Res Sim Exam

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PAPER NO. 28902B

HERIOT WATT UNIVERSITY

DEPARTMENT OF PETROLEUM ENGINEERING

Examination for the Degree of

Meng in Petroleum Engineering

Reservoir Simulation

Monday 17th April 1995 09.30 - 12.30

( 70% of Total marks )

NOTES FOR CANDIDATES

(1) Answer ALL the questions and try to confine your answer to the space provided on the

paper.

(2) The amount of space and the relative mark for the question will give you some idea of the

detail that is required in your answer.

(3) If you need more space in order to answer a question then continue on the back of the

same page indicating clearly (by PTO) that you have done so.

(4) The total number of marks in this examination is 262; this will be rescaled to give an

appropriate weighted percentage for the exam. The marks are relative and, together with

the space available, should give an approximate guide to the level of detail required.

(5) There is a compulsory 15 minute reading time on this paper during which you must not

write anything.

(6) You will be allocated 3 hours to complete this paper.


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Q1. List two uses of numerical reservoir simulation for each of the following stages of field

development.

(i) At the appraisal/early field development stage

1.

(2)

2.

(2)

(ii) At a stage well beyond the maximum oil production in a large North Sea field:

1.

(2)

2.

(2)

Q2. At any stage in a reservoir development by waterflooding, the engineer may use material

balance calculations and/or numerical reservoir simulation. Under which particular cir cumstances would you use each of these approaches?

(i) Material Balance?

(3)

(ii) Reservoir simulation?

(3)

Q3. Given all the problems and inaccuracies, which are known to exist in the application of

reservoir simulation, why do engineers still use it?

(2)


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Q4

Waterinjector

Waterinjector

High k Low k

Producer

2000 mVertical scale100 m

Continuous or

DiscontinuousShales ???

OWC

Reservoir X is a light oil reservoir (35º API) being developed by waterflooding. The reservoir

comprises a high average permeability massive sand overlying lower average permeability

laminated sands. The thickness of each sand is approximately equal and there are shales at the

interface of these two sands. However, the operator is uncertain if these shales are continuous or

discontinuous.

The following questions refer to Figure 1 above.

(i) What would the main differences be between the cases where the shales in the abovereservoir were continuous and where they were discontinuous?

(4)

(ii) Say briefly how you would go about investigating this using reservoir simulation.

(4)


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(iii) Suppose a reservoir engineer took 10 vertical grid blocks (NZ=10) in a simulation model

of this system. Would you expect the local (kv.kh) values in each of the main reservoir

sands to be similar or different? Explain your answer briefly.

Similar/different

(1)

Explain

(4)

(iv) If this reservoir well had a gas cap, then gas coning might be a problem.

What is gas coning? Draw a rough sketch.

(4)

How would you use reservoir simulation to investigate this problem?

(4)


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(v) In which two ways would the grid used to investigate gas coning be different from that

which was used in the full field waterflooding simulation?

1.

(2)

2.

(2)

Q5. Two of the main numerical problems/errors that arise in reservoir simulators are due to

numerical dispersion and grid orientation.

Explain each of these terms briefly saying - what it means, its origin and how we might get

round it. Draw a simple hand drawn sketch illustrating each.

(i) Numerical Dispersion: Sketch

(5)

(ii) Numerical Dispersion - Explanation?

(5)


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(iii) Grid Orientation - sketch

(4)

(iv) Grid orientation - Explanation?

(4)

Q6. A very simple single phase pressure equation is given by Eq. 1 below.

∂

∂

Ê Ë Á

ˆ ¯ ˜ =

∂

∂

Ê Ë Á

ˆ ¯ ˜

P

t

P

x

2

2Eq. 1

(i) Write down how this equation is discretised in an explicit finite difference scheme - briefly

explain your notation.

(4)


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(ii) If an implicit finite difference scheme was used to solve Eq. 1, then a set of linear

equations would arise which could be solved using either a direct or an iterative linear

equation solution technique. Briefly explain each of the bold terms above:

• Implicit finite difference scheme

(4)

• Set of linear equations

(4)

• Direct linear equation solution technique

(4)

• Iterative linear equation solution technique

(4)


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Q7. Statement: “The Equations of Two Phase Flow can be derived easily simply by using

Material Balance and Darcy’s Law”.

Explain this statement with reference to two phase flow - you do not need to actually derive the

equations and, indeed, you may not use any equations other than Darcy’s law.

(8)

Q8. (i) Draw a schematic sketch of a single grid block of size Dx by Dy by Dz, showing the

porosity f, the oil and water saturations So and S

w (only 2 phases present).

(2)


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(ii) Using the sketch in part (i) above, derive expressions for (a) the volume of oil in the grid

block, Vo; (b) the mass of oil in the grid block, M

o, introducing the formation volume

factor, Bo.

(a) Vo?

(3)

(b) Mo?

(3)

(iii) Write an expression for the oil flux, Jo, saying briefly what it is, any units it might be

expressed in and explaining any terms you introduce.

(6)


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Q9. (i) Name three ways in which a Black Oil reservoir simulation differs from a

Compositional simulation model.

1.

2.

3.

(6)

(ii) Draw a simple sketch of a single grid block showing what is meant by a component and a

phase.

(4)

(iii) Using the notation CIJ to denote the mass composition of component I per unit volume of

phase J (dimensions of CIJ are mass/volume), derive an expression - based on the

quantities labelled in your sketch in (ii) above - for the mass of component I in the grid

block.

(6)


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(iv) Give one example of (a) where you would use a Black Oil model and (b) where you would

use a Compositional simulation model.

(a) Use Black Oil model?

(3)

(b) Use Compositional model?

(3)

Q10. Figure 2: The figure below shows the basic idea of “upscaling” or “Pseudo-isation”.

"Fine" Grid Cross-Sectional Model

"Coarse" Grid Upscaled or Pseudo-ised Model

"Rock"Propts.

OIL

"Pseudo-"Propts.

With reference to Figure 2 above, answer the following:


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(i) What is meant by “Upscaling” with reference to the modelling of say a waterflood.

(2)

(ii) What is the difference between “rock” relative permeabilities and pseudo-relative

permeabilities?

(4)

(iii) In order to perform upscaling in reservoir simulation, we need both an Upscaling

Methodology and Upscaling Mathematical Techniques. Explain very briefly the

meaning of the bold terms.

• Methodology

(4)

• Techniques?

(4)


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Q11. (i) Sketch (roughly) a semi variogram for each of the following permeability models:

(a) a correlated random field with a range of 100m and a sill of 10,000 mD2; and

(b) a laminated system where the laminae are of constant width of 1cm and where the high

permeability = 2D and the low permeability = 1D. Label your sketches clearly.

(a)

(6)

(b)

(6)

(ii) What can you deduce about the standard deviation of the correlated random field in (i)(a)

above.

(3)


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(iii) Sketch the correlogram for case (i) above.

(5)

Q12. Figure 3 below shows the sketch of simple 3 layer model.

2 cm

5 cm

1 cm

k = 0.5 D

k = 2.0 D

k = 1.0 D y

x

(i) Calculate the effective permeability of the above model in the x-direction; show your working.

(5)


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(ii) Calculate the effective permeability of the above model in the y-direction, show your

working.

(6)

(ii) Suppose we put a very find grid (say of size 0.1 cm x 0.1 cm) on the 3 layer model in Figure 3

above. If we jumbled up all the grid blocks randomly so that the new model had no discernable

structure, would the new effective permeability be: greater than that in (i) and (ii)?; less than that in (i)

and (ii)?; in between these values? Explain your answer.

(6)


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Q13. In miscible flow in a random correlated field, explain how the mixing zone grows with

time in each of the following cases (illustrate your answers with simple sketches):

(i) dispersive flow

(4)

(ii) fingering flow

(4)

(iii) channelling flow

(4)

(iv) On the same diagram below, sketch the expected type of fractional flow curve f(c) vs c) you

would expect for each type of flow.

(6)


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Q14. In the Kyte and Berry pseudo-isation (upscaling) method, describe briefly (using a

diagram) how numerical dispersion is taken into account (no detailed mathematics is

required).

(10)


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Q15. (i) List the main categories in the hierarchy of stratal sedimentary elements - give one

short sentence explaining each of these.

(8)

(iii) Describe which of the above length scales of sedimentary heterogeneity are likely to have

most significance for the following reservoir flow phenomena:

* Reservoir pay-zone connectivity:

(3)

* Gravity slumping or water over-ride:

(3)

* Vertical sweep efficiency:

(3)

* Residual/Remaining oil saturation

(3)


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Q16. You have been given the following distribution of core-plug permeabilities in a particular

reservoir unit which includes a higher permeability a fluvial channel sand overlying a

lower permeability deltaic sand:

100 400 600 800

F r e q u e n c y

Permeability (md)

With reference to Figure 4 above: (a) explain the probable reason that the permeabilitydistribution has the above form; (b) sketch the sort of permeability models (laminar, bed and

formation scale) you might use for the flow simulation of this unit.

(a)

(3)

(b)

(continue on the back of this sheet if necessary) (10)


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Q17. (i) Draw a sketch of water displacement of oil across the laminae in a water-wet

laminated system at (a) “low” flow rate (capillary dominated) and (b) “high” flow rate

(viscous dominated); in this sketch show where the residual remaining oil is and

give a sentence or two of explanation.

(a)

(8)

(b)

(8)


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