This document describes the Van Everdingen-Hurst (VEH) model for simulating water influx into oil reservoirs from surrounding aquifers. The VEH model considers two geometries: radial flow and linear flow. For the radial model, flow is assumed to be strictly radial between a cylindrical reservoir and surrounding aquifer. For the linear model, flow is strictly linear between adjacent rectangular reservoir and aquifer volumes. The document provides detailed equations for calculating water influx over time using the VEH model for both radial and linear geometries and both infinite and finite aquifer extents.
All hydrocarbon reservoirs are surrounded by water-bearing rocks called aquifers which they effect on reservoir performance. it's a key role for production evaluation and therefore it should be managed.
All hydrocarbon reservoirs are surrounded by water-bearing rocks called aquifers which they effect on reservoir performance. it's a key role for production evaluation and therefore it should be managed.
B.TECH. DEGREE COURSE
SCHEME AND SYLLABUS
(2002-03 admission onwards)
MAHATMA GANDHI UNIVERSITY,mg university, KTU
KOTTAYAM
KERALA
Module 1
Introduction - Proprties of fluids - pressure, force, density, specific weight, compressibility, capillarity, surface tension, dynamic and kinematic viscosity-Pascal’s law-Newtonian and non-Newtonian fluids-fluid statics-measurement of pressure-variation of pressure-manometry-hydrostatic pressure on plane and curved surfaces-centre of pressure-buoyancy-floation-stability of submerged and floating bodies-metacentric height-period of oscillation.
Module 2
Kinematics of fluid motion-Eulerian and Lagrangian approach-classification and representation of fluid flow- path line, stream line and streak line. Basic hydrodynamics-equation for acceleration-continuity equation-rotational and irrotational flow-velocity potential and stream function-circulation and vorticity-vortex flow-energy variation across stream lines-basic field flow such as uniform flow, spiral flow, source, sink, doublet, vortex pair, flow past a cylinder with a circulation, Magnus effect-Joukowski theorem-coefficient of lift.
Module 3
Euler’s momentum equation-Bernoulli’s equation and its limitations-momentum and energy correction factors-pressure variation across uniform conduit and uniform bend-pressure distribution in irrotational flow and in curved boundaries-flow through orifices and mouthpieces, notches and weirs-time of emptying a tank-application of Bernoulli’s theorem-orifice meter, ventury meter, pitot tube, rotameter.
Module 4
Navier-Stoke’s equation-body force-Hagen-Poiseullie equation-boundary layer flow theory-velocity variation- methods of controlling-applications-diffuser-boundary layer separation –wakes, drag force, coefficient of drag, skin friction, pressure, profile and total drag-stream lined body, bluff body-drag force on a rectangular plate-drag coefficient for flow around a cylinder-lift and drag force on an aerofoil-applications of aerofoil- characteristics-work done-aerofoil flow recorder-polar diagram-simple problems.
Module 5
Flow of a real fluid-effect of viscosity on fluid flow-laminar and turbulent flow-boundary layer thickness-displacement, momentum and energy thickness-flow through pipes-laminar and turbulent flow in pipes-critical Reynolds number-Darcy-Weisback equation-hydraulic radius-Moody;s chart-pipes in series and parallel-siphon losses in pipes-power transmission through pipes-water hammer-equivalent pipe-open channel flow-Chezy’s equation-most economical cross section-hydraulic jump.
Speaks about the different aspects of flow measurement i.e. flow types, fluid types, its units, selection parameters; definition of common terms, coanda effect coriolis effect . it also speaks about the factors affecting flow measurement.
B.TECH. DEGREE COURSE
SCHEME AND SYLLABUS
(2002-03 admission onwards)
MAHATMA GANDHI UNIVERSITY,mg university, KTU
KOTTAYAM
KERALA
Module 1
Introduction - Proprties of fluids - pressure, force, density, specific weight, compressibility, capillarity, surface tension, dynamic and kinematic viscosity-Pascal’s law-Newtonian and non-Newtonian fluids-fluid statics-measurement of pressure-variation of pressure-manometry-hydrostatic pressure on plane and curved surfaces-centre of pressure-buoyancy-floation-stability of submerged and floating bodies-metacentric height-period of oscillation.
Module 2
Kinematics of fluid motion-Eulerian and Lagrangian approach-classification and representation of fluid flow- path line, stream line and streak line. Basic hydrodynamics-equation for acceleration-continuity equation-rotational and irrotational flow-velocity potential and stream function-circulation and vorticity-vortex flow-energy variation across stream lines-basic field flow such as uniform flow, spiral flow, source, sink, doublet, vortex pair, flow past a cylinder with a circulation, Magnus effect-Joukowski theorem-coefficient of lift.
Module 3
Euler’s momentum equation-Bernoulli’s equation and its limitations-momentum and energy correction factors-pressure variation across uniform conduit and uniform bend-pressure distribution in irrotational flow and in curved boundaries-flow through orifices and mouthpieces, notches and weirs-time of emptying a tank-application of Bernoulli’s theorem-orifice meter, ventury meter, pitot tube, rotameter.
Module 4
Navier-Stoke’s equation-body force-Hagen-Poiseullie equation-boundary layer flow theory-velocity variation- methods of controlling-applications-diffuser-boundary layer separation –wakes, drag force, coefficient of drag, skin friction, pressure, profile and total drag-stream lined body, bluff body-drag force on a rectangular plate-drag coefficient for flow around a cylinder-lift and drag force on an aerofoil-applications of aerofoil- characteristics-work done-aerofoil flow recorder-polar diagram-simple problems.
Module 5
Flow of a real fluid-effect of viscosity on fluid flow-laminar and turbulent flow-boundary layer thickness-displacement, momentum and energy thickness-flow through pipes-laminar and turbulent flow in pipes-critical Reynolds number-Darcy-Weisback equation-hydraulic radius-Moody;s chart-pipes in series and parallel-siphon losses in pipes-power transmission through pipes-water hammer-equivalent pipe-open channel flow-Chezy’s equation-most economical cross section-hydraulic jump.
Speaks about the different aspects of flow measurement i.e. flow types, fluid types, its units, selection parameters; definition of common terms, coanda effect coriolis effect . it also speaks about the factors affecting flow measurement.
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IJRET : International Journal of Research in Engineering and Technology is an international peer reviewed, online journal published by eSAT Publishing House for the enhancement of research in various disciplines of Engineering and Technology. The aim and scope of the journal is to provide an academic medium and an important reference for the advancement and dissemination of research results that support high-level learning, teaching and research in the fields of Engineering and Technology. We bring together Scientists, Academician, Field Engineers, Scholars and Students of related fields of Engineering and TechnologyIJRET : International Journal of Research in Engineering and Technology is an international peer reviewed, online journal published by eSAT Publishing House for the enhancement of research in various disciplines of Engineering and Technology. The aim and scope of the journal is to provide an academic medium and an important reference for the advancement and dissemination of research results that support high-level learning, teaching and research in the fields of Engineering and Technology. We bring together Scientists, Academician, Field Engineers, Scholars and Students of related fields of Engineering and Technology
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The function of membrane-embedded proteins such as ion channels depends crucially on their conformation. We demonstrate how conformational changes in asymmetric membrane proteins may be inferred from measurements of their diffusion. Such proteins cause local deformations in the membrane, which induce an extra hydrodynamic drag on the protein. Using membrane tension to control the magnitude of the deformations and hence the drag, measurements of diffusivity can be used to infer--- via an elastic model of the protein--- how conformation is changed by tension. Motivated by recent experimental results [Quemeneur et al., Proc. Natl. Acad. Sci. USA, 111 5083 (2014)] we focus on KvAP, a voltage-gated potassium channel. The conformation of KvAP is found to change considerably due to tension, with its `walls', where the protein meets the membrane, undergoing significant angular strains. The torsional stiffness is determined to be 26.8 kT at room temperature. This has implications for both the structure and function of such proteins in the environment of a tension-bearing membrane.
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A Strategic Approach: GenAI in EducationPeter Windle
Artificial Intelligence (AI) technologies such as Generative AI, Image Generators and Large Language Models have had a dramatic impact on teaching, learning and assessment over the past 18 months. The most immediate threat AI posed was to Academic Integrity with Higher Education Institutes (HEIs) focusing their efforts on combating the use of GenAI in assessment. Guidelines were developed for staff and students, policies put in place too. Innovative educators have forged paths in the use of Generative AI for teaching, learning and assessments leading to pockets of transformation springing up across HEIs, often with little or no top-down guidance, support or direction.
This Gasta posits a strategic approach to integrating AI into HEIs to prepare staff, students and the curriculum for an evolving world and workplace. We will highlight the advantages of working with these technologies beyond the realm of teaching, learning and assessment by considering prompt engineering skills, industry impact, curriculum changes, and the need for staff upskilling. In contrast, not engaging strategically with Generative AI poses risks, including falling behind peers, missed opportunities and failing to ensure our graduates remain employable. The rapid evolution of AI technologies necessitates a proactive and strategic approach if we are to remain relevant.
Honest Reviews of Tim Han LMA Course Program.pptxtimhan337
Personal development courses are widely available today, with each one promising life-changing outcomes. Tim Han’s Life Mastery Achievers (LMA) Course has drawn a lot of interest. In addition to offering my frank assessment of Success Insider’s LMA Course, this piece examines the course’s effects via a variety of Tim Han LMA course reviews and Success Insider comments.
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1. WATER INFLUX-2: VEH Model
Prof. K. V. Rao
Academic Advisor
Petroleum Courses
JNTUK
2. Van Everdingen-Hurst (VEH) model
van Everdingen and Hurst considered two geometries:
radial- and linear-flow systems. The radial model assumes
that the reservoir is a right cylinder and that the aquifer
surrounds the reservoir. Fig. 1 illustrates the radial aquifer
model, where:
• ro = reservoir radius
• ra = aquifer radius
4. Flow between the aquifer and reservoir is strictly radial. This model is
especially effective in simulating peripheral and edgewater drives but also
has been successful in simulating bottomwater drives.
In contrast, the linear model assumes the reservoir and aquifer are
juxtaposed rectangular parallelepipeds. Fig. 2 shows examples. Flow
between the aquifer and reservoir is strictly linear.
This model is intended to simulate edgewater and bottomwater drives. The
model definition depends on the application. For edgewater drives, the
thicknesses of the reservoir and aquifer are identical; the widths of the
reservoir and aquifer are also the same, and the aquifer and reservoir
lengths are La and Lr, respectively (Fig. 2a).
For bottomwater drives, the width of the reservoir and aquifer are identical;
the length (L) of the reservoir and aquifer are also the same; the aquifer
depth is La, and the reservoir thickness is h (Fig. 2b).
5. Fig. 2 – Linear aquifer model for (a) an edge water drive
(b) a bottom water drive.
6. van Everdingen and Hurst solved the applicable differential equations
analytically to determine the water influx history for the case of a
constant pressure differential at the aquifer/reservoir boundary.
This case assumes the reservoir pressure is constant. They called this
case the "constant terminal pressure" and reported their results in
terms of tables and charts.
This solution is not immediately applicable to actual reservoirs because
it does not consider a declining reservoir pressure. To address this
limitation, van Everdingen and Hurst applied the superposition theorem
to a specific reservoir pressure history.
This adaptation usually requires that the reservoir’s pressure history be
known. The first step in applying their model is to discretize the time
and pressure domains.
7. Discretization
The time domain is discretized into (n+1) points (t0, t1, t2, …., tn), where
t0 < t1 < t2 < …..> tn and t0 corresponds to t = 0. The average reservoir
pressure domain also is discretized into (n+1) points (𝑝0, 𝑝1, 𝑝2 …., 𝑝𝑛)
where 𝑝0 is the initial pressure pi. The time-averaged pressure between
levels j and j-1 is
The time-averaged pressure at level j = 0 is defined as the initial
pressure pi. Table 1 shows discretization of t, 𝑝, and 𝑝. The time-
averaged pressure decrement between levels j and j-1 is
[1]
[2]
8. No value is defined for j = 0. Table 1 shows the complete discretization
of t, 𝑝, 𝑝, and p.
Table 1- Time and pressure domain discretization for
van Everdingen-Hurst model.
9. Cumulative water influx
The cumulative water influx at kth level is
where U is the aquifer constant and WD is the dimensionless
cumulative water influx. This equation is based on the superposition
theorem. The term WD (tDk – tDj) is not a product but refers to the
evaluation of WD at a dimensionless time difference of (tDk – tDj). If we
apply Eq. 3 for k = 1, 2, and 3, we obtain
[3]
10. The length of the equation grows with the time. The aquifer
constant, U, and the dimensionless cumulative water influx, WD(tD),
depend on whether the radial or linear model is applied.
11. Radial model
The radial model is based on the following equations. The effective
reservoir radius is a function of the reservoir PV and is
where:
• ro is expressed in ft
• Vpr is the reservoir PV expressed in RB
• ϕr is the reservoir porosity (fraction)
• h is the pay thickness in ft
[4]
12. The constant f is θ/360, where θ is the angle that defines the portion of
the right cylinder. Fig. 3 illustrates the definition of θ for a radial aquifer
model.
The dimensionless time is
where:
• ka = aquifer permeability (md)
• μw = water viscosity (cp)
• ct = total aquifer compressibility (psi–1)
• ϕa = aquifer porosity (fraction)
• t is expressed in years
where U is in units of RB/psi if h is in ft, ro is in ft, and ct is in psi–1.
[5]
[6]
13. Fig. 3 – Definition of angle, ϕ, for radial aquifer model.
14. The dimensionless aquifer radius is
The dimensionless water influx, WD, is a function of tD and reD and
depends on whether the aquifer is infinite acting or finite.
[7]
15. Infinite radial aquifer
The aquifer is infinite acting if re approaches infinity or if the
pressure disturbance within the aquifer never reaches the aquifer’s
external boundary. If either of these conditions is met, then WD is
where a7 = 4.8534 × 10–12, a6 = –1.8436 × 10–9, a5 = 2.8354 × 10–
7, a4 = –2.2740 × 10–5, a3 = 1.0284 × 10–3, a2 = –2.7455 × 10–2,a1 =
8.5373 × 10–1, a0 = 8.1638 × 10–1, or
[8]
[9]
[10]
16. Finite radial aquifer
For finite aquifers, Eqs. 8 through 10 apply if tD < tD*, where
Where
If tD > tD*, then
Where
[11]
[7]
[12]
[13]
17. Marsal[7] gave Eqs. 11 through 13. These equations are effective in
approximating the charts and tables by van Everdingen and Hurst.
Minor discontinuities exist at some of the equation boundaries. A
slightly more accurate but much more lengthy set of equations has
been offered by Klins et al.[6] Fig. 4 shows WD as a function
of tD for reD = 5, 7.5, 10, 20, and ∞. These equations simplify the
application of the VEH model enormously.
18. Fig. 4 – WD vs. tD for a radial aquifer model.
19. A finite aquifer can be treated effectively as an infinite aquifer if
[14]
[15]
where tDmax is the maximum value of tD. These equations follow
from Eq. 11. For example, if tDmax is 540 and corresponds to a time
of 8 years, then Eq. 15 yields ≥ reD = 38. Therefore, if the aquifer has
a dimensionless radius greater than 38, then the aquifer acts
indistinguishably from and equivalent to an infinite aquifer at all
times less than 8 years.
20. Linear aquifer
The aquifer size in the linear model is given in terms of the
aquifer/reservoir pore-volume ratio, Vpa/Vpr.
The aquifer constant is
For edge water drives, the aquifer length is
[16]
[17]
[18]
21. where La and Lr are defined in Fig. 2a. For bottom water drives, the
aquifer depth is
where La is defined in Fig. 2b. The dimensionless time is
Eqs. 20 and 5 use the same units except La is given in ft. One difference
between the linear and radial models is that tD is a function of the aquifer
size for the linear model, whereas tDis independent of the aquifer size for
the radial model. This difference forces a recalculation of tD in the linear
model if the aquifer size is changed.
[19]
[20]
22. The dimensionless cumulative water influx is an
and
Eq. 21 is by Marsal, and Eq. 22 is by Walsh. Fig. 5 shows WD as a
function of tD. The aquifer can be treated as infinite if the aquifer
length is greater than the critical length
where tmax is the maximum time expressed in years and Lac is in units
of ft.
[21]
[22]
[23]
23. Eqs. 20 and 23 use the same units. Alternatively, the aquifer is
infinite-acting if tD ≤ 0.50. If infinite-acting and an edge water
drive, We can be evaluated directly without computing WD and is
where the units in Eq. 5 apply, and We is in units of RB
and h and w are in units of ft.
[24]
25. Calculation procedure
1. Discretize the time and average reservoir pressure domains and
define tj and 𝑝𝑗 for (j=0, 1, …n) according to table 1.
2. Compute the time-averaged reservoir pressure 𝑝𝑗 for (j = 1, 2, ….,
n) with eq. 1. Note that 𝑝0 = pi.
3. Compute the time-averaged incremental pressure differential pj for
(j=1, 2, …., n) with eq. 2.
4. Compute tDj for (j=0, 1, …, n) with eq. 5 for radial aquifers or with
eq. 20 for linear aquifers.
5. Steps 5 through 9 create a computational loop that is
repeated n times. The loop index is k, where k = 1, ..., n. For
the kth time level, compute (tDk – tDj) for (j = 0, ..., k – 1).
26. 6. For the kth time level, compute WD(tDk – tDj) for (j = 0, ..., k – 1).
7. For the kth time level, compute Δpj + 1 WD(tDk – tDj) for (j = 0,
..., k – 1).
8. For the kth time level, compute Wek with Eq. 3.
9. Increment the time from level k to k + 1, and return to Step 5
until k > n.
This procedure is highly repetitive and well suited for spreadsheet
calculation. The example below illustrates the procedure.