| Abstract |
An outstanding degree of wellbore-flow asymmetry was encountered at the Klaipeda geothermal field in Lithuania. Wells that sustainably produce copious aquifer fluids are observed to clog when the wells are used as injectors -- e.g., well flow asymmetric can reach factors to 10 to 40 (a well with productivity index PI can be reduced to having injectivity index II ~ PI/40 to PI/10). A degree of reversibility is observed for freely flowing producer wells in that, while declining during temporary use as injectors, the wells can then recover full productivity. However, attempts at treatment of long-term injector wells – including sidetracking – fail to reverse the injectivity decline. The observed wellbore flow asymmetry is logically due to small scale particulate matter in the injected fluid: clean produced aquifer fluids sustain flow while particulate-bearing injected fluids degrade flow. The micro-scale details of particulate clogging have not, however, been established for the Klaipeda wells, thus complicating or defeating attempts at remediation. It is typically assumed that well injectivity clogging proceeds by continuous transport of particulate matter that feeds a mass deposit that grows radially outward according to some radial profile -- a process that is often called ‘deep-bed filtration’. Deep-bed filtration, with origins in the use of unconsolidated sand filters, has been given a mathematical expression involving empirical parameters that codify the unconsolidated sand filter process. Using those parameters, deep-bed filtration injectivity of large scale well flow is often assessed (‘predicted’) by conducting well-core-scale injectivity decline experiments using core from the given or similar well. In our experience at Klaipeda, the deep filtration expression does not reproduce the observed decline curve. To understand this impasse, we note a fundamental distinction between filtration in (i) spatially uncorrelated porous media such as unconsolidated sands and (ii) spatially-correlated porous media such as consolidated rock. We find that an alternative physical process describes Klaipeda injector wellbore decline curve when the spatial correlation properties of the flow medium are those of rock. No match is possible for our model when the flow medium spatial correlation properties are reduced to negligible values characteristic of unconsolidated sands. In our computation, macroscopic injectivity declines are attributed to the effects of clogging of pore-throats in proportion to the pore-throat connectivity: the greater the connectivity, the greater the flow; and the greater flow, the greater the time rate of particulate transport, and hence the greater the rate of clogging the most important flow channels. When pore connectivity distributions are lognormal, the clogging mechanism has the exponential flow decline over time, V(t) ∠exp(-t/τ), characteristic of Klaipeda data. In contrast, when the connectivity distributions are normally distributed as in unconsolidated sands, the decline curve is more characteristic of deep-bed filtration, typically of order V(t) ∠1/(1+t/τ), that does not fit Klaipeda data. In support of our Klaipeda decline curve modelling, we note that Klaipeda well-logs show that the geological section has crustal porosity fluctuations with power-spectra that scale inversely as a power-law in k, Pφ(k) ~ 1/k, as is observed worldwide. It is highly attested that crustal permeability κ in groundwater and other crustal flow systems is closely associated with crustal porosity φ, κ ~ exp(αφ), where the value of α is such that mean product quantity has value ~ 3-4. When porosity is spatially correlated, permeability is lognormally distributed. Such connectivity distributions lead directly to our Klaipeda decline curve results. If actual crustal wellbore decline curves are due to spatially-correlated permeability, then using well-core as diagnostic of model parameters for deep-bed filtration predictions is likely to be faulty. |