methods and analysis : de-convolution and reservoir surveillance 26 - - PowerPoint PPT Presentation

Society of Petroleum Engineers – London Piers Johnson C.Eng

Managing Director of OPC 26th November 2013

Innovations in pressure transient test methods and analysis : de-convolution and reservoir surveillance

What we will cover in this talk…

• A Brief history of well testing and techniques
• Gauges
• De-convolution: Theory and Application
• Permanent Downhole Gauges (PDH) and using De-

convolution

• Other Applications of De-convolution (multi-stage

fraccing in horizontal wells)

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Well Testing as we used to know it

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A little bit of operational history….

• Onshore Well Testing (1950’s) Drill Stem Tests (DST’s)
• Open hole testing with an MFE (Multi Flow Evaluator –

mechanically operated tool) and mechanical pressure gauges – Amerada gauge. (1960’s)

• Burners allowed offshore testing (1970’s)
• Introduction of Electronic gauges and powerful personal

computers (1980’s)

26/11/2013 OPC 4

A little bit of operational history….

• Sub Sea Testing equipment (1980’s)
• Deep water Sub Sea Testing equipment (1990’s)
• Permanent down hole gauges (1990’s)
• Wireless communication with gauges (2000’s)

26/11/2013 OPC 5

And some theoretical history….

• Darcy’s law (flow in a porous medium) 19th Century
• Drawdown analysis.
• Build up analysis in the 1950’s and 1960’s. Miller

Dyes & Hutchison – MDH Plot, One single constant rate drawdown followed by a build up (Horner Plot) 1960’s – Straight line analysis generally by hand.

• Many flow periods at different rates with many

build ups. (Superposition theory) 1970’s

• Derivative Type Curve Analysis (Bourdet et al +

Computers & Software) 1980’s

• De-convolution (a few clever people!) 2000’s

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Schlumberger

Gauges and Gauge Performance – and cost

26/11/2013 OPC 7

26/11/2013 OPC 8

10 20 30 40 50 60 70 80 90 100 10 20 30 40 50 60 70 80 90 100 1980 1985 1990 1995 2000 2005 2010 2015 Costs Costs Year Cost of Wells Cost of Gauges

Gauge and Well Costs over the last 30 years

Diagrammatic only

Exploration well test Gauge Data

BIGASCI Example Data

0. 20. 40. 60. 80.

• 200.

600.

Time (hours) STB/D

BIGASCI Example Data

0. 20. 40. 60. 80. 0. 2000. 6000. 10000.

PSI

SET PACKER PRESSURE TEST TUBING WHEN RUNNING IN HOLE (RIH) INITIAL FLOW CLEAN UP FINAL BUILD UP MAIN FLOW POOH

REVERSE CIRCULATE

26/11/2013 OPC 9

Permanent Down hole Gauge Data

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De-Convolution in Simple Terms

Convolution and De-convolution can be thought of as simplified multiplication and division. Given: “P” is a set of measured pressure data “q” is a measured rate-history “pd” is the theoretical reservoir type-curve or drawdown function (as shown in next slide) Convolution: De-convolution:

d

p q P   q P pd  

Note that these equations are just a schematic of the

• process. The “multiplication” operator is the convolution

integral, and the “division” operator is a messy iterative solution as shown in the following slides...

26/11/2013 OPC 11

Some explanation of terms: for a Draw-Down Type-Curve Model (or response function)

0. 50. 100. 150.

• 20.

40. 80.

Time (hours)

0. 50. 100. 150. 4800. 4900. 5000.

q*pd(t) t +q The pressure change at the well bore, caused by production at a constant rate is characterised by a “type-curve model”, pd(t)

Note: the “d” in “pd” stands for “draw-down”. This “pd” has dimensions of psi/stb/d.

Pi

26/11/2013 OPC 12

Draw-Down Type-Curve Model

Given the following definitions:

t = time k = a characteristic permeability h = a characteristic thickness L = a characteristic length S = a constant “skin” x = a list of model parameters α,β = conversion factors

                    S x , L c kt f kh B ) t ( p

2 t d



For radial flow in an infinite reservoir, the above general equation translates into the classic drawdown equation as follows:

                  S r c k t kh B t p

w t d

87 . 23 . 3 log ) log( 6 . 162 ) (

2

 

26/11/2013 OPC 13

In order to understand Deconvolution, we need to understand Convolution.

The “Convolution” integral describes the pressure change for an arbitrary rate-history, “q(t)”:

   

     

 t d d i

d dt t dp q t p P ) (



  

 

 

 



 

   

n i i d i i d i

t t p q q t p P

1 1

For “q(t)” made up of ‘n’ constant-rate flow-periods which start at times “ti” and are less than “t”: “Convolution” is just “Superposition” by another name.

26/11/2013 OPC 14

So… what is De-Convolution?

• De-convolution is a mathematical solution that

characterises the reservoir.

• The objective of “de-convolution” is to:

– find the draw-down response function, pd, such that... – a best-fit is obtained between a type-curve simulation using pd and a set of pressure measurements, p(t)

• And the result from de-convolution is a derivative plot of

the response function, pd

• Note: pd is a completely arbitrary function! Which makes

this exercise difficult.

• This is possibly better explained as follows….

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Superposition

26/11/2013 OPC 16

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Deconvolution

Wrong Reservoir (dinosaur) model RIGHT Reservoir (dinosaur) model

So, Convolution is like a Multi-rate Simulation

0. 50. 100. 150. 200. 250.

• 100.

300.

Time (hours)

0. 50. 100. 150. 200. 250. 4000. 4400. 4800.

t > tq1 t > tq2 Pi-p(t) = [q1-q0]pd(t-tq1) Pi-p(t) = [q1-q0]pd(t-tq1) + [q2-q1]pd(t-tq2) note: q0=0

p(t) tq1 tq2 t tq3

Type-curve simulation computes “p(t)” by convolving a rate-history (qn) with a draw-down response, pd

Pi

q1 q2

Drawdown Build up

26/11/2013 OPC 18

De-convolution Recovers “pd”

Pi-p(t11) = [q1-q0]pd(t11-tq1) Pi-p(tq2) = [q1-q0]pd(tq2-tq1)



Pi-p(t21) = [q1-q0]pd(t21-tq1) + [q2-q1]pd(t21-tq2) Pi-p(tq3) = [q1-q0]pd(tq3-tq1) + [q2-q1]pd(tq3-tq2)



Given pressure points:

p(t11) to p(tq2) in 1st flow p(t21) to p(tq3) in 2nd flow

10 -2 10 -1 10 0 10 1 10 2 10 -2 10 -1 10 0

Delta-T (hr) Draw-Down Response (PSI/STB/D)

Solve this system of equations to recover pd from the measured rates and pressure points

pd(Δt) derivative of pd

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So what De-convolution does…

Pi-p(t11) = [q1-q0]pd(t11-tq1) Pi-p(tq2) = [q1-q0]pd(tq2-tq1)



Pi-p(t21) = [q1-q0]pd(t21-tq1) + [q2-q1]pd(t21-tq2) Pi-p(tq3) = [q1-q0]pd(tq3-tq1) + [q2-q1]pd(tq3-tq2)



Given pressure points:

p(t11) to p(tq2) in 1st flow p(t21) to p(tq3) in 2nd flow

10 -2 10 -1 10 0 10 1 10 2 10 -2 10 -1 10 0

Delta-T (hr) Draw-Down Response (PSI/STB/D)

tq2-tq1 tq3-tq1

…..is allow the de- convolved response to span the entire test duration!

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Is De-convolution useful then…?

• Does de-convolution derive more information from

the test data?

– No – a skilled engineer can eventually get the same answers using a regular analysis given some time…

• Does de-convolution make the analysis more

straight-forward?

– Yes – gives a direct “view” of the underlying model controlling the well. Get to the right answer faster.

• Does de-convolution help estimate reserves?

– Oh Yes! – provides a way of defining an “equivalent” radius-of-investigation for the whole test.

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De-convolution extends duration of analysis data

10-3 10-2 10-1 100 101 102 103 10-2 10-1 100 Delta-T (hr)

Well production history spans 5000 hours because Permanent Down hole gauges record the pressures and rates are recorded at surface (usually). Down hole Rate measurement devices are good too (another presentation). Response function (or Deconvolved Type curve) spans 5000 hours too! So we are no longer relying on build ups alone.

However….

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De-convolution doesn’t always work!

Pi-p(t11) = [q1-q0]pd(t11-tq1) Pi-p(tq2) = [q1-q0]pd(tq2-tq1)



Pi-p(t21) = [q1-q0]pd(t21-tq1) + [q2-q1]pd(t21-tq2) Pi-p(tq3) = [q1-q0]pd(tq3-tq1) + [q2-q1]pd(tq3-tq2)



Given real pressures:

p(t11) to p(tq2) in 1st flow p(t21) to p(tq3) in 2nd flow

10 -2 10 -1 10 0 10 1 10 2 10 -2 10 -1 10 0

Delta-T (hr) Draw-Down Response (PSI/STB/D)

Changes in behaviour between flow periods “pollutes” the algorithm which destroys the solution for pd

26/11/2013 OPC 23

“All-Together” De-convolution

The preceding slides described de-convolution of the entire set of analysis-data “all together” in a single

• peration of the algorithm.

De-convolving real data “all-together” will usually fail for these reasons:

• well-bore storage changes (e.g. change shut-in procedure)
• the skin-factor changes (e.g. clean-up)
• pressure interference from offset wells
• reservoir mobility changes (e.g. multi-phase flow)
• ...anything that changes the well behaviour!

26/11/2013 OPC 24

“All-Together” De-convolution does not always work

10-3 10-2 10-1 100 101 102 103 10-3 10-2 10-1 100

Delta-T (hr)

10-3 10-2 10-1 100 101 10-2 10-1 100

Delta-T (hr)

0. 500. 1000. 1500. 2000. 2500. 3000.

• 100.

300.

Time (hours)

0. 500. 1000. 1500. 2000. 2500. 3000. 3000. 3500. 4000. 4500.

Derivative plot comparison PBU#1 PBU#2 De-Convolution of both PBU’s ..”all-together” fails Bottom Hole Shut in vs Surface shut in – different well bore storage so De-convolution fails

26/11/2013 OPC 25

Choosing Data to De-convolve

Can de-convolution be applied to a test consisting of pressure measurements for a single flow-period? (e.g. a single PBU)

– Yes – de-convolution can be applied to any set of data, from a single PBU to an entire well history.

Are we free to choose the amount of data to use in de- convolution?

– Yes, up to a point. Too few points or not enough history will lead to failure.

Is the Initial Reservoir Pressure, Pi, important?

– Oh yes! Because the derived drawdown function, Pd, is based

• n drawdown dictated by a Pi.

26/11/2013 OPC 26

“Conditioned” De-convolution

0. 500. 1000. 1500. 2000. 2500. 3000.

• 100.

300.

Time (hours)

0. 500. 1000. 1500. 2000. 2500. 3000. 3000. 3500. 4000. 4500.

PBU#1 PBU#2

10-3 10-2 10-1 100 101 102 10-2 10-1 100

Delta-T (hr)

De-convolve PBU#1

10-2 10-1 100 101 102 103 10-2 10-1 100

Delta-T (hr)

De-convolve PBU#2

compare each de-convolved response for consistency

...over the TOTAL duration of the test

subject to points from PBU#1

10-2 10-1 100 101 102 103 10-2 10-1 100

Delta-T (hr)

.05 .05 .03 .03

26/11/2013 OPC 27

...a trick to guess the Initial-Pressure

10-3 10-2 10-1 100 101 102 103 10-3 10-2 10-1 100

Delta-T (hr)

.05 .05 .03

Pi too low

10-3 10-2 10-1 100 101 102 103 10-3 10-2 10-1 100

Delta-T (hr)

.05 .05 .03 .03

Pi too high

10-3 10-2 10-1 100 101 102 103 10-3 10-2 10-1 100

Delta-T (hr)

.05 .05 .03 .03

Pi just right

But the Rate History, and accurate rate measurement is as important too!

26/11/2013 OPC 28

De-convolution - Summary

• De-convolution extracts the underlying draw-down

response function, pd, given:

– a rate-history – the initial reservoir pressure – pressure data in one or more flow-periods

• “All-together” de-convolution is sensitive to changes

in behaviour between flow periods, and usually fails.

• “Conditioned” de-convolution is more reliable and

allows the consistency of the data to be checked.

26/11/2013 OPC 29

De-convolution – Important points to note

• The rate-history should be reasonably complete
• The initial-pressure at the start of production is

known (Note: important!).

• Select the pressure data that will be used for de-
• convolution. Usually, this is one or more PBU’s.
• Use “conditioned” de-convolution to derive the main
• results. Select flow periods and adjust the

conditioning factor to get consistent response curve.

• Adjust all of the above to get a sensible response

function.

26/11/2013 OPC 30

Example – Revealing the “Truth”

A Field B Well

0. 100. 200. 300. 400. 500.

• 5000.

5000. 15000.

Time (hours)

A Field B Well

0. 100. 200. 300. 400. 500.

• 2700. 2800. 2900. 3000. 3100. 3200. 3300.

ANALYSE

2003/10/23-2014 : OIL

26/11/2013 OPC 31

Example – Revealing the “Truth”

A Field B Well

10-3 10-2 10-1 100 101 10-4 10-3 10-2

Delta-T (hr) ENDWBS

2003/10/23-2014 : OIL

Homogeneous Reservoir ** Simulation Data **

• well. storage = 0.084581 BBLS/PSI

skin = -1.8893 permeability = 190.79 MD Areal Ky/Kx = 1.0000 Perm-Thickness = 5342.1 MD-METER +x boundary = 40.0 METER (1.00)

• x boundary = 60.0 METER (1.00)

+y boundary = 380. METER (1.00)

• y boundary = 780. METER (1.00)

Initial Press. = 7841.27 PSI Average Press. = 3499.28 PSI Pore-Volume = 779240. METER^3 Smoothing Coef = 0.,0. Static-Data and Constants Volume-Factor = 1.490 vol/vol Thickness = 28.00 METER Viscosity = 0.2980 CP Total Compress = .2310E-04 1/PSI Rate = 8000. STB/D Storivity = 0.0001552 METER/PSI Diffusivity = 2829. METER^2/HR Gauge Depth = N/A METER

• Perf. Depth = N/A METER

Datum Depth = N/A METER Analysis-Data ID: DCADJ Based on Gauge ID: A2 M51 PFA Starts: 2003-10-04 00:00:00 PFA Ends : 2003-10-24 21:18:36

A Field B Well

20000. 30000. 40000. 50000. 3000. 3100. 3200. 3300. 3400. 3500. 3600. Superposition(T) P PSI 6.0 HR 0.73 HR 0.048 HR ENDWBS 2003/10/23-2014 : OIL

A Field B Well

0. 100. 200. 300. 400. 500.

• 5000.

5000. 15000. Time (hours)

A Field B Well

0. 100. 200. 300. 400. 500. 2000. 3000. 4000. 5000. 6000. 7000. 2003/10/23-2014 : OIL

26/11/2013 OPC 32

Example – Revealing the “Truth”

A Field B Well

10-3 10-2 10-1 100 101 102 10-3 10-2 10-1

Delta-T (hr)

2003/10/23-2014 : OIL

Pi for this model is 7840psia. But if Pi is known to be 4155 psia, this cannot be the correct model

26/11/2013 OPC 33

All is not as it seems…!!

A Field B Well

10-3 10-2 10-1 100 101 102 10-3 10-2

Delta-T (hr) ENDWBS

2003/10/23-2014 : OIL

Linear-Composite 3-Zone ** Simulation Data **

• well. storage = 0.030000 BBLS/PSI

skin = -2.8000 permeability = 164.00 MD Areal Ky/Kx = 1.0000 X-Interface(1) = 45.000 METER Mob.ratio(1) = 0.15000 Stor.ratio(1) = 0.80000 X-Interface(2) = -45.000 METER Mob.ratio(2) = 0.15000 Stor.ratio(2) = 0.80000 Perm-Thickness = 4592.0 MD-METER +x boundary = 450. METER (1.00)

• x boundary = 450. METER (1.00)

+y boundary = 300. METER (1.00) Initial Press. = 4155.00 PSI

• Deconv. Initial Press. = 4155.00 PSI

Conditioning Coeff. = 0.0100000 [23-OCT-2003] Obj.Func. = 1501.20 Static-Data and Constants Volume-Factor = 1.490 vol/vol Thickness = 28.00 METER Viscosity = 0.2980 CP Total Compress = .2310E-04 1/PSI Rate = 8000. STB/D Storivity = 0.0001552 METER/PSI Diffusivity = 2432. METER^2/HR Gauge Depth = N/A METER

• Perf. Depth = N/A METER

Datum Depth = N/A METER Analysis-Data ID: DCADJ Based on Gauge ID: A2 M51 PFA Starts: 2003-10-04 00:00:00 PFA Ends : 2003-10-24 21:18:36

26/11/2013 OPC 34

Hydraulically Fractured Tight Gas Reservoir example using De-convolution

0. 500. 1000. 1500. 2000. 2500. 3000.

• 2000.

4000. 10000.

Time (hours)

0. 500. 1000. 1500. 2000. 2500. 3000. 1000. 2000. 3000. 4000. 5000. 6000. 2010/01/24-0000 : GAS (PSEUDO-P with Mat.Bal.)

Data showing large draw-down over a long time. Note the detailed rate-history with a flow-period for each pressure point.

26/11/2013 OPC 35

Deconvolved data for tight gas reservoir

10-1 100 101 102 103 10-3 10-2 10-1

Delta-T (hr) STABIL

2010/01/24-0000 : GAS (PSEUDO-P with Mat.Bal.)

permeability = 4.0000 MD Perm-Thickness = 400.00 MD-FEET R(inv) at 1.035 hr = 226. FEET Mat.Bal Correction

• Deconv. Initial Press. = 7763.00 PSI
• Deconv. Pore-Volume = 5266200. FEET^3
• Deconv. Ct = .7704E-04 1/PSI

Conditioning Coeff. = 1.0000 [24-JAN-2010] Obj.Func. = 22304.7 Static-Data and Constants Volume-Factor = 0.8104 RB/MSCF Thickness = 100.0 FEET Viscosity = 0.02702 CP Total Compress = .7704E-04 1/PSI Rate = 29.00 MSCF/D Storivity = 0.0003082 FEET/PSI Diffusivity = 12670. FEET^2/HR Gauge Depth = N/A FEET

• Perf. Depth = N/A FEET

Datum Depth = N/A FEET Analysis-Data ID: ALLQ2 Based on Gauge ID: THP PFA Starts: 2009-09-11 00:00:00 PFA Ends : 2010-01-25 00:00:00

De-convolution (note: with a material-balance correction) based on a specified reservoir pore-volume. Note that the de- convolution excludes the clean- up and gap in the data at 2000

• hours. Iterate on pore-volume

until response-function agrees with unit-slope line.

26/11/2013 OPC 36

De-convolution to obtain connected pore volume

10-1 100 101 102 103 10-3 10-2 10-1 Delta-T (hr) 2010/01/24-0000 : GAS (PSEUDO-P with Mat.Bal.)

Horizontal Well and Homogeneous Reservoir ** Simulation Data **

• well. storage = 0.010001 BBLS/PSI

Sk(mech.darcy) = 3.6228 permeability = 0.36946 MD Areal Ky/Kx = 1.0000 Kv/Kh = 0.100000 Drain Length/2 = 2250.0 FEET Zw/H = 0.50000 Sk(Global+DQ) = -7.7993 Skin(geom.) = -8.0538 Perm-Thickness = 36.946 MD-FEET Turbulence = 0. 1/MSCF/D +x boundary = 2300. FEET (1.00)

• x boundary = 2300. FEET (1.00)

+y boundary = 143. FEET (1.00)

• y boundary = 143. FEET (1.00)

Initial Press. = 7763.00 PSI Mat.Bal Correction

• Deconv. Initial Press. = 7763.00 PSI
• Deconv. Pore-Volume = 5266200. FEET^3

Model Pore-Volume = 5267600. FEET^3

• Deconv. Ct = .7704E-04 1/PSI

Model Ct = .7704E-04 1/PSI Conditioning Coeff. = 1.0000 [24-JAN-2010] Obj.Func. = 22304.7 Static-Data and Constants Volume-Factor = 0.8104 RB/MSCF Thickness = 100.0 FEET Viscosity = 0.02702 CP Total Compress = .7704E-04 1/PSI Rate = 29.00 MSCF/D Storivity = 0.0003082 FEET/PSI Diffusivity = 1170. FEET^2/HR Gauge Depth = N/A FEET

• Perf. Depth = N/A FEET

Datum Depth = N/A FEET Analysis-Data ID: ALLQ2 Based on Gauge ID: THP PFA Starts: 2009-09-11 00:00:00 PFA Ends : 2010-01-25 00:00:00

Match with a horizontal-well in a narrow box enclosing the well-bore i.e. the staged fracs "stimulated" a reservoir volume. The model pore- volume corresponds to the de- convolution pore-volume. The skin, permeability, kv/kh, etc. are just nominal values to get a stabilisation below the first point in the response- function.

26/11/2013 OPC 37

Connected Pore Volume

0. 500. 1000. 1500. 2000. 2500. 3000.

• 2000.

4000. 10000.

Time (hours)

0. 500. 1000. 1500. 2000. 2500. 3000. 1000. 2000. 3000. 4000. 5000. 6000. 2010/01/24-0000 : GAS (PSEUDO-P with Mat.Bal.)

Horizontal Well and Homogeneous Reservoir ** Simulation Data **

• well. storage = 0.0100000 BBLS/PSI

Sk(mech.darcy) = 3.6228 permeability = 0.36946 MD Areal Ky/Kx = 1.0000 Kv/Kh = 0.10000 Drain Length/2 = 2250.0 FEET Zw/H = 0.50000 Sk(Global+DQ) = -7.7993 Skin(geom.) = -8.0538 Perm-Thickness = 36.946 MD-FEET Turbulence = 0. 1/MSCF/D +x boundary = 2300. FEET (1.00)

• x boundary = 2300. FEET (1.00)

+y boundary = 143. FEET (1.00)

• y boundary = 143. FEET (1.00)

Initial Press. = 7763.00 PSI Average Press. = 2147.28 PSI Pore-Volume = 5262400. FEET^3 Sk(mech.darcy)+DQ = 3.6228 Static-Data and Constants Volume-Factor = 0.8104 RB/MSCF Thickness = 100.0 FEET Viscosity = 0.02702 CP Total Compress = .7704E-04 1/PSI Rate = 29.00 MSCF/D Storivity = 0.0003082 FEET/PSI Diffusivity = 1170. FEET^2/HR Gauge Depth = N/A FEET

• Perf. Depth = N/A FEET

Datum Depth = N/A FEET Analysis-Data ID: ALLQ2 Based on Gauge ID: THP PFA Starts: 2009-09-11 00:00:00 PFA Ends : 2010-01-25 00:00:00

Regular simulation with the results

• f the previous slides showing that

the model does make some sense. But only as an indication of the well behaviour i.e. the rate and pressure data are consistent with depletion

• f a rectangular reservoir with a

length equal to the length of the horizontal-well and a width equal to twice a sensible hydraulic-fracture half-length. In other words, the well is depleting a zone "broken and

• pened up" by the staged hydraulic-

fracture treatment. (see SPE paper 115766: Slick water Fracturing: Food for thought)

26/11/2013 OPC 38

De-convolution References

Three key papers describe the correct approach to de- convolution:

– SPE 71574, “De-convolution of Well Test Data as a Nonlinear Total Least Squares Problem”, October, 2001 – SPE 84290, “Practical Application of Pressure-Rate De- convolution to Analysis of Real Well Tests”, October, 2002 – SPE 90680, “Practical Considerations for Pressure-Rate De- convolution of Well Test Data”, September, 2004 I also want to thank Mike Wilson of Well Test Solutions who are responsible for PIE, the software used in this presentation and Bill Roberts of OPC USA in Houston, who helps me a lot! And others……

26/11/2013 OPC 39