An Alternative Approach to Predicting Reservoir Performance in a Coalbed Methane (CBM) Well Flowing Under Dominant Matrix Shrinkage Effect

Coalbed methane (CBM) reservoirs contain gas molecules in adsorbed state into the solid matrix of coal. The pressure depletion in CBM reservoir causes the matrix gas to desorb into the cleat system which leads to matrix shrinkage. The pore volume of the cleat network changes as coal matrix shrinks. Consequently, cleat porosity and permeability of reservoir change as reservoir pressure depletes. The change in cleat porosity and permeability due to shrinkage of coal matrix with depletion of reservoir pressure invalidates the underlying assumptions made in the derivation of diffusivity equation. Under the conditions of changing porosity and permeability, the utility of the standard method of inflow performance relationship (IPR), paired with \(\frac{P}{Z^{*}}\) method suggested by King (in: SPE Annual Technical Conference and Exhibition, New Orleans, 1990), for performance prediction diminishes. In this paper, an effort has been made to predict reservoir performance of such CBM reservoirs with an alternative approach. The method suggested by Upadhyay and Laik (Transp Porous Media, 2017. doi: 10.1007/s11242-016-0816-6) has been leveraged to describe pseudo-steady-state flow in the form of a new equation that relates stress-dependent pseudo-pressure function with time. The analytical equation derived in this paper is useful in predicting reservoir pressure and flowing bottom hole pressure of a CBM well under the situation when coal matrix shrinks below desorption pressure. The paper aims to predict production performance of CBM reservoirs producing under the influence of matrix shrinkage effect with an approach alternative to conventional IPR approach paired with \(\frac{P}{Z^{*}}\) method. The results of this analytical solution have been validated with the help of numerical simulator CMG–GEM as well as in-field production data. The equations and workflow suggested in this paper can be easily implemented in spreadsheet applications like Microsoft Excel tools.     

A Computational Approach to Controllability Issues for Flow-Related Models. (I): Pointwise Control of the Viscous Burgers Equation

We discuss the numerical solution of some controllability problems for time-dependent flow models. The emphasis is on algorithmic aspects, discretization issues, and memory-saving devices. In the first part of the article, we investigate the controllability of the viscous Burgers equation. In part two, we shall discuss the boundary controllability of a linear advection-diffusion equation and then the distributed controllability of the unsteady Stokes equations.     

A Collaboration-based Approach to CFD Model Validation and Uncertainty Quantification (VUQ) Using Data from a Laminar Helium Plume

An effective approach to the model VUQ process by means of direct collaboration between computationalist and experimental data analyst is proposed. An analysis of data from a laminar helium plume experiment provides a demonstration of the proposed collaboration process. Consistency analysis serves a central role in the collaboration. It takes the data and uncertainties from both analyst and computationalist and provides an objective and quantifiable measure of agreement between the two. Despite the simplicity of the laminar helium system and the computational model, certain phenomena brought to light in the collaboration process make it difficult to find quantitative agreement in the data. These phenomena include the unsteady behavior of air flow in an open room, and the presence of helium permeation to the region near the plume. Important sources of error in the simulation include uncertainty in the room temperature (295.15 to 305.15 K), uncertainty in the helium inlet velocity (0.1215 \(\frac {m}{s}\) to 0.1415 \(\frac {m}{s}\)), and uncertainty in local helium permeation (0 % to 3 % by mass.) The collaboration process allows for a better understanding of the phenomena affecting the plume and the relative sensitivies of the system to these phenomena.     

A new approach to investigate the nonlinear dynamics in a (3 + 1)-dimensional nonlinear evolution equation via Wronskian condition with a free function

This paper proposes a new approach to investigate the nonlinear dynamics in a (3 + 1)-dimensional nonlinear evolution equation via Wronskian condition with a free function. Firstly, a Wronskian condition involving a free function is introduced for the equation. Secondly, by solving the Wronskian condition, some exact solutions are presented. Thirdly, the dynamical behaviors are analyzed by choosing specific functions in the Wronskian condition. In addition, some exact solutions are graphically illustrated by using Mathematica symbolic computations. The dynamical behaviors include stationary y-breather, line-soliton resonance, line-soliton-like phenomenon, parabola–soliton interaction, cubic–parabola–soliton resonance, kink behavior, and singular waves. These results not only illustrate the merits of the proposed method in deriving new exact solutions but also novel dynamical behaviors in the (3 + 1)-dimensional nonlinear evolution equation.

     

A numerical study on the use of liquid metals (gallium and mercury) as agents to enhance heat transfer from hot water in a co-flow mini-channel system

Enhancement in the heat removal from hot water co-flowing in a mini-channel in a direct contact manner with two liquid metals, gallium and mercury, is investigated numerically. Results show that the liquid metals lead to superior heat removal from hot water co-flowing in the channel as compared to the case when only water flows in the channel. Moreover, it is found that gallium yields higher heat removal from water than mercury by about 15 %. This percentage, representing the superiority of gallium over mercury increases to about 20?% under conditions when the mass flow rate of both the liquid metal and the co-flowing water are doubled. The results reported showed numerical mesh independence. However, the results show much dependence on the spatial discretization scheme adopted where it is found that first order upwind scheme yields somewhat over predicted heat exchange rates in the channel, as compared with the case when a second order scheme is used. It is found further that the channel efficiency in removing heat from the water is remarkable in the first half of the overall channel length where in general the heat removed in the first 10?mm of the channel length is found to be about 70?% of the total heat removed. This percentage is a bit less than that when only water flows in the channel.