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Annular Pressure Loss, ) Frictional pressure loss calculations in narrow annuli of slim-hole and coiled tubing operations require more accuracy than before. For higher drilling fluid flow rates, the annular pressure loss first decreases and then it increases. Experimental Download scientific diagram | Calculation of pressure loss in the annulus and ECD. What Does Annular Pressure Mean? Annular pressure is the pressure that builds up in the spaces between the drill string and the external casing or borehole wall. Two pipe and one concentric annular test sections were considered for this investigation. Experimental In this paper, the flow field characteristics and the annular pressure loss in the coupling movement between the Flow experiments with polymer-based fluids were carried out using the Dynamic Testing Facility. It refers to the pressure drop that occurs as fluids move through the annular space between the drill Learn the fundamentals of annulus pressure in well completion, its importance, and how to manage it effectively for optimal well performance. Jin et al. Based on these review, a new general correlation is . What to do, A new prediction method for the frictional pressure drop in annular two-phase flow is presented. In In oil and gas drilling operations, predictions of pressure losses and cuttings concentration in the annulus are very complex due to the A larger rate of penetration contributes to an increased annular pressure loss. ) d 1 d1 : Outer This study focused on the modelling of the pressure losses in the annulus and Equivalent Circulating Density (ECD) at low shear rate yield API RP 90 provides guidelines for managing annular casing pressure in offshore wells to determine if the pressure poses an unacceptable risk. The annulus pressure changes can occur by one of the following mechanisms: thermal expansion of the This thesis studies the correlation between various causes and corresponding changes in annular pressure loss of drilling fluid, using response in stand pipe The document provides data on annular pressure loss from drilling including mud weight, length, flow rate, pipe diameter, pressure difference, velocity, and Pressure loss caused by the flow of fluid up the annulus (also referred to as annular friction loss). It is similar in scope and Model description: This model of component calculates the major head loss (pressure drop) of a horizontal straight pipe of annular and constant cross-section. The analysis details the physical principle for generation of a direct stiffness in these mechanical components. from publication: Dependence of the Equivalent Circulation Density of Formate Monitoring downhole annular pressure during drilling operations can significantly enhance drilling performance and safety by providing critical real-time data on Experiments and unsteady numerical simulation conducted show that the total pressure loss reduction caused by the delayed boundary layer separation exceed the vortex-induced Drill cuttings accumulate in the wellbore during drilling and form a cutting bed,which results in the increase of annulus pressure loss. Input these values into the Annular pressure loss is a concept most often encountered in the oil and gas industry, especially in drilling operations. This would be similar to a shaft running in a bushing with fluid as Experimental results show that annulus pressure loss does not always rise with the increase in the flow rate in extended reach wells and Controlling the annular frictional pressure losses is important in order to drill safely with overpressure without fracturing the formation. This document contains an annular pressure loss calculation for a drill string operating at 30 GPM. It was developed Calculating pressure losses in a pipe (Fluid Dynamics with Olivier Cleynen) Pressure and Flow in a Hydraulic System and Their Basic Relationship Subsea wells use annular-pressure-buildup (APB) mitigation devices to ensure well integrity. To predict these pressure losses, however, is not Potential Issues with Annular Pressure: Pressure Buildup: Uncontrolled pressure build-up in the annular space can lead to wellbore instability, cementing issues, and potential well control problems. Calculating annular pressure losses is essential in wellbore engineering to ensure safe and efficient drilling operations. Among the various factors that need careful Trapped annular pressure is caused by thermal expansion due to heat transfer and has become one of the serious challenges to well safety. This loss is mainly due to frictional Calculate annular pressure loss from flow rate, geometry, fluid properties and roughness, with pressure gradient, velocity, Reynolds number and ECD. , 2014 all studied the theoretical calculation of annular pressure and annular temperature, which each then used to propose a series of predictive analysis A new prediction method for the frictional pressure drop in annular two-phase flow is presented. The present study investigates the effects of The topic of annular frictional pressure loss modeling has been a challenge in drilling engineering. In such systems, pressure loss due to friction between the Therefore, in this study, an annular drilling fluid flow model is established by using numerical simulation technology. 13 Annular pressure management 13. , 2013, Huang et al. In all these applications, it is often required to predict the frictional pressure gradient to sustain a fixed flow rate or vice versa. Sustained annulus pressure is an increasingly common well integrity issue encountered particularly in aging platforms. Monitoring of the annulus pressure during injection ensures the well integrity. The annular pressure The wear rings are annular flow path provided in pumps, which offer significant resistance to the leakage flow. In this work, a three layer feed-forward neural network For arbitrary temporal distributions of the flow, the inverse Laplace transform of the relation between pressure loss and flow velocity has to be derived. Managed pressure drilling (MPD) as a drilling system is the product of elevated cost of Non Productive Time (NPT) caused by the closeness The calculated total pressure loss and airflow distribution data presented in this re port for the annular combustor agreed quite well with comparable calculated data from a previous report on the tubular Each question is based on the strokes, pump rate, drill pipe and casing gauge readings at a specific point in time during a well kill operation. The use of core-annular flow pattern, where a thin fluid surrounds a very viscous one, has been suggested as an attractive artificial lifting method for heavy oils in the current Brazilian On the basis of conventional annular pressure loss model, this paper establishes a modified model of single-phase annular pressure loss which is suitable for slim hole considering the correction factors Annular pressure losses have received substantial attention in theoretical analyses, laboratory assessment and actual well measurements. The lecture details the physical principle for generation of a direct stiffness in annular Request PDF | Frictional pressure loss of drilling fluids in a fully eccentric annulus | It is common practice when drilling oil and gas wells to assume that the drillstring is placed In such systems, accurately predicting the pressure gradient is essential for understanding flow stability, equipment performance, and system design under counter-current conditions. Measurement while Abstract. Understanding and calculating annular pressure loss is crucial for Sustained annular pressure (SAP) is a primary indicator and hazard of wellbore integrity failure, commonly observed in deep oil and gas The obtained results show that in the laminar flow regime, the annular frictional pressure loss in a fully eccentric annulus is considerably less than a concentric annulus, on Abstract: Large difference exists between largesize annular hydraulics and conventional well's. It defines annulus as the space between two concentric circles or rings. To solve problem of large annular pressure loss from insufficient Summary Annular (damper) seals restrict secondary leakage between stages in a centrifugal pump or compressor . Due to its large opening angle the diffuser is susceptible The pressure loss for laminar flow in concentric and eccentric annular annulus is predicted using SVM. Any one or a combination of these readings could indicate Graph of high-pressure gas wells and gas storage wells These available researches are helpful in determining the sources of annular pressure, Formulas and Calculations: Bottomhole annulus pressure Bottomhole annulus pressure Input (s) ρ a ρa: Annulus Fluid Density (ppg) D a v Dav: Vertical Height in the Annulus (ft) Output (s) P b h Pbh: In high-temperature wells, annular pressure buildup (APB) caused by temperature increase is a widespread phenomenon in production, The American Petroleum Institute (API) has recently updated its safety standard for measuring annular casing pressure at offshore energy facilities, publishing the 2nd Edition of Recommended Practice Increase of production rate and decrease of bottom pressure can be considered as potential measures to reduce the rising rate and maximum sustained annular pressure under both Such measures have been shown to decrease total pressure losses as well. Excess pressure Consequently, the annular frictional pressure loss is increased even though the drilling fluid becomes thinner because of added shear rate. Therefore, an accurate The management of annulus pressure becomes more significant as the industry develops deeper, hotter, and more complex subsea wells. Annular pressure loss, abbreviated as AP, is the reduction in pressure that occurs when fluid flows through the annulus, the space between two concentric cylindrical objects, such as the drill string To reduce the threat of trapped annular pressure on deepwater wells safe production, this study established a model of calculating trapped annular pressure, examined the The total pressure loss is an equally important diffuser design parameter. We define annular pressure loss or APL as the pressure lost while circulating drilling mud in the annulus. , mud loss height) can be expressed in terms of the volume of the low-density fluid pumped to balance Effective management of annulus pressure is essential to ensure the integrity and performance of the well. This new prediction method focuses on the Pressure loss calculations for an annulus flow path require some extra steps to complete, since the standard cylindrical tube model cannot be directly applied. The annular frictional performance of non-Newtonian fluids is among the major considerations during development of hydraulic programs for drilling operations. It is strongly linked to the pressure recovery and the residual kinetic In this study the pressure-drop, mean and rms axial velocity data are measured using a differential pressure transducer and a laser Doppler anemometer for the flow of Newtonian and non-Newtonian Ensuring well integrity throughout a well’s lifecycle is essential for maintaining safe and efficient operations in the oil and gas industry. These problems are exasperated if the primary cement job was The sustained casing pressure on developed wells induce stresses that transmits to the annular cement sheaths intended to isolate from formation fluids. Discover how annular casing pressure (ACP) monitoring supports well integrity and safer operations throughout the well lifecycle. Monitoring annulus pressures is During oil and gas drilling operations, frictional pressure loss is experienced as the drilling fluid transports the drilled cuttings from the bottom Download Citation | Experimental Study of Slimhole Annular Pressure Loss and Its Field Applications | Large difference exists between slimhole annular hydraulics and conventional By analyzing the properties of Wells with high sulfur content and high temperature and pressure, this paper studies the mechanism of causing annular zoning pressure, and puts forward the safety 1) Pressure drop through an eccentric annulus is significantly less than pressure drop through perfectly centered (100% standoff) geometry, while cross-sectional area remains constant. This guide provides a clear, step-by-step process to determine 1. This new prediction method focuses on the aerodynamic This document is meant to be used for existing ofshore wells that exhibit annular casing pressure, including thermally induced casing pressure, sustained casing pressure (SCP) and operator-imposed Friction pressure losses in annular space during tripping and casings operations can cause an increase in mud weight while moving pipe downward into the fluid column (surge pressures) and a decrease The pressure loss changes in non-Newtonian fluids through annulus are attributed to shear-thinning, inertial effects and formation of Abstract. A comparative study between model-calculated and PWD-measured values of APL for 15 points along Drilling Fluids – Frictional Pressure Loss Formulas Flow rate, flow regime, rheological properties, and conduit geometry are among the key In order to have a better control over the drilling process and reduce the overall cost of this drilling operation, engineers have tried to use soft computing (SC) techniques to conduct the Packer or cement seal If the open lap is cemented sealed with cement or covered with mud or other fluid loss control material, the ability is lost to bleed off the pressure and the outside annulus becomes a Estimation of pressure losses and deposition velocities is vital in the hydraulic design of annular drill holes in the petroleum industry. Methods for Monitoring Annulus Pressure There are several methods for Annular Friction Loss → Excessive pressure drop in the annulus indicates poor hole cleaning. In Simulation results indicate that drillstring rotation speed, annular gap, and eccentricity greatly influence flow field and pressure losses at drillstring joints. Pressure required to break circulation - Annulus Input (s) y: Gel strength of drilling fluid (l b / 100 f t 2) (lb/100ft2) L L: Length of Drill String (f t) (ft) Dh: Diameter of hole (in. The first linear model involves the reduction in pressure drop in the drill collar-casing annulus and the second linear model involves the reduction in pressure drop in the drill pipe-casing annulus. e. The annular pressure loss would increase with The annular pressure loss would increase with the decrease of the annular gap and eccentricity but decrease with the increase of the Based on evaluating the calculation model of power-law fluid pressure in eccentric annulus, the constitutive equation of the four-parameter rheological model is extended, and the Existing predictive methods are also limited because gas dissolution, transient annular flow, and managed pressure drilling (MPD) pressure control are often treated separately. Check out my back of the napkin note below for Annulus pressure loss due to friction during hydraulic fracturing (laminar flow) Input (s) v: Average Velocity (f t / s) (ft/s) L: Pipe Length (ft) d 0 d0 : Inner Diameter of the Outer Pipe (in. In addition, the flow is assumed fully Model description: This model of component calculates the major head loss (pressure drop) of a horizontal straight pipe of annular and constant cross-section. Using numerical simulation, this article analyze annular Hello, I was looking for an equation to calculate flow and pressure loss in an annulus. It is regarded as a loss because the pressure is applied at If cementitious barriers become compromised, integrity issues proliferate and transmit downhole pressures to the surface. In this paper, we show that the benefit of total pressure loss re- duction in vortex-stabilised diffusers becomes more pronounced Predicting the pressure behavior of annular fluids during production and injection operations in oil wells became a major research topic in the exploration of deep-water reservoirs. Historically, drilling engineers have encountered considerable difficulties estimating annular pressure losses in a well annulus for drilling operations. The To address the risk of annular pressure relief channel blockage caused by solid deposition in the B and C annulus of deepwater wells, Annular Pressure Loss Calculations In Drilling - DRILLING MANUAL | #drilling_manual Pressure loss is a crucial factor in the drilling process. Cuttings bed building? Your annular pressure will show it before the pack-off does. It provides mud weight, length, flow rate, pipe diameters, and velocity to determine that the Deepwater oil and gas wells have complex well body structure, and the multi-layer closed annulus structure formed by free section and sealed section tubing column is easy to absorb An important characteristic of managed pressure drilling (MPD) technology is use of a closed, pressurizable mud returns system that provides the ability to drill ahead and make jointed-pipe con This paper uses experimental and numerical simulation methods to study the frictional pressure drop in the annular space under actual rough wellbore conditions. This guide provides a clear, step-by-step process to determine This approximate calculation gives an idea of annular pressure loss, however this should just be used as a guide as it ignores variables such as, length of BHA, washouts in the open hole and solids loading What is Annular Pressure Loss? Annular pressure loss refers to the pressure drop that occurs in the annular space between two concentric cylinders, such as in a wellbore during drilling operations. 5 inches, pressure difference of 4 Optimal Annular Frictional Loss Modelling In Constant Bottom Hole Pressure Variant of Managed Pressure Drilling John Lander Ichenwo Department of Petroleum & Gas Engineering, University of The mam purpose of th1S paper is to shed the light on the effect of these parameters on annular pressure loss and equivalent circulation densities during drilling with Incompressible drilling fluids. In order to assess and mitigate this risk, Annular pressure losses are a critical factor in drilling operations, affecting wellbore stability and safety. In that case, the length of the annulus (i. One of the major concerns in developing 环空压力损失计算是流体动力学中的一个关键过程,特别是在钻井作业和管道流动分析中。了解流速、摩擦系数和压力损失之间的关系,能够让工程师设计出更高效的系统,并防止可 In the past years, a number of wellbore hydraulic studies have been conducted to predict the annular pressure losses. ) Dp: Diameter of drill pipe (in. from publication: A mechanistic model for minimizing pressure loss in the wellbore Simulation results indicate that drillstring rotation speed, annular gap, and eccentricity greatly in uence ow eld fl fl fi and pressure losses at drillstring joints. During the process of natural gas development, sustained casing pressure (SCP) frequently occurs within the annulus of the gas wells; we Annulus Pressure Management refers to an engineered approach ensuring that casing annulus pressures do not challenge the well’s The sustained casing pressure on developed wells induce stresses that transmits to the annular cement sheaths intended to isolate from formation fluids. Annuli pressure if not controlled and managed may result in uncontrolled release of high-pressure hydrocarbon fluids from reservoir to the surface. It is easy to form belly shaped arc Introduction to Annular Pressure In the world of petroleum engineering and drilling, maintaining control over the wellbore is crucial. The momentum equation in axial direction is solved in the Laplace domain to On the basis of conventional annular pressure loss model, this paper establishes a modified model of single-phase annular pressure loss which is suitable for slim hole considering the In oil and gas drilling operations, predictions of pressure losses and cuttings concentration in the annulus are very complex due to the A larger rate of penetration contributes to an increased annular pressure loss. In addition, the flow is assumed fully The exact calculation and control for cementing annulus flow pressure is very important, especially for formations with narrow density windows. 4. We define mitigation techniques that control APB by reducing lateral heat loss from the In order to analyze the effect of changes in the casing-free section and the sealed section on the variation in annulus volume, a new annular Circulating pressure created by friction when fluid moves in the annulus between the drillstring and casing or openhole. This article provides insights into its management and reCAPTCHA v3 Verification The document provides data on annular pressure loss from drilling including mud weight of 13 ppg, a length of 8000 feet, a flow rate of 320 GPM, inner diameter of 6. Trapped annular pressure remains a Significant pressure losses occur as the mud flows through the drillpipe and the annulus. This article, written by Dennis Denney, contains highlights of paper SPE 166103, ’Evaluation of Annular-Pressure Losses While Casing Drilling,’ by Vahid Dokhani and Mojtaba P. Model description: This model of component calculates the major head loss (pressure drop) of a horizontal straight pipe of annular and constant cross-section. February 24, 2021 Annular Pressure While Drilling – What is it good for? Managing equivalent circulating density (ECD) is one the key success factors in extended February 24, 2021 Annular Pressure While Drilling – What is it good for? Managing equivalent circulating density (ECD) is one the key success factors in extended While improvements in fully automated annular pressure control systems are continually being made, allowance for disruption in the operation must still be made. 1 Any change of annulus pressure, increase or decrease, can be indicative Introduction to the problem of unsteady pressure loss What is an annular channel? An annular channel is created by mounting a cylinder within a pipe: Key design parameter: radius ratio = Radius ratio In this paper, the flow field characteristics and the annular pressure loss in the coupling movement between the Flow experiments with polymer-based fluids were carried out using the Dynamic Testing Facility. Experimental In drilling a deepwater well, the mud density window is narrow, which needs a precise pressure control to drill the well to its designed depth. Annular pressure loss, abbreviated as AP, is the reduction in pressure that occurs when fluid flows through the annulus, the space between two concentric cylindrical objects, such as the drill string Assess the length of the annulus where the fluid is flowing, as this directly impacts the frictional pressure drop. When This pressure loss is influenced by factors such as the flow rate of the drilling fluid, the friction factor, and the geometry of the annular space. Since finding the inverse Laplace transform of the This paper focuses on the total pressure losses in the boundary layer of a highly loaded annular diffuser. ABSTRACT The lecture introduces annular seals and hydrostatic bearings in liquid pumps. Fares (2018). Annular Pressure Loss Calculations In Drilling - DRILLING MANUAL | #drilling_manual Pressure loss is a crucial factor in the drilling process. Deepwater oil and gas wells are under the influence of high-temperature formation fluid after put into production, so that the shaft Deepwater oil and gas wells are under the influence of high-temperature formation fluid after put into production, so that the shaft This guide is meant to be used for offshore wells that exhibit annular casing pressure, including thermal casing pressure, sustained casing pressure (SCP) and operator- imposed pressure. It refers Monitoring annular pressure while drilling is one of important subjects to avoid drilling problems, such as pack off, formation fracture and hole cleaning issues. Macroscopic flow characteristics of annulus channels are studied more extensively in engineering practice. Understanding and calculating annular pressure loss is crucial for Predicting pressure loss and flow regimes in complex air-water-oil three-phase flows through pipe directional changes, such as 90° elbows, poses a significant challenge for industrial pipeline syst The Annular Pressure Loss Calculator is a critical tool in the petroleum engineering and drilling industry. The Estimation of pressure losses and deposition velocities is vital in the hydraulic design of annular drill holes in the petroleum industry. The issue is normally discovered via periodic wellhead Scope of RP 90 Guideline for managing annular casing pressure in offshore wells Modeled after GOM OCS wells, but applicable to similar type wells worldwide Performance and risk based methodology For the “three-high” gas wells in Sichuan Basin which are often regulated for production rate and shut-in for maintenance, annular pressure by temperature effect is a kind of Request PDF | The Hydraulic Effect of Tool-Joint on Annular Pressure Loss | For a successful drilling operation, downhole pressure or equivalent circulating density (ECD) control is Pressure loss calculations have a vital role for determining hydraulic horsepower requirements and to predict bottomhole treating pressure. It measures surface equipment pressure losses of 65 psi Reservoir Engineering Formulas Pressure Loss in Annulus (ΔP) Looking for essential reservoir engineering formulas? Access our comprehensive collection of equations with clear explanations and In oil and gas drilling operations, predictions of pressure losses and cuttings concentration in the annulus are very complex due to the This document calculates annular pressure loss for a drilling operation. Flow experiments with polymer-based fluids were carried out using the Dynamic Testing Facility. Com-pared to their effect on the drilling uid density, cuttings have a greater Laminar flow through an annulus occurs when a fluid flows through a circular pipe with an annular space between the pipe and an inner cylinder. It measures surface equipment pressure losses of 65 psi Reservoir Engineering Formulas Pressure Loss in Annulus (ΔP) Looking for essential reservoir engineering formulas? Access our comprehensive collection of equations with clear explanations and This document contains an annular pressure loss calculation for a drill string operating at 30 GPM. The pressure loss in annulus is composed of inlet loss at the entrance The main purpose of this paper is to shed the light on the effect of these parameters on annular pressure loss and equivalent circulation Flow path = annulus; Pressure source = tubing The underlying logic for pressure-drop calculations is essentially the same for both multilayer and single-layer wells. This document provides guidance for managing annular casing pressure in o昀shore wells of various types to ensure that well integrity is maintained, and risks are managed. The BHP, which is a critical parameter in any drilling operation, is a function of the Le calcul de la perte de charge annulaire est un processus crucial en dynamique des fluides, notamment dans les opérations de forage et l'analyse des écoulement an annular die, and the flow in double-pipe heat exchangers. This paper presents a In the present work, a computational fluid dynamic simulation has been performed to investigate core annular flow through sudden contraction and expan This document provides a formula and example calculation for determining annular pressure loss. Estimating friction pressure This pressure loss is influenced by factors such as the flow rate of the drilling fluid, the friction factor, and the geometry of the annular space. This phenomenon Learn the fundamentals of annulus pressure, its importance in well control, and strategies for effective management to ensure safe and efficient drilling operations. The paper describes a method to calculate pressure Combinations of casing motion, annular eccentricities, wall roughness and fluid temperatures along the length of the annulus affect fluid flow te the Annular Pressure Loss (APL) on a deep well with polymer Water-Base Mud (WBM). In addition, the flow is assumed fully The Annulus Pressure Buildup (APB) problems in shale gas wells is mainly caused by the crack at casing-cement interface. The stresses on casing-cement It is necessary to carry out analysis of annulus flow pressure drop loss in coiled tubing annular with the methods of theoretical analysis and numerical simulation. Pressure loss calculations for an annulus flow path require some extra steps to complete, since the standard cylindrical tube model cannot be directly applied. 4 Annulus pressure monitoring and testing 13. These Annular pressure loss is a critical factor in the drilling and production of deep wells. In this section, the Simulation results indicate that drillstring rotation speed, annular gap, and eccentricity greatly influence flow field and pressure losses at Annular pressure buildup (APB) is induced by high-temperature tubing fluid heating the trapped annular fluid, which leads to liquid Annular pressure buildup (APB) is induced by high-temperature tubing fluid heating the trapped annular fluid, which leads to liquid #drillingengineering #iwcf #iadc #petroleumengineering #petrobarrel In this video you will know what is the ECD in drilling engineering and APL. It is designed to estimate the The paper presents a methodology for calculating the pressure loss in unsteady flows through concentric annular channels. The predicted values for the training This study aims to develop correction factors for determining the frictional pressure losses accurately in eccentric horizontal annulus for non The results show that fl an increased concentration of cuttings in the annulus contributes to an increased annular pressure loss. I have found very limited information on the web, but from what I've found the pressure drop is different than that This document discusses annulus pressure management. Introduction Predictions of pressure losses and cuttings concentration in annular wells are strongly afected by varying drilling parameters such as fluid velocity, fluid properties (density, viscosity), Annular-Pressure Losses While Casing Drilling Casing drilling is a method by which the well is drilled and cased simultaneously. Proper estimation of ECD is influenced by both hole section length and flow rate amongst other factors which contribute to the annular pressure loss (APL). The effects of drillpipe rotation speed, borehole geometry, and This pressure is necessary to overcome the Read more The post Annular Pressure Loss Calculations In Drilling appeared first on DRILLING MANUAL. Combinations of casing motion, Download scientific diagram | Effect of the flow rate on annulus pressure loss. Anyone have a formula for pressure drop through an annular ring. The formula uses mud weight, length of annular, annular velocity, hole inner diameter, and drill pipe outer This paper presents a review of correlations used for pressure drop calculation in narrow annular clearances with rotation of inner cylinder. It refers Calculating annular pressure losses is essential in wellbore engineering to ensure safe and efficient drilling operations. This may cause loss of life, Discover the significance of annulus pressure in maintaining well control and ensuring the safety of drilling operations. Understanding how these losses occur and how to calculate them helps This means the efficiency of the CBHP-MPD is determined by the accuracy of the applied Surface Back Pressure, SBP which is just a reflective of the accuracy of the frictional loss estimation. Effective Annular pressure monitoring and testing can improve well safety by detecting problems before they threaten people or the environment. To be able to select drilling fluids with proper chemical composition to avoid un Finally, considering the influence of drill string eccentricity and drill string joint on the annulus pressure loss of slim hole, a model of annulus pressure loss is suitable for slim hole.