scholarly journals Diffusive Mass Transfer and Gaussian Pressure Transient Solutions for Porous Media

Fluids ◽  
2021 ◽  
Vol 6 (11) ◽  
pp. 379
Author(s):  
Ruud Weijermars
Keyword(s):  
Porous Media ◽  
Mass Transport ◽  
Performance Testing ◽  
Step Function ◽  
Cumulative Probability ◽  
Hydraulic Fractures ◽  
Pressure Transient ◽  
Numerical Solution Methods ◽  
Transient Solutions ◽  
Pressure Depletion

This study revisits the mathematical equations for diffusive mass transport in 1D, 2D and 3D space and highlights a widespread misconception about the meaning of the regular and cumulative probability of random-walk solutions for diffusive mass transport. Next, the regular probability solution for molecular diffusion is applied to pressure diffusion in porous media. The pressure drop (by fluid extraction) or increase (by fluid injection) due to the production system may start with a simple pressure step function. The pressure perturbation imposed by the step function (representing the engineering intervention) will instantaneously diffuse into the reservoir at a rate that is controlled by the hydraulic diffusivity. Traditionally, the advance of the pressure transient in porous media such as geological reservoirs is modeled by two distinct approaches: (1) scalar equations for well performance testing that do not attempt to solve for the spatial change or the position of the pressure transient without reference to a well rate; (2) advanced reservoir models based on numerical solution methods. The Gaussian pressure transient solution method presented in this study can compute the spatial pressure depletion in the reservoir at arbitrary times and is based on analytical expressions that give spatial resolution without gridding-meaning solutions that have infinite resolution. The Gaussian solution is efficient for quantifying the advance of the pressure transient and associated pressure depletion around single wells, multiple wells and hydraulic fractures. This work lays the basis for the development of advanced reservoir simulations based on the superposition of analytical pressure transient solutions.

Mass Transport Modelling in Porous Media Using Delay Differential Equations

2006 ◽  
Vol 258-260 ◽  
pp. 586-591
Author(s):  
António Martins ◽  
Paulo Laranjeira ◽  
Madalena Dias ◽  
José Lopes
Keyword(s):  
Porous Media ◽  
Differential Equations ◽  
Mass Transport ◽  
Delay Differential Equations ◽  
Dispersion Model ◽  
Flow Characteristics ◽  
Convective Transport ◽  
Transport Modelling ◽  
Flow Field Characteristics ◽  
Delay Differential

In this work the application of delay differential equations to the modelling of mass transport in porous media, where the convective transport of mass, is presented and discussed. The differences and advantages when compared with the Dispersion Model are highlighted. Using simplified models of the local structure of a porous media, in particular a network model made up by combining two different types of network elements, channels and chambers, the mass transport under transient conditions is described and related to the local geometrical characteristics. The delay differential equations system that describe the flow, arise from the combination of the mass balance equations for both the network elements, and after taking into account their flow characteristics. The solution is obtained using a time marching method, and the results show that the model is capable of describing the qualitative behaviour observed experimentally, allowing the analysis of the influence of the local geometrical and flow field characteristics on the mass transport.

Laboratory Experiments of Mass Transfer in the London Clay

1988 ◽  
Vol 127 ◽  
Author(s):  
P. J. Bourke ◽  
D. Gilling ◽  
N. L. Jefferies ◽  
D. A. Lever ◽  
T. R. Lineham
Keyword(s):  
Mass Transfer ◽  
Porous Media ◽  
Radioactive Waste ◽  
Mass Transport ◽  
Mathematical Models ◽  
Laboratory Experiments ◽  
Naturally Occurring ◽  
Diffusion And Convection ◽  
Waste Repository ◽  
London Clay

ABSTRACTAqueous phase mass transfer through the rocks surrounding a radioactive waste repository will take place by diffusion and convection. This paper presents a comprehensive set of measurements of the mass transfer characteristics for a single, naturally occurring, clay. These data have been compared with the results predicted by mathematical models of mass transport in porous media, in order to build confidence in these models.

Pressure-Transient Tests and Flow Regimes in Fractured Reservoirs

2015 ◽  
Vol 18 (02) ◽  
pp. 187-204 ◽  
Author(s):  
Fikri Kuchuk ◽  
Denis Biryukov
Keyword(s):  
History Matching ◽  
Fractured Reservoirs ◽  
Flow Regimes ◽  
Naturally Fractured Reservoirs ◽  
Dual Porosity ◽  
Hydraulic Fractures ◽  
Fractured Reservoir ◽  
Pressure Transient ◽  
Matrix Block ◽  
Naturally Fractured

Summary Fractures are common features in many well-known reservoirs. Naturally fractured reservoirs include fractured igneous, metamorphic, and sedimentary rocks (matrix). Faults in many naturally fractured carbonate reservoirs often have high-permeability zones, and are connected to numerous fractures that have varying conductivities. Furthermore, in many naturally fractured reservoirs, faults and fractures can be discrete (rather than connected-network dual-porosity systems). In this paper, we investigate the pressure-transient behavior of continuously and discretely naturally fractured reservoirs with semianalytical solutions. These fractured reservoirs can contain periodically or arbitrarily distributed finite- and/or infinite-conductivity fractures with different lengths and orientations. Unlike the single-derivative shape of the Warren and Root (1963) model, fractured reservoirs exhibit diverse pressure behaviors as well as more than 10 flow regimes. There are seven important factors that dominate the pressure-transient test as well as flow-regime behaviors of fractured reservoirs: (1) fractures intersect the wellbore parallel to its axis, with a dipping angle of 90° (vertical fractures), including hydraulic fractures; (2) fractures intersect the wellbore with dipping angles from 0° to less than 90°; (3) fractures are in the vicinity of the wellbore; (4) fractures have extremely high or low fracture and fault conductivities; (5) fractures have various sizes and distributions; (6) fractures have high and low matrix block permeabilities; and (7) fractures are damaged (skin zone) as a result of drilling and completion operations and fluids. All flow regimes associated with these factors are shown for a number of continuously and discretely fractured reservoirs with different well and fracture configurations. For a few cases, these flow regimes were compared with those from the field data. We performed history matching of the pressure-transient data generated from our discretely and continuously fractured reservoir models with the Warren and Root (1963) dual-porosity-type models, and it is shown that they yield incorrect reservoir parameters.

Experimental Investigation of Asphaltene-Induced Formation Damage Caused by Pressure Depletion of Live Reservoir Fluids in Porous Media

SPE Journal ◽  
2018 ◽  
Vol 24 (01) ◽  
pp. 01-20 ◽  
Author(s):  
Omid Mohammadzadeh ◽  
Shawn David Taylor ◽  
Dmitry Eskin ◽  
John Ratulowski
Keyword(s):  
Porous Medium ◽  
Porous Media ◽  
Flow Rate ◽  
Formation Damage ◽  
Bulk Fluid ◽  
Asphaltene Content ◽  
Pressure Depletion ◽  
Asphaltene Deposition ◽  
Permeability Impairment ◽  
Live Oil

Summary One of the complex processes of permeability impairment in porous media, especially in the near-wellbore region, is asphaltene-induced formation damage. During production, asphaltene particles precipitate out of the bulk fluid phase because of pressure drop, which might result in permeability reduction caused by both deposition of asphaltene nanoparticles on porous-medium surfaces and clogging of pore throats by larger asphaltene agglomerates. Experimental data will be used to identify the parameters of an impairment model being developed. As part of a larger effort to identify key mechanisms of asphaltene deposition in porous media and develop a model for asphaltene impairment by pressure depletion, this paper focuses on a systematic design and execution of an experimental study of asphaltene-related permeability damage caused by live-oil depressurization along the length of a flow system. An experiment was performed using a custom-designed 60-ft slimtube-coil assembly packed with silica sands to a permeability of 55 md. The customized design included a number of pressure gauges at regular intervals along the coil length, which enabled real-time measurement of the fluid-pressure profile across the full length of the slimtube coil. The test was performed on a well-characterized recombined live oil from the Gulf of Mexico (GOM) that is a known problematic asphaltenic oil. Under a constant differential pressure, the injection flow rate of the live oil through the slimtube coil decreased over time as the porous medium became impaired. During the impairment stage, samples of the produced oil were collected on a regular basis for asphaltene-content measurement. After more than 1 month, the impairment test was terminated; the live oil was purged from the slimtube coil with helium at a pressure above the asphaltene-onset pressure (AOP); and the entire system was gently depressurized to bring the coil to atmospheric conditions while preserving the asphaltene-damaged zones of the coil. The permeability and porosity of the porous medium changed because of asphaltene impairment that was triggered by pressure depletion. Results indicated that the coil permeability was impaired by approximately 32% because of pressure depletion below the AOP, with most of the damage occurring in the latter section of the tube, which operated entirely below the AOP. Post-analytical studies indicated lower asphaltene content of the produced-oil samples compared with the injecting fluid. The distribution of asphaltene deposits along the length of the coil was determined by cutting the slimtube coil into 2- to 3-ft-long sections and using solvent extraction to collect the asphaltenes in each section. The extraction results confirmed that the observed permeability impairment was indeed caused by asphaltene deposition in the middle and latter sections of the coil, where the pressure was less than the AOP. With the success of this experiment, the same detailed analysis can be extended to a series of experiments to determine the effects of different key parameters on pressure-induced asphaltene impairment, including flow rate, wettability, and permeability.

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