Horizontal well production profile interpretation method and device based on DTS data and inversion algorithm

Abstract

The invention discloses a horizontal well output profile interpretation method and device based on DTS data and an inversion algorithm and a computer readable storage medium, and belongs to the technical field of oil and gas field development. In order to solve the problems that in the prior art, the water outlet position of a horizontal well is difficult to determine, the output profile interpretation cost is high, and the precision is low, the method comprises the steps of obtaining distributed optical fiber temperature sensing data; establishing a multi-phase flow horizontal well temperature profile prediction composite model considering the micro-thermal effect and the formation damage as a forward model; establishing an inversion model based on the forward model and an inversion algorithm; and through inversion model iterative calculation, the formation permeability distribution is taken as a recognition target, the optimization target is to reduce actually measured and predicted shaft temperature and / or pressure profile difference, the formation permeability distribution and the output profile are finally obtained, and the water outlet position is determined. According to the method, the output profile interpretation precision is improved, the applicability to complex well conditions is enhanced, and the inversion algorithm is optimized.

Description

Technical Field

[0001] The present invention relates to the technical field of oil and gas field development, and in particular to a method and device for interpreting a horizontal well output profile based on distributed optical fiber temperature sensing data, DTS data and an inversion algorithm. Background Art

[0002] At present, most oil fields in my country have entered the development period of medium and high water content, and horizontal wells are widely used because of their large contact area with the reservoir. However, the rapid decline in horizontal well production and the uneven distribution of production profiles along the wellbore can easily lead to problems such as premature water breakthrough and rapid increase in water content, which seriously affect its development benefits. Accurately determining the water production position of horizontal wells and taking targeted water control measures are the keys to improving the development effect of horizontal wells. The existing solutions mainly include: 1. Conventional production logging technology: including indirect testing (such as C / O logging) and direct testing (such as production profile testing). However, the multiphase flow pattern in the horizontal wellbore is complex, and the wellbore trajectory often fluctuates, resulting in conventional production logging tests that are difficult, time-consuming, have large errors, and high costs. Especially for low-liquid production horizontal wells, the accuracy of the test results is difficult to guarantee. 2. Theoretical calculation models and numerical simulations: such as semi-analytical models based on the coupling of reservoir seepage and wellbore flow or commercial numerical simulation software (such as ECL). These models typically assume isothermal formation and wellbore flow, or quasi-single-phase flow, making it difficult to directly predict oil and water production. More importantly, these models presuppose a known permeability distribution along the horizontal wellbore for production profile prediction, a data lacking for the vast majority of horizontal wells in my country. The recently developed distributed fiber temperature sensing (DTS) technology provides continuous, accurate, and real-time downhole temperature data, making it possible to invert production profiles from temperature profiles. However, for horizontal wells, surrounding formation temperature variations are relatively small compared to vertical wells, and wellbore temperature variations are primarily governed by microthermal effects such as thermal expansion, viscous dissipation, and heat conduction. This makes the measurement and interpretation of horizontal well temperature profiles more complex than for vertical wells. Currently, research on interpreting horizontal well production profiles using DTS technology is insufficient, particularly in China, where mature theories and interpretation methods are lacking. Therefore, a technical solution is urgently needed to accurately and efficiently interpret horizontal well production profiles and determine water production locations to address the aforementioned challenges of existing technologies. Summary of the Invention

[0003] The purpose of the present invention is to provide a method and device for interpreting the production profile of a horizontal well based on DTS data and an inversion algorithm, so as to solve the problems in the prior art of difficulty in determining the water outlet position of a horizontal well, high cost and low accuracy of the production profile interpretation.

[0004] To achieve the above-mentioned objectives, the present invention provides the following technical solutions: a method for interpreting a horizontal well production profile based on DTS data and an inversion algorithm, comprising interpreting the production profile based on distributed optical fiber temperature sensing data and an inversion algorithm; characterized in that the method comprises the following steps: acquiring distributed optical fiber temperature sensing data collected along the horizontal well; establishing a composite model for predicting the temperature profile of a multiphase flow horizontal well that takes into account microthermal effects and formation damage as the forward model; establishing the inversion model based on the forward model and the inversion algorithm; using the inversion model, identifying a target using the formation permeability distribution along the horizontal well as a parameter, and performing iterative inversion calculations with an objective function that reduces the difference between the measured wellbore temperature profile and / or measured wellbore pressure profile obtained using the distributed optical fiber temperature sensing data and the predicted wellbore temperature profile and / or predicted wellbore pressure profile calculated by the forward model as the optimization objective; obtaining the formation permeability distribution and production profile of the horizontal well based on the results of the iterative inversion calculations, and determining the water production location based on the production profile.

[0005] Furthermore, both the reservoir thermal model and the wellbore thermal model in the composite model further consider the influence of the microthermal effect.

[0006] Furthermore, the composite model further considers the influence of formation damage, and in the consideration of the influence of formation damage, includes the simultaneous solution of fluid flow from the reservoir to the formation damage zone and fluid flow from the formation damage zone to the wellbore.

[0007] Furthermore, the composite model further includes thermodynamically coupling the reservoir model and the wellbore model to calculate temperature distribution.

[0008] Furthermore, the micro-thermal effect is selected from at least one of thermal expansion effect, thermal conduction effect, thermal convection effect or viscous dissipation effect.

[0009] Furthermore, the inversion algorithm is at least one of the Levenberg-Marquardt method or the Markov Chain Monte Carlo method.

[0010] More specifically, the inversion algorithm is a Markov chain Monte Carlo method, which performs a random search on the formation permeability parameter space to avoid the iterative inversion calculation from falling into a local optimal solution.

[0011] Furthermore, when the distributed optical fiber temperature sensing data further includes a measured wellbore pressure profile, the objective function is further based on reducing the difference between the measured wellbore pressure profile and the predicted wellbore pressure profile calculated by the forward model, and different weights are set for the difference term related to the measured wellbore temperature profile and the difference term related to the measured wellbore pressure profile.

[0012] As a preferred solution, the method further includes: based on the composite model, analyzing the influence of at least one factor among the inflow fluid type, formation permeability, water content, wellbore trajectory or completion method on the temperature distribution, and obtaining an explanatory map of the relationship between the water outlet position and the temperature distribution.

[0013] To achieve the above-mentioned objectives, the present invention also provides a horizontal well production profile interpretation device based on distributed optical fiber temperature sensing data and inversion algorithm, characterized in that it includes a processor and a memory; wherein the memory stores a computer program; and when the computer program is executed by the processor, it implements the technical solution of any of the methods described above.

[0014] Compared with the prior art, the present invention has the following beneficial effects:

[0015] 1. This invention builds a complex forward model that takes into account micro-thermal effects, formation damage, and reservoir-wellbore coupling, which is closer to the real physical process of horizontal wells. It combines the continuous high-precision temperature / pressure data obtained by distributed fiber temperature sensing (DTS) and optimizes parameters through an inversion algorithm. It can more accurately invert the formation permeability distribution and production profile along the wellbore, and then accurately determine the water production location. Figure 9 To the attached Figure 11 The MCMC inversion results shown in the figure have significantly improved the temperature and pressure fitting effects compared to the LM method that does not use MCMC or has inappropriate initial values, and the output profile interpretation results are closer to reality.

[0016] 2. The present invention enhances the applicability to complex well conditions: This method does not rely on pre-known permeability profile data, but directly obtains it through inversion. Therefore, it is applicable to a large number of existing horizontal wells with missing permeability data. At the same time, for horizontal wells with complex well trajectories and low fluid production, the adaptability and data quality of DTS testing are better than those of traditional logging tools. For example, Figure 17 To the attached Figure 19 The actual oil field case shown successfully used limited DTS data to interpret the production profile and identify the water production location of a horizontal well with a complex trajectory.

[0017] 4. The present invention optimizes the application of inversion algorithms: In particular, when the Markov chain Monte Carlo (MCMC) inversion method is used, the random search in the parameter space can effectively avoid falling into the local optimal solution, thereby improving the global reliability and stability of the inversion results. Figure 9 To the attached Figure 11 The MCMC inversion results shown are more accurate than LM.

[0018] 5. The present invention provides a decision-making basis for refined reservoir management: accurate production profile and water location information can provide direct technical support for formulating targeted water control and water plugging measures, optimizing production parameters, and evaluating completion effects in oil fields, thus helping to achieve refined management and efficient development of horizontal wells. Figure 19 The example well water flow distribution shown clearly indicates the high-water-yielding well section, providing an accurate target for subsequent water plugging operations. BRIEF DESCRIPTION OF THE DRAWINGS

[0019] In order to more clearly illustrate the technical solution of the present invention, the following briefly describes the drawings used in implementing the embodiments of the present invention or the prior art:

[0020] Figure 1 A schematic diagram of a process embodiment of the present invention;

[0021] Figure 2 A schematic diagram of a composite model for predicting temperature profiles of multiphase flow horizontal wells taking into account microthermal effects and formation damage in an embodiment of the present invention;

[0022] Figure 3 Schematic diagram of the structure of the inversion model in an embodiment of the present invention;

[0023] Figure 4 A schematic diagram of the module structure of an embodiment of a device of the present invention;

[0024] Figure 5 This is a schematic diagram of a micro-element section of a wellbore according to the present invention;

[0025] Figure 6 This is a schematic diagram of the wellbore, casing, cement sheath and formation of the present invention.

[0026] Figure 7 is the reservoir temperature profile under different fluid types of the present invention;

[0027] Figure 8 The temperature profile of the horizontal wellbore at different water outlet positions in the same oil and water layer of the present invention;

[0028] Figure 9 The inversion results of wellbore temperature and pressure using the MCMC method in the present invention when water is produced from a bottom water reservoir;

[0029] Figure 10 This is the inversion result of the formation permeability distribution under the condition of water production in the bottom water reservoir using the MCMC method in the present invention;

[0030] Figure 11 This is the inversion interpretation result of the horizontal well production profile under the condition of water production in the bottom water reservoir using the MCMC method in the present invention;

[0031] Figure 12This is a distribution diagram of formation permeability along the horizontal wellbore when water is produced in the middle of a horizontal well in the same oil and water layer according to the present invention;

[0032] Figure 13 This is the inversion interpretation result of the production profile under the condition of water production in the middle of the horizontal well in the oil-water layer of the present invention;

[0033] Figure 14 The distribution of six different formation permeabilities along the horizontal wellbore of the present invention;

[0034] Figure 15 is the formation permeability distribution inversion result under formation permeability distribution situation 6 of the present invention;

[0035] Figure 16 This is the inversion interpretation result of the horizontal well production profile under formation permeability distribution scenario 6 of the present invention;

[0036] Figure 17 The wellbore temperature and pressure observation data of the example well of the present invention;

[0037] Figure 18 The inversion result of the formation permeability distribution of the example well of the present invention is shown;

[0038] Figure 19 This is a comparison chart of the oil and water flow distribution inversion results of the example well of the present invention and the measured data. DETAILED DESCRIPTION

[0039] To make the objectives, technical solutions, and advantages of the present invention more clear, 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 merely for the purpose of explaining the present invention and are not intended to limit the scope of protection of the present invention. When writing the examples, the language should be clear, complete, and accurate, and should support each technical feature of the claims so that those skilled in the art can understand and implement the present invention.

[0040] Example 1

[0041] This embodiment provides a method for interpreting horizontal well production profiles based on DTS data and inversion algorithms. Figure 1 , the method may specifically include the following steps:

[0042] Step S101: Acquire distributed fiber temperature sensing (DTS) data collected along a horizontal well. The DTS data may include a continuously (or discretely) measured temperature profile along the horizontal wellbore. Preferably, the DTS data may also include a measured pressure profile along the horizontal wellbore. The DTS system can acquire data by being permanently installed on the outer wall of the oil pipe or temporarily deployed. Table 1 shows a comparison of DTS technology with other monitoring technologies for monitoring oil and gas well production / injection profiles.

[0043] Table 1: Comparison of various monitoring technologies

[0044]

[0045] Step S102: Establish a multiphase flow horizontal well temperature profile prediction composite model taking into account micro-thermal effects and formation damage as a forward model. Figure 2 The composite model is used to simulate the temperature and pressure distribution in a horizontal wellbore under given reservoir parameters, wellbore parameters, fluid properties, and production regime. The establishment of this composite model mainly includes the following aspects:

[0046] 1. Reservoir model construction:

[0047] Based on the principles of conservation of mass, conservation of momentum (Darcy's law), and conservation of energy, a mathematical model was developed to describe the flow and heat transfer of multiphase fluids (such as oil and water) in reservoirs. The reservoir flow model describes the flow of fluids in porous media, and its basic differential equation can be expressed as follows (using the oil phase as an example).

[0048]

[0049] Among them, ρ o is the oil phase density, k is the absolute permeability, k ro is the relative permeability of the oil phase, μ o is the oil phase viscosity, p o is the oil phase pressure, g is the acceleration of gravity, D is the vertical depth, φ is the porosity, S o is the oil phase saturation, t is the time. The water phase has a similar equation.

[0050] The reservoir thermal model describes the temperature distribution in the reservoir, taking into account heat conduction, heat convection, and microthermal effects caused by fluid expansion and viscous dissipation. Its energy conservation equation can be expressed as:

[0051]

[0052] Among them, the left side is the energy accumulation term, U i ,U r are the internal energies of fluid phase i and rock, ρ i ,ρ r Its density, S i is the saturation of fluid phase i. The first term on the right is the convective energy transport term, u i is the Darcy velocity of fluid phase i, H i is its enthalpy; the second term is the heat conduction term, λ is the effective total thermal conductivity of the reservoir (W / (m·℃)), which reflects the overall heat conduction capacity of the saturated porous medium; T res is the reservoir temperature.

[0053] According to the definition of internal energy and enthalpy U=Hp / ρ and the relationship between enthalpy change and temperature and pressure And the relationship between rock internal energy and temperature dU r ≈C pr dT, and these relationships are substituted into the reservoir energy conservation equation. Considering the energy accumulation of fluids and rocks within the pores, convective energy transport, thermal conduction in the formation, and source terms (including viscous dissipation and work done by volume change), ignoring the kinetic energy term, and considering that the potential energy term cancels out the convection and accumulation terms on both sides of the equation, after a series of transformations and arrangements, the partial differential equation describing the reservoir temperature field distribution can be obtained:

[0054]

[0055] Among them, C p is the specific heat capacity, β is the isobaric thermal expansion coefficient (1 / C), defined as The subscripts o, w, and r represent oil, water, and rock, respectively. The second term on the right side of this equation is the viscous dissipation term, and the third term is the thermal expansion term caused by the pressure gradient, both of which are microthermal effects.

[0056] 2. Wellbore model construction:

[0057] Refer to the attached Figure 5 Based on the principles of conservation of mass, momentum, and energy, a steady-state multiphase flow wellbore model is established. The wellbore model consists of two parts: the wellbore flow model and the wellbore thermal model. Taking any microelement of the wellbore, the fluid flow includes two parts: flow along the axial direction of the wellbore and radial inflow. In the wellbore coordinate system (axial x, radial r), the fluid velocity vector v can be expressed as:

[0058] v=(v x ,v r )

[0059] Among them, v x is the velocity of the fluid along the axial direction of the wellbore (m / s), v r is the radial velocity of the fluid (m / s). For the fluid flowing from the reservoir into the wellbore, its velocity can be approximated as the radial velocity v1 (m / s) perpendicular to the wellbore wall.

[0060] In order to describe different completion methods (such as open hole completion and perforation completion), the wellbore opening degree γ is defined here.

[0061]

[0062] For open hole completion, γ = 1, and for perforated completion, the wellbore is partially open with γ < 1.

[0063] The wellbore flow model establishes the wellbore pressure gradient equation based on the principles of conservation of mass and momentum, enabling dynamic simulation of multiphase flow pressure in horizontal wells. The following explanation begins with single-phase flow and then expands to multiphase flow in the wellbore.

[0064] The principle of conservation of mass can be described as mass change = inflow mass - outflow mass in any micro-element of the wellbore. The mass change in any micro-element of the wellbore can be expressed as

[0065]

[0066] Where R is the wellbore radius (m). The mass inflow and outflow are expressed as

[0067] m in =2πRγΔx(ρv r ) r＝R +πR 2 (ρv x ) x Formula 6

[0068] m out =πR 2 (ρv x ) x+Δx Formula 7

[0069] Substituting equations 5, 6, and 7 into the mass conservation principle, we can obtain

[0070]

[0071] Divide both sides of the equation by And sorted

[0072]

[0073] When Δx→0, Equation 9 can be expressed as

[0074]

[0075] Therefore, the steady-state mass conservation equation of the wellbore is:

[0076]

[0077] This form of the steady-state single-phase mass conservation equation is also applicable to multiphase flow mixtures, where ρ and v represent the density and axial velocity of the mixture, respectively.

[0078] The principle of conservation of momentum can be described as the change in momentum = inflow momentum - outflow momentum + the net external force acting on the fluid. The change in momentum in any micro-element of the wellbore can be expressed as

[0079]

[0080] The momentum flux can be expressed as

[0081] Φ=ρvv+pδ-τ Formula 13

[0082] Where Φ is the momentum flux tensor; δ is the Kronecker tensor; and τ is the shear stress tensor. Thus, the momentum inflow and outflow can be expressed as

[0083]

[0084] Assuming the fluid is Newtonian, the shear stress can be expressed as

[0085]

[0086] Where ε is the deformation rate tensor. Then the axial shear stress can be expressed as

[0087]

[0088] The shear stress on the wellbore wall is expressed by the Fanning friction coefficient as

[0089]

[0090] Where f is the friction coefficient. Assuming that there is no slip effect on the well wall, the axial velocity at r = R can be expressed as

[0091] v x | r＝R =0 Formula 19

[0092] Substituting Equations 17, 18, and 19 into Equations 14 and 15 and rearranging them, we get

[0093]

[0094] The momentum generated by the external force acting on the fluid can be expressed as

[0095] P p =-πR 2 Δxρgsinθ Equation 22

[0096] Substituting equations 12, 20, 21, and 22 into the momentum conservation principle, we can obtain

[0097]

[0098] Divide both sides of the equation by And sorted

[0099]

[0100] When Δx→0, Equation 25 becomes

[0101]

[0102] Under steady-state conditions, ignoring the second-order derivative of velocity, Equation 25 can be written as the pressure gradient equation for single-phase flow.

[0103] The friction coefficient f in laminar flow state is expressed as

[0104]

[0105] The expression of friction coefficient f in turbulent state is:

[0106]

[0107] Re and Re w is the Reynolds number and the Reynolds number on the well wall, respectively defined as

[0108]

[0109] f0 is the friction coefficient when there is no radial inflow, which can be obtained from the Moody chart or Chen's empirical formula. Its expression is:

[0110] Where ε is the relative roughness of the wellbore. The pressure gradient equation for single-phase flow is still applicable to multiphase flow. According to equation (26), for multiphase flow in the wellbore, the pressure gradient equation can be expressed as

[0111]

[0112] Where v m —Multiphase mixed fluid velocity (m / s); ρ m —Multiphase mixed fluid density (kg / m 3 ). From Equation (32), we can see that to solve the wellbore pressure distribution of multiphase flow, we must first know the average velocity and density of the multiphase mixed fluid. In the oil-water two-phase flow, assuming that the slippage between the oil and water phases is ignored, the phase holding ratio can be expressed as

[0113]

[0114] h w =1-h o Formula 34

[0115] The average density of the multiphase mixed fluid can be expressed as

[0116] ρ m =h o ρ o +h w ρ w Formula 35

[0117] The average velocity of the multiphase mixed fluid can be expressed as

[0118]

[0119] Where h o -Oil phase holdup; h w -water phase hold-up; v so - oil phase apparent velocity (m / s); v sw— The superficial velocity of the water phase (m / s). The viscosity of the oil-water mixture can be expressed by the relationship proposed by Jayawardena:

[0120] μ m =μ o (1-h w ) -2.5 Formula 37

[0121] Where μ m —Oil-water mixture viscosity (mPa·s).

[0122] Wellbore thermal model In any microelement of the wellbore, the energy conservation principle can be described as: Energy change = energy inflow - energy outflow + work done by external force on the fluid + heat transferred to the fluid. Among them, each item can be expressed as

[0123]

[0124] E in =2πRΔx(e r ) r＝R +πR 2 (e x ) x Formula 39

[0125] E out =πR 2 (e x ) x+Δx Formula 10

[0126] E 外力做功 =-πR 2 Δxρvgsinθ Equation 11

[0127] Where e is the energy flux vector, defined as

[0128]

[0129] Where q is the heat flux vector. Substituting equations (38) to (41) into the energy conservation principle, we can obtain

[0130]

[0131] Divide both sides of the equation by And sorted

[0132]

[0133] When Δx→0, Equation 44 can be expressed as

[0134]

[0135] Among them, the radial energy flux at the wellbore wall (e r ) r＝R After considering the wellbore opening degree γ, the contributions of the open section and the closed section are included. x It mainly includes the convection energy, pressure work and viscous shear work of axial fluid flow.

[0136] For steady-state flow Ignoring the contributions of kinetic energy and viscous shear terms in the axial gradient and radial inflow of the wellbore (these terms are usually small relative to the enthalpy term), and relating the enthalpy change, radial heat transfer and temperature difference (radial heat q1 = α(T1-T)), we can finally derive the steady-state multiphase flow wellbore temperature equation that describes the temperature distribution along the wellbore:

[0137]

[0138] Where, the subscript M represents all phases of the fluid, T wb is the wellbore temperature (℃); p wb is the wellbore pressure (MPa); x is the axial distance along the wellbore (m); R wb is the wellbore radius (m); θ is the wellbore inclination angle; γ is the wellbore opening degree; α is the total heat transfer coefficient; T I is the inflow temperature (℃); g is the acceleration due to gravity. (ρv) T is the axial component of the total mass flow rate of the multiphase mixed fluid, defined as (ρv) T =∑ i ρ i v i h i ;(ρvC p ) T is the axial component of the total heat capacity flow rate of the multiphase mixed fluid, defined as (ρvC p ) T =∑ i ρ i v i h i C pi ;(ρvC p K JT ) T The thermodynamic term of the multiphase mixed fluid considering the Joule-Thomson effect is defined as (ρvCp K JT ) T =∑ i ρ i v i h i C pi K JT,i ; where i is the fluid phase (such as oil, water), ρ i ,v i ,h i ,C pi ,K JT,i are the density, axial velocity, retention rate, specific heat capacity and Joule-Thomson coefficient of the i-th phase respectively. (ρ i v i C p ) I,i is the heat capacity flow rate of the i-th phase flowing radially. Joule-Thomson coefficient K JT,i Expressed as (Usually evaluated at the inflow temperature). (ρv) T =∑ i ρ i v i h i

[0139] (ρvC p ) T =∑ i ρ i v i h i C pi

[0140] (ρvC p ) T,l =∑ i ρ i,I v i,I h i,I C pi

[0141] (ρvC p K JT ) T =∑ i ρ i v i h i C pi K JT,i

[0142] α T,I =γ(ρvC p ) T,I +(1-γ)α

[0143] Refer to the attached Figure 6As shown in Figure 1, the thermal resistance between the wellbore, casing, cement sheath and formation determines the total heat transfer coefficient α. If natural convection and thermal radiation in the oil-casing annulus are not considered, the expression for α can be simplified to:

[0144]

[0145] Where λ c ——Thermal conductivity of casing (W / (m·℃)); λ cem ——thermal conductivity of cement sheath (W / (m·℃)); R——wellbore radius (m); r c ——Casing outer radius (m); r w ——Wellbore radius (m).

[0146] 3. Consideration of formation damage:

[0147] The composite model further considers the impact of formation damage. Formation damage refers to the reduction in permeability of the formation near the wellbore during drilling, completion, or production. The model quantifies the additional pressure drop caused by formation damage by introducing the contamination skin factor s. The contamination skin factor s can be defined as:

[0148]

[0149] Where k is the original formation permeability, k d is the damage zone penetration rate, r d is the radius of the damage zone, r w is the wellbore radius. Defined as the permeability damage rate. In model calculations, the pressure and temperature equations for fluid flow from the reservoir bulk to the formation damage zone and from the formation damage zone to the wellbore are solved simultaneously to more accurately simulate the impact of formation damage on the production and temperature profiles. This impacts pressure and temperature calculations in both the reservoir model and the coupled wellbore-reservoir model.

[0150] 4. Thermodynamic coupling between reservoir and wellbore:

[0151] The reservoir model and the wellbore model are determined by the temperature T of the fluid flowing into the wellbore. inflow Coupled with the inflow flow. inflow It is the key parameter that connects the reservoir temperature field and the wellbore temperature field. Its calculation requires solving the energy equation of radial flow in the reservoir and the wellbore boundary conditions simultaneously. For example, for the equivalent radius r e (represents the reservoir grid influence boundary) to the wellbore radius r w In the radial flow region, the second-order ordinary differential equation of the steady-state temperature distribution T(r) is derived as follows: The reservoir temperature equation (3) is simplified to the radial steady-state temperature equation:

[0152]

[0153] The first term on the left side of Equation 49 describes the heat convection term, the second and third terms are viscous dissipation terms, and the fourth term is the heat conduction term.

[0154] According to Darcy's law, the pressure distribution equation from the equivalent radius to the wellbore is established (i.e. in ) to obtain the radial seepage velocity:

[0155]

[0156] Substituting Equation 50 into Equation 49, the coupled temperature equation obtained after sorting is:

[0157]

[0158] Right now

[0159]

[0160] The coefficients C1, C2 and C3 are considered constant.

[0161]

[0162] Among them, k ri represents the relative permeability of the i-th phase.

[0163] The equation is a second-order linear ordinary differential equation with variable coefficients. By assuming that the coefficients C1, C2, and C3 are constants in the calculation area, the equation is similar to the Euler-Cauchy equation, and the solution of the homogeneous part is in the form of r p , we can get the characteristic equation λp(p-1)+C1p-C2=0, or λp 2 +(λ+C1)p-C2=0. The general solution is:

[0164]

[0165] Where p1 and p2 are characteristic roots, the constant term b is the special solution of the inhomogeneous part, and:

[0166]

[0167] The coefficients l1 and l2 are determined by the boundary conditions. The boundary conditions are:

[0168]

[0169] Where T e is the equivalent radius r e The reservoir temperature at , T is the wellbore temperature, is the inflow temperature. Substitute the general solution into the boundary conditions and consider the formation damage zone (radius r d , permeability k d ) exists (Formulas 4-180 and 4-181 in the technical disclosure document), the expressions of coefficients l1 and l2 (or c1, c2, c3, c4 in the technical disclosure document) can be derived, and then the wellbore wall (r = r w ) of the fluid inflow temperature T inflow When considering formation damage, the temperature distribution is a piecewise function:

[0170]

[0171] Where n1 and n2 are the characteristic roots of the equation based on the original permeability k, and n3 and n4 are based on the permeability k of the damage zone. d The characteristic root of the equation is expressed as:

[0172]

[0173] The coefficients c1, c2, c3, c4 are determined by the boundary conditions and the damage zone boundary (r = r d ) and the temperature gradient continuity condition are determined. Inflow temperature T I That is T(r w ), according to the formula r=r w Calculated at:

[0174]

[0175] This coupling process ensures that the calculation of heat transfer from the reservoir to the wellbore and the temperature change within the wellbore are correlated and consistent. By iteratively solving the reservoir model, wellbore model, and inflow temperature model, the temperature and pressure profile along the horizontal wellbore is finally obtained.

[0176] Based on the above model, the present invention predicts the influence of different factors on the temperature profile. Figure 7The data shows the changes in reservoir temperature when different fluid types (oil, gas, and water) flow into the wellbore. Due to the Joule-Thomson effect and viscous dissipation, the temperatures of different fluids entering the wellbore deviate from the original formation temperature. Gas temperature generally decreases, while oil and water temperature increases. However, water temperature increases less than oil due to its larger specific heat capacity. Higher flow rates, greater production pressure differentials, or higher crude oil density increase the wellbore temperature, and the temperature variation increases with the axial direction of the wellbore. Higher formation permeability reduces the pressure drop at the same flow rate, weakens the microthermal effect caused by the pressure drop, and reduces the inflow temperature. The presence of formation damage (e.g., a higher skin coefficient) creates an additional pressure drop near the wellbore, increasing the inflow temperature. The more severe the damage, the more pronounced the temperature anomaly. Wellbore trajectory significantly influences wellbore temperature. Fluids flowing upward encounter lower ground temperatures, while those flowing downward encounter higher ground temperatures. This is compounded by changes in hydrostatic pressure and momentum. The impact of different completion methods on wellbore temperature is primarily reflected in differences in wall friction and the overall heat transfer coefficient. The position and degree of wellbore opening affect the fluid inflow distribution and heat exchange pattern. The slope of the temperature curve will change significantly in the open section. The greater the opening degree, the greater the temperature increase. Water breakthrough in horizontal wells will cause wellbore temperature changes. When water is produced in the same layer, the temperature decreases due to the larger specific heat capacity of water than oil. The temperature decreases less near the heel due to the influence of axial flow mixing and frictional heat generation (see Appendix). Figure 8 ); when bottom water breaks through, water carrying higher ground temperatures flows into the wellbore, causing the temperature to rise. These influencing patterns form the basis for interpreting the relationship between water outlet location and temperature distribution.

[0177] Step S103: Establish an inversion model based on the forward model and inversion algorithm. Figure 3 The goal of the inversion model is to use the measured DTS data acquired by S101 to optimize the temperature / pressure profiles predicted by the forward model and the measured profiles by adjusting the unknown parameters in the forward model (here, primarily the formation permeability distribution k along the wellbore). The core of this process is to establish an objective function O(k) that quantifies the difference between the predicted and measured values. The objective function uses a least squares form, taking into account the temperature and / or pressure measurements:

[0178]

[0179]

[0180] where k is a parameter vector representing the distribution of formation permeability along the wellbore; T wb,calc,j and p wb,calc,j are the wellbore temperature and pressure at the jth observation point calculated by the forward model; T wb,obs,j and p wb,obs,j is the corresponding measured value; N T and N P are the number of observation points for temperature and pressure respectively.T and W P is a weight factor used to balance the contribution of temperature and pressure data in the objective function. When pressure data is included, it can be set according to the magnitude of their influence on the objective function. For example, the magnitude of their influence on the objective function can be set to be roughly the same, such as W T / W P ≈(1 / K JT ) 2 of magnitude.

[0181] The inversion algorithm uses the Markov Chain Monte Carlo (MCMC) method. The MCMC method is a random sampling method based on Bayesian theory. It explores the posterior probability distribution of parameters by constructing a Markov chain. Generally, considering a homogeneous Markov chain, its transition probability is independent of time t. At this time, from state s to s * The transition probability can be expressed as P(s,s * ) represents. For a distribution π(s), if

[0182] π(s)=∫P(s,s * )π(s)ds Formula 32

[0183] Then π(s) is called the transition probability P(s,s * ) is a stationary distribution. A very important property of Markov chains is their stationary distribution. Mathematically, there is the Markov chain convergence theorem, which states that when the number of iterations n is large enough, a non-periodic Markov chain with any connected states can converge to a stationary distribution π(s). This theorem is the theoretical foundation of the MCMC method.

[0184] Another property of the Markov chain is used here. If the Markov chain with transition probability P and distribution π(x) satisfies the following relationship for all states i, j:

[0185] π(i)P(i,j)=π(j)P(j,i) Formula 33

[0186] Equation 63 is called the detailed equilibrium equation. The distribution π(x) that satisfies the detailed equilibrium equation is stationary. We hope that the sampled Markov chain is stationary, so we can use the detailed equilibrium equation as a starting point. However, in general, any given distribution π(x) is not necessarily stationary. In order to make the detailed equilibrium equation valid, we can introduce a function α(i,j) (0<α(i,j)≤1) such that

[0187] π(i)P(i,j)α(i,j)=π(j)P(j,i)α(j,i) Formula 34

[0188] According to the symmetry, we can take

[0189] α(i,j)=π(j)P(j,i) Formula 35

[0190] remember

[0191] Q(i,j)=P(i,j)α(i,j) Formula 36

[0192] In this way, a new Markov chain with q(i,j) as the transition probability is obtained, and it has a stationary distribution π(x). Here, α(i,j) is called the acceptance probability, that is, the state probability of accepting the transition probability P(i,j) from state i to state j with probability α(i,j) on the original Markov chain. If the acceptance probability is too small, it will cause the Markov chain to reject too many state probabilities, so the convergence speed of the Markov chain will be very slow. Therefore, it is possible to consider amplifying the acceptance probability so that the larger of the acceptance probabilities α(i,j) and α(j,i) in Equation 64 is taken to be 1, and the smaller one is amplified by the same proportion. In this way, the acceptance probability can be expressed as

[0193]

[0194] This is the MH algorithm. Its operation is as follows:

[0195] We want to build a Markov chain with π(x) as a stationary distribution, and choose an irreducible transition probability q(·,·) and an acceptance probability α(·,·). For any state combination (x,y) (x≠y), we have the following definition:

[0196] p(x,y)=p(x→y)=q(x,y)α(x,y) Formula 37

[0197] If a Markov chain {X t :t≥0} is in state x at time t. First, a potential transition x→y is generated based on q(x,y). Then, the acceptance probability α(x,y) is used to decide whether to transfer. In other words, after the potential transition state y is found, y is accepted as the state value of the Markov chain at the next moment with the acceptance probability α(x,y), and the transition from state x to state y is rejected with the probability [1-α(x,y)]. Then, after finding y, a random number u can be drawn from the uniform distribution U(0,1). The state of the Markov chain at the next moment is

[0198]

[0199] The q(·,·) mentioned above is called the proposed distribution. Since our goal is to make π(x) a stationary distribution, after having the proposed distribution q(·,·), we need to choose an acceptance probability α(·,·) so that the new transition probability p(x,y) takes π(x) as its stationary distribution. According to formula (5-27), we can get

[0200]

[0201] According to Equation 67 and Equation 69, we can get p(x,y) as

[0202]

[0203] The suggested distribution q(x,y) can take different forms. Two commonly used distributions are:

[0204] 1) Random Walk Sampling

[0205] Random walk sampling selects a symmetric proposal distribution, i.e.

[0206] Here α(x,y) can be simplified to

[0207] In this case, the MH algorithm is actually the random walk Metropolis algorithm, and the normal distribution is usually chosen as its recommended distribution.

[0208] 2) Independent Sampling

[0209] If q(x,y) is independent of the current state x, that is, q(x,y) = q(y), it is called independent sampling. Here α(x,y) can be changed to

[0210] in

[0211] Generally, to achieve good results in independent sampling, q(x) should be close to π(x).

[0212] Next, we will prove that the Markov chain generated by the MH algorithm is stationary with respect to π(x). Because the distribution π(x) that satisfies the detailed equilibrium equation is stationary, we only need to prove that the transition probabilities of the MH algorithm satisfy the detailed equilibrium equation. We will illustrate this with three cases.

[0213] 1)π(x)q(x,y)=π(y)q(y,x)

[0214] According to formula (5-30), α(x,y)=α(y,x)=1

[0215] According to formula (5-28), we can derive p(x,y)π(x)=q(x,y)π(x) and p(y,x)π(y)=q(y,x)π(y)

[0216] Then there is p(x,y)π(x)=p(y,x)π(y)

[0217] This shows that the detailed equilibrium equation is satisfied.

[0218] 2)π(x)q(x,y)<π(y)q(y,x)

[0219] According to formula (5-30), α(x,y)=1,

[0220] According to formula (5-28), we have

[0221]

[0222] This shows that the detailed equilibrium equation is satisfied.

[0223] 3)π(x)q(x,y)>π(y)q(y,x)

[0224] According to formula 69, we have α(y,x)=1

[0225] According to formula 67, we have

[0226]

[0227] This shows that the detailed equilibrium equation is satisfied.

[0228] Step S104: Using the inversion model, the formation permeability distribution along the horizontal well is used as a parameter to identify the target, and the above objective function is used as the optimization target to perform iterative inversion calculations. Initialize the formation permeability parameter vector k. In each MCMC iteration:

[0229] Sample k from the current penetration rate according to the proposed distribution (e.g. random walk) current Generate a new candidate permeability sample k candidate .

[0230] Use k candidate As input to the forward model, the predicted wellbore temperature profile T is calculated. wb,calc (k candidate ) and pressure profile p wb,calc (k candidate ).

[0231] ·Calculate the objective function value O(k candidate ).

[0232] ·According to the formula, the acceptance probability α(k candidate |k current ).

[0233] Generate a random number u in the interval [0,1]. If u≤α, accept the candidate sample and let knext =k candidate Otherwise, reject the candidate sample and let k next =k current .

[0234] This process is repeated until the Markov chain converges (e.g., a preset number of iterations is reached, or the posterior distribution of the parameters stabilizes).

[0235] In the iterative inversion calculation process, the Markov chain Monte Carlo method is preferably used to avoid the iterative inversion calculation from falling into a local optimal solution by performing a random search in the parameter space.

[0236] The specific operations are as follows:

[0237] 1) Construct a suitable suggestion distribution q(x) t ,·), generate the initial point x0 in the distribution q;

[0238] 2) Iterate the following steps: t ,·) to generate new samples y;

[0239] 3) Calculate the acceptance probability Where f is the target distribution;

[0240] 4) Draw a random number u from the uniform distribution U(0,1); if u≤α(x t ,y), then let x t+1 =y (transfer to new state), otherwise, x t+1 =x t (status unchanged);

[0241] 5) Increase the t value and proceed to the next iteration.

[0242] Therefore, when solving inversion problems such as output profile interpretation, we use the MH algorithm in the MCMC method to perform inversion to minimize the objective function. The algorithm flow of this inversion method is:

[0243] 1) Assume an initial value of formation permeability k0;

[0244] 2) Under state n, for formation permeability k n , calculate the horizontal wellbore temperature and pressure through the forward model;

[0245] 3) Calculate the objective function f(k n );

[0246] 4) From the proposed distribution q(k n ,k n+1 ) generates k n+1 ,Here, uniform distribution is adopted to generate new formation permeability;

[0247] 5) Similarly, the horizontal wellbore temperature and pressure are calculated by the forward model, and the objective function f(k n+1 );

[0248] 6) Decide whether to accept the newly generated formation permeability k based on the acceptance probability n+1 ;

[0249]

[0250] 7) Draw a random number u from the uniform distribution U(0,1); if u≤α(k n ,k n+1 ), then the new formation permeability k n+1 If it is accepted, keep the permeability as the permeability for the next state and return to step 2; otherwise, return to step 4.

[0251] After a series of sampling (after the "burn-in" stage), samples k0, k1, k2, ..., k n ,k n+1 ,…, these are the possible solutions to the inverse problem.

[0252] The selection of the recommended distribution in step 4 is directly related to the convergence speed and coverage of the entire Markov chain and the simulation efficiency of the MCMC inversion method.

[145] As mentioned previously, independent sampling is a proposed distribution that generates samples from a uniform distribution without being constrained by the current state. This can slow down the inversion process and affect the simulation efficiency of the MCMC inversion method. Another proposed distribution is random walk sampling, which first generates random numbers from a uniform distribution and then generates new samples by perturbing the current sample. This generally has a higher probability of acceptance.

[0253] k n+1 =k n ±δ Formula 72

[0254] The small perturbation δ can be set to 0.1k n If a new sample generated from a uniform distribution does not satisfy Equation 72, it is rejected and new samples need to be generated until the constraint is satisfied. This paper chooses random walk sampling, a symmetrical proposal distribution.

[0255] As mentioned above, in the MCMC method, whether to accept a new sample is determined by the acceptance probability in Equation 66 of the MH algorithm. Therefore, the acceptance probability is affected by the value of the objective function. In this study, the temperature weight D T It can be set between 200 and 2000, and the pressure weight can be estimated by Equation 72.

[0256]

[0257] Step S105: Based on the results of the iterative inversion calculation, the formation permeability distribution and production profile of the horizontal well are obtained, and the water production location is determined based on the production profile. After the MCMC iteration is completed, a series of permeability parameter samples will be obtained. These samples approximately obey their posterior probability distribution. The mean, median or mode of these samples can be selected as the formation permeability distribution k obtained by the final inversion. final . final Substituting this into the forward model not only yields the final fitted temperature and pressure profiles, but also allows calculation of the oil, water (or other phase) production along each section of the wellbore, known as the production profile. By analyzing the flow distribution of each phase (especially the water phase) in the production profile, the location and water production of the water-producing well section (i.e., the section with significant water production) can be quantitatively determined.

[0258] Optionally, the method may further include step S106: Based on the composite model, analyzing the influence of at least one of the following factors on temperature distribution: inflow fluid type, formation permeability, water content, wellbore trajectory, or completion method, to obtain an interpretation chart of the relationship between water production location and temperature distribution. This helps to gain a priori understanding of possible water production patterns and corresponding temperature characteristics before inversion.

[0259] Analysis of simulation and case application results

[0260] In order to verify the effectiveness of the method of the present invention, we conducted tests using synthetic data and actual oil field data.

[0261] Synthetic data testing

[0262] Taking the water production of horizontal wells in bottom water reservoirs as an example, under the set real formation permeability distribution, the temperature and pressure profiles obtained by the forward model are used as measured data. We compared the inversion results of the LM method and the MCMC method. The results show that although the LM method converges quickly when the initial permeability is close to the true value, it is sensitive to the initial value and is prone to falling into local optimality. The use of the MCMC inversion method can effectively avoid local optimality and obtain inversion results that are closer to the actual situation by randomly searching the parameter space. As shown in the attached figure, Figure 9 As shown in Figure 2, the wellbore temperature and pressure profiles obtained by MCMC method inversion are in good agreement with the measured (observed) data, which is better than the fitting effect of LM method. Figure 10 ) is relatively close to the true value, and the inversion interpretation of the output profile (see Appendix Figure 11) can accurately identify the water-yielding location (for example, the section 315 to 375 meters from the horizontal well's heel) and quantify the water production rate. This demonstrates that the inversion interpretation results of this production profile can truly reflect the horizontal well's fluid production and enable quantitative evaluation of the water-yielding location.

[0263] The method of the present invention can also effectively explain the water production of horizontal wells in the case of oil and water in the same layer. Different water production positions (toe, middle, heel) lead to different wellbore temperature profile characteristics (see Appendix Figure 8 We used synthetic data to test different water-out locations, multi-stage water-out, and different production liquid contributions. For example, in the case of water-out in the middle of a horizontal well with oil and water in the same layer (the real formation permeability distribution used in the simulation is shown in the attached figure). Figure 12 ), the output profile obtained by MCMC inversion (see Appendix Figure 13 ) accurately identified the middle water outlet position (255m-315m well section), and the water production was estimated accurately (inversion value 27.2m 3 / dvs observed value 29.1m 3 For the more complex multi-stage water production scenario with different production fluid contributions, the inversion results show that the horizontal wellbore temperature and pressure profiles are generally well-fitted. The inverted formation permeability distribution is close to the true value, and the interpretation of the horizontal well production profile is also relatively accurate, which can effectively identify the locations of multi-stage water production.

[0264] In addition, this method is also applicable to identifying the formation permeability distribution along the horizontal wellbore, even if only single-phase oil is produced. For the permeability distribution caused by different heterogeneities, the formation permeability distribution obtained by inversion is consistent with the true value trend, and the inverted production profile can reflect the difference in liquid production contribution in different permeability areas (such as the attached Figure 14 To the attached Figure 16 The corresponding wellbore pressure derivative and temperature derivative curves also show different changing trends. According to their changing trends, the formation permeability distribution characteristics can be inverted or reflected.

[0265] Practical application verification

[0266] The method of the present invention has been applied and verified in an actual horizontal well in a certain oil field. The horizontal section of the well is 960m long and is completed with a liner. The wellbore trajectory has fluctuations. By collecting the DTS temperature and pressure data of the well (see attached Figure 17 ), the inversion interpretation is performed using the method of the present invention to obtain the formation permeability distribution along the wellbore (see Appendix Figure 18 ) and output profiles (see Appendix Figure 19 The inversion-derived production profile was compared with the flow rate data measured by conventional production logging. The results showed that the trends and values of the two were relatively close (see Appendix Figure 19), especially in the identification of high-yield water sections. The inversion determined that the main water production location is located in the well section 1850m-1930m away from the bottom of the horizontal well, and the water production of this well section accounts for about 85% of the total water production.

[0267] Example 2

[0268] This embodiment provides a horizontal well production profile interpretation device based on distributed optical fiber temperature sensing data and inversion algorithm. Figure 4 , the device may include: a processor; a memory; wherein the memory stores a computer program; when the computer program is executed by the processor, it implements the horizontal well production profile interpretation method based on DTS data and inversion algorithm as described in Example 1. The computer program can be stored on the storage medium and executed when running on the processor. Specifically, the computer program can instruct the processor to perform the following operations: obtain distributed optical fiber temperature sensing data collected along the horizontal well, which may include measured wellbore temperature profile and / or measured wellbore pressure profile; use the model parameters and algorithm program stored in the memory to establish a multiphase flow horizontal well temperature profile prediction composite model considering micro-thermal effect and formation damage as a forward model; establish an inversion model based on the forward model and a preset inversion algorithm (such as MCMC or LM), the algorithm program is also stored in the memory; by executing the inversion model program, to The formation permeability distribution is used as the parameter identification target, and an objective function of reducing the difference between the measured wellbore temperature profile and / or the measured wellbore pressure profile obtained by using the distributed optical fiber temperature sensing data and the predicted wellbore temperature profile and / or the predicted wellbore pressure profile calculated by the forward model is used as the optimization target, and an iterative inversion calculation is performed; based on the results of the iterative inversion calculation, the formation permeability distribution and production profile of the horizontal well are obtained, and the results are stored in a memory, and finally the water output position is determined according to the production profile and output (for example, displayed on a user interface or generated as a report).

[0269] The processor may be a central processing unit (CPU), a graphics processing unit (GPU), or any other hardware capable of executing a computer program. The memory may be a random access memory (RAM), a read-only memory (ROM), a hard disk drive (HDD), a solid-state drive (SSD), or any other type of non-transitory storage medium.

[0270] 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 interpreting horizontal well production profiles based on DTS data and inversion algorithms, characterized in that: The method comprises the following steps: acquiring distributed optical fiber temperature sensing data collected along the horizontal well; establishing a multiphase flow horizontal well temperature profile prediction composite model taking into account microthermal effects and formation damage as the forward model; and establishing the inversion model based on the forward model and an inversion algorithm. Through the inversion model, the formation permeability distribution along the horizontal well is used as a parameter to identify the target, and an objective function of reducing the difference between the measured wellbore temperature profile and / or measured wellbore pressure profile obtained using the distributed optical fiber temperature sensing data and the predicted wellbore temperature profile and / or predicted wellbore pressure profile calculated by the forward model is used as the optimization target, and an iterative inversion calculation is performed; based on the results of the iterative inversion calculation, the formation permeability distribution and production profile of the horizontal well are obtained, and the water production position is determined based on the production profile.

2. The method according to claim 1, characterized in that The reservoir thermal model and the wellbore thermal model in the composite model both further consider the influence of the microthermal effect.

3. The method according to claim 2, characterized in that The compatible model further considers the influence of formation damage, and in the consideration of the influence of formation damage, includes simultaneously solving the fluid flow from the reservoir to the formation damage zone and the fluid flow from the formation damage zone to the wellbore.

4. The method according to claim 3, characterized in that The composite model further includes thermodynamically coupling the reservoir model and the wellbore model to calculate temperature distribution.

5. The method according to claim 4, characterized in that The micro thermal effect is selected from at least one of thermal expansion effect, thermal conduction effect, thermal convection effect or viscous dissipation effect.

6. The method according to claim 4, characterized in that The inversion algorithm is at least one of a Levenberg-Marquardt method or a Markov Chain Monte Carlo method.

7. The method according to claim 6, characterized in that The inversion algorithm is a Markov chain Monte Carlo method, which performs a random search on the formation permeability parameter space to avoid iterative inversion calculation from falling into a local optimal solution.

8. The method according to claim 1, characterized in that When the distributed optical fiber temperature sensing data further includes a measured wellbore pressure profile, the objective function is further based on reducing the difference between the measured wellbore pressure profile and the predicted wellbore pressure profile calculated by the forward model, and different weights are set for the difference term related to the measured wellbore temperature profile and the difference term related to the measured wellbore pressure profile.

9. The method according to claim 1, characterized in that The method further includes: based on the composite model, analyzing the influence of at least one factor among the inflow fluid type, formation permeability, water content, wellbore trajectory or completion method on temperature distribution, and obtaining an interpretation chart of the relationship between water outlet position and temperature distribution.

10. A horizontal well production profile interpretation device based on distributed optical fiber temperature sensing data and inversion algorithm, characterized in that: The method comprises a processor and a memory; wherein the memory stores a computer program; and when the computer program is executed by the processor, the method for interpreting a horizontal well production profile based on DTS data and an inversion algorithm as claimed in claim 1 is implemented.

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