Numerical Study on Lost Circulation Mechanism in Complex Fracture Network Coupled Wellbore and Its Application in Lost-Circulation Zone Diagnosis

Abstract

Deep and ultra-deep drilling operations commonly encounter fractured and fracture-vuggy formations, where weak wellbore strength and well-developed fracture networks lead to frequent lost circulation, presenting a key challenge to safe and efficient drilling. Existing diagnostic practices mostly rely on drilling fluid loss dynamic models of single fractures or simplified discrete fractures to invert fracture geometry, which cannot capture the spatiotemporal evolution of loss in complex fracture networks, resulting in limited inversion accuracy and a lack of quantitative, fracture-network-based loss-dynamics support for bridge-plugging design. In this study, a geologically realistic wellbore–fracture-network coupled loss dynamic model is constructed to overcome the limitations of single- or simplified-fracture descriptions. Within a unified computational fluid dynamics (CFD) framework, solid–liquid two-phase flow and Herschel–Bulkley rheology are incorporated to quantitatively characterise fracture connectivity. This approach reveals how instantaneous and steady losses are controlled by key geometrical factors, thereby providing a computable physical basis for loss-zone inversion and bridge-plugging design. Validation against experiments shows a maximum relative error of 7.26% in pressure and loss rate, indicating that the model can reasonably reproduce actual loss behaviour. Different encounter positions and node types lead to systematic variations in loss intensity and flow partitioning. Compared with a single fracture, a fracture network significantly amplifies loss intensity through branch-induced capacity enhancement, superposition of shortest paths, and shortening of loss paths. In a typical network, the shortest path accounts for only about 20% of the total length, but contributes 40–55% of the total loss, while extending branch length from 300 mm to 1500 mm reduces the steady loss rate by 40–60%. Correlation analysis shows that the instantaneous loss rate is mainly controlled by the maximum width and height of fractures connected to the wellbore, whereas the steady loss rate has a correlation coefficient of about 0.7 with minimum width and effective path length, and decreases monotonically with the number of connected fractures under a fixed total width, indicating that the shortest path and bottleneck width are the key geometrical factors governing long-term loss in complex fracture networks. This work refines the understanding of fractured-loss dynamics and proposes the concept of coupling hydraulic deviation codes with deep learning to build a mapping model from mud-logging curves to fracture geometrical parameters, thereby providing support for lost-circulation diagnosis and bridge-plugging optimisation in complex fractured formations.

1. Introduction

Deep and ultra-deep drilling operations commonly encounter fractured and fracture-vuggy formations. The wellbore’s pressure-bearing capacity is weak, and fractures develop at multiple scales, so drilling fluid loss occurs frequently and in diverse forms. This has become one of the key challenges restricting safe and efficient drilling. Fracture channels exhibit differences in aperture, roughness, and stress sensitivity over multiple spatial scales, which makes the loss behaviour highly nonlinear; thus, single empirical charts can no longer support accurate diagnosis and loss-control design [1,2,3]. In field practice, bridging and plugging with specially formulated slurries remains the most widely used and economical technology for controlling lost circulation in fractured formations. The material systems have evolved from early single-size solid particles to blended systems of fibres, flaky materials, gels, and adaptive particles, and the plugging mechanism has developed from simple bridging to a multi-stage cooperative process of bridging, filling, and cementing. Previous studies have shown that whether a bridging and plugging slurry can form a stable sealing layer inside the target fractures depends strongly on the understanding and inversion accuracy of fracture geometric parameters, in situ stress conditions, and fluid-dynamic processes [4,5,6]. Therefore, improving the diagnostic accuracy of drilling fluid loss and achieving reliable identification of fracture geometry have become prerequisites for successful bridging and plugging operations and are one of the current research hotspots in both domestic and international communities.

For the quantitative characterisation of drilling fluid loss in fractured formations, many studies have developed drilling fluid loss dynamic models under different assumptions. The cubic law for non-parallel fractures and a yield–power-law rheological equation were used, and a transient drilling fluid loss model for a single fracture was built, which revealed the combined effects of pressure differential, fracture width, and rheological parameters on the loss-rate evolution curves, providing a basis for inverting fracture aperture from these curves [7,8]. CFD was applied to solve the three-dimensional flow field of a non-Newtonian fluid in rough fractures, achieving coupled analysis of the instantaneous loss rate and pressure drop under a prescribed inlet flow-rate boundary [9]. A drilling fluid loss model for fracture-porous reservoirs in a dual-media flow framework was proposed, which considered wall filtration and fracture closure and could invert both fracture permeability and matrix permeability [10]. A transient analytical solution for mud loss in a fracture set was further derived and used to evaluate the segmental mechanism of complex loss curves in long-reach wells [11]. For deep shale and carbonate formations, the effects of fracture deformation and yield stress on the loss-termination mechanism in polymer drilling fluid systems were studied, and a dynamic model suitable for high-temperature and high-pressure conditions was developed [12]. In recent years, some studies started to couple axial wellbore flow with lateral fracture flow. They built three-dimensional coupled drillstring–wellbore–fracture models and combined these with Spearman correlation analysis or sensitivity analysis. They used the quantitative relationships between instantaneous loss rate, steady-state loss rate and cumulative loss and fracture geometrical parameters for integrated diagnosis of lost-circulation zone location and fracture scale [13,14,15,16,17,18]. These contributions have significantly improved the physical understanding of the loss process and have provided a computable dynamic basis for subsequent intelligent diagnosis and lost-circulation control optimisation.

On the basis of abundant dynamic models and field data, artificial intelligence methods have gradually become an important tool for diagnosing lost-circulation zone information. Artificial neural networks (ANNs) have been used to learn from historical lost-circulation cases, achieving early prediction of the risk level of lost circulation and the volume of loss and providing data support for wellbore design and lost-circulation material pre-planning [19]. Seismic attributes and engineering parameters were input into a gradient boosting tree model, establishing a seismic-engineering integrated framework for lost-circulation probability prediction and significantly improving the identification accuracy of loss-prone intervals at the block scale [20]. XGBoost (Extreme Gradient Boosting) combined with statistical feature selection was applied, 29 loss-related features were mined from 105 wells, and an intelligent prediction model for lost-circulation zones in deep complex formations was built, achieving high-accuracy estimates of lost-circulation depth and loss severity [21]. A Mixture Density Network (MDN) was proposed, in which the loss volume is treated as a probabilistic output, effectively addressing the difficulty of describing multi-modal uncertainty with conventional regression models [22]. CTGAN (Conditional Tabular Generative Adversarial Network) was used to augment imbalanced loss samples, the performance of ANN, LSTM (Long Short-Term Memory), and TCN (Temporal Convolutional Network) time-series networks for loss-state recognition was compared, and an intelligent monitoring workflow suitable for imbalanced samples was proposed [23]. Ensemble learning and multi-model fusion were adopted, enabling lost-circulation severity classification and continuous loss prediction based on well logs and real-time drilling data [24,25]. A hybrid “physical model & deep network” framework was constructed for inverting thief-zone depth and equivalent permeability in fractured reservoirs [26]. XGBoost was used for operating-condition recognition and Particle Swarm Optimisation (PSO)-LSTM to predict bottomhole pressure evolution, achieving joint early warning of kicks and lost-circulation events [27]. Cepstral features of transient pressure waves and the Short-Time-Average/Long-Time-Average (STA/LTA) algorithm were employed, enabling automatic detection of the onset time of lost circulation [28,29]. A machine learning framework for carbonate drilling was developed, in which an MDN is coupled with a physical model to simultaneously predict loss volume and complex downhole conditions, providing a representative example for intelligent diagnosis of lost circulation in deep carbonate wells [30].

Existing studies have developed various drilling fluid loss dynamic models that simultaneously consider fracture deformation, wall filtration, and solid bridging. These models provide a basis for quantitatively describing loss-rate evolution and inverting fracture geometrical parameters. However, most of them still focus on a single fracture or simplified discrete fractures. Consequently, they cannot realistically represent loss behaviour within complex fracture networks that exhibit multi-scale and multi-topology features. At the same time, a wide range of machine-learning and deep-learning methods have achieved significant progress in predicting lost-circulation zone location, loss severity, and plugging risk, yet these models usually take field drilling and logging parameters as inputs, which are jointly affected by mud density, flow rate, well deviation, hole size, and other factors, and are easily masked by strong signals and noise, leading to missed detections, misclassifications, and poor interpretability under complex conditions. To address these two limitations, this study develops a wellbore–fracture network coupled loss dynamic model that incorporates solid–liquid two-phase flow and Herschel–Bulkley rheology. Based on graph theory, fracture networks are reconstructed with realistic geological statistical characteristics. Through parametric numerical experiments, the study systematically reveals the controlling mechanisms of the shortest flow path and bottleneck width on loss behaviour. Furthermore, an intelligent diagnosis framework combining hydraulic deviation fingerprints with deep learning is proposed, aiming to achieve reliable mapping between complex fracture-network geometrical parameters and field mud-logging responses.

2. CFD Modelling

The flow of drilling fluid in the wellbore–fracture coupled system is a typical solid–liquid two-phase flow. In the drilling fluid loss model for fractures coupled with the wellbore, no mass transfer occurs between the solid and liquid phases in the drilling fluid, and the mass of each phase remains constant [31]. The mass conservation equation for the solid phase is

$${\displaystyle \frac{\mathsf{\partial }}{\mathsf{\partial }t}}\left({\mathsf{\epsilon }}_s{\mathsf{\rho }}_s\right)+\nabla \cdot \left({\mathsf{\epsilon }}_s{\mathsf{\rho }}_s{\mathit{v}}_s\right)=0$$

(1)

where ${\mathsf{\epsilon }}_s$ is the volume fraction of the solid phase, %; ${\mathsf{\rho }}_s$ is the density of the solid phase, g/cm³; and ${\mathit{v}}_s$ is the velocity of the solid phase in the drilling fluid, m/s.

In practical applications, drilling fluids typically exhibit good suspension stability and dispersion, which means that solid particles generally do not experience a significant relative slip with the liquid phase during flow. Therefore, based on these practical conditions, it is assumed that the relative velocity between the solid and liquid phases is zero, particularly under the multiphase flow conditions considered in this study. Therefore, the mass conservation equation for the solid phase can be simplified as follows:

$${\displaystyle \frac{\mathsf{\partial }}{\mathsf{\partial }t}}\left({\mathsf{\epsilon }}_s{\mathsf{\rho }}_s\right)=0$$

(2)

Given that the study focuses on deep formations with low porosity, poor permeability, and high density, the contribution of fracture wall fluid loss is relatively minor under these geological conditions. It is unlikely to significantly alter the primary controlling factors of lost circulation behaviour. Therefore, this effect was neglected in the present model. The mass conservation equation for the liquid phase is given by

$${\displaystyle \frac{\mathsf{\partial }}{\mathsf{\partial }t}}\left({\mathsf{\epsilon }}_l{\mathsf{\rho }}_l\right)+\nabla \cdot \left({\mathsf{\epsilon }}_l{\mathsf{\rho }}_l{\mathit{v}}_l\right)=0$$

(3)

where ${\mathsf{\epsilon }}_l$ is the volume fraction of the liquid phase, %; ${\mathsf{\rho }}_l$ is the density of the liquid phase, g/cm³; and ${\mathit{v}}_l$ is the velocity of the liquid phase, m/s.

The volume fractions of the solid and liquid phases in the drilling fluid satisfy the following condition:

$${\mathsf{\epsilon }}_l+{\mathsf{\epsilon }}_s=1$$

(4)

The momentum conservation equations describe the governing equations for the interaction between the solid and liquid phases. For the solid phase, the momentum conservation equation is given by

$${\displaystyle \frac{\mathsf{\partial }}{\mathsf{\partial }t}}\left({\mathsf{\epsilon }}_s{\mathsf{\rho }}_s{\mathit{v}}_s\right)+\nabla \cdot \left({\mathsf{\epsilon }}_s{\mathsf{\rho }}_s{\mathit{v}}_s{\mathit{v}}_s\right)=-{\mathsf{\epsilon }}_s\nabla p_l+{\mathsf{\epsilon }}_s{\mathsf{\rho }}_s\mathit{g}+\nabla \cdot {\mathsf{\tau }}_s+{\mathit{F}}_{ip,s}$$

(5)

where ${\mathsf{\tau }}_s$ denotes the stress tensor of the solid phase, Pa, and ${\mathit{F}}_{ip,s}$ denotes the interphase momentum exchange acting on the solid phase.

For the liquid phase, the momentum conservation equation is given by

$${\displaystyle \frac{\mathsf{\partial }}{\mathsf{\partial }t}}\left({\mathsf{\epsilon }}_l{\mathsf{\rho }}_l{\mathit{u}}_l\right)+\nabla \cdot \left({\mathsf{\epsilon }}_l{\mathsf{\rho }}_l{\mathit{u}}_l{\mathit{u}}_l\right)=-{\mathsf{\epsilon }}_l\nabla p_l+{\mathsf{\epsilon }}_l{\mathsf{\rho }}_l\mathit{g}+\nabla \cdot {\mathsf{\tau }}_l+{\mathit{F}}_{ip,l}$$

(6)

where $p_l$ is the pressure of the liquid phase, Pa; $\mathit{g}$ is the gravitational acceleration, m/s²; ${\mathsf{\tau }}_l$ is the stress tensor of the liquid phase, Pa; and ${\mathit{F}}_{ip,l}$ is the interphase momentum exchange term acting on the liquid phase.

The stress tensor of the liquid phase is calculated as follows:

$${\mathsf{\tau }}_l={\mathsf{\mu }}_l\left\{\left[\nabla {\mathit{u}}_l+{\left(\nabla {\mathit{u}}_l\right)}^T\right]-{\displaystyle \frac{2}{3}}\left(\nabla \cdot {\mathit{u}}_l\right)\mathbf{I}\right\}$$

(7)

where ${\mathsf{\mu }}_l$ is the viscosity of the fluid phase, given as the sum of the laminar viscosity $\eta$ and the turbulent viscosity ${\mathsf{\mu }}_t$, mPa·s.

The flow of drilling fluid in the wellbore and fractures may be laminar or low-Reynolds-number turbulent. Therefore, for the selection of the turbulence model, this study adopts a low-Reynolds-number corrected $k-\omega$ turbulence model that best reflects the flow behaviour of drilling fluid in the annulus [32]. In this model, the turbulent viscosity ${\mathsf{\mu }}_t$ is given by

$${\mathsf{\mu }}_t={\displaystyle \frac{{\mathsf{\rho }}_1{C}_{\mathsf{\mu }}{k}^2}{{\mathsf{\epsilon }}_k}}$$

(8)

where $C_{\mathsf{\mu }}$ = 0.09, and $k$ and ${\mathsf{\epsilon }}_k$ are the turbulent kinetic energy and the turbulent dissipation rate of the drilling fluid, respectively. The transport equations for the turbulence quantities are expressed as

$${\displaystyle \frac{\mathsf{\partial }}{\mathsf{\partial }t}}\left({\mathsf{\epsilon }}_1{\mathsf{\rho }}_{1}k\right)+\nabla \cdot \left({\mathsf{\epsilon }}_1{\mathsf{\rho }}_1{\mathit{u}}_{1}k\right)=\nabla \cdot \left({\mathsf{\epsilon }}_1{\displaystyle \frac{{\mathsf{\mu }}_t}{{\mathsf{\sigma }}_k}}\nabla \cdot k\right)+{\mathsf{\epsilon }}_1{\mathsf{\tau }}_1\nabla \cdot {\mathit{u}}_1-{\mathsf{\epsilon }}_1{\mathsf{\rho }}_1{\mathsf{\epsilon }}_k$$

(9)

$${\displaystyle \frac{\mathsf{\partial }}{\mathsf{\partial }t}}\left({\mathsf{\epsilon }}_1{\mathsf{\rho }}_1{\mathsf{\epsilon }}_k\right)+\nabla \cdot \left({\mathsf{\epsilon }}_1{\mathsf{\rho }}_1{\mathsf{\epsilon }}_k{\mathit{u}}_1\right)=\nabla \cdot \left({\mathsf{\epsilon }}_1{\displaystyle \frac{{\mathsf{\mu }}_t}{{\mathsf{\sigma }}_{\mathsf{\epsilon }}}}\nabla \cdot {\mathsf{\epsilon }}_k\right)+{\mathsf{\epsilon }}_1{\displaystyle \frac{{\mathsf{\epsilon }}_k}{k}}\left(C_{1\mathsf{\epsilon }}{\mathsf{\tau }}_1\nabla \cdot {\mathit{u}}_1-{\mathsf{\rho }}_1{C}_{2\mathsf{\epsilon }}{\mathsf{\epsilon }}_k\right)$$

(10)

where ${\mathsf{\sigma }}_k$, ${\mathsf{\sigma }}_{\mathsf{\epsilon }}$, $C_{1\mathsf{\epsilon }}$, and $C_{2\mathsf{\epsilon }}$ are empirical constants in the model.

The rheology of drilling fluid is a fundamental indicator for evaluating its performance, and selecting an appropriate rheological behaviour under different field conditions is very important for improving drilling efficiency. In calculations related to drilling fluid loss, the rheology of the drilling fluid needs to be represented by mathematical constitutive equations. At present, three rheological models are widely used in drilling practice, namely the Bingham plastic model, the power-law model, and the Herschel–Bulkley model [33]. A rheological equation is a physical constitutive equation that describes the relationship between shear stress and shear rate. For one-dimensional shear flow, the three rheological equations are expressed as follows:

$$\mathsf{\tau }={\mathsf{\tau }}_y+{\mathsf{\mu }}_p\mathsf{\gamma }$$

(11)

$$\mathsf{\tau }=K{\mathsf{\gamma }}^n$$

(12)

$$\mathsf{\tau }={\mathsf{\tau }}_y+K{\mathsf{\gamma }}^n$$

(13)

where $n$ is the flow behaviour index of the drilling fluid, dimensionless; ${\mathsf{\mu }}_p$ and $K$ are the plastic viscosity and the consistency index of the drilling fluid, Pa·sⁿ; ${\mathsf{\tau }}_y$ is the yield stress of the drilling fluid, Pa; $\mathsf{\gamma }$ is the shear rate of the fluid, s⁻¹; and $\mathsf{\tau }$ is the shear stress, Pa.

For convenience in field applications, drilling fluid engineers usually select the two-parameter Bingham and power-law models to represent drilling fluid behaviour. In most drilling operations, the Bingham model is commonly used, and the plastic viscosity and yield point are obtained by simple linear processing of the data measured with a six-speed rotational viscometer. However, laboratory studies have shown that, compared with the Bingham and power-law models, the three-parameter Herschel–Bulkley model matches the rheological behaviour of drilling fluids more accurately at low, medium, and high shear rates. To perform hydraulic calculations of drilling fluid flow in the wellbore–fracture coupled system more accurately, the rheological model of the drilling fluid in this study is therefore specified as the Herschel–Bulkley model.

The stress tensor of the solid phase is expressed as

$${\mathsf{\tau }}_s=\left(-p_s+{\mathsf{\mu }}_b\nabla \cdot {\mathit{v}}_s\right)\mathbf{I}+{\mathsf{\mu }}_s\left\{\left[\nabla {\mathit{v}}_s+{\left(\nabla {\mathit{v}}_s\right)}^T\right]-{\displaystyle \frac{2}{3}}\left(\nabla \cdot {\mathit{v}}_s\right)\mathbf{I}\right\}$$

(14)

where the pressure $p_s$, shear viscosity ${\mathsf{\mu }}_s$, and bulk viscosity ${\mathsf{\mu }}_b$ of the solid phase are defined, and their expressions are given as follows:

$$p_s={\mathsf{\epsilon }}_s{\mathsf{\rho }}_s{\mathsf{\theta }}_s+2{\mathit{g}}_0{\mathsf{\epsilon }}_s^2\left(1+e\right){\mathsf{\rho }}_s{\mathsf{\theta }}_s$$

(15)

$${\mathsf{\mu }}_s={\displaystyle \frac{4}{5}}{\mathsf{\epsilon }}_s{\mathsf{\rho }}_s\mathit{g}{d}_s\left(1+e\right)\sqrt{{\displaystyle \frac{{\mathsf{\theta }}_s}{\pi }}}+{\displaystyle \frac{10{\mathsf{\rho }}_s{d}_s\sqrt{\pi {\mathsf{\theta }}_s}}{96\left(1+e\right){\mathsf{\epsilon }}_s\mathit{g}}}{\left[1+{\displaystyle \frac{4}{5}}\mathit{g}{\mathsf{\epsilon }}_s\left(1+e\right)\right]}^2$$

(16)

$${\mathsf{\mu }}_b={\displaystyle \frac{4}{3}}{\mathsf{\epsilon }}_s{\mathsf{\rho }}_s{d}_s\mathit{g}\left(1+e\right)\left({\displaystyle \frac{{\mathsf{\theta }}_s}{\pi }}\right)$$

(17)

In the above model, the concept of a solid-phase “pseudo-temperature” is introduced. This approach yields hydrodynamic equations that are consistent with experimental observations and is used to describe the relevant transport coefficients of the solid phase [34].

Momentum transfer between the solid and liquid phases in the drilling fluid is realised through interphase interaction forces, including drag force, lift force, virtual mass force, buoyancy, Brownian force, Basset force, Saffman force, and so on, among which the drag force is the most important. In this model, when defining the interphase interaction forces, other forces that have only a minor influence on the solid phase are neglected, and only the drag force and the virtual mass force are considered, with their expressions given as follows [35]:

$${\mathit{F}}_{ip}={\mathit{F}}_{dra\mathit{g}}+{\mathit{F}}_{\mathit{v}m}$$

(18)

where ${\mathit{F}}_{dra\mathit{g}}$ is the interphase drag force, and ${\mathit{F}}_{\mathit{v}m}$ is the virtual mass force.

For the drag-force model, the Huilin–Gidaspow model, which combines the Wen–Yu model and the Ergun model, is adopted and can more accurately describe the interaction between the two phases in the drilling fluid within the wellbore–fracture coupled system under different flow regimes. The specific expressions are as follows:

$${\mathit{F}}_{dra\mathit{g}}=\mathsf{\beta }\left({\mathit{u}}_1-{\mathit{v}}_s\right)$$

(19)

$$\mathsf{\beta }=\mathsf{\phi }{\mathsf{\beta }}_{\mathrm{Ergun}}+\left(1-\mathsf{\phi }\right){\mathsf{\beta }}_{\mathrm{Wen}\text{\&}\mathrm{Yu}}$$

(20)

$${\mathsf{\beta }}_{\mathrm{Ergun}}=150{\displaystyle \frac{{\mathsf{\epsilon }}_s^2{\mathsf{\mu }}_l}{{\mathsf{\epsilon }}_1{d}_s^2}}+1.75{\displaystyle \frac{{\mathsf{\epsilon }}_s{\mathsf{\rho }}_1}{d_s}}\left|{\mathit{v}}_1-{\mathit{v}}_s\right|$$

(21)

$${\mathsf{\beta }}_{\mathrm{Wen}\text{\&}\mathrm{Yu}}={\displaystyle \frac{3C_d{\mathsf{\epsilon }}_1{\mathsf{\epsilon }}_s{\mathsf{\rho }}_1}{4d_s}}{\mathsf{\epsilon }}_1^{-2.65}$$

(22)

where the drag coefficient $C_d$ is given by

$$C_d=\left\{\begin{array}{l}{\displaystyle \frac{24}{R{e}_s}}\left(1+0.15R{e}_s^{0.687}\right),R{e}_s\le 1000\\ 0.44,R{e}_s>1000\end{array}\right.$$

(23)

The Reynolds number of the solid phase is expressed as

$$R{e}_s={\displaystyle \frac{d_s{\mathsf{\epsilon }}_1{\mathsf{\rho }}_1\left|{\mathit{v}}_1-{\mathit{v}}_s\right|}{{\mathsf{\mu }}_1}}$$

(24)

At this point, a mathematical model describing drilling fluid flow in the wellbore–fracture coupled system has been fully established. It is explicitly clarified that the proposed model is principally applicable to non-Newtonian fluids exhibiting good suspension stability and to deep tight formations where lost circulation is dominated by fractures. Conversely, for high-permeability formations or slurries containing ultra-large settling particles, such as plugging slurry, the relative slip between solid and liquid phases, as well as the early bridging effect of large particles, must be considered, and ignoring fracture wall leak-off may lead to an underestimation of the drilling fluid loss volume. In the next section, a physical model of drilling fluid flow in the wellbore–fracture coupled system will be constructed, and a computational study will be carried out.

3. Simulation Setup

3.1. Physical Model of the Fracture Network Coupled Wellbore

During drilling, the formation fracture network is a key factor controlling drilling fluid loss, and the complexity of the network is reflected in the spatial relationships between branch fractures, fracture orientation, and size distribution. Accurate description and modelling of the fracture network are therefore essential for analysing drilling fluid loss behaviour within fractures and for clarifying the loss mechanisms in fractured formations. Based on downhole core data and outcrop interpretation from carbonate formations in the Sichuan Basin, a graph-theory-based “basic unit assembly” approach for discrete fracture network modelling is adopted. The length, width, intersection angle, and endpoint position of individual fractures, as well as their connectivity with neighbouring fractures, are statistically analysed, and probability models and geometrical parameter distributions are established for three types of nodes, namely L-type, T-type, and X-type nodes. Each fracture is then treated as an edge and each intersection as a vertex. The topological structure is described by attributes such as node degree, node type, and fracture width variation, and the geometrical shape is described by edge length, strike, dip, and width, so that the fracture network is abstracted as a weighted undirected graph (Figure 1). Finally, this weighted undirected graph is used to generate multiple fracture network models that honour the measured statistical characteristics but differ in spatial geometry, as summarised in

Table 1. Typical fracture network models and their geometrical characterization parameters.

Fracture Network	Node Type	D	NB/NL	CB
	2”L” + 2”X”	1.361	3.00	1.33
	2”T” + 1”X”	1.202	2.25	1.22
	2”T” + 2”X”	1.202	2.25	1.22
	2”L” + 2”T”	1.352	2.33	1.43
	5”T”	1.295	3.67	0.68
	1”T” + 3”X”	1.985	2.4	1.25
	2”L” + 2”T”	1.567	3.00	1.00
	2”L” + 1”T”	1.229	2.5	1.4
	1”L” + 4”T”	1.986	2	1.4

. Fractal dimensions and topological structures are the most commonly used quantitative methods to describe the complexity of fracture networks, reflecting the spatial morphological complexity and seepage capacity of the networks, respectively. Therefore, by introducing fractal dimension and topological theory, it is possible to not only quantitatively characterize the spatial geometric features of fracture networks, but also establish a relationship between the drilling fluid loss behaviour and the quantitative parameters that represent the complexity of the fracture network.

3.2. Simulation Conditions

The computational domain used in this study is shown in Figure 2. In this study, the computational mesh represents a virtual flow system consisting of a wellbore and a fracture system. A three-dimensional structured mesh composed entirely of hexahedral elements is generated. To ensure that the results are independent of the mesh, three mesh densities (168,000, 270,000, and 420,000 cells) are tested for comparison. Experimental measurements are used to validate the numerical simulation results. The two finer meshes give almost identical predictions. Although the predictions obtained with the coarse mesh are close to those of the finer meshes, a mesh with 270,000 cells is finally selected as the optimal compromise between accuracy and computational cost in order to avoid possible numerical diffusion during interface tracking. All simulation input parameters are summarised in

Table 2. Simulation parameter settings for drilling fluid loss in complex wellbore-coupled fracture networks.

	Characteristics	Value	Units
Hole	Wellbore size	215.9	mm
	Outer diameter of drill pipe	127.0	mm
	Inner diameter of drill pipe	108.6	mm
	Wellbore length	10	m
Drilling fluid	Type	Incompressible non-Newtonian fluid	/
	Density, ρ	1.15	g/cm3
	Solid content	20	%
	Particle size distribution, D90	78.85	μm
	Apparent viscosity, AV	13.5	mPa·s
	Plastic viscosity, PV	11	mPa·s
	Yield Stress, YP	4.0	Pa
Initial and boundary conditions	Liquid volume fraction in wellbore	100	%
	Liquid volume fraction in fracture	0	%
	Outer pressure of wellbore	0	MPa
	Inlet flow rate of drill pipe	Variable parameter	L/s
	Drill pipe rotational speed	45	rad/min
	Outer pressure at fracture outlet	0	MPa
CFD	Solution scheme	First-order windward scheme	/
	Fluid-solid interaction	Drag force, etc	/
	Time step	Δt = 10−1 s, and the coupling step size is 1000 steps	/

. Unlike plugging slurries, the solid phase particles in drilling fluids typically have a D90 of a few tens of microns, whereas the fracture width considered in the simulation is at least 1 mm. According to various bridging principles, such as the 1/3 bridging and D90 matching, particles of this size are unlikely to form early bridging in the fracture. Therefore, the possibility of solid particles forming bridges within the fracture is minimal, and the early bridging effect of particles is neglected. A fully open boundary condition is applied at the outlet, and a no-slip condition (zero wall velocity) is imposed on solid walls. Under these boundary conditions, governing partial differential equations are solved in a cylindrical coordinate system. For all simulation cases, the inlet velocity and the rotation speed of the inner pipe are kept constant. The SIMPLE algorithm is used for pressure–velocity coupling to ensure the stability and convergence of the calculation results. The PISO algorithm is employed for velocity field solving to improve the accuracy of low-speed flow simulations by updating both pressure and velocity fields in each iteration. The residual tolerance for all equations is set to 1 × 10⁻⁶, ensuring high computational accuracy and numerical stability. The stability of the numerical solution is ensured through the Gauss–Seidel relaxation method, with the relaxation factor set between 0.3 and 0.5 to avoid numerical oscillations and ensure convergence. The solver checks the residuals for each physical quantity in every iteration, with residuals for velocity and pressure required to reach 1 × 10⁻⁶.

3.3. Model Validation

To assess the reliability of the numerical simulations, a multiphase flow migration experimental setup incorporating a coupled wellbore–fracture system was used for lost circulation testing. The system is designed with a wellbore diameter of 150 mm and a length of 1.5 m, consisting of three integrated modules: the wellbore–fracture coupling module, the mud preparation-pumping integration module, and the unified control-data acquisition module. The fracture module includes parallel vertical fractures, each 1 m in length, 30 cm in height, and adjustable within a 0–10 mm width range. Physical and schematic representations of the setup are provided in Figure 3.

Water, with a density of 0.998 g/cm³ and a viscosity of 1.01 mPa·s, was used as the test fluid. Detailed experimental and simulation conditions are listed in

Table 3. A comparison of experimental conditions and simulation parameters [17].

Physical Model	Experiment	Simulation	Operation Parameter	Experiment	Simulation
Wellbore diameter	150 mm	150 mm	Fluid type	Water	Water
Wellbore length	1.5 m	1.5 m	Fluid density	0.998 g/cm3	0.998 g/cm3
Fracture width	5 mm	5 mm	Fluid viscosity	1.01 mPa·s	1.01 mPa·s
Fracture height	30 cm	30 cm	Pumping rate	10/20/30 L/min	10/20/30 L/min
Fracture length	1 m	1 m

. To minimise operational errors associated with single-group tests, lost circulation experiments were performed at three different flow rates, allowing for the measurement of bottom-hole pressure (BHP) and drilling fluid loss rate within the coupled wellbore–fracture system under varied flow conditions. The experimental data were compared to the simulation results, as shown in Figure 4. The close agreement between the simulated and experimental loss data, with a maximum error of 7.26%, confirms the reliability and accuracy of the model’s calculations.

Real drilling fluids are typically high-solid multiphase systems falling within the category of non-Newtonian fluids. To further substantiate the model’s validity and its applicability to such fluids, numerical simulations of flow in natural radial fractures were performed, excluding fracture wall leak-off, where the model’s accuracy was corroborated against established numerical results from the literature (

Table 4. The parameters used for the model validation based on non-Newtonian fluids.

	Properties	Value	Units
Fracture	Width	2	mm
	Length	5	m
Drilling fluid	Fluid type	Herschel-Bulkley model
	Flow behaviour index	0.75	Dimensionless
	Consistency coefficient	0.4	Pa·sn
	Yield stress	6.0	Pa
	Density	1.15	g/cm3

). As illustrated in Figure 5, a comparison with the simulation data reveals that the relative error of the present results remains below 10% [36]. These findings demonstrate that the established model achieves high computational accuracy for non-Newtonian fluid flow problems within fractured media.

4. Results and Discussion

The fracture network is the main flow path for drilling fluid loss, and its spatial distribution is often random. During drilling, differences in the position where the bit intersects the fracture network will change the way the loss channels are connected to the wellbore. As illustrated in Figure 6, three typical intersection modes can be distinguished: (i) intersection at the edge of the fracture network, (ii) intersection with a branch fracture, and (iii) intersection at different types of fracture nodes. In the following section, the differences in drilling fluid loss behaviour under these different intersection modes are discussed in detail.

4.1. Intersection at the Edge of the Fracture Network

When the bit intersects the edge of a fracture network, the network is in essence connected to the wellbore only through a terminal branch fracture. To compare this case with a single-fracture case, a fracture network and a single fracture are configured with identical and uniform width and height at the inlet, and the differences between the intersection at the edge of the fracture network and the intersection with a single fracture are analysed. Under edge-intersection conditions, Figure 7 shows that for the same inlet width and height, the instantaneous loss rate for the single fracture and for the fracture network is almost the same. However, the fracture network has a longer connected length and more branches, which provides a larger effective flow volume and a wider pressure-propagation range, significantly reduces flow resistance in the near-wellbore region, enhances the flow-conducting and storage capacity of the wellbore–fracture network system, and leads to a more sufficient and longer-lasting loss process. The correlation matrix (Figure 8a) indicates that the steady-state loss rate is strongly and positively correlated with node types that represent high connectivity, such as X-type nodes, and strongly and negatively correlated with terminal or isolated nodes. The correlations with fractal dimension and connectivity index are weakly positive, with coefficients of only 0.2-0.4, and the correlations with average path length and tortuosity are negative. These results indicate that a fracture network with higher effective dimensionality, tighter connectivity, and shorter, straighter flow paths provides larger effective flow volume and a broader pressure-transmission range, allowing drilling fluid in the near-wellbore region to leak off more easily into the deep formation, and thus producing a higher and more persistent loss rate.

The flow paths of drilling fluid in a complex fracture network provide the most direct representation of the spatial geometrical structure. The branch-fracture intersection closest to the inlet is defined as the first branching point, and the path between each outlet and the first branching point is referred to as a branch path (Figure 9a). Taking fracture network #6 as an example, the branch that is closest to the outlet and has the shortest total path length accounts for only about 20% of the total network length, but contributes approximately 40–55% of the total loss (Figure 9e,f). For different fracture networks, the relationship between path length and loss fraction is shown in Figure 10. Under equal inlet and outlet pressure conditions and with uniform fracture width, branches with path lengths shorter than about 300–400 mm generally contribute more than 60% of the total loss, whereas when the path length increases to 900–1500 mm, the corresponding loss fraction decreases to below 20–30%.

Under a constant-pressure outlet boundary, each branch can be regarded as a parallel capillary tube. As shown in Equation (25), the flow resistance coefficient of a single channel is proportional to the channel length and inversely proportional to the cube of the equivalent diameter. A shorter and less tortuous path has lower flow resistance and therefore carries a larger portion of the total flow. Once the shortest path first establishes the pressure-drop connection between the wellbore and the outlet, most of the pressure drop is consumed along this path, the driving force available for far-end long paths is greatly reduced, and only weak side flows or quasi-dead-end zones are formed (Figure 9b–d). Consequently, in a complex fracture network, the shortest path naturally evolves into the dominant seepage channel, and its contribution to drilling-fluid loss generally exceeds 50%.

Fracture geometrical parameters are an important factor controlling the intensity of drilling fluid loss. In this study, branch fractures between nodes are treated as the basic building blocks of the fracture network, and the influence of geometrical changes on network-scale loss behaviour is examined by varying branch-fracture width, height, and length. When the fracture width increases from 1 mm to 5 mm, the instantaneous loss rate rises almost linearly from about 1 L/s to 5–6 L/s, and when the fracture height increases from 10 cm to 50 cm, the instantaneous loss rate also increases from about 1 L/s to 7–8 L/s (Figure 11). In contrast, extension of the branch length leaves the instantaneous loss rate essentially unchanged. Instantaneous loss is therefore mainly controlled by the inlet geometry and is independent of the downstream channel length and can be regarded as an instantaneous response to the hydraulic size at the inlet. As shown in Figure 12, an increase in fracture width produces a much larger increment in the steady-state loss rate than an increase in fracture height, whereas an increase in branch length leads to a 40–60% reduction in the steady-state loss rate.

In reality, the fracture width is not uniformly distributed along the fracture length. To investigate the characteristics of drilling fluid loss in fracture networks with non-uniform width distribution, the widths of the branch fractures upstream and downstream of the first branching point in the network are varied, and branch widths of 1 mm and 5 mm are selected to represent the width contrast. When both upstream and downstream branches at the first branching point have a width of 1 mm, the steady-state loss rate of each fracture network is only about 0.3–0.8 L/s. When either the upstream or downstream section is widened to 5 mm, the increase in steady-state loss rate is limited to about 10–40% (Figure 13a). Only when both the upstream and downstream sections are widened to 5 mm does the steady-state loss rate jump significantly, with a maximum value of about 7 L/s, corresponding to an increase of nearly 500%.

A closer examination of the upstream or downstream segment that varied alone is shown in Figure 13b. When the upstream width increases from 1 mm to 5 mm, the average steady-state loss rate increases by about 2.65 times, whereas widening the downstream segment from 1 mm to 5 mm leads to an increase as high as 5.17 times, indicating that the narrow section close to the constant-pressure outlet exerts stronger control over the flow resistance of the whole path. According to Equation (25), the local minimum width corresponds to a flow resistance much larger than that of the other sections and acts as a throttling orifice in the loss channel. If only the non-bottleneck region is widened, the change in overall flow resistance is limited, and the increase in loss rate is insignificant. Only when the narrowest section, especially the bottleneck immediately upstream of the outlet, is widened can the overall flow-conducting capacity of the path be significantly enhanced and the drilling fluid loss capacity be increased several times.

$$R\propto L/w^3$$

(25)

4.2. Intersection at the Middle of a Branch Fracture

Next, the second intersection mode between the wellbore and the fracture network is considered, namely, intersection at the middle of a branch fracture, which in essence corresponds to two fractures connecting symmetrically to the wellbore. Compared with the intersection at the edge of the fracture network, the intersection at the middle of a branch fracture increases the number of loss-conducting fractures connected to the wellbore. For all fracture networks, the instantaneous drilling fluid loss rate shows an approximately twofold increase, while the steady-state loss rate increases to different extents depending on the network geometry, and the resulting drilling fluid loss is more severe in all cases (Figure 14).

In a fracture network, the width of branch fractures is not constant along the entire length, and intersection at the middle of such a branch fracture leads to different loss channel widths on the two sides of the wellbore. Based on the analysis in Section 4.1, the fracture network on one side of the wellbore is simplified to two fractures with different widths in order to investigate the influence of two unequal-width fractures connected to the wellbore on drilling fluid loss, and the specific simulation design is summarised in

Table 5. Simulation design table for width differences between the two fractures connected to the wellbore.

Rgw	0	0.11	0.25	0.43	0.67	1
Narrower (mm)	0	0.5	1	1.5	2	2.5
Wilder (mm)	5	4.5	4	3.5	3	2.5

. The ratio of the widths of the two fractures is defined as R_gw. Under the condition of a fixed total width, when the widths of the two symmetric fractures change from highly unequal to nearly equal, the total instantaneous loss rate remains almost unchanged, and only the contribution of each fracture to the total instantaneous loss is redistributed according to the width proportion (Figure 15a). The steady-state loss rate is more sensitive to the width ratio distribution. When R_gw = 0, the total steady-state loss rate is about 0.7 L/s. As the width ratio increases into the range 0.4–0.5, the total steady-state loss rate decreases to 0.3–0.4 L/s, and when R_gw > 0.7, a slight increase is observed (Figure 15b). The corresponding contribution curves can be divided into three regimes. For 0 ≤ R_gw ≤ 0.11, a high-contribution regime exists in which the overall loss is almost equivalent to that of a single wide fracture. For 0.11 ≤ R_gw ≤ 0.67, a transition regime appears in which the loss contribution of the wide fracture is clearly higher than its width proportion. When R_gw > 0.67, an equal-width regime is reached, and the loss contributions of the wide and narrow fractures are approximately proportional to their respective widths.

When two fractures connect symmetrically to the wellbore, the system essentially has two fractures in parallel under the same pressure drop, and the flow rate in each fracture follows the cubic law. When one side is significantly wider, its flow resistance is much lower than that of the narrow fracture, and the total loss is therefore dominated by a wide fracture. As the width contrast between the two fractures decreases, their flow resistances become comparable, while the equivalent hydraulic diameter decreases instead (Equation (26)), leading to a reduction in the total steady-state loss rate, which reaches a minimum when the two widths are equal and the flow is then distributed according to the width ratio. Overall, for an intersection at the middle of a branch fracture, a more uneven width distribution causes the network to behave as a single dominant loss channel with strong loss, whereas a more uniform width distribution results in more dispersed loss and a lower overall loss intensity.

Assumed that the sum of the widths of the connected fractures is 5 mm.

4.3. Intersection at Fracture-Network Nodes

Compared with the intersection at the middle of a branch fracture, the intersection at fracture-network nodes involves a larger number of connected fractures and a non-symmetric connection pattern. Intersection at the edge of the fracture network, at the middle of a branch fracture (L-type node), and at T-type and X-type nodes corresponds to one, two, three, and four fractures connected to the wellbore, respectively, so both the instantaneous and steady-state drilling fluid loss rates increase from the edge case to the X-type node (Figure 16). As shown in Figure 17a, when the fracture width is the same in all connection directions, the instantaneous and steady-state loss rates are approximately linear with the number of connected fractures, indicating that, under a fixed pressure drop, multiple fractures behave as parallel capillaries, and the total flow capacity is the sum of the capacities of each path, so more fractures lead to more severe loss. When the total fracture width is constrained to remain constant, however, the instantaneous loss rate changes little, whereas the steady-state loss rate decreases markedly as the number of fractures increases from one to four, by about 50–70%, and a single wide fracture induces much more loss than a combination of multiple narrow fractures (Figure 17b). Under a fixed total width, the width is equally shared by each fracture, and the governing expression for the total flow rate in Equation (26) shows that the total flow decays rapidly as the number of fractures increases. Thus, when the width of each fracture is fixed, increasing the number of fractures intensifies drilling fluid loss, whereas for a fixed total width, one wide fracture causes more severe loss than several narrow fractures. In field loss-control practice, priority should be given to identifying and sealing a small number of major wide fractures.

$$Q_t=n{\left({\displaystyle \sum w/n}\right)}^3={\displaystyle \sum w^3/n^2}$$

(26)

Asymmetry between the connected fractures is another typical feature of intersections at network nodes, and two single fractures are used to investigate the influence of the angle between connected loss channels on drilling fluid loss. As shown in Figure 18, when the angle between the connected fractures increases from 30° to 180°, the loss rate and cumulative loss volume in the two single fractures remain identical, indicating that the spatial angle at which the connected fractures intersect the wellbore does not affect drilling fluid loss. Compared with intersection at the network edge or at the middle of a branch fracture, intersection at network nodes influences drilling fluid loss mainly by changing the number of connected fractures.

4.4. Mechanism of Drilling Fluid Loss Within Fracture Networks

In a fracture network, the shortest loss path connected to the wellbore largely controls the intensity of drilling fluid loss. Under a constant positive pressure differential, the remaining branch fractures provide additional flow channels and storage space for the drilling fluid, and the superposition of losses through multiple branches results in a total loss greater than that caused by a single fracture, which can be regarded as the “loss-capacity enhancement mechanism” of fracture networks (Figure 19). When the intersection position moves from the edge of the fracture network to the middle of a branch fracture, the network is segmented by the wellbore into several parts. Each part contains a shortest loss path connected to the wellbore, the single shortest loss path is therefore transformed into multiple shortest loss paths, and the drilling fluid loss becomes more severe, which can be interpreted as the “shortest-path superposition mechanism” of fracture networks. The closer the wellbore intersects the centre of the fracture network, the higher the probability of intersecting various types of nodes, and, compared with intersections at the network edge or at the middle of a branch fracture, the number of shortest loss paths connected to the wellbore further increases, and the lengths of the connected loss paths gradually decrease, corresponding to the “loss-path shortening mechanism” of fracture networks. For a single fracture, the impact on drilling fluid loss is mainly controlled by its geometrical parameters, whereas for a fracture network, the network morphology and the intersection position exert a much more complex influence on the loss behaviour. Compared with a single fracture, a fracture network modifies drilling fluid loss through the combined effects of branch-induced capacity enhancement, superposition of shortest loss paths, and shortening of loss paths, and consequently leads to more severe drilling fluid loss.

At the same fracture width, increasing the pressure differential leads to an approximately linear increase in the instantaneous loss rate, and under high pressure differentials, the differences in instantaneous flow rate between fractures of different widths are dominated by the pressure differential and are therefore greatly reduced. As time elapses and the pressure differential decays, along-path shear resistance and additional losses caused by local contraction and expansion become dominant, and the steady-state loss rate becomes more sensitive to fracture width and to the position of narrow sections. For any given loss path, the minimum aperture along the path forms a local throttling orifice, which corresponds to the highest pressure drop per unit length and the largest local flow resistance and strongly limits the attainable flow rate along this path. Thus, in the high-pressure-differential stage, loss behaviour mainly reflects the coupling between the overall pressure differential and the inlet geometry, whereas in the low-pressure-differential, quasi-steady stage, the upper bound of the loss rate is controlled by the bottleneck aperture and local resistance, which explains why the steady-state loss rate is always governed by the minimum width along the path and varies nonlinearly with fracture width (Figure 20 and Figure 21).

The correlation heat map shows that the instantaneous loss rate has the highest correlation coefficients with the height and maximum width of the fractures connected to the wellbore, with values of 0.64 and 0.37, respectively, and only weak correlations with the number of fractures and the path length (Figure 22), reflecting the volumetric filling process of drilling fluid invasion into the fractures during the initial stage of lost circulation. This indicates that instantaneous loss is mainly controlled by the hydraulic size at the inlet, while the macroscopic structure of the network has not yet fully come into play. In contrast, the steady-state loss rate exhibits moderate to strong positive correlations with the minimum width and the length of the loss path, with correlation coefficients of 0.76 and 0.63, a moderate positive correlation with the maximum width, and a negative correlation with the number of fractures. The physical nature of this correlation lies in the bottleneck effect, which dominates the pressure dissipation along the entire loss channel. These results are fully consistent with the preceding analysis, namely that, for a fixed total width, distributing the width among narrower fractures is equivalent to sharing the same pressure differential over multiple high-resistance channels, which reduces the overall equivalent hydraulic size and causes a marked decrease in the steady-state loss rate. Conversely, a small number of wide fractures form low-resistance main channels, leading to more severe overall loss.

5. Future Direction in Drilling Fluid Loss Diagnosis Using Artificial Intelligence

Field logging curves and numerical simulations indicate that drilling fluid loss dynamics in complex fracture networks are highly consistent with the actual lost-circulation process. Figure 23 shows the variations in bit position, inlet-outlet flow-rate difference, total pit volume, standpipe pressure, and hook load during drilling and circulation. When lost circulation occurs, the flow-rate difference jumps abruptly from zero, the total pit volume changes from a steady trend to a linear decline, and the standpipe pressure drops rapidly and then forms a new low-level plateau. The simulated drilling fluid loss dynamics in the complex fracture network (Figure 24) match the field curves well in terms of the time scale of loss-rate jump, the level of stable loss rate, and the coupled response of bottomhole pressure and standpipe pressure, indicating that the proposed wellbore–fracture network dynamic model can reasonably reproduce the field lost-circulation process.

Bridging plugging is the most frequently used method for lost circulation control in drilling operations. Effective plugging requires the optimal selection of plugging materials and the reasonable design of the plugging slurry. Therefore, precise knowledge of the geometric parameters of drilling fluid loss channels, such as fracture width, is essential. However, underground loss channels are both invisible and uncertain. Conventional drilling fluid loss diagnostic processes can only provide early warnings or identify the types of complex situations occurring underground. The response mechanism of the geometric characteristics of the loss channels to variations in real-time drilling parameters remains unclear, making it difficult to accurately obtain the geometric parameters of the drilling fluid loss channels. Additionally, comprehensive well logging methods require a large number of loss data samples, and the recognition accuracy of field monitoring instruments for different real-time drilling parameters may lead to delayed underground information responses, resulting in untimely diagnostics.

From an engineering perspective, field drilling-fluid loss logging parameters are the combined result of many coupled factors, including formation fracture geometry, wellbore hydraulic conditions, drilling schedule, and equipment operating state. The recorded curves contain information about the loss zone, but are also superposed with operational disturbances such as pump start-stop, tripping, and density adjustment, together with instrument noise. Given that field mud-logging data are typically subject to the coupled effects of drilling operational fluctuations and instrument noise, which makes the direct inversion of complex subsurface fracture networks prone to non-uniqueness, the core value of the standardised lost-circulation case library constructed in this study through large-scale numerical simulations lies in providing a computational benchmark based on clear physical mechanisms rather than serving as the final completed form of intelligent diagnosis.

Meanwhile, based on large-scale drilling fluid loss simulations for the coupled wellbore-fracture system, the loss results of drilling fluid through different geometrically characterised loss channels can be obtained at various drilling moments (such as a specific trip or depth) under certain drilling conditions. These results are coupled with the response characteristics of real-time well logging parameters. In the simulation process, the monitored drill string inlet pressure can be equivalently considered the riser pressure, the real-time drilling fluid loss rate can be treated as the difference in the in-and-out well flow rate, and the cumulative drilling fluid loss is numerically equivalent to the total change in wellbore fluid volume. Therefore, based on the large-scale drilling fluid loss simulation for the coupled wellbore-fracture system, the previously ambiguous response mechanism of real-time well logging parameters to the geometric characteristics of the loss channels is revealed.

On this basis, a large number of parameterized simulations of drilling-fluid loss in fracture networks can be used for comparative learning with field logging curves to identify and remove high-frequency disturbances and random noise that are irrelevant to fracture geometry and to pair logging segments representing typical operating conditions with the corresponding idealized dynamic responses. In this way, a lost-circulation case library or database can be constructed that focuses on loss mechanisms, has greatly reduced noise, and possesses unified data formats and clear physical meaning. Under a unified CFD framework, such data enable standardised characterization of different well types, intervals, and loss grades, make cross-well and cross-block comparisons possible, and can be continuously expanded with new simulation scenarios and field cases in subsequent studies. By precisely matching idealized hydraulic responses with specific fracture-network geometrical characteristics, this case library essentially provides indispensable high-quality training data and prior physical constraints for future artificial intelligence algorithms. Underpinned by this cleaned, standardised, and physically meaningful database, subsequent deep learning models are enabled to effectively filter out irrelevant disturbances from field data and achieve a reliable mapping from hydraulic deviation fingerprints to fracture geometrical parameters, thereby establishing the library as a key cornerstone in the technical roadmap towards future high-precision intelligent diagnosis.

After building a clean case library or database in which dynamic simulation provides prior information and logging data serve as supplementary constraints, artificial intelligence can be further introduced to diagnose the geometry and position of the loss zone. The abrupt changes in flow-rate difference and standpipe pressure at the onset of lost circulation require the model to capture short-term local anomalies, whereas the evolution of total pit volume and pressure deviation over the drilling period requires the model to describe long time series behaviour. Therefore, deep learning frameworks that combine local feature extraction and sequence memory, such as convolution-sequence hybrid networks or attention-based sequence models, are suitable for learning the mapping between the “hydraulic deviation code” and geometric parameters such as fracture width, fracture height, and shortest path length from the case library. With a trained model, the depth of the loss zone, fracture geometry, and loss intensity can be identified when lost circulation occurs, providing support for real-time lost-circulation control and plugging design.

6. Conclusions

Targeting the challenge of wellbore-fracture coupled flow in fractured formations, this study establishes a CFD governing-equation framework that accounts for solid-liquid two-phase flow, Herschel–Bulkley rheology, and low-Reynolds-number turbulence, and, on this basis, systematically simulates the instantaneous and steady loss behaviour under different fracture-network geometries, providing a unified and reliable numerical analysis platform for investigating lost circulation in complex fractured formations.

(1) To address the limitation that fractures in conventional loss dynamic models cannot well represent actual geological characteristics, this study uses core and outcrop data from the Sichuan Basin and adopts a graph-theory-driven discrete fracture-network modelling approach. The three connection patterns, namely L-type, T-type, and X-type, are abstracted as nodes and edges in a weighted undirected graph, and the probability distributions of fracture length, width, intersection angle, and node type are systematically compiled. On this basis, nine typical fracture-network models are generated and coupled with the wellbore-fracture two-phase flow numerical model, achieving an integrated representation from geological fracture structure to drilling fluid loss dynamics.

(2) To address the unclear mechanism of drilling fluid loss within fracture networks, this study demonstrates that compared with a single fracture, a fracture network can markedly amplify loss intensity through branch-induced capacity enhancement, superposition of shortest loss paths, and shortening of effective loss paths. The instantaneous loss rate is mainly controlled by the maximum width and height of the fractures connected to the wellbore, whereas the steady-state loss rate is jointly governed by the minimum width and the effective path length and, under a fixed total width, decreases as the number of connected fractures increases. The shortest flow channel and its bottleneck width determine the pattern of pressure-drop dissipation and are the key geometrical factors controlling long-term drilling fluid loss.

(3) To address the challenge that lost-circulation logging curves are strongly affected by multi-factor coupling and are difficult to use for the quantitative inversion of loss-zone geometry, this study builds on the wellbore-complex fracture-network loss dynamics and introduces the concept of a “hydraulic deviation code”. Parameterized CFD simulations are coupled with field logging curves in a comparative manner, and a clean lost-circulation case library is constructed in which dynamic responses provide the prior information, and logging data serve as supplementary constraints. Within this framework, strong mappings are established between multi-channel time series of flow-rate difference, standpipe pressure, and total pit volume variation and key geometrical parameters such as fracture width, fracture height, and shortest path length, providing high-quality training data and physical constraints for subsequent AI-based refined diagnosis of loss zones and optimisation of bridge-plugging treatments.