/* [wxMaxima batch file version 1] [ DO NOT EDIT BY HAND! ]*/ /* [ Created with wxMaxima version 0.8.4 ] */ /* [wxMaxima: title start ] Gulf of Mexico Oil Spill Rough Calculations [wxMaxima: title end ] */ /* [wxMaxima: comment start ] This file contains some rough inputs and calculations relating to the Gulf of Mexico oil spill. The calculations are implemented using Maxima, a free computer algebra system under the terms of the GNU General Public License (http://wxmaxima.sourceforge.net/) [wxMaxima: comment end ] */ /* [wxMaxima: section start ] Setup [wxMaxima: section end ] */ /* [wxMaxima: comment start ] Prevent Maxima from converting floating point numbers to rational numbers [wxMaxima: comment end ] */ /* [wxMaxima: input start ] */ keepfloat:true; /* [wxMaxima: input end ] */ /* [wxMaxima: comment start ] Set precision for displaying floating point numbers [wxMaxima: comment end ] */ /* [wxMaxima: input start ] */ fpprintprec:6; /* [wxMaxima: input end ] */ /* [wxMaxima: section start ] Inputs [wxMaxima: section end ] */ /* [wxMaxima: subsect start ] Standard Constants [wxMaxima: subsect end ] */ /* [wxMaxima: comment start ] Acceleration due to gravity in m/s^2 [wxMaxima: comment end ] */ /* [wxMaxima: input start ] */ g:9.81; /* [wxMaxima: input end ] */ /* [wxMaxima: comment start ] Standard atmospheric pressure in Pa [wxMaxima: comment end ] */ /* [wxMaxima: input start ] */ p_atm:1.01325E5; /* [wxMaxima: input end ] */ /* [wxMaxima: subsect start ] Pressure Units and Conversion Factors [wxMaxima: subsect end ] */ /* [wxMaxima: comment start ] Pascal per psi [wxMaxima: comment end ] */ /* [wxMaxima: input start ] */ Pa_per_psi:1E5/14.5; /* [wxMaxima: input end ] */ /* [wxMaxima: comment start ] Psi per Pa [wxMaxima: comment end ] */ /* [wxMaxima: input start ] */ psi_per_Pa:14.5/1E5; /* [wxMaxima: input end ] */ /* [wxMaxima: comment start ] Bar per psi [wxMaxima: comment end ] */ /* [wxMaxima: input start ] */ bar_per_psi:1/14.5; /* [wxMaxima: input end ] */ /* [wxMaxima: comment start ] Bar per Pa [wxMaxima: comment end ] */ /* [wxMaxima: input start ] */ bar_per_Pa:1E-5; /* [wxMaxima: input end ] */ /* [wxMaxima: comment start ] Pa per bar [wxMaxima: comment end ] */ /* [wxMaxima: input start ] */ Pa_per_bar:1E5; /* [wxMaxima: input end ] */ /* [wxMaxima: subsect start ] Volume Units and Conversion Factors [wxMaxima: subsect end ] */ /* [wxMaxima: comment start ] Cubic metres per barrel of oil (source: http://en.wikipedia.org/wiki/Barrel, 1 Aug 2010) [wxMaxima: comment end ] */ /* [wxMaxima: input start ] */ cu_m_per_bbl:158.9873/1000; /* [wxMaxima: input end ] */ /* [wxMaxima: comment start ] US gallons per barrel of oil (source: (http://en.wikipedia.org/wiki/Barrel, 1 Aug 2010) [wxMaxima: comment end ] */ /* [wxMaxima: input start ] */ USg_per_bbl:42; /* [wxMaxima: input end ] */ /* [wxMaxima: comment start ] Barrels of oil per cubic metre [wxMaxima: comment end ] */ /* [wxMaxima: input start ] */ bbl_per_cu_m:1/cu_m_per_bbl; /* [wxMaxima: input end ] */ /* [wxMaxima: comment start ] Barrels of oil per US gallon [wxMaxima: comment end ] */ /* [wxMaxima: input start ] */ bbl_per_USg:1/USg_per_bbl, numer; /* [wxMaxima: input end ] */ /* [wxMaxima: subsect start ] Length Units and Conversion Factors [wxMaxima: subsect end ] */ /* [wxMaxima: comment start ] Feet per metre [wxMaxima: comment end ] */ /* [wxMaxima: input start ] */ ft_per_m:100/2.54/12; /* [wxMaxima: input end ] */ /* [wxMaxima: comment start ] Metres per foot [wxMaxima: comment end ] */ /* [wxMaxima: input start ] */ m_per_ft:12*2.54/100; /* [wxMaxima: input end ] */ /* [wxMaxima: subsect start ] Density Conversion Factors [wxMaxima: subsect end ] */ /* [wxMaxima: comment start ] ppg (pounds per US gallon) per (kg/m^3) Source http://www.onlineconversion.com/density_common.htm [wxMaxima: comment end ] */ /* [wxMaxima: input start ] */ ppUSg_per_kgpm3: 0.0083454044873; /* [wxMaxima: input end ] */ /* [wxMaxima: comment start ] (kg/m^3) per ppg) Source http://www.onlineconversion.com/density_common.htm [wxMaxima: comment end ] */ /* [wxMaxima: input start ] */ kgpm3_per_ppUSg: 1/ppUSg_per_kgpm3; /* [wxMaxima: input end ] */ /* [wxMaxima: subsect start ] Earth Crust Density [wxMaxima: subsect end ] */ /* [wxMaxima: comment start ] Density of earth crust kg/cm^3 (see (http://en.wikipedia.org/wiki/Oceanic_crust) [wxMaxima: comment end ] */ /* [wxMaxima: input start ] */ rho_e:3300; /* [wxMaxima: input end ] */ /* [wxMaxima: subsect start ] Sea Water Depth [wxMaxima: subsect end ] */ /* [wxMaxima: comment start ] Water Depth in metre (see http://en.wikipedia.org/wiki/Deep_water_Horizon_oil_spill) [wxMaxima: comment end ] */ /* [wxMaxima: input start ] */ z_water:1500; /* [wxMaxima: input end ] */ /* [wxMaxima: subsect start ] Density of Sea Water [wxMaxima: subsect end ] */ /* [wxMaxima: comment start ] Density of sea water in kg/m^3 (see (http://www.windows2universe.org/earth/water/density.html) [wxMaxima: comment end ] */ /* [wxMaxima: subsect start ] Depth of Reservoir below Seabed [wxMaxima: subsect end ] */ /* [wxMaxima: comment start ] Depth of well below seabed (underground riser depth) in m from Wikipedia (agrees with BP graphic of well and relief wells) [wxMaxima: comment end ] */ /* [wxMaxima: input start ] */ z_crust:5500; /* [wxMaxima: input end ] */ /* [wxMaxima: input start ] */ z_crust_ft:z_crust*ft_per_m; /* [wxMaxima: input end ] */ /* [wxMaxima: subsect start ] Crude Oil Density [wxMaxima: subsect end ] */ /* [wxMaxima: comment start ] Crude oil density (Mexican) kg/m^3 at 60 degF (15.6 degC) (http://www.engineeringtoolbox.com/liquids-densities-d_743.html) [wxMaxima: comment end ] */ /* [wxMaxima: input start ] */ rho_oil_mexican: 973; /* [wxMaxima: input end ] */ /* [wxMaxima: comment start ] Crude oil density (Eugene Island Block 43) kg/m^3 at 0 degC (http://www.etc-cte.ec.gc.ca/databases/Oilproperties/) [wxMaxima: comment end ] */ /* [wxMaxima: input start ] */ rho_oil_EI43: 853.1; /* [wxMaxima: input end ] */ /* [wxMaxima: comment start ] Crude oil density (Eugene Island Block 32) kg/m^3 at 0 degC (http://www.etc-cte.ec.gc.ca/databases/Oilproperties/) [wxMaxima: comment end ] */ /* [wxMaxima: input start ] */ rho_oil_EI32: 851.6; /* [wxMaxima: input end ] */ /* [wxMaxima: subsect start ] Well Head Oil Static Pressure [wxMaxima: subsect end ] */ /* [wxMaxima: comment start ] Well head oil static pressure 27 July 2010: 6928 psi (source http://twitter.com/BP_America/status/19675952967) [wxMaxima: comment end ] */ /* [wxMaxima: input start ] */ poil_well_head_static_psi:6928; /* [wxMaxima: input end ] */ /* [wxMaxima: comment start ] Well head oil static pressure in bar [wxMaxima: comment end ] */ /* [wxMaxima: input start ] */ poil_well_head_static_bar:poil_well_head_static_psi*bar_per_psi; /* [wxMaxima: input end ] */ /* [wxMaxima: comment start ] Well head oil static pressure in Pa [wxMaxima: comment end ] */ /* [wxMaxima: input start ] */ poil_well_head_static:poil_well_head_static_psi*Pa_per_psi; /* [wxMaxima: input end ] */ /* [wxMaxima: input start ] */ rho_water:1027; /* [wxMaxima: input end ] */ /* [wxMaxima: section start ] Calculations [wxMaxima: section end ] */ /* [wxMaxima: comment start ] Water pressure at seabed in Pa [wxMaxima: comment end ] */ /* [wxMaxima: input start ] */ p_water_bed:rho_water*g*z_water+p_atm; /* [wxMaxima: input end ] */ /* [wxMaxima: comment start ] Water pressure at seabed in bar [wxMaxima: comment end ] */ /* [wxMaxima: input start ] */ p_water_bed_bar:p_water_bed*bar_per_Pa; /* [wxMaxima: input end ] */ /* [wxMaxima: comment start ] Water pressure at seabed in psi [wxMaxima: comment end ] */ /* [wxMaxima: input start ] */ p_water_bed_psi:p_water_bed*psi_per_Pa; /* [wxMaxima: input end ] */ /* [wxMaxima: subsect start ] Estimated Maximum Hydrostatic Pressure at Depth of Oil Reservoir [wxMaxima: subsect end ] */ /* [wxMaxima: comment start ] Estimated maximum theoretical hydrostatic pressure at depth of oil reservoir (owing to weight of Earth's crust and pressure at sea bed) [wxMaxima: comment end ] */ /* [wxMaxima: input start ] */ p_res_max_est:p_water_bed+rho_e*g*z_crust; /* [wxMaxima: input end ] */ /* [wxMaxima: input start ] */ p_res_max_est_bar:p_res_max_est*bar_per_Pa; /* [wxMaxima: input end ] */ /* [wxMaxima: input start ] */ p_res_max_est_psi:p_res_max_est*psi_per_Pa; /* [wxMaxima: input end ] */ /* [wxMaxima: comment start ] Maximum hydrostatic pressure difference within underground riser [wxMaxima: comment end ] */ /* [wxMaxima: input start ] */ earth_riser_deltap_max:rho_oil_mexican*g*z_crust; /* [wxMaxima: input end ] */ /* [wxMaxima: input start ] */ earth_riser_deltap_max_bar:earth_riser_deltap_max*bar_per_Pa; /* [wxMaxima: input end ] */ /* [wxMaxima: input start ] */ earth_riser_deltap_max_psi:earth_riser_deltap_max*psi_per_Pa; /* [wxMaxima: input end ] */ /* [wxMaxima: comment start ] Estimated maximum hydrostatic oil pressure at sea bed (owing to weight of Earth's crust and pressure at sea bed and oil column below sea bed) [wxMaxima: comment end ] */ /* [wxMaxima: input start ] */ oil_p_seabed_max_est:p_res_max_est-earth_riser_deltap_max; /* [wxMaxima: input end ] */ /* [wxMaxima: input start ] */ oil_p_seabed_max_est_bar:oil_p_seabed_max_est*bar_per_Pa; /* [wxMaxima: input end ] */ /* [wxMaxima: input start ] */ oil_p_seabed_max_est_psi:oil_p_seabed_max_est*psi_per_Pa; /* [wxMaxima: input end ] */ /* [wxMaxima: comment start ] In fact the measured static pressure at the sea bed is much less than this, indicating that the pressure within the well is much less than the theoretical maximum value. [wxMaxima: comment end ] */ /* [wxMaxima: subsect start ] Calculated Hydrostatic Pressure at Depth of Oil Reservoir [wxMaxima: subsect end ] */ /* [wxMaxima: comment start ] Calculated hydrostatic pressure at depth of oil reservoir (from measured oil hydrostatic pressure at sea bed and underground oil column) [wxMaxima: comment end ] */ /* [wxMaxima: input start ] */ p_res:poil_well_head_static+rho_oil_EI32*g*z_crust; /* [wxMaxima: input end ] */ /* [wxMaxima: input start ] */ p_res_bar:p_res*bar_per_Pa; /* [wxMaxima: input end ] */ /* [wxMaxima: input start ] */ p_res_psi:p_res*psi_per_Pa; /* [wxMaxima: input end ] */ /* [wxMaxima: subsect start ] Density of Mud to Balance Oil Reservoir Pressure [wxMaxima: subsect end ] */ /* [wxMaxima: comment start ] If ballast mud is pumped down into the well from vessels on the surface, calculate its required density if the reservoir pressure is to be completely counterbalanced so that the pressure in the riser at the surface vessel is equal to atmospheric pressure. [wxMaxima: comment end ] */ /* [wxMaxima: input start ] */ z_water; /* [wxMaxima: input end ] */ /* [wxMaxima: input start ] */ z_crust; /* [wxMaxima: input end ] */ /* [wxMaxima: input start ] */ p_atm; /* [wxMaxima: input end ] */ /* [wxMaxima: comment start ] Pressure balance equation: [wxMaxima: comment end ] */ /* [wxMaxima: comment start ] poil_res = rho_mud_bal*g*(z_water+z_crust)+p_atm [wxMaxima: comment end ] */ /* [wxMaxima: comment start ] Required density (in kg/m^3) of ballast mud: [wxMaxima: comment end ] */ /* [wxMaxima: input start ] */ rho_mud_bal:(p_res-p_atm)/(z_water+z_crust)/g; /* [wxMaxima: input end ] */ /* [wxMaxima: comment start ] Required density in pounds per US gallon: [wxMaxima: comment end ] */ /* [wxMaxima: input start ] */ rho_mud_bal_ppUSg:rho_mud_bal*ppUSg_per_kgpm3; /* [wxMaxima: input end ] */ /* [wxMaxima: section start ] File Details [wxMaxima: section end ] */ /* [wxMaxima: comment start ] File name: GOM_Oil_Leak_r008.wxm Last updated: 3 August 2010 Updated by: Jim McGovern License: Creative Commons Attribution-ShareAlike 3.0 Unported http://creativecommons.org/licenses/by-sa/3.0/ Attribution: Calculations initiated by Jim McGovern, Fun-Engineering.net. [wxMaxima: comment end ] */ /* Maxima can't load/batch files which end with a comment! */ "Created with wxMaxima"$