# 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.

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