This exercises requires conversions from field to SI units:

$145$ psi $=1$ MPa $=10$ bar

$1$g$/$cm$3=0\mathrm{.}433$ psi$/$ft or $1$psi$/$feet $=2\mathrm{.}308$ g$/$cm$3$

$10-6/$ psi $=1\mathrm{.}45*10-4$ MPa

$1$ millistrain $=0\mathrm{.}001$ strain $=0\mathrm{.}1\%$

The design of the platform to produce the Heriot field requires an estimate of the seabed subsidence resulting from hydrocarbon production over $5$ yrs

Top of Heriot is located at $3500$ m SS with a water depth of $500$ m$.$ The derrick floor elevation is $40$ m$.$ Average sea water density is $1\mathrm{.}02$ g$/$cm$3.$

Heriot reservoir characteristics:

vertical thickness $100$ m; radius $1500$ m

composed of flat$-$lying unconsolidated sands with porosity between $25\%$ and $30\%$

samples taken from $$good quality, clean sands$$

between sands are low$-$permeable mudrocks; average N$/$G is $0\mathrm{.}67$

average overburden density is $2\mathrm{.}38$ g$/$cc; reservoir pore fluid pressure before production is $69$ MPa and; a $55$ MPa depletion planned over a period of $5$ years.

Lab tests:

$5$ vertical samples from core in a vertical $($producer$)$ well through central part of the reservoir deformed in the laboratory

pores were connected to atmospheric pressure

samples loaded by increasing the total axial stress while keeping the radial dimension of the samples constant $($uniaxial strain$).$ In order to maintain uniaxial$-$strain conditions, the total radial stress increased from $20$ MPa to about $38$ MPa when the total axial stress increased from $20$ MPa to $90$ MPa.

$1)$ What is the initial $($pre$-$production$)$ total vertical stress in the reservoir $?$

$2)$ What is the initial effective vertical stress in the reservoir $?$

$3)$ What are your observations from experiments HERIOT$-1$ to HERIOT$-5?$ What did the experimentators forget to do $?$

$4)$ What is the average value of the $$uniaxial$-$strain compressibility Cm$$ of the good$-$quality sands, purely based on the lab data from tests HERIOT$-1-5?($assume N$/$G$=1.)$

$5)$ What is the range in Cm that you can determine from the laboratory deformation experiments $?$ What would be the causes of the spread in Cm $?$

$6)$ What is the best$-$estimate, high$-$case and low$-$case Cm of the entire reservoir, i$.$e$.$ its complete thickness, including sands and shales $($the $$gross thickness$)?$

$7)$ Now determine the Biot$-$Willis coefficient a of the sands from the experimental data. What is your interpretation of its magnitude $?$

Do you need to include it in your further poro$-$elastic analyses $?$

Cg is the solid$-$grain compressibility

Pure quartz: Cg $=2\mathrm{.}7*10-5/$MPa

Pure calcite: Cg $=1\mathrm{.}8*10-5/$MPa

Cbc is the bulk volume compressibility

Poisson$$s ratio is calculated as follows:

$8)$ Determine the static Young$$s modulus of the sands, best$-$estimate and its range, using a Poisson$$s ratio of $0\mathrm{.}2$

$9)$ Which type of $$Compressibility$$ can be determined directly from the experimental stress$-$strain data from tests HERIOT$1-5?$PROTECTED VIEW Be careful$-$files from the Internet can contain viruses. Unless you need to edit, it's safer to stay in Protected View.

Enable Editing

Present in Teams