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The relations between in-situ and surface (usually SPE Standard Conditions (STP) ) flow properties are given by following equations (see Derivation):
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| q_O = \frac { q_o/B_o + R_v \cdot q_g/B_g } {1 - R_s R_v} |
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| q_G =\frac{q_g/B_g + R_s \cdot q_o/B_o}{1-R_s R_v} |
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| q_W = \frac{q_w}{B_w} |
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| q_L = q_O + q_W |
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| q_o = B_o \cdot ( q_O - R_v \, q_G) |
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| q_g = B_g \cdot ( q_G - R_s \, q_O) |
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| q_w = B_w \cdot q_W |
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rho_o\rhoo \frac{
\dotm_o}{}= \frac{\rho_O\rhoG\,R_s}{B_o}rhog\rho_g = frac{\g}{q_g}\frac{G+\rho \, R_v}{B_g}rhow\rho_w =\frac{w}{q_w}= \frac{\rho_W}{B_w}O1OOOG1G=rhocdotq
W1WW_W
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\dot m_o/B_o = \rho_O \cdot (q_ |
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o/B_o | | LaTeX Math Block |
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| \dot m_g = \rho_G \cdot q_g/B_g = \rho_O \cdot (q_G - R_s \, q_O) |
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| \dot m_w = \rho_W \cdot q_w/B_w |
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o_o
\frac{(\rhorho\, R_s)cdot ( q_O - R_v \, q_G) }{1- R_v \, R_s}
mgdot mg
frac{ (\rho_G + \ \, R_v) \cdot ( q_O - R_v \, q_G) }{1- R_v \, R_s}mwdot mwW \cdot \frac{q_w}{B_w} = \rho_W \cdot q_Wmtdot m = \dot m_o + \dot m_g + \dot mdot m_O + \dot m_G + \dot m_G qtqq_o + q_g + q_w |
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| q_t = \frac{B_o - B_g \, R_s}{1-R_v \, R_s} \cdot q_O
+\frac{B_g - B_o \, R_v}{1-R_v \, R_s} \cdot q_G
+ B_w \cdot q_W |
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| q_t = \frac{B_o - B_g \, R_s}{1-R_v \, R_s } \cdot \frac{\dot m_O }{\rho_O}
+\frac{B_g - B_o \, R_v}{1-R_v \, R_s } \cdot \frac{\dot m_G }{\rho_G}
+ B_w\cdot \frac{\dot m_W}{\rho_W}
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| \rho = \frac{\dot m}{q_t} = \frac{\dot m_O + \dot m_G + \dot m_G}{
\frac{B_o - B_g \, R_s}{1-R_v \, R_s } \cdot \frac{\dot m_O }{\rho_O}
+\frac{B_g - B_o \, R_v}{1-R_v \, R_s } \cdot \frac{\dot m_G }{\rho_G}
+ B_w\cdot \frac{\dot m_W}{\rho_W}
} |
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In-situ oil-cut: | LaTeX Math Block |
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| s_o = \frac{q_o}{q_t} = \frac{ B_o \, (q_O - R_v \, q_G)}{(B_o - B_g \, R_s) \, q_O + (Bg - B_o \, R_v) \, q_G + B_w \, (1- R_v \, R_s) \, q_W } |
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In-situ gas-cut: | LaTeX Math Block |
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| s_g = \frac{q_g}{q_t} = \frac{ B_g \, (q_G - R_s \, q_O)}{(B_o - B_g \, R_s) \, q_O + (Bg - B_o \, R_v) \, q_G + B_w \, (1- R_v \, R_s) \, q_W } |
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In-situ water-cut: | LaTeX Math Block |
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| s_w = \frac{q_w}{q_t} = \frac{ B_w \, (1- R_v \, R_s) \, q_W}{(B_o - B_g \, R_s) \, q_O + (Bg - B_o \, R_v) \, q_G + B_w \, (1- R_v \, R_s) \, q_W } |
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The total fluid density: | LaTeX Math Block |
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| \rho = s_o \, \rho_o + s_g \, \rho_g + s_w \, \rho_w |
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The total fluid compressibility: | LaTeX Math Block |
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| c = s_o \, c_o + s_g \, c_g + s_w \, c_w |
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See Also
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Petroleum Industry / Upstream / Subsurface E&P Disciplines / Fluid (PVT) Analysis / Fluid @model
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