A Model for the Apparent Gas Permeability of Shale Matrix Organic Nanopore Considering Multiple Physical Phenomena

The flow of shale gas in nano scale pores is affected by multiple physical phenomena. At present, the influence of multiple physical phenomena on the transport mechanism of gas in nano-pores is not clear, and a unified mathematical model to describe these multiple physical phenomena is still not available. In this paper, an apparent permeability model was established, after comprehensively considering three gas flow mechanisms in shale matrix organic pores, including viscous slippage Flow, Knudsen diffusion and surface diffusion of adsorbed gas, and real gas effect and confinement effect, and at the same time considering the effects of matrix shrinkage, stress sensitivity, adsorption layer thinning, confinement effect and real gas effect on pore radius. The contribution of three flow mechanisms to apparent permeability under different pore pressure and pore size is analyzed. The effects of adsorption layer thinning, stress sensitivity, matrix shrinkage effect, real gas effect and confinement effect on apparent permeability were also systematically analyzed. The results show that the apparent permeability first decreases and then increases with the decrease of pore pressure. With the decrease of pore pressure, matrix shrinkage, Knudsen diffusion, slippage effect and surface diffusion effect increase gradually. These four effects will not only make up for the permeability loss caused by stress sensitivity and adsorption layer, but also significantly increase the permeability. With the decrease of pore radius, the contribution of slippage flow decreases, and the contributions of Knudsen diffusion and surface diffusion increase gradually. With the decrease of pore radius and the increase of pore pressure, the influence of real gas effect and confinement effect on permeability increases significantly. Considering real gas and confinement effect, the apparent permeability of pores with radius of 5 nm is increased by 13.2%, and the apparent permeability of pores with radius of 1 nm is increased by 61.3%. The apparent permeability model obtained in this paper can provide a theoretical basis for more accurate measurement of permeability of shale matrix and accurate evaluation of productivity of shale gas horizontal wells.

Direct Numerical Simulation of Real-gas Effects within Turbulent Boundary Layers for Fully-developed Channel Flows

Real-gas effects have a significant impact on compressible turbulent flows of dense gases, especially when flow properties are in proximity of the saturation line and/or the thermodynamic critical point. Understanding of these effects is key for the analysis and improvement of performance for many industrial components, including expanders and heat exchangers in organic Rankine cycle systems. This work analyzes the real-gas effect on the turbulent boundary layer of fully developed channel flow of two organic gases, R1233zd(E) and MDM - two candidate working fluids for ORC systems. Compressible direct numerical simulations (DNS) with real-gas equations of state are used in this research. Three cases are set up for each organic vapour, representing thermodynamic states far from, close to and inside the supercritical region, and these cases refer to weak, normal and strong real-gas effect in each fluid. The results within this work show that the real-gas effect can significantly influence the profile of averaged thermodynamic properties, relative to an air baseline case. This effect has a reverse impact on the distribution of averaged temperature and density. As the real-gas effect gets stronger, the averaged centre-to-wall temperature ratio decreases but the density drop increases. In a strong real-gas effect case, the dynamic viscosity at the channel center point can be lower than at channel wall. This phenomenon can not be found in a perfect gas flow. The real-gas effect increases the normal Reynolds stress in the wall-normal direction by 7–20% and in the spanwise direction by 10–21%, which is caused by its impact on the viscosity profile. It also increases the Reynolds shear stress by 5–8%. The real-gas effect increases the turbulence kinetic energy dissipation in the viscous sublayer and buffer sublayer <inline-formula><mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline" overflow="scroll"><mml:mo stretchy="false">(</mml:mo><mml:msup><mml:mi>y</mml:mi><mml:mo>∗</mml:mo></mml:msup><mml:mo><</mml:mo><mml:mn>30</mml:mn><mml:mo stretchy="false">)</mml:mo></mml:math></inline-formula> but not in the outer layer. The turbulent viscosity hypthesis is checked in these two fluids, and the result shows that the standard two-function RANS model (<inline-formula><mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline" overflow="scroll"><mml:mi>k</mml:mi><mml:mo>−</mml:mo><mml:mi>ϵ</mml:mi></mml:math></inline-formula> and <inline-formula><mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline" overflow="scroll"><mml:mi>k</mml:mi><mml:mo>−</mml:mo><mml:mi>ω</mml:mi></mml:math></inline-formula>) with a constant <inline-formula><mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline" overflow="scroll"><mml:msub><mml:mi>C</mml:mi><mml:mi>μ</mml:mi></mml:msub><mml:mo>=</mml:mo><mml:mn>0.09</mml:mn></mml:math></inline-formula> is still suitable in the outer layer <inline-formula><mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline" overflow="scroll"><mml:mo stretchy="false">(</mml:mo><mml:msup><mml:mi>y</mml:mi><mml:mo>∗</mml:mo></mml:msup><mml:mo>></mml:mo><mml:mn>70</mml:mn><mml:mo stretchy="false">)</mml:mo></mml:math></inline-formula>, with an error in ±10%.

Aeolian Sand Dune Sedimentary Architecture Is Key in Determining the “Slow-Gas Effect” during Gas Field Production Performance

Summary Aeolian deposits are typically considered to act as homogeneous “tanks” of sand, which do not contain significant heterogeneities that impact the production of hydrocarbons. However, a succession of deeply buried aeolian gas reservoirs from the Permian Rotliegend exhibit a characteristic production decline profile that is typified by high initial flow rates, followed by a rapid decline in bottomhole pressure and decline in flow rate, subsequently followed by stabilization at low flow rates for an extended period (over several decades). This effect has been termed here as the “slow-gas effect,” and this production phenomenon has previously been attributed to structural compartmentalization. This paper presents an alternative, sedimentological hypothesis for the cause of the slow-gas effect based upon facies-controlled permeability differences within aeolian dune trough architectures. To test this, three interwell (km) scale models from well-studied aeolian analogs from Utah and Arizona were modeled with standard geostatistical reservoir techniques and populated with petrophysical properties from producing Rotliegend reservoirs in Germany. These models were subsequently dynamically simulated to analyze production behavior and test whether a similar “slow-gas” production profile could be reproduced. This study finds that the slow-gas effect primarily results from heterogeneities created by the complex interaction of deposition, accumulation, and erosion within aeolian strata, as opposed to the structural compartmentalization of homogeneous tanks of sand as previously thought. Structural compartmentalization and baffling through faulting where present will have an impact on fluid flow; however, it is not considered here to be the primary cause of the slow-gas effect. Results of this work demonstrate the necessity of accurately characterizing and reproducing low permeability heterogeneity in aeolian systems. These heterogeneities can either be modeled explicitly through the use of geostatistical reservoir modeling techniques as done here, or implicitly through the use of characteristic length and transmissibility multipliers. These results have significant implications on our understanding of how tight aeolian systems produce; namely, after depletion of the near-wellbore volume, production from the surrounding reservoir is baffled by a hierarchy of low permeability bounding surfaces and associated transmissibility barriers. Application for enhancing reservoir depletion strategies include optimizing well trajectories to maximize the number of dune penetrations and percentage of net reservoir facies in communication to the well; maximizing the size of the primary reservoir compartment. Neighboring wells should be placed in separate compartments to maximize the amount of fast-flowing gas production during the early production stage. Pressure management can be used to cyclically produce, deplete, and recharge the primary reservoir compartment to manage and optimize recovery during the decline phase and production tail.

Yield potential of world wheat based on ARIMA model under global warming

As the most important food crop across the world, with continuous increase in world population and steady declining farmlands, wheat has been attracting academic attention for improving its yield or potential in the future particularly under global warming. Therefore, analyzing the yield or potential of wheat at global level relevant to greenhouse gas effect is of great significance to direct future production of wheat in the world. However up to now, there are relatively few reports on potential yield of world wheat projected using ‘time series’ approach like ARIMA (Auto-regressive Integrated Moving Average) model. Thus in this paper, the crop potential yield of world wheat during 2019 to 2028 is projected using ARIMA model based on the yields from 1961 to 2018. Our results show that during 2019 to 2028, the average yields of world wheat are projected to increase from 3569 to 4257 kg ha-1 while top yields of world wheat from 9852 to 11246 kg ha-1. Annual global mean temperatures are projected to increase from 15.05 to 15.31°C. Global warming exerts positive effect on average yield of world wheat while negative effect on the top yield in 1961 to 2018 and 2028. Our study concluded that for world wheat production in 2019 to 2028, the opportunities for improving production should be mainly dependent on the advantage of highyield countries as the yield is still in low place before the turn-point of S-shaped curve in long-term trend affected partly by greenhouse gas effect.