# 春光油田储层砂岩地震岩石物理模型构建及其应用The Establishment of Seismic Rock Physics Model of Reservoir Sandstone in Chunguang Oilfield and Its Application

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Seismic rock physics model was an important tool for analyzing the rules of seismic elastic variation of reservoir rock and the prediction of hydrocarbon. The existing methods seldom considered the complex pore structure characteristics of reservoir rock when the rock physical model was established, which resulted in some errors in the prediction results. Systematical rock physics experiments were conducted on the sandstone samples of Shawan Formation of Chunguang Oilfield in Chepaizi Area of Xinjiang Province. After determining the pore system and concentration, the non-interaction approximation (NIA) was used to analyze the effects of porosity, pore shape and the concentration of micro-crack to the elastic properties of the dry frame of sandstone samples. The test results were used for calibrating the model parameters. Furthermore, a rock physical model was established to characterize the seismic elasticity of the rock skeleton of the target reservoir. The results of the model were in good agreement with the experimental results. According to the experimental results and model results, the jet flow model is used to replace the traditional Gassmann Equation for fluid replacement, which can better explain the ultrasonic frequency test results of fluid saturated sandstone samples.

1. 引言

2. 试验样品制备与测量

Figure 1. The characteristics of micro-pore structures of reservoir sandstone samples

3. 样品地震岩石物理特征

Figure 2. The variation of vp with confining pressure under dry condition of sample (a) and relationship between P-wave fitting Factor and vp (b)

${p}_{\text{close}}=\left[\frac{\text{π}{E}_{\text{s}}}{4\left(1-{\upsilon }_{\text{s}}^{2}\right)}\right]\alpha \approx {E}_{\text{s}}\alpha$ (1)

$\begin{array}{l}{v}_{\text{pd}}\left({p}_{\text{e}}\right)=-{C}_{\text{p}}\mathrm{exp}\left(-d\cdot {p}_{\text{e}}\right)+{v}_{\text{p0}}+{B}_{\text{p}}{p}_{\text{e}}\\ {v}_{\text{sd}}\left({p}_{\text{e}}\right)=-{C}_{\text{s}}\mathrm{exp}\left(-d\cdot {p}_{\text{e}}\right)+{v}_{\text{s0}}+{B}_{\text{s}}{p}_{\text{e}}\end{array}$ (2)

4. 岩石物理模型

4.1. 岩石骨架模型

4.1.1. 模型建立

$S={S}_{0}+\Delta {S}_{\text{crack}}+\Delta {S}_{\text{stiff}}$ (3)

$\begin{array}{l}{K}_{\text{stiff}}={K}_{0}{\left(1+\frac{p{\varphi }_{\text{t}}}{1-{\varphi }_{\text{s}}}\right)}^{-1}\\ {G}_{\text{stiff}}={G}_{0}{\left(1+\frac{q{\varphi }_{\text{t}}}{1-{\varphi }_{\text{s}}}\right)}^{-1}\end{array}$ (4)

$\begin{array}{l}{K}_{\text{d}}={K}_{\text{stiff}}{\left(1+\frac{P{\varphi }_{\text{c}}}{1-{\varphi }_{\text{c}}}\right)}^{-1}\\ {G}_{\text{d}}={G}_{\text{stiff}}{\left(1+\frac{Q{\varphi }_{\text{c}}}{1-{\varphi }_{\text{c}}}\right)}^{-1}\end{array}$ (5)

$\epsilon =\frac{3}{4\text{π}\alpha }{\varphi }_{\text{c}}$ (6)

$\begin{array}{l}{K}_{\text{d}}={K}_{\text{stiff}}{\left(1+\frac{16\left(1-{\upsilon }_{\text{stiff}}^{2}\right)}{9\left(1-2{\upsilon }_{\text{stiff}}\right)}\epsilon \right)}^{-1}\\ {G}_{\text{d}}={G}_{\text{stiff}}{\left(1+\frac{32\left(1-{\upsilon }_{\text{stiff}}\right)\left(5-{\upsilon }_{\text{stiff}}\right)}{45\left(2-{\upsilon }_{\text{stiff}}\right)}\epsilon \right)}^{-1}\end{array}$ (7)

4.1.2. 模型试验

Figure 3. The relationship of pore shape factor of sandstone samples in Shawan Formation of Chunguang oilfield

Figure 4. The feature of pc Change with ft and the relationship between ft, fc and ε0

$\epsilon \left({p}_{\text{e}}\right)={\epsilon }_{0}\mathrm{exp}\left(-d\cdot {p}_{\text{e}}\right)$ (8)

$\begin{array}{l}{K}_{\text{d}}={K}_{0}{\left[1+p\cdot {\varphi }_{\text{t}}+2.46\cdot {\epsilon }_{0}\mathrm{exp}\left(-d\cdot {p}_{\text{e}}\right)\right]}^{-1}\\ {G}_{\text{d}}={G}_{0}{\left[1+q\cdot {\varphi }_{\text{t}}+1.59\cdot {\epsilon }_{0}\mathrm{exp}\left(-d\cdot {p}_{\text{e}}\right)\right]}^{-1}\end{array}$ (9)

Figure 5. The comparison of measured vp, vs and theoretically calculated results under different pressures

4.2. 孔隙流体作用

$\begin{array}{l}\frac{1}{{K}_{\text{mf}}\left({p}_{\text{e}},\omega \right)}=\frac{1}{{K}_{\text{h}}}+\frac{1}{\frac{1}{\frac{1}{{K}_{\text{d}}\left({p}_{\text{e}}\right)}-\frac{1}{{K}_{\text{h}}}}+\frac{3i\omega \eta }{8{\varphi }_{\text{c}}{\alpha }_{\text{c}}^{2}}}\\ \frac{1}{{G}_{\text{mf}}\left({p}_{\text{e}},\omega \right)}=\frac{1}{{G}_{\text{d}}\left({p}_{\text{e}}\right)}-\frac{4}{15}\left(\frac{1}{{K}_{\text{d}}\left({p}_{\text{e}}\right)}-\frac{1}{{K}_{\text{mf}}\left({p}_{\text{e}},\omega \right)}\right)\end{array}$ (10)

$\begin{array}{l}\frac{1}{{K}_{\text{sat}}\left({p}_{\text{e}},\omega \right)}=\frac{1}{{K}_{0}}+\frac{{\varphi }_{\text{s}}\left(\frac{1}{{K}_{\text{f}}}-\frac{1}{{K}_{0}}\right)}{1+{\varphi }_{\text{s}}\left(\frac{1}{{K}_{\text{f}}}-\frac{1}{{K}_{0}}\right)/\left(\frac{1}{{K}_{\text{mf}}\left({p}_{\text{e}},\omega \right)}-\frac{1}{{K}_{0}}\right)}\\ {G}_{\text{sat}}\left({p}_{\text{e}},\omega \right)={G}_{\text{mf}}\left({p}_{\text{e}},\omega \right)\end{array}$ (11)

Figure 6. The procedures of seismic rock physics modeling based on porosity and pore shape

5. 结语

Figure 7. The interpretation of ultrasonic experimental results

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