Linear vs. Radial Boundary-Dominated Flow: Implications for Gas-Well-Decline Analysis

SPE Journal ◽  
2015 ◽  
Vol 20 (05) ◽  
pp. 1053-1066 ◽  
Author(s):  
Pichit Vardcharragosad ◽  
Luis F. Ayala ◽  
Miao Zhang
Keyword(s):  
Radial Flow ◽  
Transient Flow ◽  
Transient Behavior ◽  
Late Time ◽  
Gas Reservoirs ◽  
Linear Flow ◽  
Unconventional Resources ◽  
Flow Geometry ◽  
Fast Pace ◽  
The Impact

Summary Linear flow is a fundamental reservoir-flow geometry typically associated with production from unconventional resources stimulated by means of hydraulic fracturing. Recently, linear flow has been intensively studied following the fast pace of development of unconventional resources. Previous studies have mainly focused on early transient behavior and behavior of composite linear-flow systems. In this work, a density-based analysis method is extended to study decline behavior of the linear-flow system in boundary-dominated flow (BDF). In this study, we first discuss traditional approaches used to model linear flow in gas reservoirs. Second, we show the applicability of the density-based method for gas linear flow both analytically and numerically. Next, late-time solutions are discussed, and the analytical forecasting solution that best describes the BDF behavior is selected for long-term decline-behavior studies. Previously reported results on radial flow as well as early transient-flow effect are also incorporated to provide a more complete understanding of decline behavior and the impact of flow geometry. We show that boundary-dominated responses in linear-flow scenarios fully develop at much later stages of reservoir depletion compared with radial-flow scenarios. As a result, and in marked contrast with radial flow, purely hyperbolic decline behavior may be completely lost in linear-flow scenarios during boundary-dominated conditions. It is demonstrated that most of the recoverable hydrocarbons are produced during the early transient period for linear-flow conditions, whereas most of them are recovered during the BDF period for radial flow. These results suggest that the availability of accurate early transient models is much more critical for the formulation of linear-flow-decline models than had been traditionally necessary for radial-flow-decline models.

Unsteady Radial Flow of Gas Through Porous Media

1953 ◽  
Vol 20 (2) ◽  
pp. 210-214
Author(s):  
R. Jenkins ◽  
J. S. Aronofsky
Keyword(s):  
Porous Medium ◽  
Porous Media ◽  
Radial Flow ◽  
Transient Flow ◽  
Gas Reservoirs ◽  
Punch Card ◽  
Flow Rates ◽  
Pressure Distributions ◽  
History Of ◽  
Natural Gas Reservoirs

Abstract This paper presents a numerical method for describing the transient flow of gases radially inward or outward through a porous medium in which the initial and terminal pressures and/or rates are specified. Specific examples are worked out which have application in the study of natural-gas reservoirs. The computations were carried out by means of punch-card machines. The pressure distribution as a function of time has been calculated for various ratios of reservoir diameter to well diameter and for various dimensionless flow rates for a well penetrating the center of a homogeneous disk-shaped reservoir. A simple means of predicting the well pressure at any time in the history of such an idealized field has been developed. Flow rates and pressure distributions within the radial reservoir also have been calculated for the case in which the well pressure is suddenly lowered from its initial static value, and then held constant.

Influence of Flow Geometry on Sandface Temperatures During Single-Phase Oil Production: Dimensionless Analysis

SPE Journal ◽  
2016 ◽  
Vol 21 (03) ◽  
pp. 0928-0937 ◽  
Author(s):  
J. F. App
Keyword(s):  
Steady State ◽  
Flow Regime ◽  
Transient Analysis ◽  
Numerical Solutions ◽  
Temperature Behavior ◽  
Transient Temperature ◽  
Linear Flow ◽  
Dimensionless Analysis ◽  
Flow Geometry ◽  
The Impact

Summary This paper evaluates the impact of flow geometry on sandface temperature behavior under conditions of high drawdown in which Joule-Thomson thermal effects are significant. The temperature behavior of both radial- and linear-flow regimes is evaluated under steady-state and transient conditions. Through a dimensionless analysis of the thermal-energy equation, a systematic evaluation of the contributing terms is presented. The steady-state analysis is based on analytic solutions that demonstrate identical temperature behavior at asymptotic limits but are offset by a geometric factor at intermediary Péclet numbers. The transient analysis is based on a combination of analytical and numerical solutions. The transient analysis demonstrates that temperature changes occur earlier in time for the radial geometry compared with the linear geometry. The impetus behind this study is to address the impact of transient-temperature development in hydraulically fractured vs. nonhydraulically fractured vertical completions. The flow regime in nonhydraulically fractured vertical completions is radial whereas in hydraulically fractured vertical completions a linear-flow regime can dominate a significant portion of the flow history. All analyses assume that skin, wellbore-storage, and thermal-storage effects are negligible.

Pressure-Transient Behavior of Partially Penetrating Inclined Fractures With a Finite Conductivity

SPE Journal ◽  
2018 ◽  
Vol 24 (02) ◽  
pp. 811-833 ◽  
Author(s):  
Bailu Teng ◽  
Huazhou Andy Li
Keyword(s):  
Fluid Flow ◽  
Transient Flow ◽  
Flow Behavior ◽  
Transient Behavior ◽  
Finite Conductivity ◽  
Linear Flow ◽  
Pressure Transient ◽  
Proposed Model ◽  
Elliptical Flow ◽  
The Matrix

Summary Field studies have shown that, if an inclined fracture has a significant inclination angle from the vertical direction or the fracture has a poor growth along the inclined direction, this fracture probably cannot fully penetrate the formation, resulting in a partially penetrating inclined fracture (PPIF) in these formations. It is necessary for the petroleum industry to conduct a pressure-transient analysis on such fractures to properly understand the major mechanisms governing the oil production from them. In this work, we develop a semianalytical model to characterize the pressure-transient behavior of a finite-conductivity PPIF. We discretize the fracture into small panels, and each of these panels is treated as a plane source. The fluid flow in the fracture system is numerically characterized with a finite-difference method, whereas the fluid flow in the matrix system is analytically characterized on the basis of the Green's-function method. As such, a semianalytical model for characterizing the transient-flow behavior of a PPIF can be readily constructed by coupling the transient flow in the fracture and that in the matrix. With the aid of the proposed model, we conduct a detailed study on the transient-flow behavior of the PPIFs. Our calculation results show that a PPIF with a finite conductivity in a bounded reservoir can exhibit the following flow regimes: wellbore afterflow, fracture radial flow, bilinear flow, inclined-formation linear flow, vertical elliptical flow, vertical pseudoradial flow, inclined pseudoradial flow, horizontal-formation linear flow, horizontal elliptical flow, horizontal pseudoradial flow, and boundary-dominated flow. A negative-slope period can appear on the pressure-derivative curve, which is attributed to a converging flow near the wellbore. Even with a small dimensionless fracture conductivity, a PPIF can exhibit a horizontal-formation linear flow. In addition to PPIFs, the proposed model also can be used to simulate the pressure-transient behavior of fully penetrating vertical fractures (FPVFs), partially penetrating vertical fractures (PPVFs), fully penetrating inclined fractures (FPIFs), and horizontal fractures (HFs).

Type Curves for Finite Radial and Linear Gas-Flow Systems: Constant-Terminal-Pressure Case

1985 ◽  
Vol 25 (05) ◽  
pp. 719-728 ◽  
Author(s):  
Robert D. Carter
Keyword(s):  
Production Rate ◽  
Gas Flow ◽  
Late Time ◽  
Linear Flow ◽  
Type Curves ◽  
Basic Assumptions ◽  
Flow Geometry ◽  
Transient Period ◽  
Dimensionless Variables ◽  
Bottomhole Pressure

Carter, Robert D., SPE, Amoco Production Co. Abstract This paper presents gas-production-rate results in type curve form for finite radial and linear flow systems produced at a constant terminal (bottomhole) pressure. These produced at a constant terminal (bottomhole) pressure. These results can be used in the analysis of actual gas and oil rate/time data to estimate reservoir size and to infer reservoir shape. The type curves are based on dimensionless variables that are a generalized form of those presented previously. In addition, an approximate drawdown previously. In addition, an approximate drawdown parameter is presented. Example applications that parameter is presented. Example applications that demonstrate the applicability of the type curves to a variety of reservoir configurations are given. The Appendix contains derivations of the dimensionless variables and the drawdown parameter. Introduction The gas-bearing rock in some low-permeability gas fields consists of sandstone lenses of uncertain but limited size. In such fields, the reservoir area and volume drained by individual wells cannot be inferred from well spacing. Moreover, good reserve estimates using plots of p/z vs. cumulative production are often not possible because of the difficulty of obtaining reservoir pressure from buildup tests. Therefore, reserve estimation techniques that use performance data, such as production rate as a function performance data, such as production rate as a function of time, are needed. Although this problem has been recognized, the techniques proposed in the past for application to gas reservoirs have been mostly empirical. The present work offers a method that is consistent with the basic theory of gas flow in porous media for analyzing production data to estimate reserves. This method will also provide some inference about reservoir shape. Type Curves Basic Assumptions Six basic assumptions are made in generating the type curves.The flow geometry is radial; therefore, the reservoir either is circular and is produced by a concentrically located well of finite radius or is a sector of a circle produced by the corresponding sector of the well (Fig. 1). produced by the corresponding sector of the well (Fig. 1). In the limit as, the flow regime becomes a linear one.Permeability, porosity, and thickness are constant throughout the reservoir.The pressure at the well radius (usually corresponding to the bottomhole flowing pressure CBHFP]) is held constant.The initial reservoir pressure is constant (independent of position).Non-Darcy flow is neglected.The flowing fluid is either a gas with viscosity and compressibility that vary with pressure or an oil with a constant viscosity/compressibility product. Definitions. The type curves are based on specially defined dimensionless time (tD), dimensionless rate (qD), a flow geometry parameter ( ), and a drawdown parameter ( ). These variables are defined by the following parameter ( ). These variables are defined by the following equations, which are derived in the Appendix. ............................ (1) ................................(2) ...............................(3) .....................(4) Results The type curves for rate as a function of time are presented in Fig. 2. A finite-difference radial-gas-flow simulator was used to generate the data for constructing the type curves. Two flow periods can be identified. The infinite-acting (or transient) period is that period before which the curves become concave downward. The transient period ends at to values ranging from about 0.15 to about 1.0, depending on the value of 17 that characterizes the curve. The curves are concave downward during the late-time or depletion period. Notice that the primary characterizing parameter during the infinite-acting period is, and is parameter during the infinite-acting period is, and is the characterizing parameter for late-time behavior (tD >1). The curves for = 1.234 (linear flow) are straight lines with a negative half-slope during the infinite-acting period. SPEJ p. 719

scholarly journals Incremental and acceleration production estimation and their effect on optimization of well infill locations in tight gas reservoirs

2021 ◽  
Author(s):  
Atheer Dheyauldeen ◽  
Omar Al-Fatlawi ◽  
Md Mofazzal Hossain
Keyword(s):  
Transient Flow ◽  
Development Planning ◽  
Main Role ◽  
Gas Reservoirs ◽  
Type Curves ◽  
Field Development ◽  
Drilling Performance ◽  
Well Location ◽  
Infill Drilling ◽  
Tight Formations

AbstractThe main role of infill drilling is either adding incremental reserves to the already existing one by intersecting newly undrained (virgin) regions or accelerating the production from currently depleted areas. Accelerating reserves from increasing drainage in tight formations can be beneficial considering the time value of money and the cost of additional wells. However, the maximum benefit can be realized when infill wells produce mostly incremental recoveries (recoveries from virgin formations). Therefore, the prediction of incremental and accelerated recovery is crucial in field development planning as it helps in the optimization of infill wells with the assurance of long-term economic sustainability of the project. Several approaches are presented in literatures to determine incremental and acceleration recovery and areas for infill drilling. However, the majority of these methods require huge and expensive data; and very time-consuming simulation studies. In this study, two qualitative techniques are proposed for the estimation of incremental and accelerated recovery based upon readily available production data. In the first technique, acceleration and incremental recovery, and thus infill drilling, are predicted from the trend of the cumulative production (Gp) versus square root time function. This approach is more applicable for tight formations considering the long period of transient linear flow. The second technique is based on multi-well Blasingame type curves analysis. This technique appears to best be applied when the production of parent wells reaches the boundary dominated flow (BDF) region before the production start of the successive infill wells. These techniques are important in field development planning as the flow regimes in tight formations change gradually from transient flow (early times) to BDF (late times) as the production continues. Despite different approaches/methods, the field case studies demonstrate that the accurate framework for strategic well planning including prediction of optimum well location is very critical, especially for the realization of the commercial benefit (i.e., increasing and accelerating of reserve or assets) from infilled drilling campaign. Also, the proposed framework and findings of this study provide new insight into infilled drilling campaigns including the importance of better evaluation of infill drilling performance in tight formations, which eventually assist on informed decisions process regarding future development plans.

LOVE, GRIEF, FEAR, AND SHAME: MEDEA'S INTERCONNECTING EMOTIONS IN BOOK 3 OF APOLLONIUS’ ARGONAUTICA

2021 ◽  
Vol 68 (1) ◽  
pp. 45-60
Author(s):  
Ed Sanders
Keyword(s):  
Erotic Love ◽  
The Real ◽  
Fast Pace ◽  
The Impact ◽  
The Erotic

In its justly celebrated Book 3, the fast pace of action elsewhere in Apollonius’ Argonautica slows dramatically, such that Medea's erotic infatuation with Jason, and the consequent effects of this infatuation, become the central episode of the entire epic. Indeed, the role that Medea's erôs (erotic love, desire) plays in Book 3 is so great that one scholar has opined that ‘It is not the heroic as such but rather the erotic that becomes the real theme.’ However, it is not just erôs that shapes this book, but also Medea's internal battle with a number of other emotions that erôs engenders: principally grief, fear, and shame. Assessing the impact of each and understanding their interplay is complicated, however, because the text frequently presents them as occurring multifariously, or in quick succession – for example switching from erôs to grief, back to erôs, to fear, back to grief, to pity, and to grief again, all within a few lines (443–71). Accordingly I propose to disaggregate her emotions, looking at each in turn wherever it occurs, before considering how Apollonius presents them as interconnecting, and what such interconnections add to his overall presentation of Medea – especially by contrast to that of Euripides, from an emotional perspective the most important precursor.

scholarly journals Exogenous Alginate Protects Staphylococcus aureus from Killing by Pseudomonas aeruginosa

2019 ◽  
Vol 202 (8) ◽  
Author(s):  
Courtney E. Price ◽  
Dustin G. Brown ◽  
Dominique H. Limoli ◽  
Vanessa V. Phelan ◽  
George A. O’Toole
Keyword(s):  
Staphylococcus Aureus ◽  
Pseudomonas Aeruginosa ◽  
Physical Space ◽  
Late Time ◽  
Protective Effects ◽  
Content Type ◽  
Alginate Production ◽  
The Impact

ABSTRACT Cystic fibrosis (CF) patients chronically infected with both Pseudomonas aeruginosa and Staphylococcus aureus have worse health outcomes than patients who are monoinfected with either P. aeruginosa or S. aureus. We showed previously that mucoid strains of P. aeruginosa can coexist with S. aureus in vitro due to the transcriptional downregulation of several toxic exoproducts typically produced by P. aeruginosa, including siderophores, rhamnolipids, and HQNO (2-heptyl-4-hydroxyquinoline N-oxide). Here, we demonstrate that exogenous alginate protects S. aureus from P. aeruginosa in both planktonic and biofilm coculture models under a variety of nutritional conditions. S. aureus protection in the presence of exogenous alginate is due to the transcriptional downregulation of pvdA, a gene required for the production of the iron-scavenging siderophore pyoverdine as well as the downregulation of the PQS (Pseudomonas quinolone signal) (2-heptyl-3,4-dihydroxyquinoline) quorum sensing system. The impact of exogenous alginate is independent of endogenous alginate production. We further demonstrate that coculture of mucoid P. aeruginosa with nonmucoid P. aeruginosa strains can mitigate the killing of S. aureus by the nonmucoid strain of P. aeruginosa, indicating that the mechanism that we describe here may function in vivo in the context of mixed infections. Finally, we investigated a panel of mucoid clinical isolates that retain the ability to kill S. aureus at late time points and show that each strain has a unique expression profile, indicating that mucoid isolates can overcome the S. aureus-protective effects of mucoidy in a strain-specific manner. IMPORTANCE CF patients are chronically infected by polymicrobial communities. The two dominant bacterial pathogens that infect the lungs of CF patients are P. aeruginosa and S. aureus, with ∼30% of patients coinfected by both species. Such coinfected individuals have worse outcomes than monoinfected patients, and both species persist within the same physical space. A variety of host and environmental factors have been demonstrated to promote P. aeruginosa-S. aureus coexistence, despite evidence that P. aeruginosa kills S. aureus when these organisms are cocultured in vitro. Thus, a better understanding of P. aeruginosa-S. aureus interactions, particularly mechanisms by which these microorganisms are able to coexist in proximal physical space, will lead to better-informed treatments for chronic polymicrobial infections.

Abstract P481: Time to Reperfusion Determines Clinical Outcomes Independent of Post Thrombectomy Infarct Volume

Stroke ◽  
2021 ◽  
Vol 52 (Suppl_1) ◽  
Author(s):  
Shashvat Desai ◽  
Amin N Aghaebrahim ◽  
James E Siegler ◽  
Andre Monteiro ◽  
Ashutosh P Jadhav ◽  
...  
Keyword(s):  
Multivariate Analysis ◽  
Clinical Outcomes ◽  
Clinical Improvement ◽  
Functional Outcomes ◽  
Time Window ◽  
Infarct Volume ◽  
Late Time ◽  
Inclusion Criteria ◽  
Ischemic Time ◽  
The Impact

Introduction: Late time window thrombectomy trials demonstrated that good functional outcomes can be achieved up to 24 hours from stroke onset in Slow Progressors (small infarct volume and large penumbral volume). In this study, we aim to investigate whether early (<6 hours) recanalization leads to superior functional outcomes compared to delayed recanalization (>6 hours) amongst patients with similar 24-hour infarct volumes post thrombectomy. Methods: We performed a retrospective analysis of a prospectively maintained LVO stroke thrombectomy database across 3 comprehensive stroke centers. Demographic, clinical, radiological, and outcomes data were analyzed. Inclusion criteria were witnessed onset anterior circulation LVO [internal carotid or middle cerebral artery M1] strokes with a good baseline mRS score (0-1) having achieved success recanalization [mTICI 2b-3] and 24-hour infarct volume of ≤10 ml on CT head or MRI. Univariate and multivariate analysis of the impact of time to recanalization on clinical outcomes was performed. Results: Of the 499 LVO strokes undergoing thrombectomy, 30% (148) met inclusion criteria. Mean age was 70 ±14 and median NIHSS score was 17 (14-21). Early recanalization (<6h) was achieved in 65% (96) of patients. Baseline demographic (age: 73 vs 74, p=0.80) and clinical characteristics (NIHSS:16.5 vs 17, p=0.52; 24-h infarct volume: 4.4 vs 4.2 ml, p=0.60) were comparable between early versus late recanalization patients. Rates of early clinical improvement (24-h NIHSS <6) (71% vs 39%, p=0.0007) and mRS 0-2 at 90 days (68% vs 48%, p=0.019) were higher in early recanalizers compared to late recanalizers. Multivariate analysis including age, NIHSS, time to recanalization, and 24-hour infarct volume identified early recanalization as an independent predictor of mRS 0-2 at 90 days (OR-2.41 95% CI 1.89-4.50). Every 1-hour increase in time to recanalization decreased the odds of 90-day mRS 0-2 by 2.2%. Conclusion: Among patients with similar 24-hour infarct volume post thrombectomy (≤10 ml), shorter time to successful recanalization is associated with significantly higher rates of early clinical improvement and mRS 0-2 at 90 days. Increased penumbral ischemic time may have an impact on outcomes post stroke thrombectomy.

Analysis for the Effect of Inverter Ripple Current on Fuel Cell Operating Condition

2001 ◽  
Author(s):  
Randall S. Gemmen
Keyword(s):  
Boundary Condition ◽  
Fuel Cell ◽  
Mass Transport ◽  
Transient Behavior ◽  
Mechanical State ◽  
Dimensional Model ◽  
One Dimensional ◽  
Fuel Cell Stack ◽  
A Cell ◽  
The Impact

Abstract The effect of inverter ripple current on fuel cell stack performance and stack lifetime remains uncertain. This paper provides a first attempt to examine the impact of inverter load dynamics on the fuel cell. Since reactant utilization is known to impact the mechanical state of a fuel cell, it is suggested that the varying reactant conditions surrounding the cell govern, at least in part, the lifetime of the cells. This paper investigates these conditions through the use of a dynamic model for the bulk conditions within the stack, as well as a one-dimensional model for the detailed mass transport occurring within the electrode of a cell. These two independent modeling approaches help to verify their respective numerical procedures. In this work, the inverter load is imposed as a boundary condition to the models. Results show the transient behavior of the reactant concentrations within the stack, and of the mass diffusion within the electrode under inverter loads with frequencies between 30 Hz and 1250 Hz.

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