Deep high-temperature and high-pressure stratum pressure control drilling optimization design method and system

Abstract

The invention relates to a deep high-temperature and high-pressure stratum pressure control drilling optimization design method and system, and belongs to the technical field of deep oil and gas drilling. A mathematical model of the density and rheological parameters of the high-density oil-based drilling fluid along with temperature and pressure is obtained through a nonlinear multiple regression method, a drilling system is divided into three independent and correlated areas, circulation models of all the areas are established respectively, discretization of the models of all the areas is carried out through a finite difference method, and therefore the density of the high-density oil-based drilling fluid is obtained. Accurate pressure control considering the change of physical property parameters of the drilling fluid is realized, and optimal design of pressure-controlled drilling is carried out on a deep high-temperature and high-pressure stratum. According to the method, the value range of the static drilling fluid density in the pressure-controlled drilling can be effectively determined, so that the operation time of pressure-controlled drilling site construction is shortened, the operation cost is reduced, the stability of a well wall is maintained, various drilling accidents and complex conditions are avoided, and a powerful guarantee is provided for safe and efficient drilling and production of a deep high-temperature and high-pressure oil and gas reservoir.

Description

Technical Field

[0001] The present invention relates to a method and system for optimizing the design of managed pressure drilling in deep high-temperature and high-pressure formations, and belongs to the technical field of deep oil and gas drilling and production. Background Art

[0002] With the rapid advancement of drilling technology, many well sections that were previously inaccessible have been reached. Currently, global oil drilling and development are gradually shifting to deep, high-temperature, and high-pressure formations. This has led to a series of drilling problems caused by the narrow density safety window in deep areas. Drilling in deep, complex areas faces two challenges: first, high bottomhole temperatures and pressures, which increase with depth; and second, a narrow formation pressure window. High wellbore temperature and pressure, combined with a narrow formation safety density window, make wellbore pressure control difficult. Therefore, precise wellbore pressure control is key to safe and efficient drilling in deep, high-temperature, and high-pressure areas. By implementing managed pressure drilling technology, the wellbore pressure profile can be precisely controlled to remain within the narrow safety density window, thereby avoiding complex downhole situations such as "coexistence of leaks and blowouts, or both leaks and blowouts," and protecting reservoir safety.

[0003] Equivalent circulating density (ECD) of drilling fluids is a crucial parameter in managed pressure drilling (MPD) when drilling deep, high-temperature, and high-pressure formations. However, field calculations often overlook the fact that drilling fluid properties vary with temperature and pressure. Experiments have shown that high temperatures expand the fluid, reducing its density, while high pressure compresses it, increasing its density. In oil-based drilling fluids, high temperatures reduce its viscosity, while high pressure increases it. These uncertainties can lead to inaccurate ECD calculations by oilfield operators, leading to complex downhole conditions such as blowouts, leaks, collapses, and sticking during deep, narrow safety density windows, resulting in extended non-productive time. Fluid property variations in MPD for HPD wells are a key issue in the precise control of wellbore pressure and are crucial to the successful implementation of MPD in HPD wells. Chinese patent document CN107478544A discloses a managed pressure drilling system and drilling method for deep-sea deepwater drilling. Chinese patent document CN107478544A discloses a method for determining the density of drilling fluid in managed pressure drilling. However, domestic and foreign research has shown that the managed pressure drilling method and related theories that take into account the changes in the physical properties of the drilling fluid during drilling in deep, high-temperature and high-pressure formations are still imperfect, making it difficult to provide a strong scientific basis and technical support for the safe and efficient development of deep, high-temperature and high-pressure oil and gas in my country. There is an urgent need for a managed pressure drilling optimization design method that takes into account the impact of deep, high temperature and high pressure on the performance of the drilling fluid.

[0004] Therefore, clarifying the changing laws of drilling fluid in deep, high-temperature and high-pressure formations and designing a pressure-controlled drilling optimization design method that couples the changing laws of drilling fluid with temperature and pressure properties are currently one of the key research directions in the field of deep, high-temperature and high-pressure formation drilling and production technology. Summary of the Invention

[0005] In response to the shortcomings of the existing technology, the present invention provides a method for optimizing the design of pressure-controlled drilling that couples the law of changes in drilling fluid properties with temperature and pressure. A mathematical model of the density and rheological parameters of high-density drilling fluid as a function of temperature and pressure is obtained using a nonlinear multiple regression method. By considering the influence of the physical properties of drilling fluid on temperature and pressure in the deep HPHT well section, an ECD prediction model for the entire well section of a deep high-temperature and high-pressure well is established based on the law of conservation of energy. This model more accurately approaches the actual bottomhole ECD change value, thereby effectively determining the value range of the static drilling fluid density (ESD) in pressure-controlled drilling, and realizing the optimized design of pressure-controlled drilling in deep narrow density window formations.

[0006] The technical solutions of the present invention are as follows:

[0007] A method for optimizing the design of managed pressure drilling in deep, high-temperature, and high-pressure formations comprises the following steps:

[0008] Step S1: Obtain the performance parameters of high-density oil-based drilling fluid under high temperature and high pressure conditions, where the performance parameters include density, apparent viscosity AV, plastic viscosity PV, and yield value YP, and study how the performance of the high-density oil-based drilling fluid changes with temperature and pressure under high temperature and high pressure.

[0009] Step S2: obtaining a mathematical model of the density and rheological parameters of the high-density oil-based drilling fluid as a function of temperature and pressure by using a nonlinear multiple regression method.

[0010] Preferably, the density multivariate nonlinear regression model of the high-density oil-based drilling fluid is calculated according to the following formula:

[0011] ρ(P,T)=ρ0exp[φ(P,T)] (1)

[0012] in:

[0013] φ(P,T)=ξ P (P-P0)+ξ PP (P-P0) 2 +ξ T (T-T0)+ξ TT (T-T0) 2 +ξ pT (P-P0)(T-T0) (2)

[0014] Where: P0 is the surface pressure, MPa, which is generally atmospheric pressure; T0 is the surface temperature, °C, which is 15 °C; ρ(T, P) is the density of the drilling fluid under temperature and pressure control, g / cm 3 ξ P ,ξ T are the primary characteristic constants of the pressure and temperature terms of the drilling fluid respectively; ξ PP ,ξTT are the quadratic characteristic constants of the pressure and temperature terms of the drilling fluid respectively; ξ PT is the quadratic characteristic constant of the drilling fluid pressure and temperature coupling term; T and P are the wellbore temperature and pressure; ρ0 is the initial density of the drilling fluid, g / cm 3 .

[0015] Under the condition of controlling variables, when the pressure remains unchanged, the density of oil-based drilling fluid is inversely proportional to the temperature; when the temperature remains unchanged, the density of oil-based drilling fluid is directly proportional to the pressure.

[0016] The rheological multivariate nonlinear regression model of high-density oil-based drilling fluid is calculated according to the following formula:

[0017]

[0018] Where: P0 is the ground pressure, MPa, generally atmospheric pressure; T0 is the ground temperature, °C, taken as 15 °C; K is the consistency coefficient that changes with temperature and pressure, Pa·s n ; n is the fluidity index that changes with temperature and pressure; K0 is the viscosity coefficient of the drilling fluid measured under T0 and P0 conditions, Pa·s n ; n0 is the fluidity index of the drilling fluid measured under T0 and P0 conditions; γ1, γ2, γ3, and γ4 are related rheological parameter coefficients, and their values ​​are determined by the regression equation.

[0019] In step S3, the drilling system is divided into three independent and interrelated areas, namely area 1, area 2, and area 3. Area 1 is within the drill string, area 2 is the annulus of the formation section, and area 3 is within the formation. Considering the influence of the physical properties of the drilling fluid changing with the downhole temperature, the eccentricity and rotation of the drill string, the change of the drill tool assembly, and the temperature change on the pressure loss along the process, the heat transfer knowledge and the finite difference method are used to establish the temperature and pressure ECD prediction model of the slim hole vertical well section.

[0020] Preferably, the internal circulation model of the drill string in region 1 is established as follows:

[0021] For the area inside the drill string, the heat sources are mainly the heat transfer of the fluid, the heat source generated by friction, and the heat transfer from the outer wall to the inner wall of the drill string. The total heat source flux Q ap for:

[0022]

[0023] Where, T a is the temperature of the annular drilling fluid, °C; T p is the internal temperature of the drill string, °C; h po is the comprehensive convection heat transfer coefficient of the drill string outer surface, W / (m 2 ℃); h piis the comprehensive convection heat transfer coefficient of the inner surface of the drill string, W / (m 2 ·℃);λ dp is the thermal conductivity of the drill string, W·m -1 ·K -1 ;d pi is the inner diameter of the drill pipe, mm; d po is the outer diameter of the drill pipe, mm; z is the spatial coordinate in the depth direction of the wellbore; t is the time coordinate; Δz is the spatial discrete step length in the depth direction of the wellbore, indicating the depth difference between discrete grids; Δt is the temporal discrete step length, indicating the interval in time advancement.

[0024] Define U as the total heat transfer coefficient from the outside of the drill string to the inside of the drill string, then based on the inner surface of the drill string, we have:

[0025] Q ap =Uπd pi Δz[T a (z,t)-T p (z,t)]Δt (6)

[0026] The heat gain due to friction is:

[0027] Q cp ΔzΔt(7)

[0028] The total energy increment in the system is:

[0029]

[0030] Where Q cp is the heat generated by friction pressure drop, W; c p is the specific heat capacity of the fluid in the drill string, J / (kg·K); ρ p is the density of the fluid in the drill string, Kg / m 3 .

[0031] By replacing the difference with the differential, we can get the energy mathematical model of the circulation model in region 1:

[0032]

[0033] Where q m is the heat flow rate, W / (m 2 ).

[0034] Preferably, the annular circulation model of the second formation section of the region is established as follows:

[0035] For the annular area of ​​the formation section, in the small time of Δt, there is heat transfer Q from the formation to the annular area by convection heat transfer. fa The heat transfer from the fluid into the annulus microelement is caused by friction and heat Q is transferred to the inside of the drill string. ap .

[0036] Q fa =h f πd w Δz[T f (z,r w ,t)-T a (z,t)]Δt (10)

[0037] Where h f is the comprehensive convection heat transfer coefficient between the annulus and the formation, W / (m 2 ℃); T f is the formation temperature, °C; d w is the inner diameter of the well wall (or casing), mm; r w is the hydraulic radius, which is equal to the flow cross-sectional area divided by the wetted perimeter, mm.

[0038] Q ap =Uπd pi Δz[T a (z,t)-T p (z,t)]Δt (11)

[0039] The total energy increment in the system is:

[0040]

[0041] By replacing the difference with the differential, we can get the energy mathematical model of the circulation model in region 2 as follows:

[0042]

[0043] Where c a is the specific heat capacity of the fluid in the annulus, J / (kg·K); ρ a is the density of the fluid in the annulus, Kg / m 3 .

[0044] Preferably, the regional three-stratum internal circulation model is established as follows:

[0045] Inside the formation, only the change of temperature profile with radial distance from the formation is considered. Therefore, according to the law of conservation of energy, we can obtain:

[0046]

[0047] Taking the boundary point in the formation as the benchmark, the energy equation of the circulation model of region 3 can be obtained:

[0048]

[0049] Where c f is the specific heat capacity of formation rock, J / (kg·K); ρ fis the density of the formation rock, Kg / m 3 ; r is the radial distance from the wellbore center; Δr is the discrete step length in the radial direction of the wellbore; λ f is the thermal conductivity of formation rock, W·m -1 ·K -1 .

[0050] Step S4: Using the finite difference method, the differential equation is processed using a fully implicit difference format to establish a temperature and pressure ECD prediction model for the slim hole vertical well section.

[0051] Preferably, for the high temperature and high pressure well section of this block, the model discrete schematic diagram is as follows Figure 3 Among them: the first-order upwind scheme is used to deal with the first-order spatial derivative in the differential equation; the two-point backward difference method is used to deal with the first-order time derivative; the three-point central difference method is used to deal with the second-order spatial derivative, and the temperature and pressure ECD prediction model of the slim hole vertical well section is established;

[0052] The model of region 1 is discretized as:

[0053]

[0054] The model of region 2 is discretized as:

[0055]

[0056] The model of region 3 is discretized as:

[0057]

[0058] In the above formula, k represents the time step, which indicates the state of the system at the kth time step; i represents the spatial discreteness in the depth direction of the wellbore, corresponding to different depth positions in the wellbore; j represents the radial discreteness of the wellbore;

[0059] The number of nodes in the depth direction is represented by m, and the number of nodes in the radial direction is represented by n, then 0≤i≤m; 0≤j≤n.

[0060] Step S5, based on the mathematical model of the changes in density and rheological properties of high-density oil-based drilling fluid with temperature and pressure obtained in step 2 and the temperature and pressure ECD prediction model of the slim hole vertical well section obtained in step 4, determines the value range of the static drilling fluid density (ESD) in managed pressure drilling, and realizes the optimized design of managed pressure drilling in deep high-temperature and high-pressure formations.

[0061] Preferably, in managed pressure drilling, the drilling fluid is a single-phase stable flow; in a static state, the bottom hole pressure is the sum of the static fluid column pressure and the wellhead back pressure, which can be specifically expressed by a mathematical expression:

[0062] p h =ρ gh +pback (19)

[0063] Where p h is the bottom hole pressure, Pa; ρ gh is the hydrostatic column pressure, Pa; p back is the wellhead back pressure, Pa;

[0064] In the circulation state, the bottom hole pressure is the sum of the static liquid column pressure, annular pressure loss and wellhead back pressure, and the formula is:

[0065] p h =ρ gh +(p AF +p back ) (20)

[0066] Where p AF is the annular circulation pressure drop, Pa, where (p AF +p back ) must be maintained in a stable state;

[0067] That is: the drilling fluid equivalent circulating density (ECD) is the sum of the static drilling fluid equivalent density (ESD), the annular circulation pressure drop and the wellhead back pressure equivalent density;

[0068] The density (ESD) and viscosity of drilling fluid will change with the depth of the well. Therefore, when drilling in deep formations, the physical properties of the drilling fluid at the wellhead and bottom of the well cannot be equated, which will cause errors.

[0069] A deep, high-temperature, and high-pressure formation managed pressure drilling optimization design system includes a data acquisition module and a data processing module. The data acquisition module is used to obtain performance parameters of high-density oil-based drilling fluid under high-temperature and high-pressure conditions. The data processing module is used to execute a deep, high-temperature, and high-pressure formation managed pressure drilling optimization design method to obtain a mathematical model of the density and rheological parameters of the high-density oil-based drilling fluid as a function of temperature and pressure, and a temperature and pressure ECD prediction model for a slim hole vertical well section. The system determines the value range of static drilling fluid density (ESD) in managed pressure drilling, thereby realizing optimized design of managed pressure drilling for deep, high-temperature, and high-pressure formations.

[0070] The beneficial effects of the present invention are:

[0071] The present invention utilizes a nonlinear multiple regression method to obtain a mathematical model of the density and rheological parameters of high-density oil-based drilling fluid as a function of temperature and pressure. Simultaneously, knowledge of heat transfer, wellbore hydraulics, applied mathematics, computer science, and the like is utilized to consider the influence of the physical properties of drilling fluid on temperature and pressure in deep, high-temperature, and high-pressure well sections. Based on the law of conservation of energy, a full-well section ECD prediction model is established, which more accurately approaches the actual bottomhole ECD change value, thereby achieving precise pressure control in managed pressure drilling. This realizes the optimized design of managed pressure drilling in deep, narrow-density-window, high-temperature, and high-pressure formations, and provides powerful assistance for flexible selection of the static drilling fluid density range on site. BRIEF DESCRIPTION OF THE DRAWINGS

[0072] The accompanying drawings are used to provide a further understanding of the present invention and constitute a part of the specification. Together with the embodiments of the present invention, they are used to explain the present invention and do not constitute a limitation of the present invention. In the accompanying drawings:

[0073] Figure 1 A flow chart showing an embodiment of a method for optimizing the design of managed pressure drilling in deep, high-temperature and high-pressure formations according to the present invention;

[0074] Figure 2 A regional division model diagram showing an embodiment of a method for optimizing the design of managed pressure drilling in deep, high-temperature and high-pressure formations according to the present invention;

[0075] Figure 3 A model discrete diagram showing an embodiment of a method for optimizing the design of managed pressure drilling in deep, high-temperature and high-pressure formations according to the present invention;

[0076] Figure 4 A diagram showing wellbore structural parameters of an embodiment of a method for optimizing the design of managed pressure drilling in deep, high-temperature, and high-pressure formations according to the present invention;

[0077] Figure 5 The optimized design diagram of managed pressure drilling when K=0.3 is shown;

[0078] Figure 6 The optimized design diagram of the managed pressure drilling according to the present invention when K=0.4 is shown. DETAILED DESCRIPTION

[0079] The present invention will be further described below with reference to embodiments and accompanying drawings, but is not limited thereto.

[0080] Example 1:

[0081] Take a high-temperature and high-pressure well with a narrow density window in a deep area as an example. Figure 1 As shown, a method for optimizing the design of managed pressure drilling in deep high-temperature and high-pressure formations includes the following steps:

[0082] Step S1: Obtain the performance parameters of high-density oil-based drilling fluid under high temperature and high pressure conditions, where the performance parameters include density, apparent viscosity AV, plastic viscosity PV, and yield value YP, and study how the performance of the high-density oil-based drilling fluid changes with temperature and pressure under high temperature and high pressure.

[0083] Step S2: obtaining a mathematical model of the density and rheological parameters of the high-density oil-based drilling fluid as a function of temperature and pressure by using a nonlinear multiple regression method.

[0084] The density multivariate nonlinear regression model of high-density oil-based drilling fluid is calculated according to the following formula:

[0085] ρ(P,T)=ρ0exp[φ(P,T)](1)

[0086] in:

[0087] φ(P,T)=ξ P (P-P0)+ξ PP (P-P0) 2 +ξ T (T-T0)+ξ TT (T-T0) 2 +ξ pT (P-P0)(T-T0) (2)

[0088] Where: P0 is the surface pressure, MPa, which is generally atmospheric pressure; T0 is the surface temperature, °C, which is 15 °C; ρ(T, P) is the density of the drilling fluid under temperature and pressure control, g / cm 3 ξ P ,ξ T are the primary characteristic constants of the pressure and temperature terms of the drilling fluid respectively; ξ PP ,ξ TT are the quadratic characteristic constants of the pressure and temperature terms of the drilling fluid respectively; ξ PT is the quadratic characteristic constant of the drilling fluid pressure and temperature coupling term; T and P are the wellbore temperature and pressure; ρ0 is the initial density of the drilling fluid, g / cm 3 .

[0089] The drilling fluid performance parameters were processed using the multivariate nonlinear regression analysis method to obtain the corresponding density characteristic numbers of the drilling fluid, as shown in Table 1.

[0090] Table 1 Drilling fluid density model characteristic coefficients

[0091]

[0092] Under the condition of controlling variables, when the pressure remains unchanged, the density of oil-based drilling fluid is inversely proportional to the temperature; when the temperature remains unchanged, the density of oil-based drilling fluid is directly proportional to the pressure.

[0093] The rheological multivariate nonlinear regression model of high-density oil-based drilling fluid is calculated according to the following formula:

[0094]

[0095] Where: P0 is the ground pressure, MPa, generally atmospheric pressure; T0 is the ground temperature, °C, taken as 15 °C; K is the consistency coefficient that changes with temperature and pressure, Pa·s n ; n is the fluidity index that changes with temperature and pressure; K0 is the viscosity coefficient of the drilling fluid measured under T0 and P0 conditions, Pa·s n ; n0 is the fluidity index of the drilling fluid measured under T0 and P0 conditions; γ1, γ2, γ3, and γ4 are the relevant rheological parameter coefficients.

[0096] Nonlinear multiple regression analysis of the correlation coefficients γ1, γ2, γ3, and γ4 yielded the coefficients for the high-density oil-based drilling fluid rheological property prediction model shown in Table 2. This model accurately describes how the rheological properties of high-density oil-based drilling fluids change with temperature and pressure and is convenient for use in production sites.

[0097] Table 2 Drilling fluid rheological properties prediction model coefficients

[0098]

[0099] Step S3, the drilling system is divided into three independent and interrelated areas, namely area 1, area 2, and area 3. Area 1 is inside the drill string, area 2 is the annulus of the formation, and area 3 is inside the formation. Figure 2 As shown, Figure 2 In, d b The model solution range is 1. Considering the characteristics of drilling fluid physical properties changing with downhole temperature, the influence of drill string eccentricity, rotation, drilling tool assembly changes, and temperature changes on pressure loss along the drilling process, a temperature and pressure ECD prediction model for slim hole vertical well section is established using heat transfer knowledge and the finite difference method.

[0100] The internal circulation model of the drill string in region 1 is established as follows:

[0101] For the area inside the drill string, the heat sources are mainly the heat transfer of the fluid, the heat source generated by friction, and the heat transfer from the outer wall to the inner wall of the drill string. The total heat source flux Q ap for:

[0102]

[0103] Where, T a is the temperature of the annular drilling fluid, °C; T p is the internal temperature of the drill string, °C; h po is the comprehensive convection heat transfer coefficient of the drill string outer surface, W / (m2 ℃); h pi is the comprehensive convection heat transfer coefficient of the inner surface of the drill string, W / (m 2 ·℃);λ dp is the thermal conductivity of the drill string, W·m -1 ·K -1 ;d pi is the inner diameter of the drill pipe, mm; d po is the outer diameter of the drill pipe, mm; z is the spatial coordinate in the depth direction of the wellbore; t is the time coordinate; Δz is the spatial discrete step length in the depth direction of the wellbore, indicating the depth difference between discrete grids; Δt is the temporal discrete step length, indicating the interval in time advancement.

[0104] Define U as the total heat transfer coefficient from the outside of the drill string to the inside of the drill string, then based on the inner surface of the drill string, we have:

[0105] Q ap =Uπd pi Δz[T a (z,t)-T p (z,t)]Δt (6)

[0106] The heat gain due to friction is:

[0107] Q cp ΔzΔt(7)

[0108] The total energy increment in the system is:

[0109]

[0110] Where Q cp is the heat generated by friction pressure drop, W; c p is the specific heat capacity of the fluid in the drill string, J / (kg·K); ρ p is the density of the fluid in the drill string, Kg / m 3 .

[0111] By replacing the difference with the differential, we can get the energy mathematical model of the circulation model in region 1:

[0112]

[0113] Where q m is the heat flow rate, W / (m 2 ).

[0114] The annular circulation model of the second stratigraphic section in the region is established as follows:

[0115] For the annular area of ​​the formation section, in the small time of Δt, there is heat transfer Q from the formation to the annular area by convection heat transfer. faThe heat transfer from the fluid into the annulus microelement is caused by friction and heat Q is transferred to the inside of the drill string. ap .

[0116] Q fa =h f πd w Δz[T f (z,r w ,t)-T a (z,t)]Δt (10)

[0117] Where h f is the comprehensive convection heat transfer coefficient between the annulus and the formation, W / (m 2 ℃); T f is the formation temperature, °C; d w is the inner diameter of the well wall (or casing), mm; r w is the hydraulic radius, which is equal to the flow cross-sectional area divided by the wetted perimeter, mm.

[0118] Q ap =Uπd pi Δz[T a (z,t)-T p (z,t)]Δt (11)

[0119] The total energy increment in the system is:

[0120]

[0121] By replacing the difference with the differential, we can get the energy mathematical model of the circulation model in region 2 as follows:

[0122]

[0123] Where c a is the specific heat capacity of the fluid in the annulus, J / (kg·K); ρ a is the density of the fluid in the annulus, Kg / m 3 .

[0124] The internal circulation model of the three regional strata is established as follows:

[0125] Inside the formation, only the change of temperature profile with radial distance from the formation is considered. Therefore, according to the law of conservation of energy, we can obtain:

[0126]

[0127] Taking the boundary point in the formation as the benchmark, the energy equation of the circulation model of region 3 can be obtained:

[0128]

[0129] Where c f is the specific heat capacity of formation rock, J / (kg·K); ρ f is the density of the formation rock, Kg / m 3 ; r is the radial distance from the wellbore center; Δr is the discrete step length in the radial direction of the wellbore; λ f is the thermal conductivity of formation rock, W·m -1 ·K -1 .

[0130] Step S4: Using the finite difference method, the differential equation is processed using a fully implicit difference format to establish a temperature and pressure ECD prediction model for the slim hole vertical well section.

[0131] For the high-temperature and high-pressure well section in this block, the model discrete schematic diagram is as follows Figure 3 Among them: the first-order upwind scheme is used to deal with the first-order spatial derivative in the differential equation; the two-point backward difference method is used to deal with the first-order time derivative; the three-point central difference method is used to deal with the second-order spatial derivative, and the temperature and pressure ECD prediction model of the slim hole vertical well section is established;

[0132] The model of region 1 is discretized as:

[0133]

[0134] The model of region 2 is discretized as:

[0135]

[0136] The model of region 3 is discretized as:

[0137]

[0138] In the above formula, k represents the time step, which indicates the state of the system at the kth time step; i represents the spatial discreteness in the depth direction of the wellbore, corresponding to different depth positions in the wellbore; j represents the radial discreteness of the wellbore;

[0139] The number of nodes in the depth direction is represented by m, and the number of nodes in the radial direction is represented by n, then 0≤i≤m; 0≤j≤n.

[0140] Step S5, based on the mathematical model of the changes in density and rheological properties of high-density oil-based drilling fluid with temperature and pressure obtained in step 2 and the temperature and pressure ECD prediction model of the slim hole vertical well section obtained in step 4, determines the value range of the static drilling fluid density (ESD) in managed pressure drilling, and realizes the optimized design of managed pressure drilling in deep high-temperature and high-pressure formations.

[0141] For the high-temperature and high-pressure well section in this block, the designed drilling depth is 5980m. When drilling into deep high-pressure formations, in order to prevent well intrusion and well kick, the density of the drilling fluid used is 2.34sg. Its density safety window is extremely narrow, only 0.06sg. The wellbore structure diagram is shown below. Figure 4 shown.

[0142] In managed pressure drilling, the drilling fluid flows in a single-phase, stable manner. In a static state, the bottomhole pressure is the sum of the static fluid column pressure and the wellhead back pressure, which can be expressed mathematically as follows:

[0143] p h =ρ gh +p back (19)

[0144] Where p h is the bottom hole pressure, Pa; ρ gh is the hydrostatic column pressure, Pa; p back is the wellhead back pressure, Pa;

[0145] In the circulation state, the bottom hole pressure is the sum of the static liquid column pressure, annular pressure loss and wellhead back pressure, and the formula is:

[0146] p h =ρ gh +(p AF +p back )(20)

[0147] Where p AF is the annular circulation pressure drop, Pa, where (p AF +p back ) must be maintained in a stable state;

[0148] That is: the drilling fluid equivalent circulating density (ECD) is the sum of the static drilling fluid equivalent density (ESD), the annular circulation pressure drop and the wellhead back pressure equivalent density;

[0149] The density (ESD) and viscosity of drilling fluid will change with the depth of the well. Therefore, when drilling in deep formations, the physical properties of the drilling fluid at the wellhead and bottom of the well cannot be equated, which will cause errors.

[0150] For the high-temperature and high-pressure well section in this block, affected by the temperature and pressure of the entire well section, the ECD shows a trend of first decreasing and then increasing with the increase of well depth, and different drilling fluid density and viscosity will cause changes in the bottomhole ECD value. Figure 5 The optimized design scheme of managed pressure drilling under different drilling fluid viscosities is described. Figure 5 It can be seen that when k = 0.3, the optional density of the drilling fluid that can ensure that the bottomhole pressure profile is within the safe density window within different ground back pressure ranges is 2.36 g / cm 3 to 2.42g / cm3 , reasonably adjusting the wellhead back pressure range can expand the optional range of drilling fluid density. Figure 5 and Figure 6 We can conclude that increasing viscosity leads to a gradual decrease in the selectable drilling fluid density (ESD) because increased viscosity increases circulating pressure loss, thereby increasing the bottomhole ECD value. In managed pressure drilling in formations with a narrow density window, the change in selectable ESD values ​​is inversely proportional to viscosity. This conclusion can provide valuable assistance for flexible selection of ESD ranges in the field.

[0151] In summary, by fully considering the changes in drilling fluid physical properties with temperature and pressure, the established ECD model is made more realistic, and the optimized design scheme for managed pressure drilling in deep, high-temperature, high-pressure, and narrow-density window formations is completed, providing strong assistance for flexible selection of the static drilling fluid density range on site.

[0152] The above embodiments are merely illustrative of the principles and effects of the present invention and are not intended to limit the present invention. Anyone skilled in the art may modify or alter the above embodiments without departing from the spirit and scope of the present invention. Therefore, all equivalent modifications or alterations made by one of ordinary skill in the art without departing from the spirit and technical principles disclosed herein are intended to be covered by the claims of the present invention.

Claims

1. A method for optimizing the design of managed pressure drilling in deep high-temperature and high-pressure formations, characterized in that: The following steps are involved: Step S1, obtaining performance parameters of high-density oil-based drilling fluid under high temperature and high pressure conditions, the performance parameters including density, apparent viscosity AV, plastic viscosity PV and yield value YP, and obtaining the law of change of the performance of the high-density oil-based drilling fluid under high temperature and high pressure with temperature and pressure; Step S2, obtaining a mathematical model of density and rheological parameters of high-density oil-based drilling fluid as a function of temperature and pressure by a nonlinear multiple regression method; Step S3, dividing the drilling system into three independent and interrelated areas, namely area 1, area 2, and area 3, where area 1 is inside the drill string, area 2 is the annulus of the formation section, and area 3 is inside the formation; establishing a temperature and pressure ECD prediction model for the slim hole vertical well section; Step S4, using the finite difference method to process the above differential equation using a fully implicit difference format, and establishing a temperature and pressure ECD prediction model for a slim hole vertical well section; Step S5, based on the mathematical model of the changes in density and rheology of the high-density oil-based drilling fluid with temperature and pressure obtained in step 2 and the temperature and pressure ECD prediction model of the small hole vertical well section obtained in step 4, determine the value range of the static drilling fluid density (ESD) in controlled pressure drilling, and realize the optimized design of controlled pressure drilling for deep high-temperature and high-pressure formations.

2. The method for optimizing the design of managed pressure drilling in deep high-temperature and high-pressure formations according to claim 1, characterized in that: In step S2, the density multivariate nonlinear regression model of the high-density oil-based drilling fluid is calculated according to the following formula: ρ(P,T)=ρ0exp[φ(P,T)](1) in: φ(P,T)=ξ P (P-P0)+ξ PP (P-P0) 2 +ξ T (T-T0)+ξ TT (T-T0) 2 +ξ pT (P-P0)(T-T0) (2) Where: P0 is the surface pressure, MPa, generally atmospheric pressure; T0 is the surface temperature, °C, taken as 15 °C; ρ(T,P) is the density of the drilling fluid under temperature and pressure control, g / cm 3 ξ P ,ξ T are the first-order characteristic constants of the pressure and temperature terms of the drilling fluid respectively; ξ PP ,ξ TT are the secondary characteristic constants of pressure and temperature of drilling fluid respectively; ξ PT is the quadratic characteristic constant of the pressure and temperature coupling term of the drilling fluid; T and P are the wellbore temperature and pressure; ρ0 is the initial density of the drilling fluid, g / cm 3 ; Under the condition of controlling variables, when the pressure is constant, the density of oil-based drilling fluid is inversely proportional to the temperature; when the temperature is constant, the density of oil-based drilling fluid is proportional to the pressure; The rheological multivariate nonlinear regression model of high-density oil-based drilling fluid is calculated according to the following formula: Where: P0 is the ground pressure, MPa, T0 is the ground temperature, °C, which is 15 °C; K is the consistency coefficient that changes with temperature and pressure, Pa·s n ; n is the fluidity index that changes with temperature and pressure; K0 is the viscosity coefficient of the drilling fluid measured under T0 and P0 conditions, Pa·s n ; n0 is the fluidity index of the drilling fluid measured under T0 and P0 conditions; γ1, γ2, γ3, and γ4 are related rheological parameter coefficients, and their values ​​are determined by the regression equation.

3. The deep high-temperature and high-pressure formation managed pressure drilling optimization design method according to claim 1, characterized in that: In step S3, the internal circulation model of the drill string in region 1 is established as follows: Total flux of wellbore heat source Q ap for: Where, T a is the temperature of the annular drilling fluid, °C; T p is the internal temperature of the drill string, °C; h po is the comprehensive convection heat transfer coefficient of the drill string outer surface, W / (m 2 ℃); h pi is the comprehensive convection heat transfer coefficient of the inner surface of the drill string, W / (m 2 ·℃);λ dp is the thermal conductivity of the drill string, W·m -1 ·K -1 ;d pi is the inner diameter of the drill pipe, mm; d po is the outer diameter of the drill pipe, mm; z is the spatial coordinate in the depth direction of the wellbore; t is the time coordinate; Δz is the spatial discrete step length in the depth direction of the wellbore, indicating the depth difference between discrete grids; Δt is the discrete step length in time, indicating the interval in time advancement; Define U as the total heat transfer coefficient from the outside of the drill string to the inside of the drill string, then based on the inner surface of the drill string, we have: Q ap =Uπd pi Δz[T a (z,t)-T p (z,t)]Δt (6) The heat gain due to friction is: Q cp ΔzΔt(7) The total energy increment in the system is: In the formula, Q cp is the heat generated by friction pressure drop, W; c p is the specific heat capacity of the fluid in the drill string, J / (kg·K); ρ p is the fluid density in the drill string, Kg / m 3 ; Replacing the difference with the differential, the energy mathematical model of the circulation model in region 1 is obtained as follows: In the formula, q m is the heat flow rate, W / (m 2 ).

4. The deep high-temperature and high-pressure formation managed pressure drilling optimization design method according to claim 3, characterized in that: In step S3, the annular circulation model of the second formation section of the region is established as follows: For the annular space of the formation section, in the small time of Δt, there is heat transfer Q from the formation to the annular space by convection heat transfer. fa The heat transfer from the fluid into the annulus micro-element includes the heat source generated by friction and the heat Q transferred to the inside of the drill string. ap ; Q fa =h f πd w Δz[T f (z,r w ,t)-T a (z,t)]Δt(10) In the formula, h f is the comprehensive convection heat transfer coefficient between the annulus and the formation, W / (m 2 ℃); T f is the formation temperature, °C; d w is the inner diameter of the well wall, mm; r w is the hydraulic radius, which is equal to the flow cross-sectional area divided by the wetted perimeter, mm; Q ap =Uπd pi Δz[T a (z,t)-T p (z,t)]Δt(11) The total energy increment in the system is: Replacing the difference with the differential, the energy mathematical model of the circulation model in region 2 is obtained as follows: In the formula, c a is the specific heat capacity of the fluid in the annulus, J / (kg·K); ρ a is the density of the fluid in the annulus, Kg / m 3 .

5. The method for optimizing the design of managed pressure drilling in deep high-temperature and high-pressure formations according to claim 4, characterized in that: In step S3, the internal circulation model of the three strata in the region is established as follows: In the stratum, according to the law of conservation of energy, we have: Taking the boundary point in the formation as the reference, the energy equation of the circulation model of region 3 is obtained: In the formula, c f is the specific heat capacity of formation rock, J / (kg·K); ρ f is the rock density of the formation, Kg / m 3 ; r is the radial distance from the wellbore center; Δr is the discrete step length in the radial direction of the wellbore; λ f is the thermal conductivity of the formation rock, W·m -1 ·K -1 .

6. The method for optimizing the design of managed pressure drilling in deep high-temperature and high-pressure formations according to claim 1, characterized in that: In step S4, the first-order upwind scheme is used to process the first-order spatial derivative in the differential equation; the two-point backward difference method is used to process the first-order time derivative; the three-point central difference method is used to process the second-order spatial derivative, and the temperature and pressure ECD prediction model of the slim hole vertical well section is established; The model of region 1 is discretized as: The model of region 2 is discretized as: The model of region 3 is discretized as: In the above formula, k represents the time step, which indicates the state of the system at the kth time step; i represents the spatial discreteness in the depth direction of the wellbore, corresponding to different depth positions in the wellbore; j represents the radial discreteness of the wellbore; The number of nodes in the depth direction is represented by m, and the number of nodes in the radial direction is represented by n, then 0≤i≤m; 0≤j≤n.

7. The method for optimizing the design of managed pressure drilling in deep high-temperature and high-pressure formations according to claim 1, characterized in that: In step S5, in the pressure-controlled drilling, the drilling fluid is a single-phase stable flow; in a static state, the bottom hole pressure is the sum of the static liquid column pressure and the wellhead back pressure, which is specifically expressed by a mathematical expression: p h =ρ gh +p bac k (19) In the formula, p h is the bottom hole pressure, Pa; ρ gh is the hydrostatic column pressure, Pa; p back is the wellhead back pressure, Pa; In the circulation state, the bottom hole pressure is the sum of the static liquid column pressure, the annular pressure loss and the wellhead back pressure. The formula is: p h =ρ gh +(p AF +p back )(20) In the formula, p AF is the annular circulation pressure drop, Pa, where (p AF +p back ) must be maintained in a stable state; That is, the drilling fluid equivalent circulating density ECD is the sum of the static drilling fluid equivalent density ESD, the annular circulation pressure drop and the wellhead back pressure equivalent density.

8. A deep high-temperature and high-pressure formation managed pressure drilling optimization design system, characterized in that: It includes a data acquisition module and a data processing module. The data acquisition module is used to obtain the performance parameters of high-density oil-based drilling fluid under high temperature and high pressure conditions. The data processing module is used to execute the deep high temperature and high pressure formation controlled pressure drilling optimization design method described in claim 1, obtain the mathematical model of the density and rheological parameters of the high-density oil-based drilling fluid with temperature and pressure and the temperature and pressure ECD prediction model of the small hole vertical well section, determine the value range of the static drilling fluid density ESD in controlled pressure drilling, and realize the optimized design of controlled pressure drilling for deep high temperature and high pressure formations.

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