An efficient algorithm to compute transient pressure responses of slanted wells with arbitrary inclination in reservoirs

Compared with vertical and horizontal wells, the solution and computation of transient pressure responses of slanted wells are more complex. Vertical and horizontal wells are both simplified cases of slanted wells at particular inclination, so the model for slanted wells is more general and more complex than other models for vertical and horizontal wells. Many authors have studied unsteady-state flow of fluids in slanted wells and various solutions have been proposed. However, until now, few of the published results pertain to the computational efficiency. Whether in the time domain or in the Laplace domain, the computation of integration of complex functions is necessary in obtaining pressure responses of slanted wells, while the computation of the integration is complex and time-consuming. To obtain a perfect type curve the computation time is unacceptable even with an aid of high-speed computers. The purpose of this paper is to present an efficient algorithm to compute transient pressure distributions caused by slanted wells in reservoirs. Based on rigorous derivation, the transient pressure solution for slanted wells of any inclination angle is presented. Assuming an infinite-conductivity wellbore, the location of the equivalent-pressure point is determined. More importantly, according to the characteristics of the integrand in a transient pressure solution for slanted wells, the whole integral interval is partitioned into several small integral intervals, and then the method of variable substitution and the variable step-size piecewise numerical integration are employed. The amount of computation is significantly reduced and the computational efficiency is greatly improved. The algorithm proposed in this paper thoroughly solved the difficulty in the efficient and high-speed computation of transient pressure distribution of slanted wells with any inclination angle.

Experimental Study on Tensile Behavior of Cement Paste, Mortar and Concrete under High Strain Rates

Effects of the strain rate on cement paste, mortar and concrete were studied. A modified SHPB testing technique with fl attened Brazilian disc（FBD） specimen was developed to measure the dynamic tensile stress-strain curve of materials. A pulse-shaped split Hopkinson pressure bar（SHPB） was employed to determine the dynamic tensile mechanical responses and failure behavior of materials under valid dynamic testing conditions. Quasi-static experiments were conducted to study material strain rate sensitivity. Strain rate sensitivity of the materials was measured in terms of the stress-strain curve, elastic modulus, tensile strength and critical strain at peak stress. Empirical relations between dynamic increase factor（DIF） and the material properties were derived and presented.

EXACT SOLUTION FOR SPHERICAL FLOW AND TRANSIENT BEHAVIOR OF PRESSURE WITH CONSIDERATION OF EFFECTS OF QUADRATIC-GRADIENT TERM

Conventional models for fluid flow in well tests have not been consistent with material balance. According to the slightly compressible fluid assumption, the quadratic gradient term in the nonlinear partial differential equation has been usually neglected. This approach is questionable for live oil and low permeability reservoirs. We have already known that linearization by neglecting quadratic gradient terms may lead to errors for large values of well-test time. In this paper, a method that is consistent with material balance was proposed on the spherical flow system. All terms in the nonlinear partial eqiation were retained. Exact solution for the resulting nonlinear partial differential equation in an infinite reservoir was obtained by using the Laplace transform considering wellbore storage. Analytical solution for nonlinear partial differential equation are resulted by using orthogonal transforms under both closed and constant-pressure outer boundary conditions. The law of pressure changes for a fluid compressibility α and a storage coefficient C D were discussed.

Blood pressure-controlling behavior in relation to educational level and economic status among hypertensive women in Ghana

Objective:To explore the association between economic status and educational level with self-management behavior(medication adherence,controlling body weight,reducing salt intake,performing physical exercise,reducing alcohol consumption,abstaining from smoking,increasing fruit and vegetable consumption)among hypertensive women in Ghana.Methods:Cross-sectional data on 598 women were collected from the Ghana Demographic and Health Survey of 2014.The association between economic status and educational level with self-management behavior was measured by logistic regression methods.Results:Mean systolic blood pressure and diastolic blood pressure were 131.4 and 86.58 mm Hg,respectively.With regard to self-management behavior,81.8%of women reported taking medication to control high blood pressure,44.4%reported controlling body weight,22.5%reported reducing salt intake,48.3%reported performing physical exercise,74.2%reported reducing alcohol consumption,74.2%reported abstaining from alcohol and smoking,and 20.2%reported consuming more fruits and vegetables.Women living in the wealthiest households had significantly higher odds of maintaining healthy weight,reducing salt intake,and exercising.Conclusion:The findings imply that socioeconomic factors may play important roles in women’s adherence to blood pressure-controlling behavior.It is therefore suggested that policy makers focus on improving women’s economic status as a strategy to encourage cardiovascular health-promoting behavior.

Micro-scale behavior of granular materials during cyclic loading

This study presents the micro-scale behavior of granular materials under biaxial cyclic loading for differ- ent confining pressures using the two-dimensional （2D） discrete element method （DEM）. Initially, 8450 ovals were generated in a rectangular frame without any overlap. Four dense samples having confining pressures of 15, 25, 50, and 100 kPa were prepared from the initially generated sparse sample. Numeri- cal simulations were performed under biaxial cyclic loading using these isotropically compressed dense samples. The numerical results depict stress-strain-dilatancy behavior that was similar to that observed in experimental studies. The relationship between the stress ratio and dilatancy rate is almost indepen- dent of confining pressures during loading but significantly dependent on the confining pressures during unloading. The evolution of the coordination number, effective coordination number and slip coordina- tion number depends on both the confining pressures and cyclic loading. The cyclic loading significantly affects the microtopology of the granular assembly. The contact fabric and the fabric-related anisotropy are reported, as well. A strong correlation between the stress ratio and the fabric related to contact normals is observed during cyclic loading, irrespective of confining pressures.

Dynamic mechanical behavior of ultra-high strength steel 30CrMnSiNi2A at high strain rates and elevated temperatures

During high speed machining in the field of manufacture,chip formation is a severe plastic deformation process including large strain,high strain rate and high temperature.And the strain rate in high speed cutting process can be achieved to 105 s^（-1）.30CrMnSiNi2Asteel is a kind of important high-strength low-alloy structural steel with wide application range.Obtaining the dynamic mechanical properties of30CrMnSiNi2Aunder the conditions of high strain rate and high temperature is necessary to construct the constitutive relation model for high speed machining.The dynamic compressive mechanical properties of30CrMnSiNi2Asteel were studied using split Hopkinson pressure bar（SHPB）tests at 30-700°C and3000-10000s^（-1）.The stress-strain curves of 30CrMnSiNi2Asteel at different temperatures and strain rates were investigated,and the strain hardening effect and temperature effect were discussed.Experimental results show that 30CrMnSiNi2Ahas obvious temperature sensitivity at 300°C.Moreover,the flow stress decreased significantly with the increase of temperature.The strain hardening effect of the material at high strain rate is not significant with the increase of strain.The strain rate hardening effect is obvious with increasing the temperature.According to the experimental results,the established Johnson-Cook（J-C）constitutive model of 30CrMnSiNi2Asteel could be used at high strain rate and high temperature.

Analytical models & type-curve matching techniques for reservoir characterization using wellbore storage dominated flow regime

The applicability of early time data in reservoir characterization is not always considered worthy.Early time data is usually controlled by wellbore storage effect.This effect may last for pseudo-radial flow or even boundary dominated flow.Eliminating this effect is an option for restoring real data.Using the data with this effect is another option that could be used successfully for reservoir characterization.This paper introduces new techniques for restoring disrupted data by wellbore storage at early time production.The proposed techniques are applicable for reservoirs depleted by horizontal wells and hydraulic fractures.Several analytical models describe early time data,controlled by wellbore storage effect,have been generated for both horizontal wells and horizontal wells intersecting multiple hydraulic fractures.The relationships of the peak points(humps)with the pressure,pressure derivative and production time have been mathematically formulated in this study for different wellbore storage coefficients.For horizontal wells,a complete set of type curves has been included for different wellbore lengths,skin factors and wellbore storage coefficients.Another complete set of type curves has been established for fractured formations based on the number of hydraulic fractures,spacing between fractures,and wellbore storage coefficient.The study has shown that early radial flow for short to moderate horizontal wells is the most affected by wellbore storage while for long horizontal wells;early linear flow is the most affected flow regime by wellbore storage effect.The study has also emphasized the applicability of early time data for characterizing the formations even though they could be controlled by wellbore storage effect.As a matter of fact,this paper has found out that wellbore storage dominated flow could have remarkable relationships with the other flow regimes might be developed during the entire production times.These relationships can be used to properly describe the formations and quantify some of their characteristics.

Practical solution for stabilized pseudo-steady state productivity index of multiple vertical wells depleting closed reservoirs

The objective of this paper is introducing practical solutions for stabilized pseudo-steady state productivity index and pressure behaviors and flow regimes of multiple vertical wells depleting closed rectangular reservoirs.It introduces full understanding of reservoir performance during transient and pseudo-steady state flow using pressure and pressure derivative patterns and productivity index and productivity index derivative schemes.The practical solutions proposed in this study are relied on a new approach for accurate estimation of starting time of pseudo-steady state flow and stabilized productivity index by applying productivity index derivative that converges mathematically to zero at the beginning of this flow.It is also an attempt for pointing out the optimal reservoir configuration that can give maximum stabilized pseudo-steady state productivity index for different wellbore types and distributions in the drainage area.Several analytical models are used in this study for describing pressure drop and productivity index behavior of multiple vertical wells considering different reservoir configurations and different wellbore types and locations.These wells were assumed either fully or partially penetrate the formations.These pressure models are justified to generate two pressure derivatives,one represents the derivative of time dependent pressure drop and the second represents the derivative of time-invariant pressure drop.The two derivatives are used for determining the starting time of pseudo-steady state flow and stabilized productivity index when both converge and mathematically become identical.These models are used also to generate several plots for time-invariant or stabilized pseudo-steady state productivity index for different reservoir geometries considering different wellbore conditions.The maximum stabilized productivity index is illustrated in these plots and several analytical models for the expected flow regimes are developed using pressure and pressure derivative behaviors of different reservoirs and wellbore conditions.The outcomes of this study are summarized in:1)Developing new analytical solutions for pressure distribution in porous media drained by multiple vertical wells.2)Developing new practical solution for estimating stabilized pseudo-steady state productivity index.3)Understanding pressure,pressure derivative,and productivity index behavior of finite acting reservoir depleted by multiple vertical wells during transient and pseudo-steady state production.4)Investigating the impacts of different reservoir configurations and wellbore sizes and locations as well as partial penetration on stabilized pseudo-steady state productivity index.The novel points in this study are:1)The optimum reservoir configuration that gives the maximum stabilized productivity index is the rectangular shape reservoir with reservoir length to width ratio of(2-4).2)Starting time of pseudo-steady state and stabilized productivity index are impacted by wellbore numbers,sizes,and locations.3)Starting time of pseudo-steady state flow is not affected by partial penetration ratio,however,stabilized productivity index is affected by this ratio.4)Five spots pattern gives the maximum productivity index compared with other wellbore distribution patterns.5)Productivity index of diagonally distributed wellbores is greater than the index of wellbores distributed along reservoir length.