Analysis of DST flow data with Ramey type curves

Input(s)

$\mathrm{p}_{\mathrm{i}}$: Initial Pressure $(\mathrm{psi})$

$\mathrm{p}_{\mathrm{wf}}$: Well Flowing Pressure (psi)

$\mathrm{p}_{\mathrm{o}}$: Pressure at Time $T=0$ (psi)

Ø: Porosity (dimensionless)

$c_{\mathrm{t}}$: Total Compressibility $(1 / \mathrm{psi})$

$\mathrm{h}$: Formation Thickness (ft)

C: Wellbore Storage Coefficient (bbl/psi)

$r_{w}$: Radius of Wellbore $(\mathrm{ft})$

$\mu$: Viscosity $(\mathrm{cP})$

$\mathrm{t}_{\mathrm{c}}$: Dimensionless Parameter from Curve Fitting as $\frac{T_{d}}{c_{d}}$ (dimensionless)

$\mathrm{t}$: Time (h)

CES: Match Point for Dimensionless Well Bore Coefficient from Curve as (Cd E (2 s))_(mp) (dimensionless)

Output(s)

$\mathrm{p}_{\mathrm{DR}}$: Dimensionless Pressure (dimensionless)

$\mathrm{q}_{\mathrm{DR}}$: Dimensionless Flow Rate (dimensionless)

$\mathrm{C}_{\mathrm{D}}$: Dimensionless Well Bore Storage Coefficient (dimensionless)

$\mathrm{k}$: Permeability $(\mathrm{mD})$

s: Skin Factor (dimensionless)

Formula(s)

$$ \begin{gathered} \mathrm{p}_{\mathrm{DR}}=\frac{\mathrm{p}_{\mathrm{i}}-\left(\mathrm{p}_{\mathrm{wf}}\right)(\mathrm{t})}{\mathrm{p}_{\mathrm{i}}-\mathrm{p}_{\mathrm{o}}} \\ \mathrm{q}_{\mathrm{DR}}=1-\mathrm{p}_{\mathrm{DR}} \\ \mathrm{C}_{\mathrm{D}}=0.8936 * \frac{\mathrm{C}}{\varnothing * \mathrm{~h} * \mathrm{c}_{\mathrm{t}} *\left(\mathrm{r}_{\mathrm{w}}^{2}\right)} \\ \mathrm{k}=\left(3390 * \mu * \frac{\mathrm{C}}{\mathrm{h}}\right) *\left(\frac{\mathrm{t}_{\mathrm{c}}}{\mathrm{t}}\right) \\ \mathrm{s}=0.5 * \ln \left(\frac{\mathrm{CES}}{\mathrm{C}_{\mathrm{D}}}\right) \end{gathered} $$

Reference(s)

Lee, J., Rollins, J. B., \& Spivey, J. P. (2003). Pressure Transient Testing (Vol. 9). Richardson, Texas: Society of Petroleum Engineers, Page: 155.