Method for comprehensive performance analysis of deep-embedded casing

Abstract

This invention discloses a method for comprehensive performance analysis of deeply buried casing. The method includes: receiving system parameters input by a user through a human-computer interaction interface, and dividing the system parameters into a set of thermal physical parameters and a set of cost-economic parameters; performing dynamic thermal calculations using a segmented discretization method along the depth direction and a dynamic thermal resistance network method to obtain a first calculation result; calculating the total drilling cost based on the system parameters to obtain a second calculation result; and comprehensively processing and visualizing the first and second calculation results, and performing a horizontal comparison of multiple schemes. This invention deeply couples a high-fidelity dynamic thermal model with a deeply nonlinear engineering cost model at the algorithm level, enabling simultaneous evaluation of "physical performance" and "economic cost" on the same platform. This breaks down professional barriers in the traditional design process and improves the scientific nature and efficiency of decision-making.

Description

Technical Field

[0001] This invention relates to the field of geothermal energy development and utilization technology, and in particular to a method for comprehensive performance analysis of deeply buried casing. Background Technology

[0002] Deep-buried casing heat exchange technology utilizes deep geothermal heat and extracts heat through fluid circulation within the wellbore. It offers advantages such as small footprint, low environmental disturbance, suitability for building heating, and multi-energy complementarity. With the promotion of clean geothermal heating, deep-buried casing heat exchange systems have received widespread attention in scenarios such as district heating, industrial waste heat replenishment, green buildings, and low-carbon energy stations.

[0003] Existing deep-buried casing heat exchange schemes typically include an outer casing, an inner casing, an insulation layer, a cement sheath, and the surrounding formation. The working medium enters from the wellhead and flows downwards along the annulus channel, then turns back at the bottom of the well and flows upwards along the inner casing channel, exchanging heat with the formation through the pipe wall and multiple layers of solid media. The system's thermal performance is affected not only by well depth, pipe diameter, material thermal conductivity, flow rate, inlet temperature, and operating time, but also by drilling costs, well diameter class, casing outer diameter, and cost tiering rules. In practical engineering, decision-makers are not primarily concerned with how much heat a particular well can extract, but rather, given a given drilling investment, which well depth, pipe type, and structural parameter combination will yield the best heating capacity and economic return.

[0004] However, existing technologies still have significant shortcomings in the following aspects. First, thermal calculations and economic calculations are separated. Many schemes estimate heat transfer capacity and calculate drilling costs separately, failing to reflect whether the heat transfer gain is sufficient to cover the cost increase brought about by the increase in well depth within the same calculation framework. This leads to design optimization relying on empirical judgment and lacking a unified evaluation benchmark. Second, the description of multi-layer heat transfer paths is incomplete. The heat transfer process in the wellbore involves convective heat transfer between the fluid and the inner wall, heat conduction through the pipe wall, heat conduction through the insulation layer, heat conduction through the cement sheath, and heat transfer between the wellbore and the formation. If only a simplified overall coefficient approximation is used, it is often difficult to reflect the impact of changes in materials and geometric dimensions at different levels on the total heat transfer capacity. Third, the cost model is too coarse. Drilling costs are not simply linearly related to well depth. In actual engineering, they are usually affected by multiple factors such as well diameter, formation classification, construction difficulty, material consumption, well completion technology, and cost model selection, and are often expressed in the form of segments, tiers, and benchmark unit price adjustments. Existing methods often cannot flexibly switch cost models to meet the needs of different projects. Fourth, there is a lack of comparable indicators for heat exchange capacity and cost. The merits of an engineering scheme should be reflected in the heat capacity obtained per unit of input. However, existing technologies often only provide the heat capacity or cost itself, lacking evaluation metrics that can directly support the selection of the scheme, such as total heating capacity / drilling cost, net increase in heating revenue / deep increment cost. Summary of the Invention

[0005] This invention provides a method for comprehensive performance analysis of deeply buried casings to solve the technical problems in the prior art.

[0006] To address the aforementioned technical problems, this invention provides a method for comprehensive performance analysis of deeply buried casing, comprising: S10, receive system parameters input by the user through the human-computer interaction interface, and divide the system parameters into a set of thermophysical parameters and a set of cost-economic parameters; S20, using the segmented discretization along the depth direction and dynamic thermal resistance network method to perform thermal dynamic calculations and obtain the first calculation result; S30, Based on the system parameters, calculate the total drilling cost and obtain the second calculation result; S40, the first calculation result and the second calculation result are comprehensively processed and visualized, and multiple schemes are compared horizontally.

[0007] Optionally, the set of thermal physical parameters includes wellbore geometric parameters, material property parameters, operating parameters, and formation parameters, and the set of cost and economic parameters includes regression parameters of the heating performance coefficient model, drilling depth-cost model parameters, drilling aperture-cost model parameters, and billing mode options.

[0008] Optionally, step S20 includes: S201, Based on the system parameters, calculate the geometric properties of each key section; S202 uses the Dieters-Belt relation to automatically calculate the convective heat transfer coefficients of the inner and outer sides; S203, segment along the well depth direction, establish a steady-state thermal resistance network model, and calculate the total thermal resistance; S204 employs a numerical method that uses one-dimensional discretization along the depth direction and explicit or implicit propagation along the time direction to dynamically solve the fluid temperature distribution. S205: After the calculation is completed at each time step, extract the thermal performance indicators.

[0009] Optionally, step S201 includes: S2011, calculate the flow cross-sectional area of ​​the inner pipe based on the following formula: In the formula: A i D represents the cross-sectional area of ​​the inner tube. ii The inner diameter of the tube; S2012, calculate the cross-sectional area of ​​the annular flow based on the following formula: In the formula: A ann Indicates the cross-sectional area of ​​the annular flow. Doi The inner diameter of the outer tube. D io The outer diameter of the inner tube; S2013, calculate the equivalent diameter of the inner tube based on the following formula: In the formula: D h,i This represents the equivalent diameter of the inner tube, which is numerically equal to the inner diameter of the inner tube. D ii ; S2014, the equivalent diameter of the annulus is calculated based on the following formula: In the formula: D h,ann Indicates the equivalent diameter of the annulus, derived from the inner diameter of the outer tube. D oi With the outer diameter of the inner tube D io The difference is determined; S2015, calculate the inner pipe flow velocity based on the following formula: In the formula: u i This indicates the flow rate of the working fluid in the inner tube. m For the working fluid mass flow rate, r f For the working fluid density, A i This refers to the cross-sectional area of ​​the inner tube for flow. S2016, the annular velocity is calculated based on the following formula: In the formula: u ann The velocity of the working fluid in the annulus is expressed as the working fluid mass flow rate. m Divide by working fluid density r f Divide by the cross-sectional area of ​​the annular flow. A ann The calculation yielded the result.

[0010] Optionally, step S202 includes: S2021, the Reynolds number is calculated based on the following formula: In the formula: Re Represents the Reynolds number. r f For the working fluid density, u Refers to the flow rate of the working fluid. D h Equivalent diameter m f The dynamic viscosity of the working fluid; S2022, Prandtl number is calculated based on the following formula: In the formula: Pr Representing Prandtl numbers, m f The dynamic viscosity of the working fluid. c p,f The specific heat capacity of the working fluid at constant pressure k f The thermal conductivity of the working fluid; S2023, the Nusselt number is calculated based on the following formula: In the formula: No Representing the Nusselt number, derived from the Reynolds number. Re With Prandtl Pr Calculated using the Dittus-Boelter empirical correlation; S2024, the convective heat transfer coefficient is calculated based on the following formula: In the formula: h The convective heat transfer coefficient is represented by the Nusselt number. No Thermal conductivity of the working fluid k f and equivalent diameter D h To be determined jointly.

[0011] Optionally, step S203 includes: S2031, the entire well depth H is discretized into N micro-segments, and the length of each segment Δz = H / N is guaranteed; S2032, for each depth element j, j = 1, 2, ..., N, establish a steady-state thermal resistance network model; S2033, Calculate the total thermal resistance R from the center of the buried pipe to the outer boundary of the soil / rock surface. totj .

[0012] Optionally, the total thermal resistance R totj It consists of the following parts connected in series or parallel: Inner tube fluid convection thermal resistance: In the formula: R conv,i,j Representing depth infinitesimal elements j The convective thermal resistance between the fluid inside the inner tube and the inner wall surface of the inner tube. h i The convective heat transfer coefficient on the inner tube side is...D ii The inner diameter of the inner tube. Δz The length of the infinitesimal segment; Inner tube wall thermal resistance: In the formula: R pipe,i,j Representing depth infinitesimal elements j The radial thermal resistance of the inner tube wall. D io The outer diameter of the inner tube. D ii The inner diameter of the inner tube. k i The thermal conductivity of the inner tube is... Δz The length of the infinitesimal segment; Thermal resistance of insulation layer: In the formula: R ins,j Representing depth infinitesimal elements j The radial thermal resistance of the insulation layer D io The outer diameter of the inner tube. d ins For the thickness of the insulation layer, k ins The thermal conductivity of the insulation layer, Δz The length of the infinitesimal segment; Circulatory thermal resistance of the annulus fluid: In the formula: R conv,o,j Representing depth infinitesimal elements j The convective thermal resistance between the annular fluid and the inner wall of the outer tube. h o The annular side convective heat transfer coefficient is... D oi The inner diameter of the outer tube. Δz The length of the infinitesimal segment; Thermal resistance of the outer tube wall: In the formula: R pipe,o,j Representing depth infinitesimal elements j The radial thermal resistance of the outer tube wall, D oo The outer diameter of the outer tube. D oi The inner diameter of the outer tube. k o The thermal conductivity of the outer tube is... Δz The length of the infinitesimal segment; Thermal resistance of cement ring: In the formula: R cem,j Representing depth infinitesimal elements j The radial thermal resistance of the cement ring. D b The diameter of the borehole. D oo The outer diameter of the outer tube. k c The thermal conductivity of the cement ring is... Δz The length of the infinitesimal segment; Transient thermal resistance of formation: A transient thermal response model based on formations with varying thermal properties is adopted for operating time t and depth z. j The formation thermal resistance R at the location g,j(t) This can be expressed as: In the formula: E 1 is an exponential integral function; r b The radius of the borehole; α g,j strata j Thermal diffusivity at depth, and α g,j = k g,j / (ρg,j cg,j) .

[0013] Optionally, step S30 includes: S310, Based on the system parameters, calculate the diameter influence factor, as shown in the following formula: In the formula: D represents the actual pipe diameter; D0 represents the deviation from the reference pipe diameter; Indicates the cost adjustment factor; S320 calculates the unit length cost function based on the following formula: In the formula: This represents the cost per unit length of drilling. S330, calculate the total cost based on the following formula: In the formula: Represents the total drilling cost under the linear billing model, in the integral formula h For depth variables measured from the Earth's surface, C unit ( h ) for depth h The unit advance cost function at the location. a andb , respectively, represent the slope and intercept of the depth-cost linear relationship, where a Reflects the rate of change of unit cost as unit depth increases. b Based on the unit cost. H The total depth of the wellbore is represented by the upper and lower limits of the integral, which correspond to the bottom of the well and the surface, respectively. S340, Set a reference depth interval The total cost is calculated using a cost accumulation factor r greater than 1, through piecewise integration and summation, as shown in the following formula: In the formula: This represents the total drilling cost under the depth-increasing tiered billing model. K The total number of segments divided by depth intervals, satisfying the condition that the endpoints of each segment start from... h 0 = 0 to h K = H, h k and h k+1 They represent the first k The difference between the starting and ending depths of a segment and its adjacent endpoints is usually equal to... ΔH s , r k Representing the k The cumulative multiplication factor of the segments is used to achieve a step-like increase in unit cost as the depth increases; S350, Integrating the piecewise integral and summation formula yields the following explicit calculation formula: In the formula: This represents the total drilling cost under the depth-increasing tiered billing model. Indicates the cost adjustment factor. K This represents the total number of segments divided by depth intervals. r k Representing the k The cumulative factor of the segment, h k and h k+1 They represent the first k The starting and ending depths of the segment.

[0014] Optionally, step S40 includes: S401, displays the final outlet temperature in real time. Average geothermal extraction power Q E Average total heating power Q HTotal drilling cost ; S402, plotting the outlet temperature Geothermal extraction power Total heating power System in real time COP ( t The curve showing how the curve changes over time; S403, Plot the temperature distribution along the well depth at the final moment. T ( z This is to demonstrate the changes in formation temperature, annular fluid temperature, and inner tube fluid temperature along the path.

[0015] One or more technical solutions provided in the embodiments of the present invention have at least the following technical effects or advantages: This application deeply couples a high-fidelity dynamic thermal model with a deeply nonlinear engineering cost model at the algorithm level, enabling simultaneous evaluation of "physical performance" and "economic cost" on the same platform. This breaks down professional barriers in the traditional design process and improves the scientific nature and efficiency of decision-making.

[0016] The axially segmented discrete and radial thermal resistance network model used in this application has a clear physical mechanism and can accurately handle strata with varying physical properties, arbitrarily set pipe diameters and insulation layer structures, as well as transient processes during system operation. It avoids the oversimplification of geometry and boundary conditions in traditional line heat source models, resulting in more reliable calculation results.

[0017] The "depth interval cumulative cost model" proposed in this application is a significant innovation. By introducing a cumulative factor, it effectively portrays the trend of deep drilling costs increasing exponentially with depth, reflecting engineering realities better than simple linear or polynomial models, and greatly improving the accuracy of preliminary economic assessments.

[0018] This application transforms complex multivariate optimization problems into intuitive graphical selection problems. Combined with automated cost-effectiveness ranking and solution filtering functions, it greatly assists engineers in quickly locating the optimal or satisfactory solution among numerous design options, thus shortening the design cycle.

[0019] This application integrates complex simulation calculations, data processing, and visualization functions into a unified software platform. It guides users through the operation via a wizard-style interface, lowering the barrier to entry for advanced simulation tools and making the method easily accepted and applied by a wide range of users, including design institutes and project investors. Attached Figure Description

[0020] Figure 1 This is a flowchart illustrating the method for comprehensive performance analysis of deeply buried sleeves provided in this embodiment of the invention. Detailed Implementation

[0021] The technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of the present invention, and not all embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of the present invention.

[0022] In the relevant descriptions of this embodiment, the terms "including," "containing," and "possessing" are all open terms and are generally understood to include but not be limited to; the term "at least one" is generally understood to mean one or more, where "multiple" refers to two or more; the term "at least one of the following" or similar expressions refer to any combination of these items, including any combination of single or multiple items, for example, "at least one of a, b, or c", or "at least one of a, b, and c", which can all mean: a, b, c, ab (i.e., a and b), ac, bc, or abc, where a, b, and c can be single or multiple; the symbol "A / B" is used to describe the selection relationship of associated objects, generally indicating an "or" relationship.

[0023] In the following description of the embodiments, the terminology used in the embodiments of this application is for the purpose of describing particular embodiments only and is not intended to be limiting of the application. The singular forms "a" and "the" as used in the embodiments of this application and the appended claims are also intended to include the plural forms, unless the context clearly indicates otherwise.

[0024] Those skilled in the art should understand that, in the following description of the embodiments of this application, the sequence of numbers does not imply the order of execution. Some or all steps may be executed in parallel or sequentially. The execution order of each process should be determined by its function and internal logic, and should not constitute any limitation on the implementation process of the embodiments of this application.

[0025] Those skilled in the art will understand that the numerical ranges in the embodiments of this application should be understood to specifically disclose each intermediate value between the upper and lower limits of the range. Any stated value or intermediate value within a stated range, as well as any other stated value or each smaller range between intermediate values ​​within a range, are also included within this invention. The upper and lower limits of these smaller ranges may be independently included or excluded from the range.

[0026] Unless otherwise stated, the technical / scientific terms used herein have the same meaning as commonly understood by one of ordinary skill in the art to which this application pertains. While this application describes only preferred methods and materials, any methods and materials similar or equivalent to those described herein may be used in the implementation or testing of this application. All references to this specification are incorporated by way of citation to disclose and describe the methods and / or materials associated with those references. In the event of any conflict with any incorporated reference, the content of this specification shall prevail.

[0027] This invention provides a method for comprehensive performance analysis of deeply buried casing, with reference to... Figure 1 The method may include the following steps: S10: Receive system parameters input by the user through the human-computer interaction interface, and divide the system parameters into a set of thermophysical parameters and a set of cost-economic parameters.

[0028] Specifically, the set of thermal physical parameters includes wellbore geometric parameters, material property parameters, operating parameters, and formation parameters, while the set of cost and economic parameters includes regression parameters of the heating performance coefficient model, drilling depth-cost model parameters, drilling aperture-cost model parameters, and billing mode options.

[0029] The billing models are divided into two categories: linear cost model and deep incremental cost model, which will be described in detail below: I. Linear Cost

[0030] in, H Indicates the drilling depth, in meters (m). a , b This represents the coefficients of the depth-cost model (default 0.1887 yuan / m², 1213.8 yuan / m). Used to correct for the influence of borehole diameter. D The outer diameter of the outer tube. D 0 represents the base diameter of 177.8 mm. c , d This is the diameter-cost coefficient. This model treats the unit cost as a linear function of depth, multiplied by a diameter correction factor, and finally multiplied by depth.

[0031] II. Increasing Costs A segmented, tiered pricing system is adopted: When the depth is ≤500m, the linear formula is used directly for calculation. After the depth >500m, for every additional 500m (the step size is adjustable), the unit cost within the current segment is multiplied by an increment factor (default 1.23), and the total cost is the sum of the costs of each segment.

[0032] Furthermore, the wellbore geometric parameters include: borehole depth H, borehole diameter D. b Outer diameter D of the outer tubeoo Inner diameter D of outer tube oi Inner tube outer diameter D io Inner diameter D of the inner tube ii Insulation layer thickness δ ins ; Material properties include: thermal conductivity k of the outer tube material. o Thermal conductivity k of the inner tube material i Thermal conductivity k of insulation material ins Thermal conductivity k of cement sheath c Circulating working fluid density r f With specific heat capacity c p,f ; Operating parameters include: working fluid inlet temperature T in Mass flow rate (m), total simulation duration (t) total Calculate the time step Δt; Formation parameters include: the original formation temperature distribution function T with depth. g(z) Thermal conductivity k of the strata and soil g Density ρ g and specific heat capacity c g This embodiment supports importing layered formation parameters via file.

[0033] The regression parameters of the heating performance coefficient model are determined based on the following formula: COP = m + nT a Where COP represents the coefficient of performance for heating, T a denoted as the average temperature of the working fluid, and m and n are fitting coefficients.

[0034] The drilling depth-cost model parameters are determined based on the following formula: C H =aH+b, where a and b are depth regression coefficients based on drilling data.

[0035] The parameters of the borehole diameter-cost model are determined based on the following formula: C D =cD+d, where c and d are the pore diameter regression coefficients based on drilling data, and D is the pore diameter.

[0036] S20 uses a segmented discretization method along the depth direction and a dynamic thermal resistance network method to perform thermal dynamic calculations and obtain the first calculation result.

[0037] In an exemplary embodiment, step S20 may include: S201, Based on the system parameters, calculate the geometric properties of each key section; S202 uses the Dieters-Belt relation to automatically calculate the convective heat transfer coefficients of the inner and outer sides; S203, segment along the well depth direction, establish a steady-state thermal resistance network model, and calculate the total thermal resistance; S204 employs a numerical method that uses one-dimensional discretization along the depth direction and explicit or implicit propagation along the time direction to dynamically solve the fluid temperature distribution. S205: After the calculation is completed at each time step, extract the thermal performance indicators.

[0038] In an exemplary embodiment, step S201 may include: S2011, calculate the flow cross-sectional area of ​​the inner pipe based on the following formula:

[0039] In the formula: A i D represents the cross-sectional area of ​​the inner tube. ii The inner diameter of the tube; S2012, calculate the cross-sectional area of ​​the annular flow based on the following formula:

[0040] In the formula: A ann Indicates the cross-sectional area of ​​the annular flow. D oi The inner diameter of the outer tube. D io The outer diameter of the inner tube; S2013, calculate the equivalent diameter of the inner tube based on the following formula:

[0041] In the formula: D h,i This represents the equivalent diameter of the inner tube, which is numerically equal to the inner diameter of the inner tube. D ii ; S2014, the equivalent diameter of the annulus is calculated based on the following formula:

[0042] In the formula: D h,ann Indicates the equivalent diameter of the annulus, derived from the inner diameter of the outer tube. D oi With the outer diameter of the inner tube D io The difference is determined; S2015, calculate the inner pipe flow velocity based on the following formula:

[0043] In the formula: u i This indicates the flow rate of the working fluid in the inner tube. m For the working fluid mass flow rate, r f For the working fluid density,A i This refers to the cross-sectional area of ​​the inner tube for flow. S2016, the annular velocity is calculated based on the following formula:

[0044] In the formula: u ann The velocity of the working fluid in the annulus is expressed as the working fluid mass flow rate. m Divide by working fluid density r f Divide by the cross-sectional area of ​​the annular flow. A ann The calculation yielded the result.

[0045] In an exemplary embodiment, step S202 may include: S2021, the Reynolds number is calculated based on the following formula:

[0046] In the formula: Re Represents the Reynolds number. r f For the working fluid density, u Refers to the flow rate of the working fluid. D h Equivalent diameter m f The dynamic viscosity of the working fluid; S2022, Prandtl number is calculated based on the following formula:

[0047] In the formula: Pr Representing Prandtl numbers, m f The dynamic viscosity of the working fluid. c p,f The specific heat capacity of the working fluid at constant pressure k f The thermal conductivity of the working fluid; S2023, the Nusselt number is calculated based on the following formula:

[0048] In the formula: No Representing the Nusselt number, derived from the Reynolds number. Re With Prandtl Pr Calculated using the Dittus-Boelter empirical correlation; S2024, the convective heat transfer coefficient is calculated based on the following formula:

[0049] In the formula:h The convective heat transfer coefficient is represented by the Nusselt number. No Thermal conductivity of the working fluid k f and equivalent diameter D h To be determined jointly.

[0050] In an exemplary embodiment, step S203 may include: S2031, the entire well depth H is discretized into N micro-segments, and the length of each segment Δz = H / N is guaranteed; S2032, for each depth element j, j = 1, 2, ..., N, establish a steady-state thermal resistance network model; S2033, Calculate the total thermal resistance R from the center of the buried pipe to the outer boundary of the soil / rock surface. totj .

[0051] Specifically, the total thermal resistance R totj It consists of the following parts connected in series or parallel: Inner tube fluid convection thermal resistance:

[0052] In the formula: R conv,i,j Representing depth infinitesimal elements j The convective thermal resistance between the fluid inside the inner tube and the inner wall surface of the inner tube. h i The convective heat transfer coefficient on the inner tube side is... D ii The inner diameter of the inner tube. Δz The length of the infinitesimal segment; Inner tube wall thermal resistance:

[0053] In the formula: R pipe,i,j Representing depth infinitesimal elements j The radial thermal resistance of the inner tube wall. D io The outer diameter of the inner tube. D ii The inner diameter of the inner tube. k i The thermal conductivity of the inner tube is... Δz The length of the infinitesimal segment; Thermal resistance of insulation layer:

[0054] In the formula: R ins,j Representing depth infinitesimal elements j The radial thermal resistance of the insulation layer D ioThe outer diameter of the inner tube. d ins For the thickness of the insulation layer, k ins The thermal conductivity of the insulation layer, Δz The length of the infinitesimal segment; Circulatory thermal resistance of the annulus fluid:

[0055] In the formula: R conv,o,j Representing depth infinitesimal elements j The convective thermal resistance between the annular fluid and the inner wall of the outer tube. h o The annular side convective heat transfer coefficient is... D oi The inner diameter of the outer tube. Δz The length of the infinitesimal segment; Thermal resistance of the outer tube wall:

[0056] In the formula: R pipe,o,j Representing depth infinitesimal elements j The radial thermal resistance of the outer tube wall, D oo The outer diameter of the outer tube. D oi The inner diameter of the outer tube. k o The thermal conductivity of the outer tube is... Δz The length of the infinitesimal segment; Thermal resistance of cement ring:

[0057] In the formula: R cem,j Representing depth infinitesimal elements j The radial thermal resistance of the cement ring. D b The diameter of the borehole. D oo The outer diameter of the outer tube. k c The thermal conductivity of the cement ring is... Δz The length of the infinitesimal segment; Transient thermal resistance of formation: A transient thermal response model based on formations with varying thermal properties is adopted for the operating time. t ,depth z j thermal resistance of the formation R g,j(t) This can be expressed as:

[0058] In the formula: E 1 is an exponential integral function; r b The radius of the borehole; α g,j strata j Thermal diffusivity at depth, and α g,j = k g,j / (ρg,j cg,j) .

[0059] For fluid from the inner tube to the formation (temperature) T g,j Total thermal resistance R tot,j Because the fluid in the inner tube exchanges heat with the fluid in the annulus through the inner tube wall and insulation layer, and the fluid in the annulus exchanges heat with the formation, the thermal network is a complex structure. An equivalent approach is to first calculate the heat transfer coefficient from the inner tube to the annulus. U ia,j and the heat transfer coefficient from the annulus to the formation U ag,j :

[0060]

[0061] In the formula: U ia,j Representing depth infinitesimal elements j The overall heat transfer coefficient from the fluid inside the tube to the fluid in the annulus is given. R conv,i,j The convective thermal resistance between the fluid inside the tube and the inner wall of the tube. R pipe,i,j The radial thermal resistance of the inner tube wall. R ins,j The radial thermal resistance of the insulation layer wrapped around the outer wall of the inner tube; U ag,j Representing depth infinitesimal elements j Temperature from annular fluid to far-end formation T g,j Overall heat transfer coefficient, R conv,o,j The convective thermal resistance between the annular fluid and the inner wall of the outer tube. R pipe,o,j The radial thermal resistance of the outer tube wall. R cem,j The radial thermal resistance of the cement ring is given. R g,j ( t ( ) represents runtime t Time-depth infinitesimal jTransient thermal resistance of the formation at that location.

[0062] The overall heat transfer coefficient between the fluid in the inner tube and the formation. U total,j satisfy:

[0063] In the formula: A ref 、A ia 、A ag The selected reference area (e.g., based on the outer surface of the inner tube).

[0064] S30, based on the system parameters, calculate the total drilling cost and obtain the second calculation result.

[0065] In an exemplary embodiment, step S30 may include: S310, Based on the system parameters, calculate the diameter influence factor, as shown in the following formula:

[0066] In the formula: D represents the actual pipe diameter; D0 represents the deviation from the reference pipe diameter; Indicates the cost adjustment factor; S320 calculates the unit length cost function based on the following formula:

[0067] In the formula: This represents the cost per unit length of drilling. S330, calculate the total cost based on the following formula:

[0068] In the formula: Represents the total drilling cost under the linear billing model, in the integral formula h For depth variables measured from the Earth's surface, C unit ( h ) for depth h The unit advance cost function at the location. a and b , respectively, represent the slope and intercept of the depth-cost linear relationship, where a Reflects the rate of change of unit cost as unit depth increases. b Based on the unit cost. H The total depth of the wellbore is represented by the upper and lower limits of the integral, which correspond to the bottom of the well and the surface, respectively. S340, Set a reference depth interval The total cost is calculated using a cost accumulation factor r greater than 1, through piecewise integration and summation, as shown in the following formula:

[0069] In the formula: This represents the total drilling cost under the depth-increasing tiered billing model. K The total number of segments divided by depth intervals, satisfying the condition that the endpoints of each segment start from... h 0 = 0 to h K = H, h k and h k+1 They represent the first k The difference between the starting and ending depths of a segment and its adjacent endpoints is usually equal to... ΔH s , r k Representing the k The cumulative multiplication factor of the segments is used to achieve a step-like increase in unit cost as the depth increases; S350, Integrating the piecewise integral and summation formula yields the following explicit calculation formula:

[0070] In the formula: This represents the total drilling cost under the depth-increasing tiered billing model. Indicates the cost adjustment factor. K This represents the total number of segments divided by depth intervals. r k Representing the k The cumulative factor of the segment, h k and h k+1 They represent the first k The starting and ending depths of the segment.

[0071] Next, a numerical method is employed to solve the fluid temperature field using one-dimensional discretization along the depth direction and explicit or implicit advancement along the time direction. Let the current time step be n, and the fluid temperature of the j-th infinitesimal element in the inner tube be known. and annular fluid temperature For the annular downflow fluid (flowing from the wellhead j = 0 to the bottom j = N), its energy balance equation is:

[0072] In the formula: Indicates the mass of the fluid; The specific heat capacity at constant pressure refers to the amount of heat absorbed or released per unit mass of fluid when the temperature rises or falls by a unit amount under constant pressure. This represents the temperature of the annular fluid at position j in the (n+1)th iteration step; This represents the temperature of the aforementioned fluid at position j-1, in the (n+1)th iteration step; This represents the overall heat transfer coefficient of the annular fluid at position j.

[0073] For the fluid flowing upwards in the inner tube (from the bottom of the well, j = N, to the wellhead, j = 0), its energy balance equation is:

[0074] In the formula: and This represents the average temperature of the inner tube and the annular fluid within the micro-element segment (which can be the value from the previous time step or an intermediate value from the current iteration). and This represents the heat transfer area of ​​the corresponding micro-element segment.

[0075] The boundary conditions are: The annular inlet temperature (given wellhead temperature) is:

[0076] The bottom connection conditions are as follows:

[0077] The required outlet (wellhead) temperature of the inner tube is:

[0078] The above equations constitute a large linear system of equations, which can be solved using the chasing method, updating the fluid temperature across the entire depth domain step by step (n→n+1). and .

[0079] S40, the first calculation result and the second calculation result are comprehensively processed and visualized, and multiple schemes are compared horizontally.

[0080] In an exemplary embodiment, step S40 may include: S401, displays the final outlet temperature in real time. Average geothermal extraction power Q E Average total heating power Q H Total drilling cost ; S402, plotting the outlet temperature Geothermal extraction power Total heating power System in real time COP (t) is a curve that changes with time; S403, Plot the temperature distribution along the well depth at the final moment. T ( z This is to demonstrate the changes in formation temperature, annular fluid temperature, and inner tube fluid temperature along the path.

[0081] Plotting the temperature distribution along the well depth at the final moment T ( z After that, the simulation parameters and results for each completed simulation will be automatically recorded. Q H , (etc.) are stored as a "case". In a dedicated comparison view, the "average total heating power (etc.)" of all historical cases is plotted as a scatter plot. Q H Comparison of total drilling costs ( The cost-performance scatter plot is a visual representation of the distribution of different design options on a thermal economy coordinate system, helping decision-makers quickly identify the set of options.

[0082] In the above embodiments of this application, a high-fidelity dynamic thermal model and a deeply nonlinear engineering cost model are deeply coupled at the algorithm level, enabling simultaneous evaluation of "physical performance" and "economic cost" on the same platform. This breaks down professional barriers in the traditional design process and improves the scientific nature and efficiency of decision-making.

[0083] The axially segmented discrete and radial thermal resistance network model used in this application has a clear physical mechanism and can accurately handle strata with varying physical properties, arbitrarily set pipe diameters and insulation layer structures, as well as transient processes during system operation. It avoids the oversimplification of geometry and boundary conditions in traditional line heat source models, resulting in more reliable calculation results.

[0084] The "depth interval cumulative cost model" proposed in this application is a significant innovation. By introducing a cumulative factor, it effectively portrays the trend of deep drilling costs increasing exponentially with depth, reflecting engineering realities better than simple linear or polynomial models, and greatly improving the accuracy of preliminary economic assessments.

[0085] This application transforms complex multivariate optimization problems into intuitive graphical selection problems. Combined with automated cost-effectiveness ranking and solution filtering functions, it greatly assists engineers in quickly locating the optimal or satisfactory solution among numerous design options, thus shortening the design cycle.

[0086] This application integrates complex simulation calculations, data processing, and visualization functions into a unified software platform. It guides users through the operation via a wizard-style interface, lowering the barrier to entry for advanced simulation tools and making the method easily accepted and applied by a wide range of users, including design institutes and project investors.

[0087] In the description of this application, it should be noted that the terms "first", "second", and "third" are used for descriptive purposes only and should not be construed as indicating or implying relative importance.

[0088] Those skilled in the art will clearly understand that, for the sake of convenience and brevity, the specific working process of the software simulation device and unit described above can be referred to the corresponding process in the foregoing method embodiments, and will not be repeated here.

[0089] In the several embodiments provided in this application, it should be understood that the disclosed software simulation devices and methods can be implemented using other formulas. The software simulation device embodiments described above are merely illustrative. For example, the division of units is only a logical functional division, and in actual implementation, there may be other division methods. Furthermore, multiple units or components may be combined or integrated into another, or some features may be ignored or not executed. Additionally, the shown or discussed mutual couplings, direct couplings, or communication connections may be through some communication interfaces. Indirect couplings or communication connections between software simulation devices or units may be electrical, mechanical, or other forms.

[0090] The units described as separate components may or may not be physically separate. The components shown as units may or may not be physical units; that is, they may be located in one place or distributed across multiple network units. Some or all of the units can be selected to achieve the purpose of this embodiment according to actual needs.

[0091] In addition, the functional units in the various embodiments of this application can be integrated into one processing unit, or each unit can exist physically separately, or two or more units can be integrated into one unit.

[0092] If the aforementioned functions are implemented as software functional units and sold or used as independent products, they can be stored in a processor-executable, non-volatile, computer-readable storage medium. Based on this understanding, the technical solution of this application, in essence, or the part that contributes to the prior art, or a portion of the technical solution, can be embodied in the form of a software product. This computer software product is stored in a storage medium and includes several instructions to cause a computer device (which may be a personal computer, server, or network device, etc.) to execute all or part of the steps of the methods described in the various embodiments of this application. The aforementioned storage medium includes various media capable of storing program code, such as USB flash drives, portable hard drives, read-only memory (ROM), random access memory (RAM), magnetic disks, or optical disks.

[0093] Finally, it should be noted that the above-described embodiments are merely specific implementations of this application, used to illustrate the technical solutions of this application, and not to limit them. The protection scope of this application is not limited thereto. Although this application has been described in detail with reference to the foregoing embodiments, those skilled in the art should understand that any person skilled in the art can still modify or easily conceive of changes to the technical solutions described in the foregoing embodiments, or make equivalent substitutions for some of the technical features, within the technical scope disclosed in this application. Such modifications, changes, or substitutions do not cause the essence of the corresponding technical solutions to deviate from the spirit and scope of the technical solutions of the embodiments of this application, and should all be covered within the protection scope of this application. Therefore, the protection scope of this application should be determined by the protection scope of the claims.

[0094] Furthermore, although the operations of the method of this application are described in a specific order in the accompanying drawings, this does not require or imply that these operations must be performed in that specific order, or that all the operations shown must be performed to achieve the desired result. Additionally or alternatively, certain steps may be omitted, multiple steps may be combined into one step, and / or one step may be broken down into multiple steps.

Claims

1. A method for comprehensive performance analysis of deeply buried casing, characterized in that, include: S10, receive system parameters input by the user through the human-computer interaction interface, and divide the system parameters into a set of thermophysical parameters and a set of cost-economic parameters; S20, using the segmented discretization along the depth direction and dynamic thermal resistance network method to perform thermal dynamic calculations and obtain the first calculation result; S30, Based on the system parameters, calculate the total drilling cost and obtain the second calculation result; S40, the first calculation result and the second calculation result are comprehensively processed and visualized, and multiple schemes are compared horizontally.

2. The method according to claim 1, characterized in that, The set of thermal physical parameters includes wellbore geometric parameters, material property parameters, operating parameters, and formation parameters. The set of cost and economic parameters includes regression parameters of the heating performance coefficient model, drilling depth-cost model parameters, drilling aperture-cost model parameters, and billing mode options.

3. The method according to claim 1, characterized in that, Step S20 includes: S201, Based on the system parameters, calculate the geometric properties of each key section; S202 uses the Dieters-Belt relation to automatically calculate the convective heat transfer coefficients of the inner and outer sides; S203, segment along the well depth direction, establish a steady-state thermal resistance network model, and calculate the total thermal resistance; S204 employs a numerical method that uses one-dimensional discretization along the depth direction and explicit or implicit propagation along the time direction to dynamically solve the fluid temperature distribution. S205: After the calculation is completed at each time step, extract the thermal performance indicators.

4. The method according to claim 3, characterized in that, Step S201 includes: S2011, calculate the flow cross-sectional area of ​​the inner pipe based on the following formula: In the formula: A i D represents the cross-sectional area of ​​the inner tube. ii The inner diameter of the tube; S2012, calculate the cross-sectional area of ​​the annular flow based on the following formula: In the formula: A ann Indicates the cross-sectional area of ​​the annular flow. D oi The inner diameter of the outer tube. D io The outer diameter of the inner tube; S2013, calculate the equivalent diameter of the inner tube based on the following formula: In the formula: D h,i This represents the equivalent diameter of the inner tube, which is numerically equal to the inner diameter of the inner tube. D ii ; S2014, the equivalent diameter of the annulus is calculated based on the following formula: In the formula: D h,ann Indicates the equivalent diameter of the annulus, derived from the inner diameter of the outer tube. D oi With the outer diameter of the inner tube D io The difference is determined; S2015, calculate the inner pipe flow velocity based on the following formula: In the formula: u i This indicates the flow rate of the working fluid in the inner tube. m For the working fluid mass flow rate, ρ f For the working fluid density, A i This refers to the cross-sectional area of ​​the inner tube for flow. S2016, the annular velocity is calculated based on the following formula: In the formula: u ann The velocity of the working fluid in the annulus is expressed as the working fluid mass flow rate. m Divide by working fluid density ρ f Divide by the cross-sectional area of ​​the annular flow. A ann The calculation yielded the result.

5. The method according to claim 3, characterized in that, Step S202 includes: S2021, the Reynolds number is calculated based on the following formula: In the formula: Re Represents the Reynolds number. ρ f For the working fluid density, u Refers to the flow rate of the working fluid. D h Equivalent diameter μ f The dynamic viscosity of the working fluid; S2022, Prandtl number is calculated based on the following formula: In the formula: Pr Representing Prandtl numbers, μ f The dynamic viscosity of the working fluid. c p,f The specific heat capacity of the working fluid at constant pressure k f The thermal conductivity of the working fluid; S2023, the Nusselt number is calculated based on the following formula: In the formula: Nu Representing the Nusselt number, derived from the Reynolds number. Re With Prandtl Pr Calculated using the Dittus-Boelter empirical correlation; S2024, the convective heat transfer coefficient is calculated based on the following formula: In the formula: h Represents the convective heat transfer coefficient, derived from the Nusselt number. Nu Thermal conductivity of the working fluid k f and equivalent diameter D h To be determined jointly.

6. The method according to claim 3, characterized in that, Step S203 includes: S2031, the entire well depth H is discretized into N micro-segments, and the length of each segment Δz = H / N is guaranteed; S2032, for each depth element j, j = 1, 2, ..., N, establish a steady-state thermal resistance network model; S2033, Calculate the total thermal resistance R from the center of the buried pipe to the outer boundary of the soil / rock surface. totj .

7. The method according to claim 6, characterized in that, The total thermal resistance R totj It consists of the following parts connected in series or parallel: Inner tube fluid convection thermal resistance: In the formula: R conv,i,j Representing depth infinitesimal elements j The convective thermal resistance between the fluid inside the inner tube and the inner wall surface of the inner tube. h i The convective heat transfer coefficient on the inner tube side is... D ii The inner diameter of the inner tube. Δz The length of the infinitesimal segment; Inner tube wall thermal resistance: In the formula: R pipe,i,j Representing depth infinitesimal elements j The radial thermal resistance of the inner tube wall. D io The outer diameter of the inner tube. D ii The inner diameter of the inner tube. k i The thermal conductivity of the inner tube is... Δz The length of the infinitesimal segment; Thermal resistance of insulation layer: In the formula: R ins,j Representing depth infinitesimal elements j The radial thermal resistance of the insulation layer D io The outer diameter of the inner tube. δ ins For the thickness of the insulation layer, k ins The thermal conductivity of the insulation layer, Δz The length of the infinitesimal segment; Circulatory thermal resistance of the annulus fluid: In the formula: R conv,o,j Representing depth infinitesimal elements j The convective thermal resistance between the annular fluid and the inner wall of the outer tube. h o The annular side convective heat transfer coefficient is... D oi The inner diameter of the outer tube. Δz The length of the infinitesimal segment; Thermal resistance of the outer tube wall: In the formula: R pipe,o,j Representing depth infinitesimal elements j The radial thermal resistance of the outer tube wall, D oo The outer diameter of the outer tube. D oi The inner diameter of the outer tube. k o The thermal conductivity of the outer tube is... Δz The length of the infinitesimal segment; Thermal resistance of cement ring: In the formula: R cem,j Representing depth infinitesimal elements j The radial thermal resistance of the cement ring. D b The diameter of the borehole. D oo The outer diameter of the outer tube. k c The thermal conductivity of the cement ring is... Δz The length of the infinitesimal segment; Transient thermal resistance of formation: A transient thermal response model based on formations with varying thermal properties is adopted for the operating time. t ,depth z j thermal resistance of the formation R g,j(t) This can be expressed as: In the formula: E 1 is an exponential integral function; r b The radius of the borehole; α g,j strata j Thermal diffusivity at depth, and α g,j = k g,j / (ρg,j cg,j) .

8. The method according to claim 1, characterized in that, Step S30 includes: S310, Based on the system parameters, calculate the diameter influence factor, as shown in the following formula: In the formula: D represents the actual pipe diameter; D0 represents the deviation from the reference pipe diameter; Indicates the cost adjustment factor; S320 calculates the unit length cost function based on the following formula: In the formula: This represents the cost per unit length of drilling. S330, calculate the total cost based on the following formula: In the formula: This represents the total drilling cost under the linear billing model; h The depth variable is calculated from the Earth's surface. C unit ( h ) for depth h Unit advance cost function at the location; a and b Let be the slope and intercept of the depth-cost linear relationship, respectively. a Reflects the rate of change of unit cost as unit depth increases. b Basic unit cost; H The total depth of the wellbore; the upper and lower limits of integration correspond to the bottom of the well and the surface, respectively; S340, Set a reference depth interval and a cost accumulation factor greater than 1 r The total cost is calculated using a piecewise integral and summation formula, as follows: In the formula: This represents the total drilling cost under the depth-increasing tiered billing model. K The total number of segments divided by depth intervals, satisfying the condition that the endpoints of each segment start from... h 0 = 0 to h K = H, h k and h k+1 They represent the first k The difference between the starting and ending depths of a segment and its adjacent endpoints is usually equal to... ΔH s , r k Representing the k The cumulative factor of the segment; S350, Integrating the piecewise integral and summation formula yields the following explicit calculation formula: In the formula: This represents the total drilling cost under the depth-increasing tiered billing model. Indicates the cost adjustment factor. K This represents the total number of segments divided by depth intervals. r k Representing the k The cumulative factor of the segment, h k and h k+1 They represent the first k The starting and ending depths of the segment.

9. The method according to claim 1, characterized in that, Step S40 includes: S401, displays the final outlet temperature in real time. Average geothermal extraction power Q E Average total heating power Q H Total drilling cost ; S402, plotting the outlet temperature Geothermal extraction power Total heating power System in real time COP (t) is a curve that changes with time; S403, Plot the temperature distribution along the well depth at the final moment. T ( z This is to demonstrate the changes in formation temperature, annular fluid temperature, and inner tube fluid temperature along the path.

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