Analysis of DST flow data with Ramey type curves

Input(s)

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

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

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

Ø: Porosity (dimensionless)

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

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

C: Wellbore Storage Coefficient (bbl/psi)

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

μ\mu: Viscosity (cP)(\mathrm{cP})

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

t\mathrm{t}: Time (h)

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

Output(s)

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

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

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

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

s: Skin Factor (dimensionless)

Formula(s)

pDR=pi(pwf)(t)pipoqDR=1pDRCD=0.8936C hct(rw2)k=(3390μCh)(tct)s=0.5ln(CESCD)\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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