Inflow temperature calculation method and device for coupling oil reservoir-wellbore model

Abstract

The invention discloses an inflow temperature calculation method and device for a coupled oil reservoir-wellbore model.The inflow temperature calculation method comprises the steps that firstly, for an oil reservoir grid corresponding to a wellbore section, a radial flow area from the equivalent radius of the oil reservoir grid to the well wall is defined; secondly, a radial steady-state temperature second-order ordinary differential equation describing temperature distribution in the area is established, and the equation comprehensively takes heat convection, viscous dissipation caused by pressure gradient, Joule-Thomson effect, heat conduction and other micro heat effects into account; thirdly, setting boundary conditions for coupling the oil reservoir and the wellbore state for the equation; and finally, solving the equation with complete configuration to obtain radial temperature distribution, and determining the temperature at the well wall as the accurate inflow temperature. Compared with the prior art, the method has the advantages that the inflow temperature model with more complete mechanism and more accurate solution is established, so that the accuracy and reliability of output profile inversion interpretation are remarkably improved.

Description

Technical Field

[0001] The present invention relates to the technical field of oil and gas field development, in particular to a horizontal well output profile interpretation technology based on distributed temperature sensing data, and more particularly to an inflow temperature calculation method and device for a coupled reservoir-wellbore model. Background Art

[0002] Horizontal wells have been widely used in the efficient development of various oil and gas reservoirs due to their large contact area with the reservoir and their ability to achieve high production with fewer wells. However, as oil fields enter the medium-to-high water-cut stage, horizontal well development faces severe challenges such as rapid production decline, uneven flow distribution along the well section, and premature water or gas breakthrough. Accurately determining the location of water production and implementing targeted water control measures is key to improving the efficiency of horizontal well development, but it also presents a technical challenge.

[0003] Existing solutions primarily include the following: 1. Conventional production logging technology: Such as Schlumberger's production profile testing technology, which directly measures oil, gas, and water production at various downhole sections to obtain information. However, in horizontal wells, the extremely complex multiphase flow patterns caused by gravity differentiation, coupled with the undulating wellbore trajectory, make conventional instrument installation difficult, measurement accuracy difficult to guarantee, and testing costs high. 2. Theoretical models and numerical simulations: While semi-analytical models based on reservoir seepage and wellbore flow or commercial numerical simulation software (such as ECLIPSE) can predict production profiles, they typically assume isothermal flow and their accuracy is highly dependent on permeability distribution data along the wellbore. Unfortunately, in actual oil fields, a large number of producing horizontal wells lack this type of detailed logging data, resulting in significant discrepancies between theoretical predictions and actual conditions. 3. Distributed fiber temperature logging (DTS) technology: DTS technology provides real-time, continuous, and accurate temperature profiles along the entire wellbore, opening up new possibilities for inversion solutions to production profiles. However, unlike vertical wells, where geothermal gradients vary significantly, the formation temperature around horizontal wells is relatively constant. Temperature variations within the wellbore are primarily governed by microthermal effects such as fluid thermal expansion, viscous dissipation, and heat conduction, resulting in very small temperature variations. Therefore, accurately inferring the fluid production profile from these weak temperature signals remains a pressing challenge in the field, particularly in the absence of mature theories and interpretation methods.

[0004] In coupled reservoir-wellbore models, the temperature of the fluid flowing from the reservoir into the wellbore (i.e., inflow temperature) is the key physical quantity connecting the two sub-models. The accuracy of its calculation directly impacts the prediction accuracy of the entire coupled model and the reliability of the production profile inversion. Existing methods for calculating inflow temperature either simply equate it with formation temperature or only consider the Joule-Thomson effect, ignoring the combined effects of other important microthermal effects such as viscous dissipation, resulting in inaccurate results. Therefore, a theoretical method for accurately calculating inflow temperature is urgently needed to improve the overall level of production profile interpretation technology. Summary of the Invention

[0005] The purpose of the present invention is to provide a method and device for calculating the inflow temperature of a coupled reservoir-wellbore model, so as to solve the problem of low accuracy of horizontal well output profile interpretation caused by inaccurate inflow temperature calculation in the prior art.

[0006] To achieve the above-mentioned object, the present invention provides the following technical solution: a method for calculating inflow temperature for a coupled reservoir-wellbore model, characterized in that it comprises the following steps: for a wellbore section corresponding to a reservoir grid, defining a radial flow region in which a fluid flows from an equivalent radius of the reservoir grid to a wellbore wall of the wellbore section, wherein the pressure and temperature at the equivalent radius are determined by the pressure and temperature of the reservoir grid; establishing a radial steady-state temperature second-order ordinary differential equation for describing the temperature distribution in the radial flow region, wherein the equation takes into account the thermal effect caused by the radial flow of the fluid. flow, viscous dissipation and Joule-Thomson effect caused by radial pressure gradient, and heat conduction; setting boundary conditions for the second-order ordinary differential equation, the boundary conditions including: at the equivalent radius, the temperature is equal to the temperature of the reservoir grid; and at the wellbore wall, a heat flow boundary condition determined based on the fluid temperature in the wellbore section and a total heat transfer coefficient; solving the second-order ordinary differential equation configured with the boundary conditions to obtain the radial temperature distribution in the radial flow region; and determining the temperature at the wellbore wall as the inflow temperature based on the radial temperature distribution.

[0007] Furthermore, the method further includes determining the radial pressure gradient by solving the pressure distribution equation in the radial flow region before establishing the radial steady-state temperature second-order ordinary differential equation, wherein the boundary conditions of the pressure distribution equation are the pressure of the reservoir grid and the fluid pressure in the wellbore section.

[0008] Furthermore, when there is a formation damage zone in the radial flow area, the steps of establishing and solving the second-order ordinary differential equation include: dividing the radial flow area into adjacent damage zone areas and non-damage zone areas; establishing respective second-order ordinary differential equations for the damage zone areas and non-damage zone areas; and at the junction of the damage zone area and the non-damage zone area, coupling and solving the two second-order ordinary differential equations by ensuring the continuity of temperature and heat flow.

[0009] Furthermore, the method further includes: using the determined inflow temperature as a boundary condition to solve the wellbore thermal model in the coupled reservoir-wellbore model to calculate the fluid temperature in the wellbore section; and iteratively updating the fluid temperature in the wellbore section and the inflow temperature until convergence.

[0010] To achieve the above-mentioned purpose, the present invention also provides an inflow temperature calculation device for a coupled reservoir-wellbore model, characterized in that it includes: a region definition module, used to define, for a wellbore section corresponding to a reservoir grid, a radial flow region in which a fluid flows from the equivalent radius of the reservoir grid to the wellbore wall of the wellbore section; a temperature equation establishment module, used to establish a radial steady-state temperature second-order ordinary differential equation describing the temperature distribution in the radial flow region, wherein the equation takes into account heat convection, viscous dissipation, Joule-Thomson effect and heat conduction; a boundary condition setting module, used to set boundary conditions for the second-order ordinary differential equation, including a temperature boundary condition at the equivalent radius and a heat flow boundary condition at the wellbore wall; an inflow temperature determination module, used to solve the second-order ordinary differential equation configured with the boundary conditions to obtain a radial temperature distribution, and determine the temperature at the wellbore wall as the inflow temperature based on the radial temperature distribution.

[0011] Furthermore, when there is a formation damage zone in the radial flow area, the temperature equation establishment module and the inflow temperature determination module are further used to: divide the radial flow area into a damage zone area and a non-damage zone area, and establish and couple the second-order ordinary differential equations for the two areas to determine the inflow temperature.

[0012] Compared with the prior art, the present invention has the following beneficial effects:

[0013] 1. This invention establishes a radial steady-state temperature equation that comprehensively considers multiple micro-thermal effects such as heat convection, viscous dissipation, Joule-Thomson effect, and heat conduction. The physical mechanism is more complete and can more accurately describe the temperature changes during the process of fluid flowing from the reservoir into the wellbore. It overcomes the calculation deviation caused by model simplification in existing methods.

[0014] 2. This invention specifically considers the existence of formation damage zones. Through regional modeling and coupled solution, it can accurately handle the additional pressure drop and temperature changes caused by formation damage, making the model closer to the actual operating conditions of the oil field. It is particularly suitable for old oil fields and horizontal wells that have undergone operational transformation.

[0015] 3. Accurate inflow temperature is a prerequisite for accurately predicting wellbore temperature profiles using coupled reservoir-wellbore models. This method, through iterative solution, ensures the self-consistency and convergence of inflow temperature and wellbore temperature, thereby providing a highly reliable forward model for subsequent inversion interpretation of production profiles based on DTS data. Ultimately, this significantly improves the accuracy of interpretation of production profiles and water production locations. BRIEF DESCRIPTION OF THE DRAWINGS

[0016] In order to more clearly illustrate the technical solution of the present invention, the following briefly describes the drawings used to implement the embodiments of the present invention:

[0017] Figure 1 This is a flow chart of an embodiment of a method for calculating inflow temperature according to the present invention;

[0018] Figure 2 This is a structural block diagram of an embodiment of an inflow temperature calculation device of the present invention;

[0019] Figure 3 A schematic diagram of a grid for coupling a wellbore and an oil reservoir in an embodiment of the present invention;

[0020] Figure 4 Schematic diagram of the radial flow area considering the formation damage zone in an embodiment of the present invention. DETAILED DESCRIPTION

[0021] To make the purpose, technical solutions and advantages of the present invention more clear, the specific embodiments of the present invention will be described in detail below with reference to the accompanying drawings. It should be understood that the specific embodiments described herein are only used to explain the present invention and are not intended to limit the scope of protection of the present invention.

[0022] Example 1: A method for calculating inflow temperature for a coupled reservoir-wellbore model Figure 1 This embodiment provides a method for calculating inflow temperature for a coupled reservoir-wellbore model. This method is a core step in the inversion interpretation process for horizontal well production profiles, and its purpose is to provide accurate inflow temperature boundary conditions for the wellbore thermal model.

[0023] The method may specifically include the following steps:

[0024] Step S101: Define the radial flow region and determine its initial conditions. Figure 3In a coupled reservoir-wellbore numerical model, the reservoir is divided into multiple grids, and the horizontal wellbore passes through these grids along a specific trajectory. For any section of the wellbore (for example, wellbore section i), it corresponds to a grid in the reservoir (for example, reservoir grid i, j, k). This step first defines a region where fluid flows radially from the reservoir to the wellbore. The outer boundary of this region is the equivalent radius r e , the internal boundary is the well wall radius r w The equivalent radius r e Defined by the Peaceman model, its value depends on the mesh size and permeability anisotropy. For orthogonal meshes, the equivalent radius r e It can be calculated by the following formula:

[0025]

[0026] Where r y ,k z are the permeabilities of the reservoir grid in the x, y, and z directions, respectively; Δy and Δz are the dimensions of the reservoir grid in the x and z directions.

[0027] The boundary conditions in this radial flow region are determined by the state of the coupled model at the current time:

[0028] At the equivalent radius r e At pressure p e and temperature T e The pressure and temperature of the reservoir grid can be obtained by solving the macroscopic reservoir seepage model and reservoir thermal model.

[0029] · At the wellbore radius r w At pressure p wb Equal to the fluid pressure within the wellbore section, which can be obtained by solving the wellbore flow model.

[0030] Step S102: Solve the radial pressure distribution and determine the pressure gradient. Before establishing the radial steady-state temperature equation, it is necessary to determine the pressure distribution and pressure gradient in the radial flow region. Assume that the equivalent radius r e To the well wall w The fluid flow is a steady radial flow, and the pressure distribution equation can be expressed as:

[0031]

[0032] The boundary conditions of this equation are determined by step S101:

[0033]

[0034] Solving the above equations and their boundary conditions, we can obtain the analytical solution of the radial pressure distribution:

[0035]

[0036] in, is the pressure gradient correlation coefficient.

[0037] Step S103: Establish a radial steady-state temperature second-order ordinary differential equation. The core of this step is to establish a system that can accurately describe the radial steady-state temperature. e to r w Mathematical model of fluid temperature change. Based on the principle of conservation of energy and taking into account the heat convection caused by the radial flow of the fluid, the viscous dissipation and Joule-Thomson effect caused by the radial pressure gradient, and heat conduction, the steady-state radial temperature equation can be expressed as:

[0038]

[0039] ρ i represents the density of fluid phase i, u ri Refers to the radial flow velocity of fluid phase i from the reservoir to the wellbore, C pi Refers to the constant pressure specific heat capacity of fluid phase i, T represents temperature, represents the radial temperature gradient, p represents the pressure, represents the radial pressure gradient, β i It represents the coefficient of volume change with temperature when the pressure of fluid phase i remains constant, λ represents the comprehensive thermal conductivity of the porous medium saturated with fluid, r represents the radial distance, and λ represents the comprehensive thermal conductivity of the porous medium saturated with fluid.

[0040] Assuming that the effects of capillary force and gravity are ignored, the radial fluid velocity u ri Given by Darcy's law:

[0041]

[0042] k represents the permeability of reservoir rock, k ri represents the relative permeability of fluid phase i, μ i represents the viscosity of fluid phase i, and Equation 3 and the radial velocity are substituted into the energy equation, and the transformation is:

[0043]

[0044] After further arrangement, the radial steady-state temperature second-order ordinary differential equation describing the temperature distribution in the radial flow region is obtained:

[0045] The equation is of the form:

[0046]

[0047] Among them, the coefficients C1, C2 and C3 are defined as:

[0048]

[0049] The λ term in C1 represents the heat conduction effect, and the other term represents the heat convection effect caused by radial flow; the C2 term reflects the temperature change caused by the Joule-Thomson effect; and the C3 term reflects the temperature change caused by the viscous dissipation effect.

[0050] Step S104: Set the boundary conditions of the temperature equation. To solve Equation 8, two boundary conditions need to be set:

[0051] 1. At the equivalent radius r e At , the temperature is equal to the reservoir grid temperature:

[0052] 2. At the well wall radius r w The third type of boundary condition (heat flux boundary condition) is where the heat flux conducted from the formation to the wellbore wall is equal to the heat flux convected from the wellbore wall to the wellbore fluid: Where α is the total heat transfer coefficient of the wellbore, T wb is the fluid temperature in the current wellbore section. The overall heat transfer coefficient α can be given by the Willhite model, which usually takes into account the comprehensive thermal resistance of the wellbore structure (tubing, casing, cement sheath) and the surrounding formation.

[0053] Step S105: Solve the equation and determine the inflow temperature. Apply the boundary conditions of step S104 to equation 8, and the general solution of the equation is:

[0054]

[0055] Then the inflow temperature is r = r w The temperature at is expressed as

[0056]

[0057] where p e ——reservoir pressure in the grid (MPa);

[0058] p wb ——wellbore pressure (MPa);

[0059] T e ——reservoir temperature in the grid (℃);

[0060] T wb ——Wellbore temperature (℃).

[0061] The expressions corresponding to the symbols in formula (9) are:

[0062]

[0063] During the drilling, completion, and production processes, the intrusion of drilling fluids, completion fluids, and fracturing fluids into the formation can cause formation damage, resulting in additional pressure drop and reduced formation permeability. Because temperature is affected by pressure changes, the additional pressure drop caused by formation damage will also affect temperature. Therefore, the impact of formation damage on temperature is considered.

[0064] Optional option: Consider formation damage

[0065] Reference Figure 4 In many practical cases, there is a formation damage zone 10 near the well wall due to drilling and completion fluid contamination, and its permeability k d Lower than the original formation permeability k, the contamination radius is r d In this case, steps S103 and S105 are modified as follows:

[0066] Divide the radial flow area into adjacent non-damage zones 20 (from r e To the damage zone radius r d ) and damage zone area 10 (from r d to r w ).

[0067] ·Establish separate second-order ordinary differential equations for these two regions, in the same form as Equation 8. The permeability k and the integrated thermal conductivity λ are used in the non-damage zone, and the permeability k is used in the damage zone. d and the comprehensive thermal conductivity of the damage zone λ d The coefficients C1, C2, and C3 are calculated separately in two areas.

[0068] When solving, the solution of the non-damage zone area equation is The solution to the damage zone equation is Where n3, n4 and b2 are determined by the damage zone equation. Four boundary conditions need to be applied to determine the coefficients c1, c2, c3, c4:

[0069] a. At the equivalent radius r e Location: T1(r e )=T e

[0070] b. At the interface r d Temperature continuity at: T1(r d )=T2(r d )

[0071] c. At the interface r d Heat flow is continuous:

[0072] d. On the well wallw (third type of boundary conditions): By combining the above four conditions, we can construct a linear equation system. Solving this system of equations can give the expressions of coefficients c1, c2, c3, and c4.

[0073] Finally, the inflow temperature T I That is, the temperature distribution of the damage zone on the well wall r w The value at

[0074] Optional solution: Iterative solution

[0075] Inflow temperature T I The calculation depends on the wellbore temperature T wb (as boundary conditions), and the wellbore temperature T wb The calculation of the inflow temperature T I (as the source term of the wellbore thermal model). Therefore, an iterative process is required to obtain a self-consistent solution. The specific iterative solution process includes:

[0076] 1. Initialize wellbore temperature

[0077] 2. In the kth iteration, use As the fluid temperature in the wellbore section, the new inflow temperature T is calculated through steps S101-S105 (or the corresponding steps in the case of formation damage). I (k+1) .

[0078] 3. T calculated for all wellbore sections I (k+1) As the source term (i.e., the temperature of the fluid as it flows from the reservoir into the wellbore), the wellbore thermal model is solved to obtain the updated wellbore temperature profile

[0079] 4. Check convergence, such as determining the maximum temperature change of all wellbore sections Is it less than a preset threshold ∈. If it does not converge, set k = k + 1 and return to step 2; if it converges, the iteration ends and the final inflow temperature and wellbore temperature are obtained.

[0080] Example 2: An inflow temperature calculation device for coupled reservoir-wellbore model Figure 2 This embodiment provides an inflow temperature calculation device 1 for a coupled reservoir-wellbore model. The device can be integrated into oilfield numerical simulation software or implemented as an independent computing server. The device may specifically include:

[0081] Area definition module 100

[0082] :This module is used to execute step S101 of the first embodiment. Specifically, it determines the corresponding wellbore section for each reservoir grid intersecting with the wellbore based on the input reservoir grid data and wellbore trajectory data, and defines the equivalent radius r from the grid. e Radius to well wall r w The module is also responsible for obtaining and storing the pressure (p e ,p wb ) and temperature (T e )Initial conditions.

[0083] Temperature equation building module 200

[0084] This module is used to execute step S103 of Example 1. It constructs a second-order ordinary differential equation describing the temperature distribution in the radial flow region based on the input fluid physical parameters, rock physical parameters, formation permeability, and pressure gradient information provided by the region definition module 100, as shown in Equation 8. When a damaged zone is detected, this module also establishes separate equations for the damaged zone and non-damaged zone based on information such as the damaged zone's permeability and contamination radius.

[0085] Boundary condition setting module 300

[0086] :This module is used to execute step S104 of the first embodiment. It configures boundary conditions for the equation established by the temperature equation establishment module 200. Specifically, it sets the average temperature T of the reservoir grid where the wellbore is located. e Let the equivalent radius r e The Dirichlet boundary condition at the wellbore fluid temperature T wb The heat flux relationship with the total heat transfer coefficient α is set as the well wall r w When there is a formation damage zone, this module is also responsible for setting the continuity boundary conditions of the interface.

[0087] Inflow temperature determination module 400

[0088] :This module is used to execute step S105 of the first embodiment. It receives the complete mathematical problem provided by the temperature equation establishment module 200 and the boundary condition setting module 300, and calls the numerical solver or analytical solver to solve it, thereby obtaining the complete temperature distribution T(r) in the radial flow area. Subsequently, the module calculates T(r=r w ) to determine the final inflow temperature T I and outputs it to the wellbore thermal part of the coupled model. Preferably, the module further comprises an iterative controller for executing the iterative solution process described in the first embodiment until the inflow temperature and the wellbore temperature converge.

[0089] In practical applications, the above modules can be implemented by software programs and run on a general-purpose computer or a dedicated server. The processor executes the program codes corresponding to these modules to complete the inflow temperature calculation method of the present invention.

[0090] The above description is only a preferred embodiment of the present invention and is not intended to limit the present invention. For those skilled in the art, any modifications, equivalent substitutions, improvements, etc. made within the spirit and principles of the present invention should be included in the scope of protection of the present invention.

Claims

1. A method for calculating inflow temperature for a coupled reservoir-wellbore model, characterized in that: include: For a wellbore section corresponding to a reservoir grid, a radial flow region is defined in which a fluid flows from an equivalent radius of the reservoir grid to a wellbore wall of the wellbore section, wherein the pressure and temperature at the equivalent radius are determined by the pressure and temperature of the reservoir grid; a radial steady-state temperature second-order ordinary differential equation is established to describe the temperature distribution in the radial flow region, wherein the equation takes into account heat convection caused by radial flow of the fluid, viscous dissipation and Joule-Thomson effect caused by radial pressure gradient, and heat conduction; boundary conditions are set for the second-order ordinary differential equation, wherein the boundary conditions include: at the equivalent radius, the temperature is equal to the temperature of the reservoir grid; and at the wellbore wall, a heat flow boundary condition is set based on the fluid temperature in the wellbore section and a total heat transfer coefficient; the second-order ordinary differential equation configured with the boundary conditions is solved to obtain a radial temperature distribution in the radial flow region; and based on the radial temperature distribution, the temperature at the wellbore wall is determined as the inflow temperature.

2. The method according to claim 1, characterized in that The method further includes determining the radial pressure gradient by solving a pressure distribution equation in the radial flow region before establishing the radial steady-state temperature second-order ordinary differential equation, wherein the boundary conditions of the pressure distribution equation are the pressure of the reservoir grid and the fluid pressure in the wellbore section.

3. The method according to claim 1, characterized in that When a formation damage zone exists in the radial flow region, the steps of establishing and solving the second-order ordinary differential equation include: dividing the radial flow region into adjacent damage zone regions and non-damage zone regions; establishing respective second-order ordinary differential equations for the damage zone regions and non-damage zone regions; and coupling and solving the two second-order ordinary differential equations at the junction of the damage zone region and the non-damage zone region by ensuring the continuity of temperature and heat flow.

4. The method according to any one of claims 1 to 3, characterized in that The method further includes: using the determined inflow temperature as a boundary condition to solve a wellbore thermal model in the coupled reservoir-wellbore model to calculate the fluid temperature in the wellbore section; and iteratively updating the fluid temperature in the wellbore section and the inflow temperature until convergence.

5. An inflow temperature calculation device for a coupled reservoir-wellbore model, characterized in that: include: A region defining module, for defining, for a wellbore section corresponding to a reservoir grid, a radial flow region where a fluid flows from an equivalent radius of the reservoir grid to a wellbore wall of the wellbore section; a temperature equation establishing module for establishing a radial steady-state temperature second-order ordinary differential equation describing the temperature distribution in the radial flow region, wherein the equation takes into account heat convection, viscous dissipation, Joule-Thomson effect, and heat conduction; a boundary condition setting module, configured to set boundary conditions for the second-order ordinary differential equation, including a temperature boundary condition at the equivalent radius and a heat flow boundary condition at the well wall; An inflow temperature determination module is configured to solve the second-order ordinary differential equation configured with the boundary conditions to obtain a radial temperature distribution, and determine the temperature at the well wall as the inflow temperature according to the radial temperature distribution.

6. The device according to claim 5, characterized in that When there is a formation damage zone in the radial flow area, the temperature equation establishment module and the inflow temperature determination module are further used to: divide the radial flow area into a damage zone area and a non-damage zone area, establish and couple the second-order ordinary differential equations for the two areas respectively, and solve them separately to determine the inflow temperature.

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