to the insulation heat loss ratio curve obtained in the fourth step ( Figure 3 ), apply formula (8) to draw the curve of heat loss rate changing with production time ( Figure 4 ), where Δt is 50 days. When the rate of change of heat loss is less than the given value 0.0001, the production times t1, t2, and t3 corresponding to the limit heating radius of the reservoir layers Ⅰ, Ⅱ, and Ⅲ are 1200, 1350, and 1350 days respectively.

[0108] S6. Iteratively update the calculated value of steam injection rate for each oil layer.

[0109] With the continuous injection and flushing of steam, the reservoir permeability will change, which will cause the seepage resistance of each oil layer and the steam injection amount to change continuously.

[0110] Permeability correlation considering the permeability change caused by steam scouring:

[0111]

[0112] The relationship between the permeability change rate and the amount of injected steam:

[0113] rk,i =0.011ln(PV i ) (10)

[0114] In the formula, is the average permeability of the i-th layer of the reservoir at time t, mD; r k,i is the rate of change of permeability of the i-th layer in the reservoir at time t, dimensionless.

[0115] Apply formulas (7), (9) and (10), and combine with the production time t obtained in step 5, repeat the calculation process of steps 1 and 2 to calculate the steam injection volume q of each oil layer corresponding to time t s,i .q s,i Specific calculation steps: Given the initial time (t = 0) K i , calculate the time q s,i ; Calculate the Δt time Will Substitute into formulas (1) to (5) and iteratively update R i and q s,i value until the iteration reaches time t, at which time q s,i That is, the steam injection amount of each oil layer corresponding to time t.

[0116] According to the initial K1, K2, K3 values ​​and the q obtained in the second step s,1 ,q s,2 ,q s,3 , apply formulas (7), (9) and (10) to update value, Substitute into formulas (1) to (5) and iteratively update R1, R2, R3 and q s,1 ,q s,2 ,q s,3 value until the iterative calculation reaches the production time t1, t2, and t3 obtained in the fifth step. At this time, q s,1 ,q s,2 ,q s,3 That is, the steam injection volume of reservoir Ⅰ, Ⅱ, and Ⅲ corresponding to the limit heating radius, and q at the end of iteration s,1 ,q s,2 ,q s,3 They are 7.44×10 4 , 6.92×10 4 , 5.64×10 4 kg / d.

[0117] S7. Calculate the equivalent heating radius of the steam zone.

[0118] According to the energy conservation of the steam zone, the overburden effect is considered ( Figure 5 ), determine the bottom heating radius of the steam zone ( Figure 6), and then determine the equivalent heating radius of the steam zone. Prepare the crude oil density, steam density, and steam effective permeability data, combined with the steam injection volume q of the i-th layer of the reservoir at time t obtained in step 6 s,i , use formula (11) to calculate the steam overburden shape factor of the i-th layer of the reservoir at time t.

[0119]

[0120] In the formula, A rd,i is the steam overburden shape factor of the i-th layer of the reservoir at time t, dimensionless; C2 is a coefficient related to the unit, with a value of 1.157×10 7 ρ o is the density of crude oil, kg / m 3 ρ s is the steam density, kg / m 3 ; K si is the effective steam permeability of the i-th layer of the reservoir at time t (generally 1 / 4 of the average permeability of the oil layer), mD; g is the gravity acceleration, taken as 9.8m / s 2 .

[0121] The heating radius ratio of the top and bottom cap layers of the i-th steam zone in the reservoir at time t is calculated according to formula (12).

[0122]

[0123] In the formula, y i It is the ratio of the heating radii of the top and bottom cap layers of the i-th steam zone in the reservoir at time t, and is dimensionless.

[0124] Prepare the data of reservoir heat capacity, bottom hole steam temperature, reservoir initial temperature, and reservoir initial pressure. Combined with the interlayer heat loss ratio obtained in the fourth step, the bottom heating radius of the i-th steam zone in the reservoir at time t is obtained according to formulas (13) to (16).

[0125]

[0126] L v =273×(374.15-T b ) 0.38 (14)

[0127] T b =210×P i 0.21 -30 (15)

[0128] E l,s =q s,i xL v tη i (16)

[0129] In the formula, rsd,i M is the bottom heating radius of the i-th steam zone in the reservoir at time t; R is the reservoir heat capacity, kJ / (m 3 ℃); T s is the bottom steam temperature, °C; T i is the initial temperature of the reservoir, °C; L v is the latent heat of vaporization, kJ / kg; T b is the saturation temperature, °C; P i is the initial reservoir pressure, MPa; E l,s is the heat loss of the steam zone barrier, kJ.

[0130] The equivalent heating radius of the steam zone in the i-th layer of the reservoir at time t is calculated according to formula (17).

[0131]

[0132] In the formula, r s,i is the equivalent heating radius of the steam zone in the i-th layer of the reservoir at time t, m.

[0133] Crude oil density in target area ρ o 992.8kg / m 3 , steam density ρ s 20kg / m 3 , the initial effective permeability of steam in layers I, II and III of the reservoir K s,1 , K s,2 , K s,3 They are 196mD, 155mD, and 109mD respectively. Combined with the steam injection rates q of reservoir I, II, and III obtained in step 6, s,1 ,q s,2 ,q s,3 , the steam overburden shape factor A of reservoir Ⅰ, Ⅱ and Ⅲ layers is calculated by using formula (11): rd,1 , A rd,2 , A rd,3 According to formula (12), the heating radius ratios y1, y2, and y3 of the top and bottom cap layers of the steam zone of the reservoir I, II, and III are 1.76, 2.52, and 9.37, respectively. The heat capacity of the target area reservoir M R 2575 kJ / (m 3 ℃), bottom steam temperature T s is 300℃, the initial reservoir temperature T i is 40℃, the initial reservoir pressure P i is 9MPa, according to the fourth step Figure 3The heat loss ratios of the interlayers η1, η2, and η3 of the reservoir Ⅰ, Ⅱ, and Ⅲ at the time t1, t2, and t3 are determined to be 0.67, 0.57, and 0.46, respectively. By applying formulas (13) to (16), the bottom heating radius r of the steam zone of the reservoir Ⅰ, Ⅱ, and Ⅲ can be obtained. sd,1 、r sd,2 、r sd,3 The equivalent heating radius r of the steam zone of the reservoir Ⅰ, Ⅱ and Ⅲ layers is calculated by using formula (17): s,1 、r s,2 、r s,3 They are 58, 48 and 31m respectively.

[0134] S8. Calculate the limit heating radius of the combined production of steam injection directional wells in multi-layer heavy oil reservoirs. Assume that the heating radius of the hot water area in the i-th layer of the reservoir at time t is r h,i Initial value, combined with the equivalent heating radius of the steam zone determined in step 7, the temperature distribution function T of the hot water zone of the i-th layer of the reservoir at time t under this condition is obtained by applying formula (18): h,i (r). h,i Substitute (r) into formula (19), combine formula (20) to (22), and iteratively solve the heating radius r of the hot water zone in the i-th layer of the reservoir at time t h,i , until the iteration error F(r h,i ) is less than the allowed accuracy ε, at which point r h,i It is the heating radius of the hot water zone in the i-th layer of the reservoir at time t, that is, the limit heating radius of the layer.

[0135]

[0136] Where, T h,i (r) is the temperature distribution function of the hot water area in the i-th layer of the reservoir at time t; T f is the front edge temperature of the hot water area, °C; r h,i is the heating radius of the hot water area in the i-th layer of the reservoir at time t, m; A and B are the fitting coefficients of the dimensionless temperature distribution correlation formula of the hot water area, dimensionless; r is the heating radius, m.

[0137]

[0138] h ws =1.08×(T b +17.78) 1.24 (20)

[0139] h wr =1.08×(T i +17.78) 1.24 (twenty one)

[0140] E l,h =qs,i (h ws -h wr )tη i (twenty two)

[0141] In the formula, F(r h,i ) is the iteration error, dimensionless; h ws is the enthalpy of saturated hot water, kJ / kg; h wr is the thermal enthalpy of water at the initial reservoir temperature, kJ / kg; E l,h Heat absorbed by the hot water zone insulation, kJ.

[0142] The fitting coefficients A and B of the dimensionless temperature distribution correlation equation in the hot water area of ​​the target area are 1 and -5.21 respectively, and the front edge temperature T f is 60℃, combined with the equivalent heating radius r of the steam zone determined in step 7 s,1 、r s,2 、r s,3 , using formula (18) to obtain the temperature distribution function T of the hot water area of ​​the i-th layer of the reservoir under this condition h,i (r). Substitute formula (18) and formula (20) to (22) into formula (19). Now only r is included in formula (19). h,i is an unknown variable, and the integral can be solved by iteration. Specifically, the heating radius r of the hot water zone in the i-th layer of the reservoir is given h,i The initial value is r s,i +Δr, Δr is the iteration step, Δr = 0.001m, combined with the production time t1, t2, t3 when the reservoir Ⅰ, Ⅱ, Ⅲ layers reach the limit heating radius determined in the fifth step, and the steam injection rate q of the reservoir Ⅰ, Ⅱ, Ⅲ layers determined in the sixth step s,1 ,q s,2 ,q s,3 The proportion of heat loss of the interlayer in the reservoir Ⅰ, Ⅱ, Ⅲ determined in the seventh step is η1, η2, η3. Formula (19) is used to iteratively solve the heating radius r of the hot water area in the reservoir Ⅰ, Ⅱ, Ⅲ layers. h,1 、r h,2 、r h,3 , until the iteration error F(r h,i ) is less than 0.001, and finally the ultimate heating radius r of reservoir Ⅰ, Ⅱ, and Ⅲ layers is obtained. h,1 、r h,2 、r h,3 They are 206, 170 and 112m respectively.

[0143] The applicant declares that the above is only a specific implementation mode of the present invention, but the protection scope of the present invention is not limited thereto. Those skilled in the art should understand that any changes or substitutions that can be easily thought of by those skilled in the art within the technical scope disclosed by the present invention shall fall within the protection scope and disclosure scope of the present invention.

Claims

1. A method for calculating the limiting heating radius of a directional steam injection well in a multi-layer heavy oil reservoir, characterized in that: S1. Calculate the seepage resistance of each layer in a multi-layer heavy oil reservoir; S2, calculate the steam injection rate of each layer in the multi-layer heavy oil reservoir; S3. Design orthogonal numerical experiments based on the factors affecting thermal efficiency; S4. Establish a correlation formula for the proportion of heat absorption of the interlayer, and calculate the proportion of heat loss of each interlayer in the reservoir; S5. Calculate the production time corresponding to when the heat loss amount tends to be stable; S6, iteratively updating the calculated value of steam injection rate in each layer of the reservoir; S7. Calculate the equivalent heating radius of the steam zone; S8. Calculate the ultimate heating radius of combined production of directional steam injection wells in multi-layer heavy oil reservoirs.

2. The method for calculating the limiting heating radius of a directional steam injection well in a multi-layer heavy oil reservoir according to claim 1, characterized in that: The method for calculating the seepage resistance of each oil layer in the multi-layer heavy oil reservoir in step S1 is specifically as follows: Prepare the viscosity of the injected steam, the thickness and average permeability of each oil layer, the total thickness of the oil layer, the skin factor, the wellbore radius, and the supply radius data of the target area production layer, and use formulas (1) to (4) to calculate the seepage resistance of the i-th layer of the reservoir; Where: C1 is the coefficient related to the unit, and its value is 11.574; K i is the average permeability of the i-th layer of the reservoir, in mD; h i is the thickness of the i-th layer of the reservoir, in m; R i is the seepage resistance of the i-th layer of the reservoir, in MPa·d / m 3 ; are the internal, middle and external seepage resistance of the i-th layer of the reservoir, respectively, in MPa·d / m 3 ;μ s is the steam viscosity, in mPa·s; H is the total thickness of the oil layer, in m; r w is the borehole radius, in meters; S is the skin factor, dimensionless; r e is the supply radius, in m.

3. The method for calculating the limiting heating radius of a directional steam injection well in a multi-layer heavy oil reservoir according to claim 1, characterized in that: The method for calculating the steam injection rate of each layer in the multi-layer heavy oil reservoir in step S2 is specifically as follows: Prepare the total steam injection volume data of the production layer section in the target area, combine the seepage resistance of each layer of the reservoir determined in step S1, and use formula (5) to calculate the steam injection rate of the i-th layer of the reservoir; Where: q s,t is the total steam injection rate, in kg / d; q s,i is the steam injection rate of the i-th layer of the reservoir, in kg / d; n is the number of oil layers in the reservoir, dimensionless; R i is the seepage resistance of the i-th layer of the reservoir, in MPa·d / m 3 .

4. The method for calculating the limiting heating radius of a directional steam injection well in a multi-layer heavy oil reservoir according to claim 1, characterized in that: The design method of the orthogonal numerical experiment in step S3 is as follows: select four static parameters and four dynamic parameters, conduct eight-factor orthogonal design, each factor contains five levels, design L50(5 8 ) with a total of fifty sets of numerical simulation schemes.

5. The method for calculating the limiting heating radius of a directional steam injection well in a multi-layer heavy oil reservoir according to claim 4, characterized in that: The static parameters include the oil layer / interlayer thickness ratio, the number of interlayers, oil saturation and permeability extreme difference; the dynamic parameters include steam injection dryness, steam injection speed, cycle injection volume and production-injection ratio.

6. The method for calculating the limiting heating radius of a directional steam injection well in a multi-layer heavy oil reservoir according to claim 1, characterized in that: The method for establishing the correlation equation of the heat absorption ratio of the insulation layer in step S4 is specifically as follows: The CMG thermal recovery numerical simulation software was used to calculate the fifty numerical simulation schemes designed in step S3. The three main control factors affecting thermal efficiency, namely, the oil layer / interlayer thickness ratio, steam injection dryness, and steam injection speed, were used as variables. The heating efficiency was used as the evaluation index. Multiple linear regression was carried out to establish a correlation formula for the proportion of interlayer heat loss. The correlation formula is shown in formula (6). The specific method for calculating the proportion of interlayer heat loss of each layer in the reservoir is: Combined with the oil layer / interlayer thickness ratio, steam injection dryness, steam injection rate, and reservoir pore volume multiples in the target area, the heat loss ratio of the i-th interlayer in the reservoir is calculated; η i =a+bx+hp s,i +dr (6) Where: η i is the heat loss ratio of the i-th interlayer in the reservoir, decimal; x is the steam injection dryness, decimal; v s,i is the steam injection rate of the i-th layer of the reservoir, in m 3 / d; r is the ratio of oil layer / interlayer thickness, decimal; a, b, c, d are regression coefficients, and PV is the pore volume multiple of the i-th layer of the reservoir. i A function of , dimensionless; Where, is the steam injection rate v in the i-th layer of the reservoir s,i The calculation formula is v s,i =q s,i / ρ w , ρ w is the density of water, kg / m 3 ; In the formula, q s,i is the steam injection rate of the i-th layer of the reservoir, in kg / d; Among them, the calculation formula of the pore volume multiple of the i-th layer of the reservoir is formula (7), Where, PV i is the multiple of the pore volume of the i-th layer of the reservoir, dimensionless; ρ w is the density of water, kg / m 3 ; φ is porosity, decimal; t is production time, d; h i is the thickness of the i-th layer of the reservoir, in m; q s,i is the steam injection rate of the i-th layer of the reservoir, in kg / d; r e is the supply radius, in m.

7. The method for calculating the limiting heating radius of a directional steam injection well in a multi-layer heavy oil reservoir according to claim 1, characterized in that: The specific calculation method of the production time corresponding to when the heat loss amount in step S5 tends to be stable is: According to the heat loss ratio of each layer of the reservoir obtained in step S4, a curve of the heat loss ratio of the interlayer versus the production time is plotted, and then the heat loss change rate η′ is calculated using formula (8), and a curve of the heat loss change rate versus the production time is plotted. When the heat loss change rate is less than a given value ε′, it is approximately considered that the heat loss tends to be stable, and the injected heat and the heat loss are balanced. At this time, the corresponding heating radius is the limit heating radius, and the corresponding production time t is calculated. Where Δη is the difference between the heat loss ratio of the next time node and the previous time node, which is dimensionless; Δt is the time step, in units of d.

8. The method for calculating the limiting heating radius of a directional steam injection well in a multi-layer heavy oil reservoir according to claim 1, characterized in that: The specific method of iteratively updating the calculated value of steam injection rate of each oil layer in step S6 is: S61. The permeability correlation formula considering the permeability change caused by steam scouring is formula (9): S62, the relationship between the permeability change rate and the amount of injected steam is as follows: r k,i =0.011ln(PV i ) (10) Where: is the average permeability of the i-th layer of the reservoir at time t, in mD; r k,i is the permeability change rate of the i-th layer of the reservoir at time t, dimensionless; PV i is the multiple of the pore volume of the i-th layer in the reservoir, dimensionless; S63, apply formulas (7), (9) and (10), and combine with the production time t obtained in step S5, repeat the calculation process of steps S1 and S2, and calculate the steam injection volume q of each oil layer corresponding to time t s,i , q s,i The specific calculation steps are: given the initial time K of t = 0 i , calculate the time q s,i ; Calculate the Δt time Will Substitute into formulas (1) to (5) and iteratively update R i and q s,i value until the iteration reaches time t, at which time q s, i That is, the steam injection amount of each oil layer corresponding to time t.

9. The method for calculating the limiting heating radius of a directional steam injection well in a multi-layer heavy oil reservoir according to claim 1, characterized in that: The calculation method of the equivalent heating radius of the steam zone in step S7 is specifically as follows: S71, prepare crude oil density, steam density, steam effective permeability data, and combine the steam injection volume q of the i-th layer of the reservoir at time t obtained in step S6 s,i , use formula (11) to calculate the steam overburden shape factor of the i-th layer of the reservoir at time t; Where: A rd,i is the steam overburden shape factor of the i-th layer of the reservoir at time t, dimensionless; C2 is a coefficient related to the unit, with a value of 1.157×10 7 ;μ s is the steam viscosity, in mPa·s; ρ o is the density of crude oil, in kg / m 3 ρ s is the steam density, in kg / m 3 ; K s,i is the effective steam permeability of the i-th layer of the reservoir at time t, which is 1 / 4 of the average permeability of the oil layer, in mD; g is the gravity acceleration, which is 9.8 m / s 2 ;q s,i is the steam injection rate of the i-th layer of the reservoir, in kg / d; S72, calculating the heating radius ratio of the top and bottom cap layers of the i-th steam zone of the reservoir at time t according to formula (12); Where: A rd,i is the steam overburden shape factor of the i-th layer of the reservoir at time t, dimensionless; i It is the ratio of the heating radius of the top and bottom cap layers of the i-th steam zone in the reservoir at time t, dimensionless; S73, prepare the data of reservoir heat capacity, bottom hole steam temperature, reservoir initial temperature, and reservoir initial pressure, combine the data with the interlayer heat loss ratio obtained in step S4, and obtain the bottom heating radius of the i-th steam zone of the reservoir at time t according to formulas (13) to (16); L v =273×(374.15-T b ) 0.38 (14) E l,s =q s,i xL v tη i (16) Where: r sd,i is the bottom heating radius of the steam zone of the i-th layer of the reservoir at time t, in meters; q s,i is the steam injection rate of the i-th layer of the reservoir, in kg / d; x is the steam injection dryness, in decimal; t is the production time, in d; y i M is the ratio of the heating radius of the top and bottom cap layers of the i-th steam zone in the reservoir at time t, dimensionless; R is the reservoir heat capacity, in kJ / (m 3 ℃); T s is the bottom steam temperature, in °C; T i is the initial temperature of the reservoir, in °C; L v is the latent heat of vaporization, in kJ / kg; T b is the saturation temperature, in °C; P i is the initial reservoir pressure, in MPa; E l,s is the heat loss of the steam zone barrier, in kJ; η i is the proportion of heat loss in the i-th interlayer of the reservoir, decimal; S74, calculating the equivalent heating radius of the steam zone of the i-th layer of the reservoir at time t according to formula (17); In the formula, r s,i is the equivalent heating radius of the steam zone in the i-th layer of the reservoir at time t, in meters; y i It is the ratio of the heating radii of the top and bottom cap layers of the i-th steam zone in the reservoir at time t, and is dimensionless.

10. The method for calculating the limiting heating radius of a directional steam injection well in a multi-layer heavy oil reservoir according to claim 1, characterized in that: The method for calculating the combined production limit heating radius of the steam injection directional well in the multi-layer heavy oil reservoir in step S8 is specifically as follows: S81, assuming that the heating radius r of the hot water zone in the i-th layer of the reservoir at time t h,i Initial value, combined with the equivalent heating radius of the steam zone determined in step S7, formula (18) is used to obtain the temperature distribution function T of the hot water zone of the i-th layer of the reservoir at time t under this condition. h,i (r); T h,i Substitute (r) into formula (19), combine formula (20) to (22), and iteratively solve the heating radius r of the hot water zone in the i-th layer of the reservoir at time t h,i , until the iteration error F(r h,i ) is less than the allowed accuracy ε, at which point r h,i is the heating radius of the hot water zone in the i-th layer of the reservoir at time t, i.e., the limiting heating radius of the layer; Where: T h,i (r) is the temperature distribution function of the hot water area in the i-th layer of the reservoir at time t; T f is the front edge temperature of the hot water area, in °C; r h,i is the heating radius of the hot water zone in the i-th layer of the reservoir at time t, in m; A and B are the fitting coefficients of the dimensionless temperature distribution correlation equation in the hot water area, which are dimensionless; r is the heating radius, in m; h ws =1.08×(T b +17.78) 1.24 (20) h wr =1.08×(T i +17.78) 1.24 (21) E l,h =q s,i (h ws -h wr )tη i (22) Where: F(r h,i ) is the iteration error, dimensionless; h ws is the enthalpy of saturated hot water, in kJ / kg; h wr is the thermal enthalpy of water under the initial reservoir temperature, in kJ / kg; E l,h It is the heat loss of the hot water zone insulation, in kJ.

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