Well Testing

Well test types and transient pressure

A well test changes the production or injection rate of one well in a controlled way and records the bottomhole pressure against time. The shape of the pressure record identifies the test, so each test is best learned through its characteristic pressure profile.

• Flow-after-flow test — a series of constant-rate steps with increasing rate and no shut-in between them, so the pressure declines within every step.
• Modified isochronal test — flow periods of equal duration, each followed by a shut-in long enough for the pressure to stabilize before the next, higher rate.
• Fall-off test — the pressure recorded after injection or production stops, so the pressure falls back toward the static value.
• Interference test — the rate is changed at an active well and the response is observed at a separate observation well, where it appears later and is weaker than at the active well.

Tests are also classified by scope. A single well productivity test gives skin, formation damage and well deliverability, but it cannot reveal vertical or horizontal reservoir heterogeneity, which requires descriptive reservoir tests that sample the reservoir beyond the wellbore. Fluid types and their volume ratios come from surface measurements rather than from the pressure response. Pressure transient analysis yields skin, average reservoir pressure and drainage pore volume, but the solution gas-oil ratio is a PVT property measured in the laboratory and cannot be obtained from pressure data.

The flow regime at a given radius is identified by the rate of pressure change (\partial P/\partial t)_r. It is zero in steady-state flow, constant in pseudo-steady-state flow, and a function f(r,t) in transient flow. On a log-log plot of pressure derivative against time, each regime leaves a characteristic slope: spherical flow -1/2, linear flow 1/2, bilinear flow 1/4, and boundary-dominated (pseudo-steady) flow 1. Recognizing these slopes is the basis of type-curve matching.

Gringarten type curves plot dimensionless pressure P_D against t_D/C_D. After a match point (\Delta p, t) is chosen with a known (P_D, t_D/C_D), permeability follows from k = 141.2\,q\,\mu\,P_D/(h\,\Delta p) when q is in reservoir barrels per day. If q is in stock tank barrels per day, the formation volume factor must be included as k = 141.2\,qB\mu P_D/(h\,\Delta p).

On a semilog plot of pressure against \log t, the slope m of the middle-time straight line gives permeability through k = 162.6\,qB\mu/(mh), with m in psi per log cycle.

Bourdet pressure-derivative type curves are drawn on two logarithmic axes. The horizontal axis is t_D/C_D, each curve is labelled by C_D e^{2s}, and the vertical axis carries the derivative as well as P_D. In middle-time radial flow the dimensionless derivative equals 0.5 for every curve, so all curves merge in that region.

Infinite-acting behaviour ends when the pressure transient reaches the nearest no-flow boundary. For a given drainage area, a well located far from all boundaries sustains infinite-acting flow longest, while a well close to two boundaries reaches pseudo-steady state earliest and depletes fastest. Analysis of a drawdown test with a permeability-skin model also relies on identifying which period of the record is radial and which is boundary-controlled.

Skin factor from formation damage

The skin factor s is a dimensionless measure of the extra pressure drop near the wellbore, caused by a zone whose permeability differs from that of the undamaged formation. For a uniform altered zone of permeability k_s extending to radius r_s, the Hawkins formula gives s = \left(\dfrac{k}{k_s} - 1\right)\ln\dfrac{r_s}{r_w}, where r_w is the wellbore radius. The radii are measured from the centre of the wellbore.

The sign of the skin is the key to many questions. A positive skin means damage, in which the near-wellbore permeability is reduced by mud invasion, fines migration, clay swelling, asphaltene deposition or scale. A negative skin means stimulation. Hydraulic fracturing creates a highly conductive path that bypasses the damaged zone and lowers the skin, sometimes to negative values. Successful hydraulic fracturing therefore decreases the skin, whereas formation damage near the wellbore increases it.

The additional pressure drop caused by the damage exists only in the annulus between r_w and r_s. At r = r_s the formation is undamaged, so the additional drop is zero there, and it is largest near the wellbore.

When a problem gives the damage distance measured from the sand face instead of from the centre of the well, the true radius of the altered zone is r_s = r_w + (\text{distance from sand face}). Substituting this r_s into the Hawkins formula gives the correct skin.

The skin also changes the productivity index. In pseudo-steady radial flow the productivity index is inversely proportional to \ln(r_e/r_w) - 0.75 + s, so a more negative skin increases the productivity index sharply. Stimulation of a damaged zone and a larger undamaged permeability in the near-wellbore region both raise the ratio of productivity indices after the treatment.

Pressure buildup test analysis

In an ideal pressure buildup test, the shut-in bottomhole pressure plots as a single straight line against \log[(t_p + \Delta t)/\Delta t] for all times, where t_p is the producing time and \Delta t the shut-in time. In an actual test the curve is non-linear and divides into three regions.

• Early-time region — dominated by wellbore storage and skin effects, while the transient moves through the formation nearest the wellbore. It carries no information about boundaries, because the transient has not reached them.
• Middle-time region — the infinite-acting radial flow period, reached after wellbore storage has ended and while the transient is still inside the bulk reservoir. Its straight-line slope gives permeability, and the data here are not affected by boundaries or sealing faults.
• Late-time region — the radius of investigation has reached the drainage boundaries, and boundaries, sealing faults and other heterogeneities control the response.

The Horner pseudo-producing time for a multi-rate production history is t_{pH} = N_p / q_{last}, where N_p is the cumulative production before shut-in and q_{last} is the rate immediately before shut-in. Each rate period contributes to N_p as rate times duration, so the rate history must be summed before dividing by the last rate.

The absolute open flow potential is estimated from a single stabilized test with a linear inflow relation. The productivity index is J = q/(\bar{p} - p_{wf}), where \bar{p} is the static pressure found by buildup and p_{wf} is the flowing bottomhole pressure. The AOF is the rate at zero bottomhole pressure, q_{AOF} = J\bar{p}. Both pressures must be on the same basis, either gauge or absolute, before the difference is taken.

Productivity index and inflow

The productivity index J relates the production rate to the drawdown, J = q/(\bar{p} - p_{wf}) for a single-phase liquid with linear inflow. It is the measure of a well's ability to deliver fluid from the reservoir, and it is the slope of the inflow performance curve.

Deliverability is governed by the flow capacity kh/\mu. This quantity is obtained from transient pressure analysis of a flow test. A drill stem test in an exploration or appraisal well, and a drill stem test in a development well, both record the pressure and rate needed to compute kh/\mu. Openhole wireline logs give permeability and thickness only indirectly, through correlations, and they do not measure the flow capacity under flowing conditions.