The prediction of recovery percent of water-free stage and its application in the correction of theoretical water cut

ABSTRACT

Water-free oil production period is an important stage for oil production, prediction and water cut prediction. Because there are many factors affecting the water-free oil production period and the influencing mechanism is complex, it is very difficult to calculate the water-free oil production period. In this paper, the main influencing factors of water-free oil production period are analyzed by the stream tube approach method. The influence law of four influencing factors on water-free oil production period was analyzed and the quantitative relationship between four influencing factors and water-free oil production period were established. The average water saturation of reservoir and water saturation near producers are different which is important for the calculation of theoretical water cut. The quantitative relationship between average water saturation of reservoir and water saturation near producers is established. On this basis, a new method for calculating theoretical water cut is built and is applied to BZ reservoir. The result shows the theoretical water cut calculated by this method is consistent with field data.

KEYWORDS:

• Water-free oil production period
• influencing factor
• water index
• oil index
• average water saturation
• water saturation near producers

Disclosure statement

No potential conflict of interest was reported by the author(s).

Annotation

$\mathrm{\Delta q}$——flow rate of a stream tube,m³/s; $\mathit{A}\left(\mathit{\zeta }\right)$——sectional area of tube in the position of $\mathit{\zeta }$,m²; $\mathit{\zeta }$——the lengh of a stream tube ,m; $\mathit{f}{{\mathit{ }}^{\mathrm{\prime }}}_{\mathit{w}}\left(S_{\mathrm{w}}\right)$——water cut increasing rate; $\mathit{\phi }$——porosity,%; $\mathit{r}\left(\mathit{i}\right)$——percolating resistance of a stream tube, MPa·(m³/s)⁻¹; $\mathit{t}$——time, s; $r_w$——radius, m; ${\zeta }_2$——the length of stream tube in the position of ${\zeta }_2$,m; ${\zeta }_1$——the Length of a stream tube of water area，m; $l_i$——the Length of a stream tube, m; $K_{\mathit{ro}}$——oil relative permeability, f; $K_{\mathit{rw}}$——oil relative permeability, f; ${\mu }_o$——formation water viscosity,mPa·s; ${\mu }_w$——formation water viscosity,mPa·s; $\mathit{K}$——permeability,mD; $\mathit{Q}$——flow rate of a permeable unit,m³/s; $\mathit{\lambda }$—water oil mobility ratio; $n_w$—water index; $n_o$—oil index; $S_{\mathit{wi}}$—irreducible water saturation, f; $S_{\mathit{or}}$—residual oil saturation,f; $R_0$—recovery percent of water-free stage,%; ${\bar{S}}_{\mathit{w}}$—average water saturation,%; $S_w$—water saturation of outlet end, f; $\mathit{a}$, $\mathit{b}$—the regression coefficient of the relation between average water saturation and outlet end water saturation; $f_w$—water cut,%; $f_w^{\prime }$—water cut increasing rate; $R_{\mathit{\hspace{0.17em}}}$—recovery percent,%; $f_{\mathit{w}\left(\mathit{i}\right)}$、$f_{\mathit{w}\left(\mathit{i}-1\right)}$—the outlet water saturation at two adjoining times, %; $R_{\mathit{w}\left(\mathit{i}\right)}$、$R_{\mathit{w}\left(\mathit{i}-1\right)}$—the recovery percent at two adjoining time, %; $f_{w0}^{\prime }$—water cut increasing rate calculated by traditional method; $S_{\mathit{w}\left(\mathit{i}\right)}$、$S_{\mathit{w}\left(\mathit{i}-1\right)}$—water cut at two adjoining time, f; $R_1$—recovery percent at the end of first step,%; $\mathrm{\Delta }{f}_w$—the water cut variation of a step,%; $f_{\mathit{w}1}$、$f_{\mathit{w}0}$——water cut at the beginning of the first step and the end of the first step, %; $\overline{{\mathit{f}}_{\mathit{w}1}}$—the average water cut of the first step,%; $R_1$—recovery percent at the end of the first step,% $f_{w1}^{\prime }$—water cut increasing rate of the first step;

Additional information

Funding

This work was supported by the National Major Science and Technology Special Project for the 13th Five Year Plan [2016ZX05058001].