A Streamline Approach for Integrating Transient Pressure Data into High Resolution Reservoir Models
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AbstractStreamline models have shown significant potential in integrating dynamic data into high-resolution reservoir models in a computationally efficient manner. However, previous efforts towards production data integration using streamline models have been limited to tracer data and multiphase production history such as water-cut at the wells. In this paper we generalize the streamline approach to transient pressure applications by introducing a diffusive time of flight along streamlines. We show that the diffusive time of flight allows us to define drainage areas or volumes associated with primary recovery and compressible flow under the most general conditions. We then utilize developments in seismic tomography and waveform imaging to formulate an efficient approach to integrating transient pressure data into high-resolution reservoir models.Our proposed approach exploits an analogy between a propagating wave and a propagating pressure front. In particular, we adopt a high frequency asymptotic solution to the transient pressure equation to compute travel times associated with a propagating pressure front. The asymptotic approach has been widely used in modeling wave propagation phenomena. A key advantage of the asymptotic approach is that parameter sensitivities required for solving inverse problems related to production data integration can be obtained analytically using a single streamline simulation. Thus, the approach can be orders of magnitude faster than current techniques that can require multiple flow simulations.We have applied our proposed approach to both synthetic and field examples. The synthetic example utilizes transient pressure response from an interference test in a nine-spot pattern. The spatial distribution of permeability is estimated by matching arrival times of the pressure front in each of the observation wells. The field example is from the Conoco Borehole Test Facility in Kay County, Oklahoma. A series of pressure interference tests were performed in a skewed five-spot pattern to identify the distribution and orientation of the natural fracture system at the Fort Riley formation. We have inverted the pressure drawdowns at the observation wells to create a conceptual model for the Fort Riley formation. The predominant fracture patterns emerging from the inversion are shown to be consistent with outcrop mapping and crosswell seismic imaging.
