Sheik S. Rahman

The lattice Boltzmann method for isothermal micro-gaseous flow and its application in shale gas flow: A review

Abstract The lattice Boltzmann method (LBM) has experienced tremendous advances and been well accepted as a popular method for simulating various fluid flow problems in porous media. With the introduction of an effective relaxation time and slip boundary conditions, the LBM has been successfully extended to solve micro-gaseous transport phenomena. As a result, the LBM has the potential to become an effective numerical method for gas flow in shale matrix in slip flow and transition flow regimes. Additionally, it is very difficult to experimentally determine the permeability of extremely low permeable media like shale. In this paper an extensive review on a number of slip boundary conditions and Knudsen layer treatments used in LB models for micro-gaseous flow is carried out. Furthermore, potential applications of the LBM in flow simulation in shale gas reservoirs on pore scale and representative elementary volume (REV) scale are evaluated and summarized. Our review indicates that the LBM is capable of capturing gas flow in continuum to slip flow regimes which cover significant proportion of the pores in shale gas reservoirs and identifies opportunities for future research.

Apparent permeability prediction of organic shale with generalized lattice Boltzmann model considering surface diffusion effect

Abstract Gas flow in shale is associated with both organic matter (OM) and inorganic matter (IOM) which contain nano-pores ranging in size from a few to hundreds of nano-meters. In addition to the non-continuum effect which leads to an apparent permeability of gas higher than the intrinsic permeability, the surface diffusion of adsorbed gas in organic pores also can influence the apparent permeability through its own transport mechanism. In this study, a generalized lattice Boltzmann model (GLBM) is employed for gas flow through the reconstructed shale matrix consisting of OM and IOM. The Expectation–Maximization (EM) algorithm is used to assign the pore size distribution to each component, and the dusty gas model (DGM) and generalized Maxwell–Stefan model (GMS) are adopted to calculate the apparent permeability accounting for multiple transport mechanisms including viscous flow, Knudsen diffusion and surface diffusion. Effects of pore radius and pressure on permeability of both IOM and OM as well as effects of Langmuir parameters on OM are investigated. The effect of total organic content and distribution on the apparent permeability of the reconstructed shale matrix at different surface diffusivity is also studied. It is found that the influence of pore size and pressure on the apparent permeability of organic matter is affected by the surface diffusion of adsorbed gas. Moreover, surface diffusion plays a significant role in determining apparent permeability and the velocity distribution of shale matrix.

An Analytical Model of Apparent Gas Permeability for Tight Porous Media

Simulation of fluid flow in tight rocks, such as shale gas reservoirs, has been a challenging task because of the coexistence of various flow regimes, including the continuum flow, slippage, transition flow, and Knudsen diffusion within the porous structure. Currently, both numerical and analytical methods have been applied to address this issue. In this paper, we have extended the application of most widely used analytical solution for single uniform capillary proposed by Beskok and Karniadakis (Microscale Thermophys Eng 3(1):43–77,1999) to the porous media. The porous structure is represented by a bundle of tortuous capillary tubes with different diameters. Fractal theory is applied to mathematically express the capillary diameter distribution and their tortuosity. For shale gas and coal seam gas formations where adsorption gas is present, the effect of surface diffusion is also included in the analytical solution. Thus, the presented analytical model has allowed us to study the effect of pore size distribution, fractal dimensions for pore size and tortuosity, porosity, surface diffusivity and Langmuir parameters on flow processes. Experimental data from 100 tight gas sand samples and one shale sample, with equivalent liquid permeability ranging from nanodarcy to millidarcy, are used to effectively evaluate the application of the analytical model in the study of flow behavior of gas in tight rocks. The results of this study also show that in tight formation, there has been an increase in apparent gas permeability through the life of production by a factor of 2.2.

Integrated conditional global optimisation for discrete fracture network modelling

This paper presents a methodology to simulate discrete fracture networks for naturally fractured reservoirs by combining statistical and spatial analyses, object-based modelling and conditional global optimisation. The methodology examines and utilises both continuum and discrete fracture information, such as spatial distribution of fracture density, statistical and geostatistical distributions of fracture size and orientation. The output is a network of discrete fractures, with their corresponding details of location, size and orientation. The methodology is illustrated by a case study on the surface fault system in New York region. The results show that it is able to produce discrete fracture network that match closely to the target fault map, even in the case where data are limited. The results show that it is also able to improve results of several recent fracture models, such as integrated stochastic simulations as well as grid-based simulations.

Effective permeability calculation using boundary element method in naturally fractured reservoirs

Abstract A model is presented to calculate the effective permeability tensor in naturally fractured reservoirs using Boundary Element Methods (BEM). Arbitrary fractures of different scales based on their length are considered. Interface boundary condition is used to model the short fractures as an enhancement of matrix permeability. Long fractures, on the other hand are treated as source/sink in the corresponding blocks. Periodic boundary condition is applied to the grid-block boundaries to calculate the elements of effective permeability tensor. Darcys law and Navier-stokes equation are applied to fluid flow in rock matrix and fractures, respectively. An important feature of this approach is that the fluid flow in matrix-fracture interface is coupled by Poissons equation and fluid flow in the rest of the matrix is formulated by Laplaces equation. This paper also presents an innovative approach to optimization and parallelization of the model by High Performance Computing (HPC) techniques. The model has been validated against analytical results and applied to a typical case where arbitrary fractures of different sizes are assumed within the grid blocks. The effective block permeability tensors can be implemented into a reservoir simulator to calculate fluid flow through the naturally fractured reservoirs.

Stress concentration incorporated fatigue analysis of die-marked drill pipes

Fatigue damage of drill pipes occurs in the pipe section at the dogleg region (where the drill pipe changes its drilling direction) due to alternating bending stress during rotation of the pipe. The pipe section may fail due to the cumulative effect of fatigue damage in a single drilling event, or in a number of drilling events. Moreover, dies of gripping systems mark the pipe surface during making and breaking operations (screwed and unscrewed to connect and disconnect two pipes). These marks on the pipe surface cause stress concentration. This paper develops a method for fatigue analysis of drill pipes taking into account the alternating bending stress at the dogleg, the direct axial stress due to hanging weight of drill pipes and the stress concentration due to die-marks on the pipe surface. The application of the method is demonstrated by evaluating cumulative fatigue damage for a number of drilling events and different gripping systems which produce die-marks of different depths. Results have revealed that higher die-mark depths accelerate fatigue failure, which can be predicted more accurately by the method presented in this paper.

A Holistic Approach to the Design and Evaluation of Hydraulic-Fracture Treatments in Tight Gas Reservoirs

This paper presents a comprehensive approach to the design of hydraulic-fracture treatments. accounting for anisotropic stress conditions, rock properties, and the effect of pore-pressure changes caused by production in tight gas reservoirs. This has allowed its, among other opportunities, to design a refracture treatment. The poroelastic model is also coupled with a production-optimization scheme to optimize the design parameters for hydraulic-fracture treatments. A case Study of refracture treatment has been carried out for a typical tight gas reservoir. This Study has shown that the fracture treatment can be optimized successfully to increase the net present Value and/or ultimate gas recovery. This study also has demonstrated that a second fracture treatment can be performed after a period of production from the same treated interval to maintain production without the drilling of additional wells.

A Study of Permeability Changes Due to Cold Fluid Circulation in Fractured Geothermal Reservoirs

Reservoir behavior due to injection and circulation of cold fluid is studied with a shear displacement model based on the distributed dislocation technique, in a poro-thermoelastic environment. The approach is applied to a selected volume of Soultz geothermal reservoir at a depth range of 3600 to 3700 m. Permeability enhancement and geothermal potential of Soultz geothermal reservoir are assessed over a stimulation period of 3 months and a fluid circulation period of 14 years. This study-by shedding light onto another source of uncertainty-points toward a special role for the fracture surface asperities in predicting the shear dilation of fractures. It was also observed that thermal stress has a significant impact on changing the reservoir stress field. The effect of thermal stresses on reservoir behavior is more evident over longer circulation term as the rock matrix temperature is significantly lowered. Change in the fracture permeability due to the thermal stresses can also lead to the short circuiting between the injection and production wells which in turn decreases the produced fluid temperature significantly. The effect of thermal stress persists during the whole circulation period as it has significant impact on the continuous increase in the flow rate due to improved permeability over the circulation period. In the current study, taking into account the thermal stress resulted in a decrease of about 7 °C in predicted produced fluid temperature after 14 years of cold fluid circulation; a difference which notably influences the potential prediction of an enhanced geothermal system.

Modeling Time-Dependent Pore Pressure Due to Capillary and Chemical Potential Effects and Resulting Wellbore Stability in Shales

During drilling operations, the mud filtrate interacts with the pore fluid around the wellbore and changes pore pressure by capillary and chemical potential effects. Thus the change in pore pressure around borehole becomes time-dependent, particularly in extremely low permeability shaley formations. In this paper, the change in pore pressure due to capillary and chemical potential effects are investigated experimentally. Analytical models are also developed based on the experimental results. A wellbore stability analysis model incorporating the time-dependent change in pore pressure is applied to a vertical well in a shale formation under normal fault stress regime.

Survival assessment of die-marked drill pipes:: integrated static and fatigue analysis

Abstract Drill pipes under operational loads may fail in static or fatigue mode. Static failures are evaluated at two critical levels: the rotary table level (surface level) and the dogleg level, whereas fatigue failure occurs in a pipe section at the dogleg level due to the cumulative effect of fatigue damage in a number of drilling events. The current practice of static and fatigue failure analyses is based on a smooth pipe surface condition. In practice, however, dies of gripping systems mark the pipe surface during making and breaking operations (screwed and unscrewed to connect and disconnect two pipes). These marks on the pipe surface cause stress concentrations, which make a pipe more susceptible to both failure modes. This paper presents an integrated approach for static and fatigue failure analysis, considering the effects of stress concentrations due to die-marks from different gripping systems. Thus, the approach is intended to assist engineers in assessing the overall survivability of drill pipes through a detailed failure evaluation considering the effect of die-mark related stress concentrations in representative field conditions.